Physics of Dark Gauge Interaction (KPS 2016 spring Open...

U(1)’ instead of R-parity

1

Physics of Dark Gauge Interaction (with an emphasis on low-energy parity test implications)

Hye-Sung Lee IBS Center for Theoretical Physics of the Universe

KPS 2016 Meeting (Open KIAS Session) Daejeon, April 20, 2016

Outline

1. Brief history of sin2 θW physics [mixing angle of SU(2)L & U(1)Y]

2. Dark Force Models (Dark Photon, Dark Z)

3. Typical Dark force searches (based on dilepton decay channels)

4. Invisibly decaying Dark gauge boson case (Z’ → 𝝌𝝌)

5. Importance of Low-Energy parity test (precise measurement of sin2 θW)

6. General message

* Dark force searches at the LHC (e.g. using rare Higgs decay) will not be covered in this talk.

Brief History of sin2 θW physics

CERN Gargamelle

1961. Glashow introduced SU(2)L×U(1)Y symmetry (W±, W0, B).

1967. Weinberg added the Higgs mechanism (with a Higgs doublet and a vev). and also predicted the weak neutral currents mediated by Z.

1973. Neutral currents (predicted in the SM) were discovered in 𝜈 scatterings. But is the SM a correct theory for the neutral currents?

Parity Test (weak mixing angle) can tell.

1978. SLAC E122 (polarized eD scattering) measured Parity Violation asymmetry (σR-σL / σR+σL), which gave sin2 θW ≈ 0.22(2).

Parity Test established SU(2)L×U(1)Y as the EW interaction structure.

History of sin2 θW physics

mW = mZ cos ✓W

Aµ = cos ✓WBµ + sin ✓WW 0µ , Zµ = � sin ✓WBµ + cos ✓WW 0

µ

(mass relation with θW is given)

g

cos ✓WZµ

¯f�µ�T3f � 2Qf sin

2 ✓W � T3f�5�f

(Agreed with the SM)

Lessons from the historyEstablishment of the SU(2)L×U(1)Y by the parity test (1978) at SLAC occurred much earlier than the direct discovery of the W±/Z boson resonances (1983) at CERN SPS.

LESSONS from the history: (i) Parity Test (by precise measurement of sin2 θW) can be a critical way to search for a new gauge interaction. (ii) Its finding may precede the direct discovery of a gauge boson (by bump search).

Neutral Current

Parity Test

In the Press release from Nobel foundation:

Weak mixing angle running and current constraints

!3 !2 !1 0 1 2 3

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Log10 Q !GeV"

sin2Θ W#Q2 $

SM prediction


APV!Cs"

Qweak !first"E158

SLAC

LEP

Ν"DIS

PVDIS

"3 "2 "1 0 1 2 3

0.230

0.232

0.234

0.236

0.238

0.240

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Log10 Q #GeV$

sin2Θ W!Q2 "

APV!Cs"

Qweak !first"E158

SLAC

LEP

Ν"DIS

PVDIS

APV!Ra#" MollerP2Qweak

SOLID

''Anticipated sensitivities''

"3 "2 "1 0 1 2 3

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Log10 Q #GeV$

sin2 ΘW!Q2 "


Dark force (Light Z’) models

Dark gauge boson : a gauge boson with very small mass and very small coupling, with motivations from the Dark matter physics [e.g. positron excess, self-interacting dark matter] and others [e.g. gµ-2 anomaly].

Dark gauge boson

- Roughly, MeV - GeV scale - Extremely weak couplings to the SM particles

Z’ (Dark Force carrier)

(Ex: Dark Photon)

⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ ⎮ MeV GeV TeV PeV

(Z’ mass)

Heavy Z’ (~ TeV scale) : Traditional target of discovery.

Light Z’ (~ MeV - GeV scale) : Recently highlighted subject with growing interest.

(i) Popular Model: “Dark Photon” • Z’ mass = MeV - GeV • Z’ coupling = ε×(Photon coupling)

f

f̄Z ′Z

×εZ

f

f̄Z ′γ

×ε Light Z’ models

(ii) New Model: “Dark Z” • Z’ mass = MeV - GeV (cf. Z mass = 91 GeV) • Z’ coupling = ε×(Photon coupling) + εZ×(Z coupling)

[Davoudiasl, LEE, Marciano (2012)]

inherits properties of Z boson like parity violation. (different couplings for left/right-handed particles)

[Arkani-Hamed et al (2008); and others]

Z’ : a gauge boson of dark sector U(1).

couples to the SM particles only through small mixing with SM gauge bosons.

Lkin = �1

4

Bµ⌫Bµ⌫+

1

2

"

cos ✓WBµ⌫Z 0µ⌫ � 1

4

Z 0µ⌫Z 0µ⌫

model-dependent

Bµ = cos ✓W Aµ � sin ✓W Zµ

[ ]

[ ](Coupling to JNC is largely cancelled, for mZ0 ⌧ mZ .)

Higgs structure matters

Dark Force couplings depend on “Higgs sector”.

( ) (Kinetic mixing diagonalization)

(Z-Z’ mass matrix diagonalization)(for Higgs singlet)(depends on Higgs sector)

Lint = �" eJµemZ 0

µ

Lint = �[" eJµem + "Z (g/2 cos ✓W )Jµ

NC ]Z0µ JNC

µ =✓

12T3f �Qf sin2 ✓W

◆f̄�µf �

✓12T3f

◆f̄�µ�5f

Lint = �eJµemAµ � (g/2 cos ✓W )Jµ

NCZµ

! �eJµem[Aµ + "Z 0

µ]� (g/2 cos ✓W )JµNC [Zµ � " tan ✓WZ 0

µ]

! �eJµem[Aµ + "Z 0

µ]� (g/2 cos ✓W )JµNCZµ

Model-dependence in coupling comes from how Z’ gets a mass (or Higgs sector). - Dark Photon: (Example) additional Higgs singlet gives mass to Z’

coupling = ε×(Photon coupling)

- Dark Z: (Example) additional Higgs doublet (+ singlet) gives mass to Z’ coupling = ε×(Photon coupling) + εZ×(Z coupling)

(Example) Dark Photon case : Z-Z’ kinetic mixing is cancelled by Z-Z’ mass mixing (which is “induced by kinetic mixing”) at Leading Order.

Effects of New Model (Dark Z)

‧ Dark Z = Dark Photon with more general coupling. ‧Dark Photon = a special case of Dark Z (εZ = 0 limit).

Some experiments irrelevant to Dark Photon searches become relevant to Dark Z searches. They include “Low-Q2 Parity Tests”.

ε

Z’ mass

ε

Z’ mass

Lint = �" eJµemZ 0

µ

(Dark Photon) (Dark Z)

Parameter space (Z’ mass and coupling to the SM) is extended from 2D to 3D.

εZ (Z-Z’ mixing) : parity violating

Lint = �[" eJµem + "Z (g/2 cos ✓W )Jµ

NC ]Z0µ

mZ’ << mZ

(will be back to this later)

Typical Dark Force Searches (Bump hunt of a new resonance)

𝑎µ = (gµ - 2) / 2 : Always an important motivation/constraint for New Physics.

- One of the major motivations for the light Dark gauge boson (Z’). - Unlike other motivations, it is independent of the unknown DM properties. - It is independent of the Z’ decay BR.

�aµ = aexpµ � aSMµ = (288± 80)⇥ 10�11 3.6σ level discrepancy

Muon Anomalous Magnetic Moment

- Brookhaven E821 result : 3.6σ level discrepancy. (Cf. Tau data now agrees with e+e- data, confirming the deviation.)

- FermiLab E989 (with intense muon beam) will start data taking in 2017 (for 18 months) : up to 5σ level expected. (External B-field)

(-Muon spin)

Precession

𝑎µ = (gµ - 2) / 2 : Always an important motivation/constraint for New Physics.

- One of the major motivations for the light Dark gauge boson (Z’). - Unlike other motivations, it is independent of the unknown DM properties. - It is independent of the Z’ decay BR.

aΜ !3Σ"aΜ ex

plained !90# CL"

a e!3Σ"

a e!2Σ"

a e!95#"

5 10 50 100 500 10001$10%7

5$10%7

1$10%6

5$10%6

1$10%5

5$10%5

1$10%4

mdark photon #MeV$

!2

�aµ = aexpµ � aSMµ = (288± 80)⇥ 10�11 3.6σ level discrepancy

Muon Anomalous Magnetic Moment𝜺2

= 𝛼

’/𝛼

Mdark photon [MeV]

Z ′

γ

µ µ

Green band: explains the 3.6σ deviation in 𝑎µ

a possible hint of Dark Force [Gninenko, Krasnikov (2001); Pospelov (2008)]

(magnetic moment) = �gµBS

~

Bump searches of Light Z’[Current constraints]

arXiv:1507.02330

With 2015 results [CERN NA48/2 using pion decay closes the last gap (2015)]: whole green band (gµ-2 favored) is excluded now. [for a visibly-decaying case]

We need to keep probing the other parameter space (Intensity Frontier).

Mostly from the Z’ → l+l− searches

(i) Electron, Muon g-2 (ii) Beam-dumps (iii) Meson (quarkonium) decays (iv) e+e- collision (photon+Z’) (v) Fixed target experiments

[Dark Photon & Dark Z boson] (as εZ is tiny)

Bump searches of Light Z’

“Dark gauge boson” physics is a rapidly-developing field.

-210 -110 1

-1010

-910

-810

-710

-610

-510

-410

BaBar

MAMIKLOE

ea

TestAPEX

Full

HPSE774

E141

E137

DarkLight

VEPP3

A' is 'welcome'µa

A' is excludedµa

(GeV)Um-210 -110 1

α'/α

-1010

-910

-810

-710

-610

-510

-410

𝜺2 =

𝛼’/𝛼

[ 2011 constraints and plans]

arXiv:1109.4855

Unfilled curves:proposed experiments

Budker (Russia)

KEK (Japan)

BES (China)

Mainz (Germany)GSI (Germany)

CERN (Europe)INFN (Italy)

FNAL (USA)Orsay (France)

BNL (USA)JLab (USA)

SLAC (USA)

Jülich (Germany)

Dark Force searches in the Labs

Many searches for Dark Force in the Labs around the world (ongoing/proposed).

Exciting time! (With some exaggeration)

Whole world is searching for a new fundamental force.

Text

FEL: DarkLight

Hall A: APEX Hall B: HPS

A B C

Free Electron Laser

“Dark Photon” searches(Fixed target experiments)

ContinuousElectron Beam (up to 12 GeV)

Dark Force searches at Jefferson Lab Nuclear/Hadronic Physics Lab

BDX

New Fixed target (Tantalium Z=73) experiment designed for direct Dark Photon production/detection.

Example: A’ Experiment (APEX) at JLab - Hall A

180 200 220 240 2601001000104105106107108

e+e- mass HMeVL

EventsêH1

MeVL

2s5s

[APEX Collaboration]

SM bkgsignal

Dark Photon Bremsstrahlung

Z’e

fixed target

Z’ ➞ e+e- narrow resonance at Z’ mass (Direct bump search at Low-energy facility)

The High Resolution Spectrometers (HRS) at Hall A are used.

Typical Dark Force searches in meson decays are performed in flavor-conserving ones with quarkoniums (qqbar-type mesons).

d

d̄π

γ

e+

e−γ Z ′×ε

Example: Meson decays into Light Z’

π(dd) ➞ ɣ Z’ ➞ ɣ + dilepton-resonance

Flavor-conserving meson decays π(dd), η(dd) ➞ ɣ Z’ (WASA, HADES, PHENIX, NA48/2) 𝝓(ss) ➞ η Z’ (KLOE) Υ(bb) ➞ ɣ Z’ (BABAR)

: Important searches for the Dark Force

(Direct bump search)

Dark Photon from Meson decays

Invisibly decaying Dark gauge boson (Missing energy search)

Invisible Dark Gauge Boson

Visible Dark Gauge Boson

Z’ → ℓ+ℓ− is the major decay mode in an ordinary scenario.

Visible/Invisible decay of Dark gauge boson

Z’ → 𝝌𝝌 is the major decay mode, if 𝝌 (very light dark sector particle) exists.

(i) “Dilepton Resonance” search (typical search)

(ii) “Missing Energy” search

2 main categories of Dark force search (in terms of the dominant decay modes) :

0.10 1.000.500.20 2.000.30 3.000.15 1.500.70

0.10

1.00

0.50

0.20

0.30

0.15

0.70

gd Mass @GeVD

BR

gd Branching Ratio

e+e-

m+m-

Hadrons

BR(Z’ → missing energy) ≈ 1 is taken.

[Batell, Pospelov, Ritz (2009)] [Falkowski et al (2010)]

Whole green band (gµ-2 favored) is excluded.

𝝆 𝝓

Does the green band (gµ-2 favored) survive?

(ii) Missing Energy (Z’ → 𝝌𝝌) searchesa e!2Σ"

aΜ

aΜ explained

E787#E949

BR!Zd$missing" % 1

Izaguirre et al.Essig et al.

5 10 50 100 500 10001&10'7

5&10'7

1&10'6

5&10'6

1&10'5

5&10'5

1&10'4

Zd mass #MeV$

!2

[Dark Photon]

In Dark Photon model, small portion of the green band survives the constraints.

Invisibly decaying Dark gauge boson

(i) K+ → π+ + nothing (BNL E787+E949)

(ii) e+e− → 𝛾 + nothing (BABAR)

More constraints through 𝝌 interaction at detectors in some beam-dump experiments are possible, but they depend on the 𝝌 coupling (αD). (will come back to this later)

[Izaguirre et al (2013); Essig et al (2013)]

[Pospelov (2009); and others]

a e!2Σ"

aΜ

aΜ explained

E787#E949

BR!Zd$missing" % 1


5 10 50 100 500 10001&10'7

5&10'7

1&10'6

5&10'6

1&10'5

5&10'5

1&10'4

Zd mass #MeV$

!2

a e!2Σ"

aΜ

aΜ explained E787#E949

BR!Zd$missing" % 1Max suppressionMax suppression


5 10 50 100 500 10001&10'7

5&10'7

1&10'6

5&10'6

1&10'5

5&10'5

1&10'4

Zd mass #MeV$

!2

[Dark Photon] [Dark Z boson]

In Dark Z model, because of the additional term (εZ term), there can be a sizable interference in the flavor-changing meson decays. The “K ➞ π + Z’ (nothing)” constraints (orange) can be much weaker (1/7 times).

Invisibly decaying Dark gauge boson

[Davoudiasl, LEE, Marciano (2014)] (ii) Missing Energy (Z’ → 𝝌𝝌) searches

More green band survivesin the Dark Z case

�(K+ ! ⇡+Zd) = 4⇡

q�(m2

K , m2

⇡, m2

Zd)

64⇡2 m3

K

X

pol

|M|2

with

Additional term of Dark Z model

K ➞ π + Z’

dark photon !∆"0"

pure dark Z !!"0"

0.00 0.05 0.10 0.15 0.200.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

Zd mass #GeV$

BR!K# $

Π#Z d"%X2

!X"!,∆"

X

pol

|M|2 =14(f

+

)2"✓

m2

K �m2

⇡

mZd

◆2

��2m2

K + 2m2

⇡ �m2

Zd

�# ��"m

2

ZdA± �

mZd

mZB

��2

- Dark Photon : (loop-suppression with ɣ)×(small ε)

- pure Dark Z : (loop-suppression with Z)×(small εZ)×(enhancement factor) ✓

"Z =mZ0

mZ�

◆

(i) Primarily e-beam (~100 GeV). EOT ~ 1012. (ii) Detector is hermetic (catching all SM particles except for neutrinos) and measures total

energy deposit. (iii) Test “energy loss” (Missing E) by invisibly decaying Z’. (Essentially BKG free.) (iv) Does not depend on unknown αD (DM coupling).

Example: P348 (beam-dump for dark gauge boson) at CERN SPS[P348 Collaboration]

BaBar

ae

K!ΜΝA'

aΜaΜ favored

LSNDΑD%0.1

K!ΠA'E787, E949

VEPP-3

K!ΠA'ORKA

BaBarimproved

Belle IIconverted!a,b"Belle IIstandard

Belle IIlow-EΓ

DarkLight

109 1012

30 GeV100 GeV

10(2 10(1 1 1010(5

10(4

10(3

10(2

mA' #GeV$Ε

CERN experimentto test invisibly decaying Z’

They had a 2-weeks test run in September 2015 successfully, and recently got an approval for two extensive runs in 2016 that can

cover the whole green band for the invisible Z’ (NA64 experiment).Cf. PADME experiment (also missing E search)

“active dumping”

BaBar

K+

LSND E137

BDX 10

BDX 100

BDX 1000

50 100 200 500 1000

10-9

10-8

10-7

10-6

10-5

10-4

mA' HMeVLe2

Nucleon Scattering Erec > 1 MeV , aD = 0.1 , mc = 10 MeV

scattering to produce Z’(promptly decaying to 𝝌)

scattering to detect 𝝌(via Z’)

✏2/m2A0 ↵D ✏2/m2

A0

N� ⇠ ↵D ✏4

m4A0

[BDX Collaboration]

(plastic scintillator)12 GeV

unknown DM coupling

JLAB experiment (proposal)to test invisibly decaying Z’

αD

Example: JLab BDX (Beam-Dump eXperiment) proposal

There is a possibility the BDX is located in other beam facility

(e.g. INFN LNF, Mainz MESA).

(i) Test experiment at JLab Hall D with low current (0.2 µA). (ii) Full experiment at JLab Hall A or C with high current (100 µA). EOT ~ 1012. (iii) Signals: nucleon/electron recoils. (iv) 2 scatterings are required to produce and detect. (v) BKG from comic rays (neutrons, muons).

BaBar

K+

LSND E137

BDX 10

BDX 100

BDX 1000

50 100 200 500 1000

10-9

10-8

10-7

10-6

10-5

10-4

mA' HMeVLe2

Nucleon Scattering Erec > 1 MeV , aD = 0.1 , mc = 10 MeV

scattering to produce Z’(promptly decaying to 𝝌)

scattering to detect 𝝌(via Z’)

✏2/m2A0 ↵D ✏2/m2

A0

N� ⇠ ↵D ✏4

m4A0

[BDX Collaboration]

(plastic scintillator)12 GeV

unknown DM coupling

JLAB experiment (proposal)to test invisibly decaying Z’

αD

Example: JLab BDX (Beam-Dump eXperiment) proposal

There is a possibility the BDX is located in other beam facility

(e.g. INFN LNF, Mainz MESA).

(i) Test experiment at JLab Hall D with low current (0.2 µA). (ii) Full experiment at JLab Hall A or C with high current (100 µA). EOT ~ 1012. (iii) Signals: nucleon/electron recoils. (iv) 2 scatterings are required to produce and detect. (v) BKG from comic rays (neutrons, muons).

Dark matter beam experimentsOne of the most interesting types of the dark force experiment

as it is related to the light dark matter detection.

(See Prof. Suyong Choi’s talk.)

Another possible Dark force searches : Low-Energy Parity Test

(applying to Dark Z)

- Sensitive only to Low-Q2 (momentum transfer).

- Low-Q2 Parity-Violating experiments (measuring ) are good places to look.

Dark Z modifies the effective Lagrangian of Weak Neutral Current scattering.

“Dark Z” effects on Weak Neutral Current phenomenology

Dark Z effectively changes the weak neutral current scattering (including parity), but only for the “Low” momentum transfer (Q).

Le↵ = �4GFp2

JµNC(sin2 ✓W )JNC

µ (sin2 ✓W )

GF !✓

1 + �2 1

1 + Q2/m2Z0

◆GF

sin

2 ✓W !✓

1� "�mZ

mZ0

cos ✓W

sin ✓W

1

1 + Q2/m2Z0

◆sin

2 ✓W


✓"Z =

mZ0

mZ�

◆

Dark Z : Lint = �[" eJµem + "Z (g/2 cos ✓W )Jµ

NC ]Z0µ

g2Xm2

X +Q2�! 0 (for Q2 � m2

X)

sin2 ✓W

APV!Cs"

Qweak !first"E158

SLAC

LEP

Ν"DIS

PVDIS

APV!Ra#" MollerP2Qweak

SOLID


"3 "2 "1 0 1 2 3

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sin2 ΘW!Q2 "


Low-Q2 Parity Test (measuring Weinberg angle) can search for the Dark force. Atomic Parity Violation, Low-Q2 Polarized Electron Scatterings, Deep Inelastic Scattering It is independent of Z’ decay BR (good for both visibly/invisibly-decaying Z’).

mdark Z ! 100 MeVmdark Z ! 200 MeV

APV!Cs"

Qweak !first"E158

SLAC

LEP

Ν#DIS

PVDIS

APV!Ra$" MollerMESA

QweakSOLID


#3 #2 #1 0 1 2 3

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sin2 ΘW!Q2 "

Weinberg angle shift due to Dark Z (very light Z’)

Deviations from the SM prediction (due to Dark Z) can appear “only” in the Low-E experiments.


Low-Q2 Parity Test (measuring Weinberg angle) can search for the Dark force. Atomic Parity Violation, Low-Q2 Polarized Electron Scatterings, Deep Inelastic Scattering It is independent of Z’ decay BR (good for both visibly/invisibly-decaying Z’).

mdark Z ! 15 GeV

"0.0010 # !∆' # "0.0003!!∆'! % 0.0008 "light color#APV"Cs#

Qweak "first#E158

SLAC

LEP

Ν"DIS

PVDIS

APV"Ra'# MollerP2Qweak

SOLID


"3 "2 "1 0 1 2 3

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Log10 Q $GeV%

sin2 ΘW"Q2 #

Weinberg angle shift due to Dark Z (intermediate mass case)

Low-Q2 measurements (Cs APV, E158, NuTeV) show 1.8σ deviation from the SM. Introduction of Dark Z (~ 10 GeV) can help fitting. (Blue band: Less than 1σ deviation)


Summary & General Lessons

The Parity Test (precise measurement of sin2 θW) has been important in studying new gauge interactions. (Critically helped establishing the SU(2)L×U(1)Y model.)

There is a growing interest in the dark gauge interaction (mediated by a light Z’) around the world. (Partly because many existing low-energy facilities can join the searches.)

While most searches of the light Z’ are based on the direct resonance searches or missing energy searches, the parity tests in Low-Q2 (APV, Polarized e scatterings, DIS) are important and complementary searches, independent of Z’ decay BR.

History may repeat! (Dark Force evidence from Low-Q2 parity test before bump/missing?)

mdark Z ! 100 MeVmdark Z ! 200 MeV

APV!Cs"

Qweak !first"E158

SLAC

LEP

Ν#DIS

PVDIS

APV!Ra$" MollerMESA

QweakSOLID


#3 #2 #1 0 1 2 3

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sin2 ΘW!Q2 "

Extended range of parameters of the Dark Photon

Limited areadiscussedin this talk

[Jaeckel (2013)]

Energy Frontier

Inte

nsity

Fro

ntie

r

Extremely large parameter space emerges once we accept the idea of a very small coupling.

arXiv:1303.1821

The U(1)B-L model

[Heeck (2014)]

arXiv:1408.6845EP

ISR

Casim ir

RGRG!ΝHBSun

BBN

BD

SN1987A

e"Νneut ron

BaBarq"Ν

LHC

LEP

M!g’ # 100 G

eV

M!g’ # 109 GeV

Lim its on a B"L force

with Dirac neut rinos

"15 "12 "9 "6 "3 0 3 6 9 12"25

"20

"15

"10

"5

06 3 0 "3 "6 "9 "12 "15 "18

"51

"45

"39

"33

"27

"21

"15

"9

"3

Log10"M!eV#

Log 1

0"g’#Log10"Λ!m #

Log 1

0"Α’#

Relevant physics and constraints may change depending on the couplings.

Combination of the U(1)B-L & Dark photon (kinetic mixing)

ε

Z’ mass

gB-L

The most general form of the minimal gauge extension = (B-L) + xY [mini force] : effectively the same as the combination of the B-L and kinetic mixing (ε).

We need 3-dim parameter space to cover this model. [LEE, Yun (2016)]

Bµ ! Bµ +

"

cos ✓WZ 0µ

" =x

tan ✓W

gB�L

gZ

Many models are possible in the Low-energy New physics.

General message: Low-hanging Fruits

What do all these tell us?

Is the particles physics supposed to be cornered when its energy (and budget) is ultra high?

New physics (particles) may exist in the Low-energy. Light particles may be reachable relatively easily.

Last decade = Paradigm-changing period in the particle physics community. (Possibility of the new light particles is well-known, but not well-appreciated, except for few examples.)

Many theoretical studies and experimental innovations are called for in the New paradigm!

Tree of New particles

High-energy

Low-energyrelatively easy to harvest

- Thank you. -

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