DARK PHOTONS THEORY AND MOTIVATIONS · DARK PHOTONS THEORY AND MOTIVATIONS Neal Weiner NYU - CCPP...

DARK PHOTONSTHEORY AND MOTIVATIONS

Neal WeinerNYU - CCPPJune 17, 2014

HPS Collaboration Meeting

WHY DARK SECTORS• Holdom ’87: kinetic mixing gives SM particles

millicharge under a dark U(1)

ϵ

also: dark matter

in principle, numerous such particles could exist with small couplings to SM fields

WHY DARK SECTORS RECENTLY?

• New approach to WIMPs

Dark matter annihilates into a dark mediator

Dark mediator subsequently decays to SM particles

Finkbeiner, NW ’07; Pospelov, Ritz, Voloshin ‘08

Allows equilibrium with SM via phi - not a direct annihilation.=> Hidden sector models of dark matter

A dark force and an excited state:

allows excitation, followed by deexcitation into CR signalallows a cross section as large as 1/q2 or 1/m𝜙2

look for signals in the keV-MeV range

Finkbeiner, NW ‘07

DECOUPLE SIGNALS• Freezeout does not imply tight connection to SM

• “Natural” WIMP without associated weak scale particles

• Scattering signals with large enough rates to observe

• No immediate implication for direct detection or collider physics (although often associated)

• Dark photon (or other light particle) is often most accessible particle at accelerators

DECAYS OF THE DARK PHOTON

0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0

dark photon mass HMeVL

BR h˝p0˝p+p-p+p-p+p-p0p0p+p-p0wp0Æ2p0+˝K0K0K+K-p+p-mmee

tree levelphotons

radiativephotons

WHAT SIZE INTERACTION?

coefficient could be O(1) [no]

coefficient could be generated at 1-loop

but messengers may be GUT multiplets w/ 1-loop mass splittings

[2-loop]

but dark U(1) may be remnant of non-Abelian group, with same effect [3-loop]

if non-Abelian, whole thing may be like SM s-parameter op (v/M)power

ϵ

ANOMALIES

• PAMELA

• Chandra/XMM

• Fermi

A GROWING SIGNAL

It’s too great to be dark matter!PAMELA, Fermi and AMS

But antiprotons in CRs are in agreement with secondary production

A Challenging Puzzle for CR Physics

Donato et al. (PRL 102 (2009) 071301)

Ptuskin et al. (ApJ 642 (2006) 902)

Simon et al. (ApJ 499 (1998) 250)

CR Positron spectrum significantly harder than expectations from secondary production Moskalenko & Strong 98

If DM: Need rate above expected. Need harder than expected positron spectrum.

18 Emiliano Mocchiutti – INFN Trieste

International Workshop on Positrons in Astrophysics – Mürren, Switzerland, March 20th, 2012

Donato et al. PRL 102 (2009) 071301

Simon et al. - ApJ 499 (1998) 250 Ptuskin et al. - ApJ 642 (2006) 902

Antiprotons – secondaries?

Secondary production models

No associated anti-proton signal

MODELS FOR PAMELA

• Dark Matter Explanations for PAMELA:

• Large rates

• Large rates into e+e-

• Low rates into antiprotons

Sommerfeld EnhancementHigh velocity

If particles interact via a “long range” force, cross sections can be much larger than the perturbative cross section

If these signals arise from thermal dark matter, dark matter may have a long range force

m1

> (MDM )1 Hisano, Nojiri, Matsumoto, ’04; Cirelli, Strumia, Tamburini, ’07; Arkani-Hamed, Finkbeiner, Slatyer, NW, ’08; Pospelov,

Ritz, ’08

low velocity

DARK FORCE MODELS8

a)

χ

χ

φ

φ

φ...

mφ ∼ GeV

b)

χ

χ

φ

φ

FIG. 3: The annihilation diagrams χχ → φφ both with (a) and without (b) the Sommerfeld enhancements.

for ordinary WIMP annihilations, mediated by W/Z/γ exchange).

Because of the presence of a new light state, the annihilation χχ → φφ can, and naturally will, be significant. In

order not to spoil the success of nucleosynthesis, we cannot have very light new states in this sector, with a mass <∼ 10

MeV, in thermal equilibrium with the standard model; the simplest picture is therefore that all the light states in the

dark sector have a mass ∼ GeV. Without any special symmetries, there is no reason for any of these particles to be

exactly stable, and the lightest ones can therefore only decay back to standard model states, indeed many SM states

are also likely kinematically inaccessible, thus favoring ones that produce high energy positrons and electrons. This

mechanism was first utilized in [19] to generate a large positron signal with smaller π0 and p signals. Consequently, an

important question is the tendency of φ to decay to leptons. This is a simple matter of how φ couples to the standard

model. (A more detailed discussion of this can be found in [30].)

A scalar φ can couple with a dilaton-like coupling φFµνFµν , which will produce photons and hadrons (via gluons).

Such a possibility will generally fail to produce a hard e+e− spectrum. A more promising approach would be to mix

φ with the standard model Higgs with a term κφ2h†h. Should φ acquire a vev ⟨φ⟩ ∼ mφ, then we yield a small mixing

with the standard model Higgs, and the φ will decay into the heaviest fermion pair available. For mφ<∼ 200 MeV

it will decay directly to e+e−, while for 200 MeV<∼ mφ<∼ 250 MeV, φ will decay dominantly to muons. Above that

hadronic states appear, and pion modes will dominate. Both e+e− and µ+µ− give good fits to the PAMELA data,

while e+e− gives a better fit to PAMELA+ATIC.

A pseudoscalar, while not yielding a Sommerfeld enhancement, could naturally be present in this new sector. Such

a particle would typically couple to the heaviest particle available, or through the axion analog of the dilaton coupling

above. Consequently, the decays of a pseudoscalar would be similar to those of the scalar.

A vector boson will naturally mix with electromagnetism via the operator F ′µνFµν . This possibility was considered

some time ago in [40]. Such an operator will cause a vector φµ to couple directly to charge. Thus, for mφ<∼ 2mµ it

will decay to e+e−, while for 2mµ<∼ mφ

<∼ 2mπ it will decay equally to e+e− and µ+µ−. Above 2mπ, it will decay

40% e+e−, 40%µ+µ− and 20%π+π−. At these masses, no direct decays into π0’s will occur because they are neutral

and the hadrons are the appropriate degrees of freedom. At higher masses, where quarks and QCD are the appropriate

degrees of freedom, the φ will decay to quarks, producing a wider range of hadronic states, including π0’s, and, at

suitably high masses mφ>∼ 2 GeV, antiprotons as well [66]. In addition to XDM [18], some other important examples

of theories under which dark matter interacts with new forces include WIMPless models [41], mirror dark matter [42]

and secluded dark matter [43].

Note that, while these interactions between the sectors can be small, they are all large enough to keep the dark

and standard model sectors in thermal equilibrium down to temperatures far beneath the dark matter mass, and (as

mentioned in the previous section), we can naturally get the correct thermal relic abundance with a weak-scale dark

matter mass and perturbative annihilation cross sections. Kinetic equilibrium in these models is naturally maintained

down to the temperature TCMB ∼ mφ [44].

TeV

GeV

generates hard leptons by annihilations into a light mediator, no anti-protons

φ

l−

l+

Holdom ’86; Boehm+Fayet ’03; Finkbeiner+NW ’07; Pospelov, Ritz, Voloshin ’08; Arkani-Hamed, Finkbeiner,

Slatyer, NW ’09; Pospelov+Ritz ’09; Nomura+Thaler ’09…

PAMELA/FERMI

0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:2)

mχ = 1.68 TeV

mφ = 900 MeV

BF = 300

PAMELA Data

0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:2)

mχ = 1.52 TeV

mφ = 900 MeV

BF = 260

PAMELA Data

0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:1)

mχ = 1.55 TeV

mφ = 580 MeV

BF = 250

PAMELA Data

100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:2)

mχ = 1.68 TeV

mφ = 900 MeV

BF = 300

HESS Systematic Error Band (8% energy shift)HESS Data (8% energy shift)Fermi High Energy DataFermi Low Energy Data

100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:2)

mχ = 1.52 TeV

mφ = 900 MeV

BF = 260


100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:1)

mχ = 1.55 TeV

mφ = 580 MeV

BF = 250


0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:1)

mχ = 1.2 TeV

mφ = 580 MeV

BF = 244

PAMELA Data

0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-, µ+ µ- (1:1)

mχ = 1.33 TeV

mφ = 350 MeV

BF = 156

PAMELA Data

0.01

0.1

1

10 100 1000

φ e+ /

(φe+ +

φe- )

Energy (GeV)

XDM e+ e-

mχ = 1.0 TeV

mφ = 200 MeV

BF = 67

PAMELA Data

100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-, µ+ µ-, π+ π- (1:1:1)

mχ = 1.2 TeV

mφ = 580 MeV

BF = 244


100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-, µ+ µ- (1:1)

mχ = 1.33 TeV

mφ = 350 MeV

BF = 156


100

10 100 1000

E3 dN

/dE

(GeV

2 m-2

s-1

sr-1

)

Energy (GeV)

XDM e+ e-

mχ = 1.0 TeV

mφ = 200 MeV

BF = 67


Figure 3. Benchmark models fitting the PAMELA (first and third rows) and Fermi (second and fourth

rows) cosmic-ray excesses, obtained using the GALPROP program.

6.3 Comparisons with Previous Results

While we find ample regions of parameter space that provide agreement with the PAMELAand Fermi results, previous studies [35] have been more negative. In particular, [35] findsa maximum local “boost factor” (BF) of ∼ 120 from Sommerfeld-enhanced annihilation for∼ 2 TeV DM, and a BF of 90 for 1 TeV DM, compared to a best fit to the data for χχ→ φφ,with φ → µ+µ− (taken from [31, 116]) of 2.35 TeV DM with a boost factor of 1500. Weshould emphasize that our results are completely consistent with theirs, with the differentconclusions arising from our consideration of a more general parameter space. Specifically,

– 21 –

PAMELA/FERMI/AMS

7

MΧ"1.0 TeV ! 2.5 TeVΧΧ#ΦΦ#2Μ&2Μ'

1 5 10 50 100

0.02

0.05

0.10

0.20

0.50

1.00

E "GeV#

e&!"e&&e'#

MΧ"1.0 TeV ! 2.5 TeVΧΧ#ΦΦ#2Μ&2Μ'

1 10 100 10001

5

10

50

100

500

1000

E "GeV#

e&&e'E3xdiff.fluxGeV

2 "m2ssr#'

1

MΧ"1.0 TeV ! 3.0 TeVΧΧ#ΦΦ#2Π&2Π'

1 5 10 50 100

0.02

0.05

0.10

0.20

0.50

1.00

E "GeV#

e&!"e&&e'#

MΧ"1.0 TeV ! 3.0 TeVΧΧ#ΦΦ#2Π&2Π'

1 10 100 10001

5

10

50

100

500

1000

E "GeV#


2 "m2ssr#'

1

MΧ"700 GeV ! 1.6 TeVΧΧ#ΦΦ#2e), 2Μ), 2Π) at 1:1:2

1 5 10 50 100

0.02

0.05

0.10

0.20

0.50

1.00

E "GeV#

e&!"e&&e'#

MΧ"700 GeV ! 1.6 TeVΧΧ#ΦΦ#2e), 2Μ), 2Π) at 1:1:2

1 10 100 10001

5

10

50

100

500

1000

E "GeV#


2 "m2ssr#'

1

FIG. 5: The same as in Figs. 1, 2 and 4, but for a diffusion zone half-width of L = 8 kpc. For annihilations to 2µ+2µ− anda mass of 1.0 TeV (2.5 TeV), we have used a thermally averaged annihilation cross section of 2.9 × 10−24 cm3/s (1.5 × 10−23

cm3/s) providing a χ2/d.o.f. fit of 1.18(4.4) to the AMS and 15.4(5.1) to the Fermi data. For annihilations to 2π+2π− anda mass of 1.0 TeV (3.0 TeV), we have used a thermally averaged annihilation cross section of 3.5 × 10−24 cm3/s (2.3 × 10−23

cm3/s) giving a χ2/d.o.f. fit of 0.81(3.9) to the AMS and 15.2(3.8) to the Fermi data. For annihilations to a 1:1:2 ratio ofe+e−, µ+µ−, and π+π− final states with a mass of 700 GeV (1.6 TeV), we have used a thermally averaged annihilation crosssection of 1.6× 10−24 cm3/s (6.5× 10−24 cm3/s) with a χ2/d.o.f. fit of 0.83(3.0) to the AMS and 13.4(7.6) to the Fermi data.

From these results (especially those shown in Fig. 8), weconclude that for very reasonable choices of parameters,pulsars can provide a viable explanation for the observedcosmic ray positron fraction.

In addition to the integrated contribution from all pul-sars throughout the Milky Way, there are two young

and nearby pulsars which could each individually con-tribute significantly to the cosmic ray positron spectrum.The Geminga pulsar is 3.7×105 years old, 157 parsecsfrom the solar system, and pulsates with a period of 230ms. The pulsar B0656+14 (possibly associated with theMonogem supernova remnant) is considerably younger

Seems an actual tension in the data (assuming a power law fit to the background electrons)

PAMELA/FERMI/AMS8

Dot!Dashed: MΧ#2.5 TeV, ΧΧ$ΦΦ$2Μ'2Μ!

Dashed: MΧ#3.0 TeV, ΧΧ$ΦΦ$2Π'2Π!

Solid: MΧ#1.6 TeV, ΧΧ$ΦΦ$2e), 2Μ), 2Π) at 1:1:2

1 5 10 50 100

0.02

0.05

0.10

0.20

0.50

1.00

E !GeV"

e'#!e''e!"

Dot!Dashed: MΧ#2.5 TeV, ΧΧ$ΦΦ$2Μ'2Μ!Dashed: MΧ#3.0 TeV, ΧΧ$ΦΦ$2Π'2Π!Solid: MΧ#1.6 TeV, ΧΧ$ΦΦ$2e), 2Μ), 2Π) at 1:1:2

1 10 100 10001

5

10

50

100

500

1000

E !GeV"e''e!E3xdiff.fluxGeV

2 !m2ssr"!

1

FIG. 6: The same as in Figs. 1, 2, 4 and 5 but for a diffusion zone half-width of L = 8 kpc, and for broken power-law spectrumof electrons injected from cosmic ray sources (dN

e−/dE

e− ∝ E−2.65

ebelow 85 GeV and dN

e−/dE

e− ∝ E−2.3

eabove 85 GeV).

The cross sections are the same as given in the caption of Fig. 5. With this cosmic ray background, we show the dark mattermodels compared to the measurements of the cosmic ray positron fraction and the overall leptonic spectrum. Even with thepresence of a break, there is a preference towards models with softer injection e± spectra; with the 1.6 TeV to e±, µ±, π± caseproviding the best χ2/d.o.f. fit to the AMS (Fermi) lepton data of 0.82(0.51). The 2.5 TeV to 2µ+ 2µ−, gives a χ2/d.o.f. fitof 1.32(1.07) and the 3.0 TeV to 2π+ 2π− a fit of 1.00(1.03). We remind that in the Fermi error-bars we do not include anoverall shift from the energy resolution uncertainty.

(1.1×105 years), although somewhat more distant (290parsecs), and more slowly rotating (P = 390 ms). Theseparameters, combined with their measurements of P , im-ply that Geminga and B0656+14 have each lost approx-imately 3 × 1049 erg and 1 × 1049 erg of rotational en-ergy since their births, respectively. If 4-5% of this en-ergy went into the production and acceleration of ener-getic e+e− pairs, then these pulsars could be responsi-ble for the observed rise in the cosmic ray positron frac-tion [22, 23]. If we combine these two sources with thesomewhat smaller contribution expected from the sumof all more distant pulsars [22], we estimate that if 3-4% of the total energy from pulsars goes into energeticpairs, this would be sufficient to account for the observedpositrons.

IV. SUMMARY AND DISCUSSION

In this paper, we have revisited both annihilating darkmatter and pulsars as possible sources of the rising cos-mic ray positron fraction. Using the newly published,high precision data from AMS, we have considered a widerange of dark matter models and cosmic ray propagationmodels. We find that models in which the dark mat-ter annihilates directly to leptons (e+e− or µ+µ−) areno longer capable of producing the observed rise in thepositron fraction. Models in which the dark matter an-nihilates into light intermediate states which then decayinto combinations of muons and charged pions, however,can accommodate the new data (see Fig. 6). In thosedark matter models still capable of generating the ob-served positron excess, the dark matter’s mass and anni-

hilation cross section fall in the range of ∼1.5-3 TeV and⟨σv⟩ ∼ (6− 23)× 10−24 cm3/s.We have also considered pulsars as a possible source

of the observed positrons. In particular, we find that forreasonable choices of spectral parameters and spatial dis-tributions, the sum of all pulsars in the Milky Way couldaccount for the observed positrons (see Fig. 8) if, on av-erage, 10-20% of their total energy goes into the produc-tion and acceleration of electron-positron pairs (assuminga birth rate of one per century throughout the Galaxy,each with an average total energy of 1049). It may also bethe case that a small number of nearby and young pulsars(most notably Geminga and B0656+14) could dominatethe local cosmic ray positron flux at energies above sev-eral tens of GeV. Taking into account these two excep-tional sources, we estimate that if 3-4% of the total en-ergy from pulsars goes into energetic pairs, these objectscould be responsible for the observed positron fraction.Currently, we cannot yet discriminate between dark

matter and pulsars as the source of the observed positronexcess. We are hopeful, however, that future data fromAMS may change this situation. In addition to contin-uing to improve the precision of their measurement ofthe positron fraction and extending this measurement tohigher energies, AMS will also measure with unprece-dented precision a number of secondary-to-primary ratiosof cosmic ray nuclei species, which can be used to con-strain many aspects of the underlying cosmic rays propa-gation model. Of particular importance is the 10Be/9Beratio, for which existing measurements are limited to en-ergies below 2 GeV (kinetic energy per nucleon), and withlarge errors (for a compilation of such measurements, seeTables I and II of Ref. [63]). In contrast, AMS is ex-pected to measure this ratio with much greater precision,

with a broken power law…

Cholis+Hooper ‘13

SO WHAT IS UP WITH THOSE SCENARIOS?

(Also Pulsar explanation)

BEWARE: STRAWMAN CONSTRAINTS!

14

10 102 103 104

10-26

10-25

10-24

10-23

10-22

10-21

m @GeVD

<sv>@cm

3 s-1 D

ccô bb, NFW

3s, wêo background modeling, r0=0.2-0.7 GeV cm-3wêo background modelingconstrained free source fits3s, r0=0.43 GeV cm-3

5s, r0=0.43 GeV cm-3

sWIMP freeze-out

10 102 103 104

10-26

10-25

10-24

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10-22

10-21

m @GeVD

<sv>@cm

3 s-1 D

ccô bb, ISO

wêo background modelingconstrained free source fits

3s5s

sWIMP freeze-out

10 102 103 104

10-26

10-25

10-24

10-23

10-22

10-21

m @GeVD

<sv>@cm

3 s-1 D

ccô m+m-, NFW

IC+FSR, wêo background modelingFSR, wêo background modelingIC+FSR, constrained free source fits3s5s

sWIMP freeze-out

10 102 103 104

10-26

10-25

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10-22

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m @GeVD

<sv>@cm

3 s-1 D

ccô m+m-, ISO


sWIMP freeze-out

10 102 103 104

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m @GeVD

<sv>@cm

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ccô t+t-, NFW


sWIMP freeze-out

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10-23

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m @GeVD

<sv>@cm

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ccô t+t-, ISO


sWIMP freeze-out

Figure 4. Upper limits on the velocity averaged DM annihilation cross-section including a model of the astrophysical background compared with the limitsobtained with no modeling of the background. Upper panel: Limits on models in which DM annihilates into bb, for a DM distribution given by the NFWdistribution (left) and isothermal distribution (right). In the left panel we also add an uncertainty band (red dotted lines) in the 3 no-background limits whichwould result from varying the local DM density 0 in the range 0.2-0.7 GeV cm-3. A similar band, not shown in the plot for clarity, would be present for thelimits including a model of the astrophysical background (see discussion in the text). The horizontal line marks the thermal decoupling cross section expectedfor a generic WIMP candidate. Middle panel: Upper limits for DM annihilation to µ+µ-. Lower panel: The same, for DM annihilation to +-. The regionexcluded by the analysis with no model of the astrophysical background is indicated in light blue, while the additional region excluded by the analysis with amodeling of the background is indicated in light green. The regions of parameter space which provide a good fit to PAMELA Adriani et al. (2009a) (purple) andFermi LAT Abdo et al. (2009) (blue) CR electron and positron data are shown, as derived in Cirelli et al. (2010) and are scaled by a factor of 0.5, to account fordifferent assumptions on the local DM density (see text for more details).

Rare are the constraints on dark photon scenarios…

BEWARE: THE EFFECTS OF SUBSTRUCTURE

• Clumps of dark matter have lower velocity

• Often stated that substructure is O(1) effect (e.g., Kuhlen, Kamionkowski)

• With Sommerfeld enhancement, this is much larger

18

10-4 10-3 10-2 0.1 1 100.1

110-4 10-3 10-2 0.1 1 10

0.1

1

D

mfHGe

VL

20

50 100 200 500

10-4 10-3 10-2 0.1 1 10

110-4 10-3 10-2 0.1 1 10

1

D

mfHGe

VL

50

75

100

200 500

FIG. 7: The maximum local boost factor for 1 TeV DM with a 700 keV mass splitting, consistent with constraints from thethermal relic density, the CMB, self-interaction bounds, and naturalness (in the sense of not relying on the resonance peaks),in scenarios 1 (left panel) and 2 (right panel). The dark gauge boson is assumed to decay into electrons only; when the gaugeboson mass exceeds twice the muon mass, the true final state may become more complicated, so this region is indicated by cross-hatching. The regions overlaid in solid black indicate where our approximation for the multi-state Sommerfeld enhancement isexpected to break down.

Our results are shown in Figs. 6-7: in Fig. 6, we take a target boost factor of 65, a mass splitting of 700 keV,and a DM mass of 1 TeV, motivated by the lowest-mediator-mass benchmark model in [10]. The qualitative featuresare similar to the elastic case, although we cannot study the self-interaction bounds since they only apply to smallmediator masses where our approximations are expected to break down. We note that as expected, a local boost of65 is permitted for a 200 MeV mediator and 1 TeV DM in the zero- limit.

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1109.0521.[7] D. P. Finkbeiner and N. Weiner, Phys. Rev. D76, 083519 (2007), astro-ph/0702587.[8] N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer, and N. Weiner, Phys. Rev. D79, 015014 (2009), 0810.0713.[9] M. Pospelov and A. Ritz, Phys. Lett. B671, 391 (2009), 0810.1502.

[10] D. P. Finkbeiner, L. Goodenough, T. R. Slatyer, M. Vogelsberger, and N. Weiner (2010), 1011.3082.[11] M. Lattanzi and J. I. Silk, Phys. Rev. D79, 083523 (2009), 0812.0360.[12] M. Kuhlen and D. Malyshev, Phys. Rev. D79, 123517 (2009), 0904.3378.[13] M. Kuhlen, P. Madau, and J. Silk, Science 325, 970 (2009), 0907.0005.[14] J. Bovy, Phys. Rev. D79, 083539 (2009), 0903.0413.[15] Q. Yuan et al., JCAP 0912, 011 (2009), 0905.2736.[16] A. C. Vincent, W. Xue, and J. M. Cline (2010), 1009.5383.[17] M. D. Kistler and J. M. Siegal-Gaskins, Phys. Rev. D81, 103521 (2010), 0909.0519.[18] M. Kamionkowski, S. M. Koushiappas, and M. Kuhlen, Phys. Rev. D81, 043532 (2010), 1001.3144.[19] M. Pospelov, Phys.Rev. D80, 095002 (2009), 0811.1030.[20] B. Batell, M. Pospelov, and A. Ritz, Phys. Rev. D79, 115008 (2009), 0903.0363.

Maximum allowed boost

depletes signals in inner galaxy

FOCUSING ON PARAMETER SPACE

• To explain PAMELA/AMS, it seems to me that a lower boost factor is still preferable (i.e., 50-150 vs 1000-2000)

• This would motivate scenarios where the electron component is sizable

• Photon constraints would prefer models with only radiative photons (i.e., below the rho meson mass)

• Substructure boosts enhance most effectively for lighter mediators

NEW ANOMALIES

• X-rays

• Galactic Center

A LINE AT 3.55(ish) KeVSubmitted to ApJ, 2014 February 10

Preprint typeset using LATEX style emulateapj v. 04/17/13

DETECTION OF AN UNIDENTIFIED EMISSION LINE IN THE STACKED X-RAY SPECTRUM OF GALAXYCLUSTERS

Esra Bulbul

1,2

, Maxim Markevitch

2

, Adam Foster

1

, Randall K. Smith

1

Michael Loewenstein

2

, and

Scott W. Randall

1

1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138.2 NASA Goddard Space Flight Center, Greenbelt, MD, USA.

Submitted to ApJ, 2014 February 10

ABSTRACT

We detect a weak unidentified emission line at E = (3.55 3.57) ± 0.03 keV in a stacked XMMspectrum of 73 galaxy clusters spanning a redshift range 0.01 0.35. MOS and PN observationsindependently show the presence of the line at consistent energies. When the full sample is dividedinto three subsamples (Perseus, Centaurus+Ophiuchus+Coma, and all others), the line is seen at> 3 statistical significance in all three independent MOS spectra and the PN “all others” spectrum.The line is also detected at the same energy in the Chandra ACIS-S and ACIS-I spectra of the Perseuscluster, with a flux consistent with XMM-Newton (however, it is not seen in the ACIS-I spectrum ofVirgo). The line is present even if we allow maximum freedom for all the known thermal emissionlines. However, it is very weak (with an equivalent width in the full sample of only 1 eV) and locatedwithin 50–110 eV of several known faint lines; the detection is at the limit of the current instrumentcapabilities and subject to significant modeling uncertainties. On the origin of this line, we argue thatthere should be no atomic transitions in thermal plasma at this energy. An intriguing possibility isthe decay of sterile neutrino, a long-sought dark matter particle candidate. Assuming that all darkmatter is in sterile neutrinos with ms = 2E = 7.1 keV, our detection in the full sample corresponds toa neutrino decay mixing angle sin2(2) 7 1011, below the previous upper limits. However, basedon the cluster masses and distances, the line in Perseus is much brighter than expected in this model,significantly deviating from other subsamples. This appears to be because of an anomalously brightline at E = 3.62 keV in Perseus, which could be an Arxvii dielectronic recombination line, althoughits emissivity would have to be 30 times the expected value and physically dicult to understand. Inprinciple, such an anomaly might explain our line detection in other subsamples as well, though itwould stretch the line energy uncertainties. Another alternative is the above anomaly in the Ar linecombined with the nearby 3.51 keV K line also exceeding expectation by factor 10–20. Confirmationwith Chandra and Suzaku, and eventually Astro-H, are required to determine the nature of this newline.

1. INTRODUCTION

Galaxy clusters are the largest aggregations of hot in-tergalactic gas and dark matter. The gas is enrichedwith heavy elements (Mitchell et al. (1976); Serlemitsoset al. (1977) and later works) that escape from galaxiesand accumulate in the intracluster/intergalactic medium(ICM) over billions of years of galactic and stellar evo-lution. The presence of various heavy ions is seen fromtheir emission lines in the cluster X-ray spectra. Datafrom large e↵ective area telescopes with spectroscopic ca-pabilities, such as ASCA, Chandra, XMM-Newton andSuzaku, uncovered the presence of many elements in theICM, including O, Ne, Mg, Si, S, Ar, Ca, Fe, and Ni(for a review see, e.g., Bohringer & Werner 2010). Re-cently, weak emission lines of low-abundance Cr and Mnwere discovered (Werner et al. 2006; Tamura et al. 2009).Relative abundances of various elements contain valuableinformation on the rate of supernovae of di↵erent types ingalaxies (e.g., Loewenstein 2013) and illuminate the en-richment history of the ICM (e.g., Bulbul et al. 2012b).Line ratios of various ions can also provide diagnosticsof the physical properties of the ICM, uncover the pres-ence of multi-temperature gas, nonequilibrium ionization

[email protected]

states and nonthermal emission processes such as chargeexchange (Paerels & Kahn 2003).As for dark matter, 80 years from its discovery by

(Zwicky 1933, 1937), its nature is still unknown (thoughnow we do know for sure it exists — from X-ray andgravitational-lensing observations of the Bullet Cluster,Clowe et al. (2006), and we know accurately its cosmo-logical abundance, e.g., Hinshaw et al. (2013)). Amongthe various plausible dark matter candidates, one thathas motivated our present work is the hypothetical ster-ile neutrino that is included in some extensions to thestandard model of particle physics (Dodelson & Widrow(1994) and later works; for recent reviews see, e.g.,Abazajian et al. (2007); Boyarsky et al. (2009)). Ster-ile neutrinos should decay spontaneously with the rate

(ms, ) = 1.38 1029 s1

sin2 2

107

ms

1 keV

5

,

(1)where the particle mass ms and the “mixing angle” are unknown but tied to each other in any particularneutrino production model (Pal & Wolfenstein 1982).The decay of sterile neutrino should produce a photon ofE = ms/2 and an active neutrino. The mass of the ster-ile neutrino may lie in the keV range, which would place

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An unidentified line in X-ray spectra of the Andromeda galaxy and Perseus galaxy cluster

A. Boyarsky1, O. Ruchayskiy2, D. Iakubovskyi3,4 and J. Franse1,51Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Niels Bohrweg 2, Leiden, The Netherlands

2Ecole Polytechnique Federale de Lausanne, FSB/ITP/LPPC, BSP, CH-1015, Lausanne, Switzerland3Bogolyubov Institute of Theoretical Physics, Metrologichna Str. 14-b, 03680, Kyiv, Ukraine

4National University “Kyiv-Mohyla Academy”, Skovorody Str. 2, 04070, Kyiv, Ukraine5Leiden Observatory, Leiden University, Niels Bohrweg 2, Leiden, The Netherlands

We identify a weak line at E ∼ 3.5 keV in X-ray spectra of the Andromeda galaxy and the Perseus galaxycluster – two dark matter-dominated objects, for which there exist deep exposures with the XMM-Newton X-rayobservatory. Such a line was not previously known to be present in the spectra of galaxies or galaxy clusters.Although the line is weak, it has a clear tendency to become stronger towards the centers of the objects; it isstronger for the Perseus cluster than for the Andromeda galaxy and is absent in the spectrum of a very deep“blank sky” dataset. Although for individual objects it is hard to exclude the possibility that the feature is dueto an instrumental effect or an atomic line of anomalous brightness, it is consistent with the behavior of a lineoriginating from the decay of dark matter particles. Future detections or non-detections of this line in multipleastrophysical targets may help to reveal its nature.

The nature of dark matter (DM) is a question of crucial im-portance for both cosmology and for fundamental physics. Asneutrinos – the only known particles that could be dark mat-ter candidates – are known to be too light to be consistent withvarious observations (see e.g. [1] for a review), it is widely an-ticipated that a new particle should exist to extend the hot BigBang cosmology paradigm to dark matter. Although manycandidates have been put forward by particle physicists (seee.g. [2]), little is known experimentally about the propertiesof DM particles: their masses, lifetimes, and interaction typesremain largely unconstrained. A priori, a given DM candidatecan possess a decay channel if its lifetime exceeds the ageof the Universe. Therefore, the search for a DM decay signalprovides an important test to constrain the properties of DM ina model-independent way. For fermionic particles, one shouldsearch above the Tremaine-Gunn limit [3] (! 300 eV). If themass is below 2mec2, such a fermion can decay to neutrinosand photons, and we can expect two-body radiative decay withphoton energy Eγ = 1

2mDM. Such particles can be searched

for in X-rays (see [4] for review of previous searches). Foreach particular DM model, the particle’s mass, lifetime andother parameters are related by the requirement to provide thecorrect DM abundance. For example, for one very interestingDM candidate – the right-handed neutrino – this requirementrestricts the mass range to 0.5 − 100 keV [4, 5]. A large partof the available parameter space for sterile neutrinos is fullyconsistent with all astrophysical and cosmological bounds [6],and it is important to probe it still further.

The DM decay line is much narrower than the spectral res-olution of the present day X-ray telescopes and, as previoussearches have shown, should be rather weak. The X-ray spec-tra of astrophysical objects are crowded with weak atomic andinstrumental lines, not all of which may be known. Therefore,even if the exposure of available observations continues to in-crease, it is hard to exclude an astrophysical or instrumentalorigin of any weak line found in the spectrum of individual

object. However, if the same feature is present in the spectraof a number of different objects, and its surface brightness andrelative normalization between objects is consistent with theexpected behavior of the DM signal, this can provide muchmore convincing evidence about its nature.

The present paper takes a step in this direction. We presentthe results of the combined analysis of many XMM-Newtonobservations of two objects at different redshifts – the Perseuscluster and the Andromeda galaxy (M31) – together with along exposure “blank sky” dataset. We study the 2.8–8 keVenergy band and show that the only significant un-modeledexcess that is present in the spectra of both M31 and Perseusis located at ∼ 3.5 keV energy and the line in Perseus is cor-rectly redshifted as compared to Andromeda (at 95% CL). Therelative fluxes for the two objects are in agreement with whatis known about their DM distributions. We also study sur-face brightness profiles of this line and find them consistentwith expectations for a DM decay line. We do not detect sucha line in the very deep “blank sky” dataset, which disfavorssome of the scenarios for its instrumental origin (e.g. featuresin the effective area). The upper bound from this dataset isconsistent with expectations for a DM signal that would comein this case primarily from the Milky Way halo. However, asthe line is weak (∼ 4σ in the combined dataset) and the uncer-tainties in DM distribution are significant, positive detectionsor strong constraints from more objects are clearly needed inorder to determine the nature of this signal.1

Below we summarize the details of our data analysis and then

1 During our work we became aware that a similar analysis has been carriedout by different group for a collection of galaxy clusters. When this paperwas in preparation, the arXiv preprint [7] by this group appeared, claim-ing a detection of a spectral feature at the same energy from a number ofclusters.

Bulbul et al Boyarsky et al

73 Clusters, XMM, central, to z=0.35

incl Coma, Perseus

Perseus Chandra, central

Virgo Chandra, central (not seen)

M31 XMM central+non-central

Perseus XMM, non-central

3

Dataset Exposure χ2/d.o.f. Line position Flux ∆χ2

[ksec] [keV] 10−6 cts/sec/cm2

M31 ON-CENTER 978.9 97.8/74 3.53± 0.025 4.9+1.6−1.3 13.0

M31 OFF-CENTER 1472.8 107.8/75 3.53± 0.03 < 1.8 (2σ) . . .PERSEUS CLUSTER (MOS) 528.5 72.7/68 3.50+0.044

−0.036 7.0+2.6−2.6 9.1

PERSEUS CLUSTER (PN) 215.5 62.6/62 3.46± 0.04 9.2+3.1−3.1 8.0

PERSEUS (MOS) 1507.4 191.5/142 3.518+0.019−0.022 8.6+2.2

−2.3 (Perseus) 25.9+ M31 ON-CENTER 4.6+1.4

−1.4 (M31) (3 dof)BLANK-SKY 15700.2 33.1/33 3.53± 0.03 < 0.7 (2σ) . . .

TABLE I: Basic properties of combined observations used in this paper. Second column denotes the sum of exposures of individual observa-tions. The last column shows change in∆χ2 when 2 extra d.o.f. (position and flux of the line) are added. The energies for Perseus are quotedin the rest frame of the object.

0.01

0.10

1.00

10.00

Normalized count rate

[cts/sec/keV]

M31 ON-center

-6⋅10-3-4⋅10-3-2⋅10-3 0⋅100 2⋅10-3 4⋅10-3 6⋅10-3 8⋅10-3 1⋅10-2

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Data - model

[cts/sec/keV]

Energy [keV]

No line at 3.5 keV

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

Normalized count rate

[cts/sec/keV]

M31 ON-centerNo line at 3.5 keV

-4⋅10-3-2⋅10-3 0⋅100 2⋅10-3 4⋅10-3 6⋅10-3 8⋅10-3 1⋅10-2

3.0 3.2 3.4 3.6 3.8 4.0

Data - model

[cts/sec/keV]

Energy [keV]

No line at 3.5 keVLine at 3.5 keV

FIG. 1: Left: Folded count rate (top) and residuals (bottom) for the MOS spectrum of the central region of M31. Statistical Y-errorbars on thetop plot are smaller than the point size. The line around 3.5 keV is not added, hence the group of positive residuals. Right: zoom onto the lineregion.

with such a large exposure requires special analysis (as de-scribed in [16]). This analysis did not reveal any line-likeresiduals in the range 3.45−3.58 keVwith the 2σ upper boundon the flux being 7× 10−7 cts/cm2/sec. The closest detectedline-like feature (∆χ2 = 4.5) is at 3.67+0.10

−0.05 keV, consistentwith the instrumental Ca Kα line.3

Combined fit of M31 + Perseus. Finally, we have performeda simultaneous fit of the on-center M31 and Perseus datasets(MOS), keeping common position of the line (in the rest-frame) and allowing the line normalizations to be different.The line improves the fit by ∆χ2 = 25.9 (Table I), whichconstitutes a 4.4σ significant detection for 3 d.o.f.

Results and discussion. We identified a spectral feature atE = 3.518+0.019

−0.022 keV in the combined dataset of M31 andPerseus that has a statistical significance 4.4σ and does notcoincide with any known line. Next we compare its propertieswith the expected behavior of a DM decay line.

3 Previously this line has only been observed in the PN camera [9].

The observed brightness of a decaying DM line should be pro-portional to the dark matter column density SDM =

!

ρDMdℓ –integral along the line of sight of the DM density distribution:

FDM ≈ 2.0× 10−6 cts

cm2 · sec

"

Ωfov

500 arcmin2

#

× (1)"

SDM

500 M!/pc2

#

1029 s

τDM

"

keV

mDM

#

.

M31 and Perseus brightness profiles. Using the line fluxof the center of M31 and the upper limit from the off-centerobservations we constrain the spatial profile of the line. TheDM distribution in M31 has been extensively studied (see anoverview in [13]). We take NFW profiles for M31 with con-centrations c = 11.7 (solid line, [22]) and c = 19 (dash-dottedline). For each concentration we adjust the normalization sothat it passes through first data point (Fig. 2). The c = 19profile was chosen to intersect the upper limit, illustrating thatthe obtained line fluxes of M31 are fully consistent with thedensity profile of M31 (see e.g. [22, 24, 25] for a c = 19− 22model of M31).

10

0.6

0.7

0.8

Flux

(cnt

s s-1

keV

-1)

-0.02

-0.01

0

0.01

0.02

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

300

305

310

315

Eff.

Area

(cm

2 )

3.57 ± 0.02 (0.03) XMM-MOSFull Sample

6 Ms1

1.5

Flux

(cnt

s s-1

keV

-1)

-0.02

0

0.02

0.04

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

980

1000

1020

Eff.

Area

(cm

2 )

3.51 ± 0.03 (0.05) XMM-PN Full Sample

2 Ms

-0.04

0

0.04

0.08

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

280

285

Eff.

Area

(cm

2 )

XMM-MOSCentaurus +

Coma +Ophiuchus525.3 ks

-0.2

-0.1

0

0.1

0.2

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

630

640

650

Eff.

Area

(cm

2 )

XMM-PNCentaurus +

Coma +Ophiuchus

168 ks

-0.002

0

0.002

0.006

0.008

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

290

295

300

305

310

315

Eff.

Area

(cm

2 )

XMM-MOSRest of the

Sample(69 Clusters)

4.9 Ms

-0.02

0

0.02

0.04

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

1220

1240

1260

Eff.

Area

(cm

2 )

XMM-PNRest of the

Sample(69 Clusters)

1.8 Ms

Figure 5. Top panels: 34 keV band of the stacked MOS (left panel) and stacked PN (right panel) spectra of the samples. The figuresshow the energy band where the new spectral feature is detected. The Gaussian lines with maximum values of the flux normalizations of Kxviii and Ar xvii estimated using AtomDB were included in the models. The red lines in the top panels (shown only for the full sample)show the model and the excess emission. The blue lines show the total model after another Gaussian line is added, representing the newline. Middle panels shows the residuals before (red) and after (blue) the Gaussian line is added. The bottom panels show the e↵ective areacurves (the corresponding ARF). Redshift smearing greatly reduces variations of the e↵ective area in the high-z sample.

bution of each cluster i to the total DM line flux in thestacked spectrum is

!i,dm =Mproj

i,DM (< Rext)(1 + zi)

4D2i,L

eietot

. (4)

where zi is the redshift of ith cluster, and ei and etot arethe exposure time of ith cluster and the total exposuretime of the sample.The dark matter mass within the extraction radius is

16

1.9 1010, consistent with the MOS detection. Figure6 shows both XMM-Newton Perseus spectra.

4.5

5.5

6.5

Flux

(cnt

s s-1

keV

-1)

-0.2

-0.1

0

0.1

0.2

Res

idua

ls

3 3.2 3.4 3.6 3.8 4Energy (keV)

295

300

305

Eff.

Area

(cm

2 )

XMM - MOSPerseus (core cut)

317 ks

Figure 7. 34 keV band of the core-excised stacked MOS spec-trum of the Perseus cluster. The figures show the energy band,where a new spectral feature at 3.57 keV is detected. The Gaus-sian lines with peak values of the flux normalizations of K xviii

and Ar xvii estimated using AtomDB were included in the mod-els. The red lines in the top panels show the model and the excessemission in both spectra. The blue lines show the total model aftera Gaussian line is added, indicating that the unidentified spectralline can be modeled with a Gaussian.

Since this is a single-cluster spectrum, we first checkwhether the Perseus signal is not an artifact of our blue-shifting procedure. For this we fit the original, redshiftedMOS spectrum with a line-free apec model. We obtaineda best-fit 2 463 for 385 dof. Adding a Gaussian line at3.57 keV (rest energy) improved the fit by 2 of 16 foran additional degree of freedom. The best-fit flux was 5.3± 1.2 (2.0) 105 photons cm2 s1, is in agreementwith the flux obtained from the blue-shifted spectrum.We conclude that our detection is independent of shiftingthe spectrum.Not ready to abandon the sterile neutrino explanation

based on the line flux incorrectly scaling with clustermass that we see for Perseus, we tried to investigatepossible astrophysical reasons behind the excess of theline flux in Perseus. First, we investigated the depen-dence of the energy and flux of this unidentified line onthe AtomDB predicted fluxes of nearby lines, i.e., theK xviii line at 3.51 keV and the Ar xvii DR line at3.62 keV. Allowing the energy of the Gaussian compo-nent to vary produced a best-fit for an energy of 3.56+0.010.02 (+0.02

0.03) keV, with a flux of 6.0+1.81.4 (+2.4

1.7) 105

photons cm2 s1 (2 of 598.1 for 572 dof). The best-fitenergy is consistent with the energy measured from theMOS observations of the full sample. However, the fluxesof the nearby K xviii line at 3.51 keV and the Ar xvii

DR at 3.62 keV line were at their allowed upper limitspredicted from the AtomDB. Relaxing the upper limitshas shifted the line energy higher, to 3.59 +0.01

0.03 (+0.020.04)

keV with a flux of 5.5+1.70.8 (+3.7

1.5) 105 photons cm2

s1 gave a slightly better fit (2 of 594.5 for 572 dof). Wenote that the line energy of this extra line gets close tothe Ar xvii DR line at 3.62 keV. So we removed the extra

Gaussian line and re-fit the Perseus spectrum removingthe upper limits on the Ar xvii DR line. We obtainedonly a slightly worse fit than the previous case, with a 2

of 598.8 (574 dof). The measured flux of the Ar xvii DRline at 3.62 keV in this case was 4.8+0.7

0.8 (+1.31.4) 105

photons cm2 s1, which is a factor of 30 above the pre-dicted maximum flux of the Ar xvii DR line based onthe measured flux of the Ar xvii line at 3.12 keV andAtomDB line rates. The predicted maximum flux of theAr xvii DR line for the Perseus spectrum was 1.6 106

photons cm2 s1 (< 0.01 times the flux of the Ar xviitriplet at 3.12 keV).This test showed that the line detected in the Perseus

cluster could also be interpreted as an abnormally brightAr xvii DR line. We note that, however, that obtainingsuch a bright DR line relative to the He-like triplet at3.12 keV is problematic. The emissivity of the satelliteline peaks at kT=1.8 keV, and declines sharply at lowertemperatures, in addition to the change in the ionizationbalance which reduces the Ar+17 content of the plasma.The emissivity ratio for the DR/3.12 keV has its max-imum value of 0.04 at kT=0.7 keV, but the emissivityof both lines is weak here, so any hotter component willdominate and lead to a lower ratio being observed.To avoid cool gas in the Perseus core contaminating

the flux of the nearby Ar and K lines, we also tried ex-cising the central 10 region of the cluster and performedthe fit on the core-excised co-added MOS spectrum. Wefound that adding an extra Gaussian line at 3.57 keV hasimproved the fit by 2 of 12.8 for an additional degreeof freedom with a best-fit flux of 2.1 +0.7

0.6 (+1.21.1) 105

photons cm2 s1 (see Figure 7). Excising the inner-most 10 reduced the flux of the detected line by a factorof two, indicating that the most of the flux of this emis-sion originates from the cool core. The mixing angle thatcorresponds to the line flux from the core-excised Perseusspectrum is consistent within 1 2 with those for thebright clusters (Centaurus+Coma+Ophiuchus) and thefull sample, respectively (Table 5).

3.5. Refitting full sample with anomalous 3.62 keV line

With the knowledge that the 3.62 keV line can beanomalously high (at least in Perseus), we should nowtry to re-fit the stacked MOS spectrum of the full sampleto see if the line in the full sample is a↵ected by the 3.62keV excess from Perseus, which is part of the full sam-ple. We set the flux of the 3.62 keV line to the Perseuscontribution of the Ar xvii DR line to the full-samplespectrum (2.3 106 photons cm2 s1), assuming allthe new line flux in Perseus originates from the abnor-mally bright DR line. We note that this flux was alreadya factor of 30 above the predicted upper limits by theAtomDB. Adding an extra Gaussian component, repre-senting the new line, to a model with the anomalous 3.62keV line, still improves the fit by 2 of 6.52 for 2 de-grees of freedom. The best-fit energy and flux were 3.55± 0.03 (0.05) and 2.23+1.6

0.9 (+2.21.5) 105 photons cm2

s1, respectively. The new line is still required with 2.5in the full sample; however, the energy of this line getslower and its confidence interval wider. The line energycomes into agreement with the energy detected in PNfull sample (see Figure 8 left panel). If we completelyfree the normalization of the 3.62 keV line in the full-

Bulbul et al

Boyarsky et alPasses the Toro test…

BUT WHAT IS IT?

assuming it’s BSM physics, that is

DECAYING DARK MATTERDecaying dark matter

• Sterile neutrino N → ν + γνNs

e± ν

W∓

γW∓

• R-parity violating gravitinog → ν + γ

•

(a)

ℓ ℓ

ν

p − k

!G

p

γ

k

ℓ

R

• Also R-parity violating axino, . . .

• For bosonic DM axions (or axion-like particles) would decay a → γγ

Oleg Ruchayskiy DECAYING DARK MATTER IN X-RAYS 11shamelessly stolen from talk by Ruchayskiy, April 2014

5

Interaction strength Sin2(2θ)

Dark matter mass MDM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Not enough DM

Tremaine-Gunn / Lyman-α Excluded by X-ray observations



10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Not enough DM




10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Not enough DM




10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Not enough DM




10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Not enough DM


FIG. 4: Constraints on sterile neutrino DM within νMSM [4]. Theblue point would corresponds to the best-fit value from M31 if theline comes from DM decay. Thick errorbars are ±1σ limits on theflux. Thin errorbars correspond to the uncertainty in the DM distri-bution in the center of M31.

to detect the candidate line in the “strong line” regime [35]. Inparticular, Astro-H should be able to resolve the Milky Wayhalo’s DM decay signal and therefore all its observations canbe used. Failure to detect such a line will rule out the DMorigin of the Andromeda/Perseus signal presented here.

Acknowledgments. We thank D. Malyshev for collaboration;A. Neronov for useful critical comments; M. Shaposhnikovand M. Lovell for reading the manuscript and providing com-ment. The work of D. I. was supported by part by the theProgram of Cosmic Research of the National Academy of Sci-ences of Ukraine and the State Programme of Implementationof Grid Technology in Ukraine.

[1] A. Boyarsky, O. Ruchayskiy, and D. Iakubovskyi, JCAP 0903,005 (2009).

[2] J. L. Feng, ARA&A 48, 495 (2010).[3] S. Tremaine and J. E. Gunn, Phys. Rev. Lett. 42, 407 (1979).[4] A. Boyarsky, D. Iakubovskyi, and O. Ruchayskiy, Phys. Dark

Univ. 1, 136 (2012).[5] A. Boyarsky, O. Ruchayskiy, and M. Shaposhnikov, Ann. Rev.

Nucl. Part. Sci. 59, 191 (2009).[6] A. Boyarsky, J. Lesgourgues, O. Ruchayskiy, and M. Viel,

Phys. Rev. Lett. 102, 201304 (2009).[7] E. Bulbul, M. Markevitch, A. Foster, R. K. Smith, M. Loewen-

stein, et al., 1402.2301 (2014).[8] M. J. L. Turner, A. Abbey, M. Arnaud, M. Balasini, M. Barbera,

E. Belsole, P. J. Bennie, J. P. Bernard, G. F. Bignami, M. Boer,et al., A&A 365, L27 (2001).

[9] L. Struder, U. Briel, K. Dennerl, R. Hartmann, E. Kendziorra,N. Meidinger, E. Pfeffermann, C. Reppin, B. Aschenbach,W. Bornemann, et al., A&A 365, L18 (2001).

[10] Xmm-newton science analysis system,http://xmm.esa.int/sas/.

[11] A. M. Read and T. J. Ponman, A&A 409, 395 (2003).[12] K. D. Kuntz and S. L. Snowden, A&A 478, 575 (2008).[13] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, M. G. Walker,

S. Riemer-Sørensen, and S. H. Hansen, MNRAS 407, 1188(2010).

[14] A. De Luca and S. Molendi, Astron. Astrophys. 419, 837(2004).

[15] Fin over fout public script, v. 1.1,http://xmm.vilspa.esa.es/external/xmm_sw_cal/background/Fin_over_Fout.

[16] D. Iakubovskyi, Ph.D. thesis, Leiden University (2013).[17] T. Abbey, J. Carpenter, A. Read, A. Wells, Xmm Science Cen-

tre, and Swift Mission Operations Center, in The X-ray Uni-verse 2005, edited by A.Wilson (2006), vol. 604 of ESA SpecialPublication, p. 943.

[18] Xmm-newton epic mos1 ccd6 update,http://xmm.esac.esa.int/external/xmm_news/items/MOS1-CCD6/.

[19] Irby, B., The ftools webpage, HeaSoft,http://heasarc.gsfc.nasa.gov/docs/software/ftools/ftools menu.html (2008).

[20] J. A. Carter and A. M. Read, A&A 464, 1155 (2007).[21] D. B. Henley and R. L. Shelton, Astrophys.J.Suppl. 202, 14

(2012).[22] E. Corbelli, S. Lorenzoni, R. A. M. Walterbos, R. Braun, and

D. A. Thilker, A&A 511, A89 (2010).[23] A. Simionescu, S. W. Allen, A. Mantz, N. Werner, Y. Takei,

R. G. Morris, A. C. Fabian, J. S. Sanders, P. E. J. Nulsen, M. R.George, et al., Science 331, 1576 (2011).

[24] L. Chemin, C. Carignan, and T. Foster, Astrophys. J. 705, 1395(2009).

[25] M. A. Sanchez-Conde, M. Cannoni, F. Zandanel, M. E. Gomez,and F. Prada, JCAP 1112, 011 (2011).

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(2008).[30] S. Dodelson and L. M. Widrow, Phys. Rev. Lett. 72, 17 (1994).[31] X.-d. Shi and G. M. Fuller, Phys. Rev. Lett. 82, 2832 (1999).[32] M. Shaposhnikov, JHEP 08, 008 (2008).[33] M. Laine and M. Shaposhnikov, JCAP 6, 31 (2008).[34] T. Takahashi, K. Mitsuda, R. Kelley, H. Aharonian, F. Aarts,

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Astropart. Phys. 28, 303 (2007).

22

Figure 12. Recent constraints on sterile neutrino productionmodels, assuming sterile neutrinos constitute dark matter (Abaza-jian et al. 2007). Straight lines in black show theoretical predictionsassuming sterile neutrinos constitute the dark matter with leptonnumber L = 0, L = 0.003, L = 0.01, L = 0.1. Constraints from thecosmic X-ray background are shown in the solid (blue and hatchedregions). The region is solid green is excluded based upon obser-vations of the di↵use X-ray background (Abazajian et al. 2007).Individual galaxy cluster constraints from XMM-Newton observa-tions of the Coma and Virgo clusters are shown in light blue (Bo-yarsky et al. 2006). The horizontal pink band shows the mass scaleconsistent with producing a 100300 pc core in the Fornax dwarfgalaxy (Strigari et al. 2006), and limits from the Milky Way byBoyarsky et al. (2006) is indicated with BMW. The orange regionat m

s

< 0.4 keV is ruled out by an application of the Tremaine-Gunn bound (Bode et al. 2001). Our measurement obtained fromthe full sample which is marked with the star in red, is consistentwith previous upper limits.

are unable to collisionally excite any Ar XVII lines, butdielectronic recombination is still possible. Examiningthe satellite line data in the AtomDB, taken from Vain-shtein & Safronova (1980), shows that even in this casethe maximum ratio is only 7%, as there are DR satellitelines at the energies of the Ar XVII triplet as well andthese lines would also be excited in such a case. Whilenot physically impossible if there was a significant andunexpected error in the atomic physics calculations, wehave no reason to believe this has occurred.We also note that our assumptions regarding rela-

tive line strengths have assumed the ICM is in thermalequilibrium or close to it. Charge exchange (CX) be-tween highly-ionized ions and neutral hydrogen or he-lium could also create X-ray emission lines with di↵erentratios (Smith et al. 2012). This could a↵ect our assump-tion of equilibrium line ratios, although we have includeda substantial range around the equilibrium values. It isimportant to note that these CX lines are not ‘new, butrather the same lines occurring in di↵erent ratios. Dueto its large cross section relative to electron excitationrates, astrophysical CX can occur only in a thin sheetwhere ions and neutrals interact directly, limiting its to-tal emission relative to the large ICM volume. In certain

cases, such as the core of the Perseus cluster where manyneutral filaments are known, it is possible that CX couldbe large enough to create a small fraction of the totalX-ray emission, although it would not create or enhancea line at 3.57 keV or the DR line at 3.62 keV. CX couldnot dominate the overall emission, however, as it wouldalso create Fe XVII and other lines that are not detected.

5.2. Sterile neutrino decay line?

An interesting interpretation of the line is the decaysignature of the sterile neutrino, a long-sought dark mat-ter particle candidate (Boyarsky et al. (e.g., 2009), seeour §1). The mass of the sterile neutrino would be dou-ble the decay photon energy, ms =7.1 keV. The line fluxdetected in our full sample corresponds to a mixing anglefor the decay sin2(2) 7 1011. This value is belowthe upper limits placed by the previous searches, shownin Fig. 12. Our detection from the stacked XMM-NewtonMOS observations galaxy clusters are shown with a starin red in that figure. Figure 13 shows the detections andupper limits we obtained from our various subsamples weused in this work (based on the included cluster massesand distances), as well as a comparison with previous up-per limit placed using the Bullet cluster by Boyarsky etal. (2008) at 3.57 keV, which is the most relevant earlierconstraint for us. Since the mixing angle is a universalquantity, all the subsample measurements must agree.The line in the subsample of fainter 69 clusters (full

sample sans Perseus, Coma, Ophiuchus and Centaurus)corresponds to a mixing angle that is consistent withthe full sample; the same is seen (though with a mild1.5 tension) for the subsample of bright nearby clustersComa+Centaurus+Ophiuchus. However, the brightnessof the new line in the XMM-Newton spectrum of Perseuscorresponds to a significantly higher mixing angle thanthat for the full sample (by factor 8 for the MOS spec-trum), which poses a problem in need of further investi-gation.We tried to excise the central 10 region of the Perseus

cluster, to see if the flux originates in the cool core of thecluster. Indeed, this decreased the flux in the line in halfand removed most of the tension with the other measure-ments. However, this suggests that either some of the lineflux is astrophysical in origin (at least in Perseus), or thecool gas in the core of the cluster a↵ects our ability tomeasure the continuum and the fluxes of the nearby Kxviii and Ar xvii lines, in the end resulting in an over-estimate of the flux of our detected line. It appears thatin Preseus, there is an anomalously strong line at the po-sition of the Ar xvii dielectronic recombination line at3.62 keV.With this knowledge, we have tried to add this anoma-

lous 3.62 keV line in the model for the full sample, wherewe have the most statistically significant line detection.The additional line is still required, albeit at a lower sig-nificance and a slightly lower energy of 3.55± 0.03 keV.Note that the sample of bright clusters is dominated bythe emission from the cool cores of Ophiuchus and Cen-taurus cluster, if this Ar 3.62 keV line anomaly is typicalof cool cores, they may also be a↵ected. However, free-ing the flux of the 3.62 keV line in the MOS full-samplefit did not require additional contribution from clustersother than Perseus, though the constraints are obviouslyweak.

22

Figure 12. Recent constraints on sterile neutrino productionmodels, assuming sterile neutrinos constitute dark matter (Abaza-jian et al. 2007). Straight lines in black show theoretical predictionsassuming sterile neutrinos constitute the dark matter with leptonnumber L = 0, L = 0.003, L = 0.01, L = 0.1. Constraints from thecosmic X-ray background are shown in the solid (blue and hatchedregions). The region is solid green is excluded based upon obser-vations of the di↵use X-ray background (Abazajian et al. 2007).Individual galaxy cluster constraints from XMM-Newton observa-tions of the Coma and Virgo clusters are shown in light blue (Bo-yarsky et al. 2006). The horizontal pink band shows the mass scaleconsistent with producing a 100300 pc core in the Fornax dwarfgalaxy (Strigari et al. 2006), and limits from the Milky Way byBoyarsky et al. (2006) is indicated with BMW. The orange regionat m

s

< 0.4 keV is ruled out by an application of the Tremaine-Gunn bound (Bode et al. 2001). Our measurement obtained fromthe full sample which is marked with the star in red, is consistentwith previous upper limits.

are unable to collisionally excite any Ar XVII lines, butdielectronic recombination is still possible. Examiningthe satellite line data in the AtomDB, taken from Vain-shtein & Safronova (1980), shows that even in this casethe maximum ratio is only 7%, as there are DR satellitelines at the energies of the Ar XVII triplet as well andthese lines would also be excited in such a case. Whilenot physically impossible if there was a significant andunexpected error in the atomic physics calculations, wehave no reason to believe this has occurred.We also note that our assumptions regarding rela-

tive line strengths have assumed the ICM is in thermalequilibrium or close to it. Charge exchange (CX) be-tween highly-ionized ions and neutral hydrogen or he-lium could also create X-ray emission lines with di↵erentratios (Smith et al. 2012). This could a↵ect our assump-tion of equilibrium line ratios, although we have includeda substantial range around the equilibrium values. It isimportant to note that these CX lines are not ‘new, butrather the same lines occurring in di↵erent ratios. Dueto its large cross section relative to electron excitationrates, astrophysical CX can occur only in a thin sheetwhere ions and neutrals interact directly, limiting its to-tal emission relative to the large ICM volume. In certain

cases, such as the core of the Perseus cluster where manyneutral filaments are known, it is possible that CX couldbe large enough to create a small fraction of the totalX-ray emission, although it would not create or enhancea line at 3.57 keV or the DR line at 3.62 keV. CX couldnot dominate the overall emission, however, as it wouldalso create Fe XVII and other lines that are not detected.

5.2. Sterile neutrino decay line?

An interesting interpretation of the line is the decaysignature of the sterile neutrino, a long-sought dark mat-ter particle candidate (Boyarsky et al. (e.g., 2009), seeour §1). The mass of the sterile neutrino would be dou-ble the decay photon energy, ms =7.1 keV. The line fluxdetected in our full sample corresponds to a mixing anglefor the decay sin2(2) 7 1011. This value is belowthe upper limits placed by the previous searches, shownin Fig. 12. Our detection from the stacked XMM-NewtonMOS observations galaxy clusters are shown with a starin red in that figure. Figure 13 shows the detections andupper limits we obtained from our various subsamples weused in this work (based on the included cluster massesand distances), as well as a comparison with previous up-per limit placed using the Bullet cluster by Boyarsky etal. (2008) at 3.57 keV, which is the most relevant earlierconstraint for us. Since the mixing angle is a universalquantity, all the subsample measurements must agree.The line in the subsample of fainter 69 clusters (full

sample sans Perseus, Coma, Ophiuchus and Centaurus)corresponds to a mixing angle that is consistent withthe full sample; the same is seen (though with a mild1.5 tension) for the subsample of bright nearby clustersComa+Centaurus+Ophiuchus. However, the brightnessof the new line in the XMM-Newton spectrum of Perseuscorresponds to a significantly higher mixing angle thanthat for the full sample (by factor 8 for the MOS spec-trum), which poses a problem in need of further investi-gation.We tried to excise the central 10 region of the Perseus

cluster, to see if the flux originates in the cool core of thecluster. Indeed, this decreased the flux in the line in halfand removed most of the tension with the other measure-ments. However, this suggests that either some of the lineflux is astrophysical in origin (at least in Perseus), or thecool gas in the core of the cluster a↵ects our ability tomeasure the continuum and the fluxes of the nearby Kxviii and Ar xvii lines, in the end resulting in an over-estimate of the flux of our detected line. It appears thatin Preseus, there is an anomalously strong line at the po-sition of the Ar xvii dielectronic recombination line at3.62 keV.With this knowledge, we have tried to add this anoma-

lous 3.62 keV line in the model for the full sample, wherewe have the most statistically significant line detection.The additional line is still required, albeit at a lower sig-nificance and a slightly lower energy of 3.55± 0.03 keV.Note that the sample of bright clusters is dominated bythe emission from the cool cores of Ophiuchus and Cen-taurus cluster, if this Ar 3.62 keV line anomaly is typicalof cool cores, they may also be a↵ected. However, free-ing the flux of the 3.62 keV line in the MOS full-samplefit did not require additional contribution from clustersother than Perseus, though the constraints are obviouslyweak.


Dark matter mass M

DM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2

5

50

1

10

DM overproduction

Not enough DM

Tremaine-Gunn / Lyman-α

Excluded by X-ray observations


Dark matter mass M

DM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2

5

50

1

10

DM overproduction

Not enough DM




Dark matter mass M

DM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2

5

50

1

10

DM overproduction

Not enough DM




Dark matter mass M

DM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2

5

50

1

10

DM overproduction

Not enough DM




Dark matter mass M

DM [keV]

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2

5

50

1

10

DM overproduction

Not enough DM



the model we should compare all models to is the sterile neutrino…(cf Davoudiasl et al hep-ph/0405097)

CONSIDERING ALTERNATIVES

• Important to have alternatives just to ask what to test

• Other observations may motivate other scales of DM (e.g., the GeV excess in the GC)

• ?

VIRGO VS PERSEUS

1 10 1007

7.02

7.04

7.06

7.08

7.1

7.12

7.14

7.16m

s (keV

) Full Sample (MOS)

Coma + Centaurus + Ophiuchus (MOS)

Perseus (Core-Cut) (MOS)

Other Clusters (MOS)

Full Sample (PN)

Coma + Centaurus +Ophiuchus (PN)

Perseus (Core-Cut) (PN)

Other Clusters (PN)

Perseus (ACIS-I)Perseus (ACIS-S)Virgo (ACIS-I)

10 sin2 (2θ)-11

B08

H14

VIRGO VS PERSEUSmvirgo~ few 1014 M mperseus~ few 1014 M

dvirgo~ 15 Mpc dvirgo~ 75 Mpc

THE MODEL

II. MODELS

The original XDM model was based on a simple U(1) dark force with the minimal La-

grangian2,

L = χi Dχi +1

4F dµνF

dµν + ϵFµνFdµν +m2φµφ

µ +Miχiχi + δiχiχi. (1)

The kinetic mixing parameter ϵ gives SM particles ϵ charge under the dark force, allowing

equilibrium in the early universe via χχ ↔ φφ, and φe ↔ γe.

The presence of the excited state allows the possibility of upscattering χχ → χ∗χ∗.

For δ > 2me, this will be followed by χ∗ → χe+e−, potentially explaining [1, 6, 7] the

INTEGRAL/SPI positron excess [3–5].

However, for δ < 2me, it has been shown that - absent any other interaction - the excited

state is stable on cosmological timescales [8, 9]. An obvious modification to the model is

the inclusion of a dipole operator 1

Mχ∗σµνχFµν , which mediates the decay χ∗ → χγ. The

lifetime for such a decay is [10]

τ = 0.5 sec×

!

M

TeV

"2!keV

δ

"3

. (2)

Thus, even for ∼ keV splittings, dipoles with M < 108TeV lead to decays on cosmological

timescales. This then motivates us to consider the implications of this XDM scenario for

X-ray signals beyond the 511 keV line. We dub this variant of the XDM scenario “XrayDM”.

III. X-RAY SIGNALS OF XDM AND A FEATURE AT 3.56 KEV

While such a model clearly produces X-rays from DM-DM scattering, it is not clear that

it produces a detectable signal of X-rays. To understand whether such a signal is detectable,

it is helpful to study this in a specific context.

Recently, [11] reported a potential detection of an X-ray line at 3.56 keV from a stacked

combination of clusters, with a particularly bright signal from Perseus. A similar analysis

finds a line at the same energy from Perseus and M31 [12].

The cumulative flux of ∼ 4× 10−6cm−2sec−1 from [11] is difficult to interpret as it arises

from a combination of clusters at a variety of distances. However, the collaboration does

2 An additional field is assumed to Higgs the dark U(1) at the 100MeV− 1GeV scale

3

II. MODELS


grangian2,

L = χi Dχi +1

4F dµνF













τ = 0.5 sec×

!

M

TeV

"2!keV

δ

"3

. (2)














3

II. MODELS


grangian2,

L = χi Dχi +1

4F dµνF













τ = 0.5 sec×

!

M

TeV

"2!keV

δ

"3

. (2)














3

THE SIGNAL

report on the signal from the Perseus cluster individually. Thus, fitting this source gives a

simple test as to whether such a signal could arise from XDM. Similarly, the analysis of [12]

produces a fit to M31 (and a somewhat broader range of fit to Perseus), giving a second

candidate to consider. At the same time, no signal has arisen from the much closer Virgo

cluster, so this limit should be addressed.

Beginning with Perseus, [11] claims a 3.56 keV line flux of 5.2+3.70−2.13 ×

10−5photons cm−2 sec−1 (90% errors) with the cluster core or 2.14+1.12−1.05 × 10−5 without, aris-

ing from XMM MOS observations, and upper limits of 1.77× 10−5 and 1.61× 10−5 for the

same regions from the XMM PN observations. The Chandra ACIS-S and ACIS-I obser-

vations yielded fluxes of 1.02+0.48−0.47 × 10−5 and 1.86+1.2

−1.6 × 10−5.3 [12] claim a similar flux of

0.7+2.6−2.6 × 10−5 (MOS) and 0.92+3.1

−3.1 × 10−5 (PN).

For M31 [12] find a rate of 0.49+0.16−0.13 × 10−5cm−2sec−1. For Virgo [11] find an upper limit

of 0.91× 10−5cm−2sec−1.

A naive estimate of the total luminosity from Perseus can be found (assuming an NFW

profile) using the cluster parameters found in [13]

L =

! R200

0

4πr2"

ρ(r)

mχ

#2

⟨σscattv⟩

= 1.9× 1049photons/sec ×

"

⟨σscattv⟩

10−19cm3sec−1

#"

10GeV

mχ

#2

. (3)

With Perseus 78 Mpc away, this yields a local photon flux

Φ = 2.6× 10−5

"

⟨σv⟩

10−19cm3sec−1

#"

10GeV

mχ

#2

photons/sec. (4)

Clearly, this cross section is well above the conventional thermal annihilation cross section,

but since this is a scattering process, this cross section can be naturally large, as we now

describe.

The perturbative cross section for this scattering has a cross section

σ =4πM2

χα2d

m4φ

, (5)

where αd is the dark U(1) coupling constant. For αMχ/mφ ∼ 1 one must worry about non-

perturbative effects and appropriately resum the ladder diagrams, in which case a numerical

calculation becomes motivated [7].

3 While the listed 90% errors are +.12 and −.16 × 10−5, we believe this was a typo, as the errors can be

read off from the sin2 θ plot in the paper.

4

report on the signal from the Perseus cluster individually. Thus, fitting this source gives a

simple test as to whether such a signal could arise from XDM. Similarly, the analysis of [12]

produces a fit to M31 (and a somewhat broader range of fit to Perseus), giving a second

candidate to consider. At the same time, no signal has arisen from the much closer Virgo

cluster, so this limit should be addressed.

Beginning with Perseus, [11] claims a 3.56 keV line flux of 5.2+3.70−2.13 ×

10−5photons cm−2 sec−1 (90% errors) with the cluster core or 2.14+1.12−1.05 × 10−5 without, aris-

ing from XMM MOS observations, and upper limits of 1.77× 10−5 and 1.61× 10−5 for the

same regions from the XMM PN observations. The Chandra ACIS-S and ACIS-I obser-

vations yielded fluxes of 1.02+0.48−0.47 × 10−5 and 1.86+1.2

−1.6 × 10−5.3 [12] claim a similar flux of

0.7+2.6−2.6 × 10−5 (MOS) and 0.92+3.1

−3.1 × 10−5 (PN).

For M31 [12] find a rate of 0.49+0.16−0.13 × 10−5cm−2sec−1. For Virgo [11] find an upper limit

of 0.91× 10−5cm−2sec−1.

A naive estimate of the total luminosity from Perseus can be found (assuming an NFW

profile) using the cluster parameters found in [13]

L =

! R200

0

4πr2"

ρ(r)

mχ

#2

⟨σscattv⟩

= 1.9× 1049photons/sec ×

"

⟨σscattv⟩

10−19cm3sec−1

#"

10GeV

mχ

#2

. (3)

With Perseus 78 Mpc away, this yields a local photon flux

Φ = 2.6× 10−5

"

⟨σv⟩

10−19cm3sec−1

#"

10GeV

mχ

#2

photons/sec. (4)

Clearly, this cross section is well above the conventional thermal annihilation cross section,

but since this is a scattering process, this cross section can be naturally large, as we now

describe.

The perturbative cross section for this scattering has a cross section

σ =4πM2

χα2d

m4φ

, (5)

where αd is the dark U(1) coupling constant. For αMχ/mφ ∼ 1 one must worry about non-

perturbative effects and appropriately resum the ladder diagrams, in which case a numerical

calculation becomes motivated [7].

3 While the listed 90% errors are +.12 and −.16 × 10−5, we believe this was a typo, as the errors can be

read off from the sin2 θ plot in the paper.

4

Nonetheless, such a cross section is easily achievable. The unitarity bound on the S-wave

component of the cross section is σv ∼ π/(M2χv) ∼ 10−16cm3 sec−1, for cluster velocities of

∼ .003c. Moreover, for light mediators and glancing collisions, the scattering is naturally

composed of multiple partial waves [7], yielding often an approximately geometric cross

section, i.e., 1/q2 or 1/m2φ for m2

φ > q2.

Thus, for mφ ∼ 100MeV, we expect a cross section saturating at levels as large as

4×10−26cm2 yielding σv ∼ 10−17cm3sec−1 for relative velocities of 2×1000 km/sec. Clearly,

achieving this level of rate is possible.

A. Estimating Rates

We now go about more precisely attempting to address the signals observed. While a

detailed fit to the full stacked cluster analysis is beyond our scope, we can reasonably attempt

to understand the Chandra observation of the line in Perseus, M31 and the non-observation

in Virgo.

While the NFW model is a simple and convenient parametrization, it is thought that

different histories can lead to different halo profiles [14]. In particular, Virgo is thought to

be a younger cluster, and may not have fully settled into a steep profile as yet. To study

the effects on the signal, we use a variant of the NFW profile

ρ(r) =ρ0

(r/Rs)γ(1 + r/Rs)3−γ, (6)

where we hold the total mass inside the virial radius fixed by varying ρ0.

To compare signals, we approximate the Chandra ACIS-I FOV (which is a 2× 2 array of

8′ × 8′ CCDs) by a 9′ disc, which has nearly the same angular size. For cuspy profiles (as

will be necessary to explain the data), the majority of the signal is in the central region,

thus the precise boundary is not important at the leading order. For M31, whose flux has

been found by [12] from XMM data, we take a radius around the inner 15’ as our region.

We will parametrize the predicted flux as

Φperseus = F 19,10perseus ×

!

⟨σv⟩perseus10−19cm3 sec−1

"!

10GeV

mχ

"2

. (7)

For inner slope profiles γ = (0.7, 1, 1.3) we find F 19,10perseus = (1.1, 2.0, 5.9)×10−5cm−2 sec−1.

While for Virgo, we find F 19,10virgo = (2.7, 9.6, 62)× 10−5cm−2 sec−1. Finally, for M31, F 19,10

M31 =

5

(Perseus)

THE SIGNAL

5 × (1.2, 3.7, 18)× 10−5cm−2 sec−1. Note that for M31, the characteristic velocity is ∼ ×5

lower than in Perseus, and we pull out an overall factor of 5 to make the comparison clearer.

B. More detailed calculation

The above calculation assumed that ⟨σscattv⟩ is independent of location in the cluster,

and has a fixed value in each system. As a more careful estimate, we now take

⟨σscattv⟩ = σmr

!

v2 − v2thresh, (8)

where σmr is the cross section in the “moderately relativistic” limit, and v is the relative

velocity of the WIMPs. We take the (3D, single-particle) rms velocity dispersion to be"

3/2vcirc, where vcirc is the circular velocity at the scale radius. At each radius we truncate

the velocity distribution at the escape velocity, vesc(r).

Taking a reference value of σmr = 10−28cm2, we get Fperseus = (0.12, 0.29, 1.1)× 10−5 in

a 9 arcmin radius for (0.7,1.0,1.3). Fvirgo = (0.47, 2.0, 13.0)× 10−5 in a 9 arcmin radius for

(0.7,1.0,1.3). FM31 = (0.29, 1.3, 9.6)× 10−5 in a 15 arcmin radius. As we see, the variation

with the slope γ is even more pronounced for this model. But the picture is qualitatively

the same as the naive model.

As a result, we see that for “pure” NFW profiles, there seems to be a conflict between the

non-observation in Virgo and the detection in Perseus. However, because the upscattering

process is proportional to ρ2, there is a significant dependence on the halo, and moderate

variations away from NFW can easily make these results consistent. More colloquiually, the

fact that we see Perseus and not Virgo may just be a measurement of their dark matter

profiles.

For M31, assuming that Perseus is relatively steep, we would expect a signal at a similar

order, but potentially larger or smaller. The claim of [12] for a similar flux is consistent with

this. Consequently, we find that DM-DM scattering can explain the presence of an X-ray

line in Perseus, consistent with non-observation in Virgo. Moreover, a comparable signal is

possible in M31.

Up to this point, we have assumed that the X-ray signal traces the scattering. For short

lifetimes of the excited state this is true, but for longer lifetimes this would not be. For

large dipoles, the excited WIMP decays rapidly and the X-ray signal traces the ρ2 profile.

In contrast, when the lifetime is long compared to the dynamical time of the cluster, the

6







!
















profiles.





possible in M31.





6







!
















profiles.





possible in M31.





6

Nonetheless, such a cross section is easily achievable. The unitarity bound on the S-wave

component of the cross section is σv ∼ π/(M2χv) ∼ 10−16cm3 sec−1, for cluster velocities of

∼ .003c. Moreover, for light mediators and glancing collisions, the scattering is naturally

composed of multiple partial waves [7], yielding often an approximately geometric cross

section, i.e., 1/q2 or 1/m2φ for m2

φ > q2.

Thus, for mφ ∼ 100MeV, we expect a cross section saturating at levels as large as

4×10−26cm2 yielding σv ∼ 10−17cm3sec−1 for relative velocities of 2×1000 km/sec. Clearly,

achieving this level of rate is possible.

A. Estimating Rates

We now go about more precisely attempting to address the signals observed. While a

detailed fit to the full stacked cluster analysis is beyond our scope, we can reasonably attempt

to understand the Chandra observation of the line in Perseus, M31 and the non-observation

in Virgo.

While the NFW model is a simple and convenient parametrization, it is thought that

different histories can lead to different halo profiles [14]. In particular, Virgo is thought to

be a younger cluster, and may not have fully settled into a steep profile as yet. To study

the effects on the signal, we use a variant of the NFW profile

ρ(r) =ρ0

(r/Rs)γ(1 + r/Rs)3−γ, (6)

where we hold the total mass inside the virial radius fixed by varying ρ0.

To compare signals, we approximate the Chandra ACIS-I FOV (which is a 2× 2 array of

8′ × 8′ CCDs) by a 9′ disc, which has nearly the same angular size. For cuspy profiles (as

will be necessary to explain the data), the majority of the signal is in the central region,

thus the precise boundary is not important at the leading order. For M31, whose flux has

been found by [12] from XMM data, we take a radius around the inner 15’ as our region.

We will parametrize the predicted flux as

Φperseus = F 19,10perseus ×

!

⟨σv⟩perseus10−19cm3 sec−1

"!

10GeV

mχ

"2

. (7)

For inner slope profiles γ = (0.7, 1, 1.3) we find F 19,10perseus = (1.1, 2.0, 5.9)×10−5cm−2 sec−1.

While for Virgo, we find F 19,10virgo = (2.7, 9.6, 62)× 10−5cm−2 sec−1. Finally, for M31, F 19,10

M31 =

5







!
















profiles.





possible in M31.





6







!
















profiles.





possible in M31.





6

(think 10-5 for Perseus, limit of 10-5 for Virgo, few x 10-6 for M31)

THE SIGNAL

II. MODELS


grangian2,

L = χi Dχi +1

4F dµνF













τ = 0.5 sec×

!

M

TeV

"2!keV

δ

"3

. (2)














3

Signal could look like 𝝆2, could look like 𝝆

Important: presence of dipole suggests kinetic mixing atsome loop order.

S. Riemer-Sørensen in prep

Looking in the MW center

My estimate is factor of 5-10 conflict unless dipole is

weak, in which case, no conflict as excited states

propagate out of the center

INTERACTIONS THROUGH A LIGHT SECTOR

↵d↵EM 2

m4

N N

𝜙 O(GeV)

easily generates large cross sections

DIRECT DETECTION 6

mWIMP (GeV/c2)

WIM

P−nu

cleo

n cr

oss

sect

ion

(cm

2 )

101 102 103

10−45

10−44

6 8 10 12

10−44

10−42

10−40

FIG. 5. The LUX 90% confidence limit on the spin-independent elastic WIMP-nucleon cross section (blue),together with the ±1 variation from repeated trials, wheretrials fluctuating below the expected number of events forzero BG are forced to 2.3 (blue shaded). We also showEdelweiss II [44] (dark yellow line), CDMS II [45] (greenline), ZEPLIN-III [46] (magenta line), CDMSlite [47] (darkgreen line), XENON10 S2-only [20] (brown line), SIMPLE [48](light blue line) and XENON100 100 live-day [49] (orangeline), and 225 live-day [50] (red line) results. The inset(same axis units) also shows the regions measured from annualmodulation in CoGeNT [51] (light red, shaded), along withexclusion limits from low threshold re-analysis of CDMS IIdata [52] (upper green line), 95% allowed region fromCDMS II silicon detectors [53] (green shaded) and centroid(green x), 90% allowed region from CRESST II [54] (yellowshaded) and DAMA/LIBRA allowed region [55] interpretedby [56] (grey shaded). Results sourced from DMTools [57].

upper limit on the number of expected signal eventsranges, over WIMP masses, from 2.4 to 5.3. A variationof one standard deviation in detection eciency shiftsthe limit by an average of only 5%. The systematicuncertainty in the position of the NR band was estimatedby averaging the di↵erence between the centroids ofsimulated and observed AmBe data in log(S2b/S1). Thisyielded an uncertainty of 0.044 in the centroid, whichpropagates to a maximum uncertainty of 25% in the highmass limit.

The 90% upper C. L. cross sections for spin-independent WIMP models are thus shown in Fig. 5with a minimum cross section of 7.61046 cm2 for aWIMP mass of 33 GeV/c2. This represents a significantimprovement over the sensitivities of earlier searches [45,46, 50, 51]. The low energy threshold of LUX permitsdirect testing of low mass WIMP hypotheses wherethere are potential hints of signal [45, 51, 54, 55].These results do not support such hypotheses basedon spin-independent isospin-invariant WIMP-nucleoncouplings and conventional astrophysical assumptions

for the WIMP halo, even when using a conservativeinterpretation of the existing low-energy nuclear recoilcalibration data for xenon detectors.

LUX will continue operations at SURF during 2014and 2015. Further engineering and calibration studieswill establish the optimal parameters for detectoroperations, with potential improvements in appliedelectric fields, increased calibration statistics, decayingbackgrounds and an instrumented water tank vetofurther enhancing the sensitivity of the experiment.Subsequently, we will complete the ultimate goal ofconducting a blinded 300 live-day WIMP search furtherimproving sensitivity to explore significant new regionsof WIMP parameter space.

This work was partially supported by the U.S.Department of Energy (DOE) under award numbersDE-FG02-08ER41549, DE-FG02-91ER40688, DE-FG02-95ER40917, DE-FG02-91ER40674, de-na0000979, DE-FG02-11ER41738, de-sc0006605, DE-AC02-05CH11231,DE-AC52-07NA27344, and DE-FG01-91ER40618; theU.S. National Science Foundation under award numbersPHYS-0750671, PHY-0801536, PHY-1004661, PHY-1102470, PHY-1003660, PHY-1312561, PHY-1347449;the Research Corporation grant RA0350; the Centerfor Ultra-low Background Experiments in the Dakotas(CUBED); and the South Dakota School of Mines andTechnology (SDSMT). LIP-Coimbra acknowledges fund-ing from Fundacao para a Ciencia e Tecnologia (FCT)through the project-grant CERN/FP/123610/2011. Im-perial College and Brown University thank the UK RoyalSociety for travel funds under the International ExchangeScheme (IE120804). The UK groups acknowledgeinstitutional support from Imperial College London,University College London and Edinburgh University,and from the Science & Technology Facilities Council forPh.D. studentship ST/K502042/1 (AB). The Universityof Edinburgh is a charitable body, registered in Scotland,with registration number SC005336. This research wasconducted using computational resources and services atthe Center for Computation and Visualization, BrownUniversity.

We acknowledge the work of the following engi-neers who played important roles during the design,construction, commissioning, and operation phases ofLUX: S. Dardin from Berkeley, B. Holbrook, R.Gerhard, and J. Thomson from University of California,Davis; and G. Mok, J. Bauer, and D. Carr fromLawrence Livermore National Laboratory. We gratefullyacknowledge the logistical and technical support andaccess to laboratory infrastructure provided to us by theSanford Underground Research Facility (SURF) and itspersonnel at Lead, South Dakota. SURF was developedby the South Dakota Science and Technology authority,with an important philanthropic donation from T. DennySanford, and is operated by Lawrence Berkeley NationalLaboratory for the Department of Energy, Oce of HighEnergy Physics.

9

IV. A NON-ABELIAN Gdark: INTEGRAL, DIRECT DETECTION, AND DAMA

Up to this point we have focused on a situation where there is a single force-carrying boson φ, whether vector or

scalar. Already, this can have significant phenomenological consequences. In mixing with the standard model Higgs

boson, there is a nuclear recoil cross section mediated by φ. With technically natural parameters as described in [18],

the rate is unobservable, although in a two-Higgs doublet model the cross section is within reach of future experiments

[45].

In contrast, an 800 GeV WIMP which interacts via a particle that couples to charge is strongly constrained. Because

the φ boson is light and couples to the electromagnetic vector current, there are strong limits. The cross section per

nucleon for such a particle is [43]

σ0 =16πZ2αSMαDarkϵ2µ2

ne

A2m4φ

(11)

=

!

Z

32

"2!73

A

"2# ϵ

10−3

$2 # αDark

137−1

$# µne

938 MeV

$

!

1 GeV

mφ

"4

× 1.8 × 10−37 cm2,

where αDark is the coupling of the φ to the dark matter, ϵ describes the kinetic mixing, µne is the reduced mass

of the DM-nucleon system and αSM is the standard model electromagnetic coupling constant. With the parameters

above, such a scattering cross section is excluded by the present CDMS [46] and XENON [47] bounds by 6 orders

of magnitude. However, this limit can be evaded by splitting the two Majorana components of the Dirac fermion

[22] or by splitting the scalar and pseudoscalar components of a complex scalar [48, 49]. Since the vector coupling

is off-diagonal between these states, the nuclear recoil can only occur if there is sufficient kinetic energy to do so. If

the splitting δ > v2µ/2 (where µ is the reduced mass of the WIMP-nucleus system) no scattering will occur. Such

a splitting can easily arise for a U(1) symmetry by a U(1) breaking operator such as 1M ψcψh∗h∗ which generates a

small Majorana mass and splits the two components (see [23] for a discussion).

Remarkably, for δ ∼ 100 keV one can reconcile the DAMA annual modulation signature with the null results of

other experiments [22, 23, 24], in the “inelastic dark matter” scenario. We find that the ingredients for such a scenario

occur here quite naturally. However, the splitting here must be O(100 keV) and the origin of this scale is unknown, a

point we shall address shortly.

Exciting Dark Matter from a Non-Abelian Symmetry

One of the strongest motivations for a ∼ GeV mass φ particle prior to the present ATIC and PAMELA data was

in the context of eXciting dark matter [18]. In this scenario, dark matter excitations could occur in the center of the

galaxy via inelastic scattering χχ→ χχ∗. If δ = mχ∗ − mχ>∼ 2me, the decay χ∗ → χe+e− can generate the excess of

511 keV x-rays seen from the galactic center by the INTEGRAL [50, 51] satellite. However, a large (nearly geometric)

cross section is needed to produce the large numbers of positrons observed in the galactic center, necessitating a boson

with mass of the order of the momentum transfer, i.e., mφ<∼ Mχv ∼ GeV, precisely the same scale as we require for

the Sommerfeld enhancement. But where does the scale δ ∼ MeV come from? Remarkably, it arises radiatively at

precisely the appropriate scale[67].

We need the dark matter to have an excited state, and we will further assume the dark matter transforms under

a non-Abelian gauge symmetry. Although an excited state can be present with simply a U(1), this only mediates

the process χχ → χ∗χ∗. If this requires energy greater than 4me it is very hard to generate enough positrons to

explain the INTEGRAL signal. If we assume the dark matter is a Majorana fermion, then it must transform as a

real representation of the gauge symmetry. For a non-Abelian symmetry, the smallest such representation will be

three-dimensional [such as a triplet of SU(2)]. This will allow a scattering χ1χ1 → χ2χ3. If m3 is split from m2 ∼ m1

by an amount δ ∼ MeV, we have arrived at the setup for the XDM explanation of the INTEGRAL signal.

Because the gauge symmetry is Higgsed, we should expect a splitting between different states in the dark matter

multiplet. This could arise already at tree-level, if the dark matter has direct couplings to the Higgs fields breaking

the gauge symmetry; these could naturally be as large as the dark gauge breaking scale ∼ GeV itself, which would

be highly undesirable, since we need these splittings to be not much larger than the DM kinetic energies in order to

5

Total phonon energy [keV]2 4 6 8 10 12

Ioni

zatio

n en

ergy

[keV

]

-1

0

1

2

3

4Lindhard nuclear-recoil energy [keVnr]

2 3 4 5 6 7 8 9T2Z1T2Z2T5Z2T5Z3

FIG. 3. Small gray dots are all veto-anticoincident single-scatter events within the ionization-partition fiducial volumethat pass the data-quality selection criteria. Large encircledshapes are the 11 candidate events. Overlapping shaded re-gions (from light to dark) are the 95% confidence contours ex-pected for 5, 7, 10 and 15 GeV/c2 WIMPs, after applicationof all selection criteria. The three highest-energy events occuron detector T5Z3, which has a shorted ionization guard. Theband of events above the expected signal contours correspondsto bulk electron recoils, including the 1.3 keV activation lineat a total phonon energy of 3 keV. High-radius events nearthe detector sidewalls form the wide band of events with near-zero ionization energy. For illustrative purposes, an approxi-mate nuclear-recoil energy scale is provided.

a WIMP-nucleon scattering interpretation of the excessreported by CoGeNT, which also uses a germanium tar-get. Similar tension exists with WIMP interpretationsof several other experiments, including CDMS II (Si),assuming spin-independent interactions and a standardhalo model. New regions of WIMP-nucleon scatteringfor WIMP masses below 6 GeV/c2 are excluded.

The SuperCDMS collaboration gratefully acknowl-edges the contributions of numerous engineers and tech-nicians. In addition, we gratefully acknowledge assis-tance from the sta↵ of the Soudan Underground Lab-oratory and the Minnesota Department of Natural Re-sources. The iZIP detectors were fabricated in the Stan-ford Nanofabrication Facility, which is a member of theNational Nanofabrication Infrastructure Network. Thiswork is supported in part by the National Science Foun-dation, by the United States Department of Energy, byNSERC Canada, and by MultiDark (Spanish MINECO).Fermilab is operated by the Fermi Research Alliance,LLC under Contract No. De-AC02-07CH11359. SLAC isoperated under Contract No. DE-AC02-76SF00515 withthe United States Department of Energy.

FIG. 4. The 90% confidence upper limit (solid black) based onall observed events is shown with 95% C.L. systematic uncer-tainty band (gray). The pre-unblinding expected sensitivityin the absence of a signal is shown as 68% (dark green) and95% (light green) C.L. bands. The disagreement between thelimit and sensitivity at high WIMP mass is due to the eventsin T5Z3. Closed contours shown are CDMS II Si [3] (dottedblue, 90% C.L.), CoGeNT [4] (yellow, 90% C.L.), CRESST-II[5] (dashed pink, 95% C.L.), and DAMA/LIBRA [34] (dash-dotted tan, 90% C.L.). 90% C.L. exclusion limits shown areCDMS II Ge [22] (dotted dark red), CDMS II Ge low-threshold[17] (dashed-dotted red), CDMSlite [20] (solid dark red), LUX[35] (solid green), XENON10 S2-only [19, 36] (dashed darkgreen), and EDELWEISS low-threshold [18] (dashed orange).

Corresponding author: [email protected][1] J. L. Feng, Ann. Rev. Astro. Astrophys., 48, 495 (2010).[2] M. W. Goodman and E. Witten, Phys. Rev. D, 31, 3059

(1985).[3] R. Agnese et al. (CDMS Collaboration), Phys. Rev. Lett.,

111, 251301 (2013).[4] C. E. Aalseth et al. (CoGeNT Collaboration), Phys. Rev.

D, 88, 012002 (2013).[5] G. Angloher et al., Eur. Phys. J. C, 72, 1971 (2012).[6] R. Bernabei et al., Eur. Phys. J. C, 67, 39 (2010).[7] D. Hooper and T. Linden, Phys. Rev. D, 84, 123005

(2011).[8] D. B. Kaplan, Phys. Rev. Lett., 68, 741 (1992).[9] D. E. Kaplan, M. A. Luty, and K. M. Zurek, Phys. Rev.

D, 79, 115016 (2009).[10] A. Falkowski, J. Ruderman, and T. Volansky, J. High

Energy Phys., 1105, 106 (2011).[11] R. R. Volkas and K. Petraki, Int. J. Mod. Phys. A, 28,

1330028 (2013).[12] K. M. Zurek, (2013), arXiv:1308.0338.[13] R. Essig, J. Kaplan, P. Schuster, and N. Toro, (2010),

arXiv:1004.0691.[14] C. Cheung, J. T. Ruderman, L.-T. Wang, and I. Yavin,

Phys. Rev. D, 80, 035008 (2009).[15] D. Hooper and W. Xue, Phys. Rev. Lett., 110, 041302

PARAMETER SPACE

• Large self-scattering cross sections suggest light (~100 MeV) mediator

• Direct detection limits suggest small mixing unless dark matter is below ~ 5 or 6 GeV

A SIGNAL IN THE GC/IG

7

0.5-1 GeV residual

-20-1001020 00

-20

-10

0

10

20

00

0

5

10

15

20

0

5

10

15

20

10-6 counts/cm

2/s/sr

1-2 GeV residual

-20-1001020 00

-20

-10

0

10

20

00

0

2

4

6

8

10

0

2

4

6

8

10

10-6 counts/cm

2/s/sr

2-5 GeV residual

-20-1001020 00

-20

-10

0

10

20

00

0

1

2

3

4

5

0

1

2

3

4

5

10-6 counts/cm

2/s/sr

5-20 GeV residual

-20-1001020 00

-20

-10

0

10

20

00

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

10-6 counts/cm

2/s/sr

FIG. 6: Intensity maps (in galactic coordinates) after subtracting the best-fit Galactic di↵use model, Fermi bubbles, andisotropic templates. At energies between 0.5-5 GeV (i.e. in the first three frames), the dark-matter-like emission is clearlyvisible around the Galactic Center.

analysis of Ref. [8], the cut on CTBCORE significantlyhardens the spectrum at energies below 1 GeV, render-ing it more consistent with that extracted at higher lati-tudes (see Appendix A). Shown for comparison (as a solidline) is the spectrum predicted from a 35.25 GeV darkmatter particle annihilating to bb with a cross section ofv = 1.7 1026 cm3/s [(0.3GeV/cm3)/

local

]2. Thespectrum of this component is in good agreement withthat predicted by this dark matter model, yielding a fitof 2 = 26.4 over the 25 error bars between 0.3 and 100GeV. We also note that the spectral shape of the darkmatter template is quite robust to variations in , exceptat energies below 600 MeV, where the spectral shape

can vary non-negligibly with the choice of inner slope (seeAppendix C).

In Fig. 6, we plot the maps of the gamma-ray sky infour energy ranges after subtracting the best-fit di↵usemodel, Fermi Bubbles, and isotropic templates. In the0.5-1 GeV, 1-2 GeV, and 2-5 GeV maps, the dark-matter-like emission is clearly visible in the region surroundingthe Galactic Center. Much less central emission is vis-ible at 5-20 GeV, where the dark matter component issignificantly less bright.

15

any new signal is, in fact, the result of annihilating darkmatter.

There are significant reasons to conclude, however,that the gamma-ray signal described in this paper is farmore likely to be a detection of dark matter than anyof the previously reported anomalies. Firstly, this signalconsists of a very large number of events, and has beendetected with overwhelming statistical significance. Thethe excess consists of 104 gamma rays per square meter,per year above 1 GeV (from within 10 of the GalacticCenter). Not only does this large number of events en-able us to conclude with confidence that the signal ispresent, but it also allows us to determine its spectrumand morphology in some detail. And as shown, the mea-sured spectrum, angular distribution, and normalizationof this emission does indeed match well with that ex-pected from annihilating dark matter particles.

Secondly, the gamma-ray signal from annihilating darkmatter can be calculated straightforwardly, and generallydepends on only a few unknown parameters. The mor-phology of this signal, in particular, depends only on thedistribution of dark matter in the Inner Galaxy (as pa-rameterized in our study by the inner slope, ). Thespectral shape of the signal depends only on the mass ofthe dark matter particle and on what Standard Modelparticles are produced in its annihilations. The Galac-tic gamma-ray signal from dark matter can thus be pre-dicted relatively simply, in contrast to, e.g., dark mattersearches using cosmic rays, where putative signals area↵ected by poorly constrained di↵usion and energy-lossprocesses. In other words, for the gamma-ray signal athand, there are relatively few “knobs to turn”, makingit less likely that one would be able to mistakenly fit awell-measured astrophysical signal with an annihilatingdark matter model.

Thirdly, we once again note that the signal described inthis study can be explained by a very simple dark mattercandidate, without any baroque or otherwise unexpectedfeatures. After accounting for uncertainties in the overallmass of the Milky Way’s dark matter halo profile [17],our results favor dark matter particles with an annihi-lation cross section of v = (0.7 3.9) 1026 cm3/s(for annihilations to bb, see Fig. 15). This range coversthe long predicted value that is required of a thermalrelic that freezes-out in the early universe with an abun-dance equal to the measured cosmological dark matterdensity (2.2 1026 cm3/s). No substructure boost fac-tors, Sommerfeld enhancements, or non-thermal historiesare required. Furthermore, it is not dicult to constructsimple models in which a 30-40 GeV particle annihi-lates to quarks with the required cross section withoutviolating constraints from direct detection experiments,colliders, or other indirect searches (for work related toparticle physics models capable of accommodating thissignal, see Refs. [62–74]).

And lastly, the dark matter interpretation of this signalis strengthened by the absence of plausible or well moti-vated alternatives. There is no reason to expect that any

di↵use astrophysical emission processes would exhibit ei-ther the spectrum or the morphology of the observedsignal. In particular, the spherical symmetry of the ob-served emission with respect to the Galactic Center doesnot trace any combination of astrophysical components(i.e. radiation, gas, dust, star formation, etc.), but doesfollow the square of the anticipated dark matter density.

The astrophysical interpretation most often discussedwithin the context of this signal is that it might originatefrom a large population of unresolved millisecond pul-sars. The millisecond pulsars observed within the MilkyWay are largely located either within globular clustersor in or around the Galactic Disk (with an exponentialscale height of zs 1 kpc [11, 75]). This pulsar popu-lation would lead to a di↵use gamma-ray signal that ishighly elongated along the disk, and would be highly in-compatible with the constraints described in Sec. VI. Forexample, the best-fit model of Ref. [75], which is basedon the population of presently resolved gamma-ray mil-lisecond pulsars, predicts a morphology for the di↵usegamma-ray emission exhibiting an axis ratio of 1-to-6.Within 10 of the Galactic Center, this model predictsthat millisecond pulsars should account for 1% of theobserved di↵use emission, and less than 5-10% of thesignal described in this paper.

To evade this conclusion, however, one could contem-plate an additional (and less constrained) millisecondpulsar population associated with the Milky Way’s cen-tral stellar cluster. This scenario can be motivated bythe fact that globular clusters are known to contain largenumbers of millisecond pulsars, presumably as a conse-quence of their very high stellar densities. If our galaxy’scentral stellar cluster contains a large number of mil-lisecond pulsars with an extremely concentrated distribu-tion (with a number density that scales approximately asnMSP

/ r2.4), those sources could plausibly account formuch of the gamma-ray excess observed within the inner1 around the Galactic Center [2, 4–7, 10]. It is muchmore challenging, however, to imagine that millisecondpulsars could account for the more extended componentof this excess, which we have shown to be present outto at least 10 from the Galactic Center. Expecta-tions for the Inner Galaxy’s pulsar population are notconsistent with such an extended distribution. Further-more, if the required number of millisecond pulsars werepresent 10 (1.5 kpc) north or south of the GalacticCenter, a significant number of these sources would havebeen resolved by Fermi and appeared within the 2FGLcatalog (assuming that the pulsars in question have asimilar luminosity function to other observed millisecondpulsars) [11, 44, 75]. The lack of such resolved sourcesstrongly limits the abundance of millisecond pulsars inthe region of the Inner Galaxy. Furthermore, the shapeof the gamma-ray spectrum observed from resolved mil-lisecond pulsars and from globular clusters (whose emis-sion is believed to be dominated by millisecond pulsars)appears to be not-insignificantly softer than that of thegamma-ray excess observed from the Inner Galaxy. In

15










15










not hard to make models ≠ not baroque

20 40 60 80 100

-48

-46

-44

-42

-40

20 40 60 80 100

-48

-46

-44

-42

-40

20 40 60 80 100

-48

-46

-44

-42

-40

20 40 60 80 100

-48

-46

-44

-42

-40

mS [GeV]

mS [GeV]

mS [GeV]

mS [GeV]

mh = 100 GeV

mh = 140 GeV

mh = 120GeV

mh = 200GeV

log

σel(

nucl

eon)!

cm2"

log

σel(

nucl

eon)!

cm2"

log

σel(

nucl

eon)!

cm2"

log

σel(

nucl

eon)!

cm2"

Figure 4: The predictions for the elastic cross section, σel, as a function of mS, which

follows from the λ(mS) dependence dictated by the cosmic abundance. Also shown by

a dashed line is the exclusion limit from the CDMS experiment [6] .

falsify than are more complicated models, with much of the parameter space covered

by the next generation of experiments [4]. Most importantly, the projected sensitivities

of the CDMS-Soudan and Genius experiments will completely cover the range mS ≤ 50

GeV, for values of the Higgs mass between 110 and 140 GeV. As we show in the next

section, this range of masses and coupling constants has important implications for the

Higgs searches at colliders. On the other hand, there exists the possibility of completely

“hiding” the dark matter by choosing 0.4mh <∼ mS ≤ 0.5mh. In this case annihilation

at freeze-out is very efficient, requiring small λ’s which lead to elastic cross sections

suppressed to the level of 10−48 cm2. These levels of sensitivity to σel(nucleon) are not

likely to be achieved in the foreseeable future.

Our model of a singlet real scalar predicts a smaller signal for underground detectors

than does a model where the dark matter consists of N singlet scalars (including the

model considered in ref. [10], for which N = 2). This is because the abundance of every

individual species must be 1/N of the total dark matter abundance, Ωi = Ωtot/N . This

requires a larger annihilation rate at freeze-out for every species, and so an enhancement

14

Burgess, Pospelov and ter Veldhuis ‘01

LUX limits ~ 10-45cm2

bative analysis which we present. Couplings to all Standard Model fields are controlled

by the single parameter λ.

We now identify what constraints are implied for these couplings by general con-

siderations like vacuum stability or from the requirement that the vacuum produce an

acceptable symmetry-breaking pattern. These are most simply identified in unitary

gauge,√

2H† = (h, 0) with real h, where the scalar potential takes the form:

V =m2

0

2S2 +

λ

2S2h2 +

λS

4S4 +

λh

4

!

h2 − v2EW

"2. (2.2)

λh and vEW = 246 GeV are the usual parameters of the Standard Model Higgs potential.

1. The Existence of a Vacuum: This potential is bounded from below provided

that the quartic couplings satisfy the following three conditions:

λS, λh ≥ 0 and (2.3)

λS λh ≥ λ2 for negative λ.

We shall assume that these relations are satisified and study the minima of the scalar

potential.

2. Desirable Symmetry Breaking Pattern: We demand the minimum of V to have

the following two properties: It must spontaneously break the electroweak gauge group,

⟨h⟩ = 0; and it must not break the symmetry S → −S, so ⟨S⟩ = 0. The first of these

is an obvious requirement in order to have acceptable particle masses, while the second

is necessary in order to ensure the longevity of S in a natural way. (S particles must

survive the age of the universe in order to play their proposed present role as dark

matter.)

The configuration h = 0 and S = 0 is a stationary point of V if and only if v2EW

> 0,

in which case the extremum occurs at h2ext = v2

EW. This is a local minimum if and only

if

m20 + λ v2

EW> 0. (2.4)

A second local minimum, with hext = 0 and S2ext = −m2

0/λS, can also co-exist with the

desired minimum if λ > 0 and λ2 < λhλS. This second minimum is present so long

as m20 < 0 and −λm2

0 > λSλhv2EW

. Even in this case, the minimum at Sext = 0 and

h2ext = v2

EWis deeper, and so is the potential’s global minimum, provided that

0 < −m20 < v2

EW

#

λhλS. (2.5)

5

2

Therefore, we are led to consider a pseudoscalar media-tor, instead of a scalar, between the (fermionic) DM andthe SM, leading to an e↵ective dimension-six operator ofthe form

Le↵ =mb

3i5bi5b, (1)

where is the DM. This operator has been singled outpreviously as a good candidate to describe the e↵ectiveinteraction between the SM and the dark sector [12, 13].It implies s-wave DM annihilation, which allows thegamma ray excess to be fit while having a large enoughsuppression scale that it is not immediately ruled outby collider measurements of monojets/photons. The di-rect detection signal from this operator is spin-dependentand velocity-suppressed, rendering it safe from currentconstraints.

To move beyond the e↵ective, higher dimensional op-erator in Eq. (1) requires confronting electroweak sym-metry breaking because the SM portion of Le↵ is not anelectroweak singlet:

bi5b = ibLbR bRbL

. (2)

Therefore, Le↵ has to include the Higgs field (whichwould make it a singlet) which then gets a vacuum ex-pectation value (VEV), implying a mediator which cancouple to the Higgs.

It is easy to construct a scalar-scalar interaction be-tween DM and the SM using the “Higgs portal” operatorH†H, where H is the SM Higgs doublet, since it is aSM gauge singlet. This portal has been well explored inthe literature, particularly in its connection to DM [14].In this paper, however, we expand the Higgs sector ofthe SM to include a second doublet, which has enoughdegrees of freedom to allow for a pseudoscalar to mixwith the dark matter mediator. In the presence of CPviolation one could also induce a pseudoscalar-scalar cou-pling via this portal, however it is puzzling why a newboson with CP violating couplings would not also have ascalar coupling to the dark fermion. Including two Higgsdoublets allows CP to be an approximate symmetry ofthe theory, broken by the SM fermion Yukawa couplingmatrices. Tiny CP violating couplings will need to beincluded in order to renormalize the theory at high or-ders in perturbation theory, but we simply assume thatall flavor and CP violation is derived from spurions pro-portional to the Yukawa coupling matrices, and so hasminimal e↵ect on the Higgs potential and dark sector.

The outline of this paper is as follows. In Sec. II weintroduce the two Higgs doublet model (2HDM) and thepseudoscalar mediator which mixes with the Higgs sector.We also discuss CP violation in the dark sector and ininteractions between DM and SM fermions. We brieflydiscuss the annihilation cross section for our DMmodel inSec. III. In Sec. IV, we catalog constraints on this model,such as direct detection, Higgs and B meson decays, andmonojets. Section V contains our conclusions.

II. THE MODEL

A. CP-Conserving Extended Higgs Sector

As mentioned above, a straightforward way to coupledark matter to the SM through pseudoscalar exchange isby mixing the mediator with the pseudoscalar Higgs in a2HDM.For concreteness, we take the DM to be a Dirac

fermion, , with mass m, coupled to a real, gauge sin-glet, pseudoscalar mediator, a0, through

Ldark = ya0i5. (3)

The mediator couples to the SM via the Higgs portal inthe scalar potential which is

V = V2HDM +1

2m2

a0a20 +

a

4a40 + Vport, (4)

Vport = iBa0H†1H2 + h.c. (5)

with H1,2 the two Higgs doublets. B is a parameter withdimensions of mass. We assume that Ldark and V are CP-conserving (i.e. B and y are both real, and there is noCP violation in V2HDM) and we will comment on relaxingthis assumption in Sec II B. In this case, a0 does notdevelop a VEV.We write the most general CP-conserving2HDM potential as

V2HDM = 1

H†

1H1 v212

2

+ 2

H†

2H2 v222

2

+ 3

H†

1H1 v212

+

H†

2H2 v222

2(6)

+ 4

hH†

1H1

H†

2H2

H†

1H2

H†

2H1

i

+ 5

hRe

H†

1H2

v1v2

2

i2+ 6

hIm

H†

1H2

i2,

with all i real. We have also imposed a Z2 symmetryunder whichH1 ! H1 andH2 ! H2 to suppress flavor-changing neutral currents, which is only softly broken byV2HDM and Vport. The potential is minimized at hHii =(0, vi/

p2)T, i = 1, 2, and the W and Z masses fix v21 +

v22 = v2 = (246 GeV)2. The angle is defined by tan =v2/v1. In unitary gauge we can decompose the doubletsas

Hi =1p2

p2+

ivi + i + ii

. (7)

The spectrum contains a charged Higgs,

H± = sin ±1 cos ±

2 , (8)

with mass m2H± = 4v

2/2.The CP-even Higgs mass matrix in the (1, 2) basis is

2


Le↵ =mb

3i5bi5b, (1)



bi5b = ibLbR bRbL

. (2)




II. THE MODEL




Ldark = ya0i5. (3)


V = V2HDM +1

2m2

a0a20 +

a

4a40 + Vport, (4)



V2HDM = 1

H†

1H1 v212

2

+ 2

H†

2H2 v222

2

+ 3

H†

1H1 v212

+

H†

2H2 v222

2(6)

+ 4

hH†

1H1

H†

2H2

H†

1H2

H†

2H1

i

+ 5

hRe

H†

1H2

v1v2

2

i2+ 6

hIm

H†

1H2

i2,




Hi =1p2

p2+

ivi + i + ii

. (7)



2 , (8)



2


Le↵ =mb

3i5bi5b, (1)



bi5b = ibLbR bRbL

. (2)




II. THE MODEL




Ldark = ya0i5. (3)


V = V2HDM +1

2m2

a0a20 +

a

4a40 + Vport, (4)



V2HDM = 1

H†

1H1 v212

2

+ 2

H†

2H2 v222

2

+ 3

H†

1H1 v212

+

H†

2H2 v222

2(6)

+ 4

hH†

1H1

H†

2H2

H†

1H2

H†

2H1

i

+ 5

hRe

H†

1H2

v1v2

2

i2+ 6

hIm

H†

1H2

i2,




Hi =1p2

p2+

ivi + i + ii

. (7)



2 , (8)



+ harder hierarchy problem + no sannihilon (scalar annihilon)

Ipek, McKeen, Nelson ‘14

GC SIGNALS OF XDM MODELS

Liu, NW, Xue in prep

Easy to write down

determination of baroquocity left to the reader

Liu, NW, Xue in prep

0.5 1.0 5.0 10.0 50.0 100.0-1.¥ 10-6

0

1.¥ 10-6

2.¥ 10-6

3.¥ 10-6

Eg HGeVL

E2JHEL@G

eVcm-2s-1sr-1D

Dark photon best-fit

4e±

4m±

4p±Total

mDM=10.4GeV, mDF=690MeV, B=8.5

0.5 1.0 5.0 10.0 50.0 100.0-1.¥ 10-6

0

1.¥ 10-6

2.¥ 10-6

3.¥ 10-6

Eg HGeVL

E2JHEL@G

eVcm-2s-1sr-1D


e+e-

p+p-p0p0

wp0Æ2p0g

Total

mDM=7GeV, mDF=1200MeV, B=0.63

0.5 1.0 5.0 10.0 50.0 100.0-1.¥ 10-6

0

1.¥ 10-6

2.¥ 10-6

3.¥ 10-6

Eg HGeVL

E2JHEL@G

eVcm-2s-1sr-1D


e+e-˛+˛-

m+m-

p0g

Total

mDM=5GeV, mDF=6.9MeV, B=2.5

You only need to worry about this if you worry about the 3.5 keV line!

Otherwise - inelasticity solves your DD constraints

PARAMETER SPACE

• Somewhat agnostic at this point

• Differing opinions on what is “best fit”

• Maybe radiative maybe tree level signals better - not clear

• Errors not under control

• 5 GeV maybe ok?

CONCLUSIONS• Our range of Dark Matter Models has been enlarged - this is

motivated both from a simple theoretical idea as well as potential signals

• The present set of anomalies - PAMELA+, XMM/Chandra, Fermi - that motivate dark photons are intriguing but not yet smoking gun evidence for DM

• Easy to get 2 of 3, but DD constraints make hard for these to be discoverable in next round of experiments.

DARK PHOTONS THEORY AND MOTIVATIONS · DARK PHOTONS THEORY AND MOTIVATIONS Neal Weiner NYU - CCPP...

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Transcript of DARK PHOTONS THEORY AND MOTIVATIONS · DARK PHOTONS THEORY AND MOTIVATIONS Neal Weiner NYU - CCPP...