Beyond the MSSMpgl/talks/nyu_2006.pdf · 2009. 1. 28. · NMSSM nMSSM UMSSM |N 16 |2 in UMSSM •...

Beyond the MSSM

0 100 200 300M

χ0

1 (GeV)

0

0.2

0.4

0.6

0.8

1

|N15

|2 (S

ingl

ino

in χ0 1)

NMSSMnMSSMUMSSM|N16|2 in UMSSM

• Beyond the MSSM

• Heavy Z′

• Higgs

• Neutralinos

• Exotics

• Neutrino Mass in Strings

Davis (May 1, 2006) Paul Langacker (Penn)

References

• J. Kang, P. Langacker, T. j. Li and T. Liu,“Electroweak baryogenesis in a supersymmetric U(1)′ model,”Phys. Rev. Lett. 94, 061801 (2005), hep-ph/0402086.

• J. Kang and P. Langacker,“Z′ discovery limits for supersymmetric E(6) models”,Phys. Rev. D 71, 035014 (2005), hep-ph/0412190.

• J. Erler, P. Langacker and T. j. Li,“The Z−Z′ mass hierarchy in a supersymmetric model with a secluded U(1)′-breaking sector,”Phys. Rev. D 66, 015002 (2002), hep-ph/0205001.

• V. Barger, C. W. Chiang, J. Jiang and P. Langacker,“Bs − Bs mixing in Z′ models with flavor-changing neutral currents,”Phys. Lett. B 596, 229 (2004), hep-ph/0405108.

• T. Han, P. Langacker and B. McElrath,“The Higgs sector in a U(1)′ extension of the MSSM,”Phys. Rev. D 70, 115006 (2004), hep-ph/0405244.


• V. Barger, PL and H. S. Lee,“Lightest neutralino in extensions of the MSSM,”Phys. Lett. B 630, 85 (2005), hep-ph/0508027

• J. Giedt, G. L. Kane, P. Langacker and B. D. Nelson,“Massive neutrinos and (heterotic) string theory,”Phys. Rev. D 71, 115013 (2005) hep-th/0502032.

• P. Langacker and B. D. Nelson,“String-inspired triplet see-saw from diagonal embedding ofSU(2)L in SU(2)A×SU(2)B,”Phys. Rev. D 72, 053013 (2005), hep-ph/0507063.

• “Higgs Sector in Extensions of the MSSM”, V. Barger, PL, H.S. Lee and G.Shaughnessy, hep-ph/0603247.

• “Quasi-Chiral Exotics”, J. Kang, PL and B. Nelson, to appear


Beyond the MSSM

Even if supersymmetry holds, MSSM may not be the full story

Most of the problems of standard model remain (hierarchy ofelectroweak and Planck scales is stabilized but not explained)

µ problem introduced: Wµ = µHu · Hd, µ = O(electroweak)

Could be that all new physics is at GUT/Planck scale, but withremnants surviving to TeV scale

Specific string constructions often have extended gauge groups,exotics, extended Higgs/neutralino sectors

Important to explore alternatives/extensions to MSSM


Remnants Physics from the Top-Down

• Z′ or other gauge

• Extended Higgs/neutralino (doublet, singlet)

• Quasi-Chiral Exotics

• Charge 1/2 (Confinement?, Stable relic?)

• Quasi-hidden (Strong coupling? SUSY breaking? Composite family?)

• Time varying couplings

• LED (TeV black holes, stringy resonances)

• LIV, VEP (e.g., maximum speeds, decays, (oscillations) of HE γ, e, gravity

waves (ν’s))


A TeV-Scale Z′

• Strings, GUTs, DSB, little Higgs, LED often involve extra Z′

• Typically MZ′ > 600 − 900 GeV (Tevatron, LEP 2, WNC);|θZ−Z′| < few × 10−3 (Z-pole)(CDF di-electron: 850 (Zseq), 740 (Zχ), 725 (Zψ), 745 (Zη))

• Discovery to MZ′ ∼ 5 − 8 TeV at LHC, ILC,(pp→e+e−, µ+µ−, qq) (depends on couplings, exotics, sparticles)

• Diagnostics to 1-2 TeV (asymmetries, y distributions, associatedproduction, rare decays)


• String models

– Extra U(1)′ and SM singlets extremely common

– Radiative breaking of electroweak (SUGRA or gauge mediated)often yield EW/TeV scale Z′ (unless breaking along flat direction →intermediate scale)

– Breaking due to negative mass2 for scalar S (driven by largeYukawa) or by A term


_

f

f

S

~

Sf

−0.7

−0.5

−0.3

−0.1

0.1

0.3

0.5

0.7

0.9

1.1

−0.25 −0.20 −0.15 −0.10 −0.05

t


Implications of a TeV-scale U(1)′

• Natural Solution to µ problem W ∼ hSHuHd→ µeff = h〈S〉(“stringy version” of NMSSM)

• Extended Higgs sector

– Relaxed upper limits, couplings, parameter ranges (e.g., tan βcan be close to 1)

– Higgs singlets needed to break U(1)′

– Doublet-singlet mixing → highly non-standard collider signatures

• Large A term and possible tree-level CP violation (no new EDM

constraints) → electroweak baryogenesis


• Extended neutralino sector

– Additional neutralinos, non-standard couplings, e.g., lightsinglino-dominated, extended cascades

– Enhanced possibilities for cold dark matter, gµ − 2 (even small

tanβ)

• Exotics (anomaly-cancellation)

– May decay by mixing; by diquark or leptoquark coupling; or bequasi-stable

• Z′ decays into sparticles/exotics

• Constraints on neutrino mass generation

• Flavor changing neutral currents (for non-universal U(1)′ charges)

– Tree-level effects in B decay competing with SM loops (or with

enhanced loops in MSSM with large tanβ)


Models

UMSSM: SUSY-breaking scale models (Demir et al)

• MZ′ ∼ MZ, leptophobic

• MZ′ >∼ 10MZ by modest tuning

sMSSM: Secluded sector models (Erler, PL, Li)

• Approximately flat direction, broken by small (∼ 0.05) Yukawa

• Z′ breaking decoupled from effective µ term

• Four SM singlets: S, S1,2,3, doublets H1,2

• Off-diagonal Yukawas

• Can be consistent with minimal gauge unification


Superpotential : W = hSH1H2 + λS1S2S3

Potential : V = VF + VD + Vsoft

VF = h2 (|H1|2|H2|2 + |S|2|H1|2 + |S|2|H2|2)

+ λ2 (|S1|2|S2|2 + |S2|2|S3|2 + |S3|2|S1|2)

VD =G2

8

(|H2|2 − |H1|2

)2+

1

2g2Z′

(QS|S|2 + QH1|H1|2 + QH2|H2|2 +

3∑i=1

QSi|Si|2

)2

where G2 = g21 + g2

2,


Vsoft = m2H1

|H1|2 + m2H2

|H2|2 + m2S|S|2 +

3∑i=1

m2Si

|Si|2

− (AhhSH1H2 + AλλS1S2S3 + H.C.)

+ (m2SS1

SS1 + m2SS2

SS2 + m2S1S2

S†1S2 + H.C.)

• 〈Si〉 ∼ mSi/λ large for small λ

• Breaking along D(U(1)′) ∼ 0• Smaller 〈S〉, 〈Hi〉, dominated by hAh: tan β ∼ 1, 〈S〉 ∼ 〈Hi〉• Large doublet-singlet mixing

• Two sectors nearly decoupled

• Mixed soft terms break two global symmetries

• Tree-level CP breaking in S, Si sector in general (Important for

baryogenesis; little effect on EDMs)


Extended Higgs Sector

• Standard model singlets Si and additional doublet pairs Hu,d verycommon.

• Additional doublet pairs

– Richer spectrum, decay possibilities

– May be needed (or expand possibiities for) quark/leptonmasses/mixings (e.g., stringy symmetries may restrict single Higgs

couplings to one or two families)

– Extra neutral Higgs → FCNC (suppressed by Yukawas)

– Significantly modify gauge unification


Higgs singlets Si

• Standard model singlets extremely common in string constructions

• Needed to break extra U(1)′ gauge symmetries

• Solution to µ problem (U(1)′, NMSSM, nMSSM)

W ∼ hsSHuHd→ µeff = hs〈S〉

• Relaxed upper limits, couplings, parameter ranges (e.g., tanβ =vu/vd can be close to 1), singlet-doublet mixing

• Large A term and possible tree-level CP violation → electroweakbaryogenesis


Dynamical µ

• “Higgs Sector in Extensions of the MSSM”, V. Barger, PL, H.S.Lee and G. Shaughnessy, hep-ph/0603247

• V. Barger, PL and H. S. Lee,“Lightest neutralino in extensions of the MSSM,”Phys. Lett. B 630, 85 (2005), hep-ph/0508027

• Abel, Bagger, Barger, Bastero-Gil, Batra, Birkedal, Carena, Chang,Choi, Cvetic, Dedes, Delgado, Demir, Dermisek, Dobrescu, Drees,Ellis, Ellwanger, Erler, Espinosa, Everett, Fox, Godbole, Gunion,Haber, Han, Hooper, Hugonie, Kaplan, King, Landsberg, Li,Matchev, McElrath, Menon, Miller, Moretti, Morrissey, Nevzorov,Panagiotakopoulos, Perelstein, Pilaftsis, Poppitz, Randall, Rosner,Roy, Sarkar, Sopczak, Tait, Tamvakis, Vempati, Wagner, Weiner,White, Zerwas, Zhang


Models with Dynamical µ

Model Symmetry Superpotential CP-even CP-odd

MSSM – µHu · Hd H01,H

02 A0

2NMSSM Z3 hsSHu · Hd + κ

3 S3 H0

1,H02,H

03 A0

1, A02

nMSSM ZR5 , ZR7 hsSHu · Hd + ξFM

2nS H0

1,H02,H

03 A0

1, A02

UMSSM U(1)′ hsSHu · Hd H01,H

02,H

03 A0

2sMSSM U(1)′ hsSHu · Hd + λsS1S2S3 H0

1,H02,H

03, A0

1, A02, A

03, A

04

H04,H

05,H

06

• MSSM: gaugino unification but general µ

• NMSSM: may be domain wall problems (ZR2 ?)

• nMSSM: avoids domain walls; tadpoles from high order loops

• UMSSM: additional Z′ (µeff,MZ′ generated by single S)

• sMSSM: stringy NMSSM w. decoupled µeff , MZ′

(Hu, Hd, S reduces to nMSSM in Si decoupling limit → n/sMSSM)


A Unified Analysis of Higgs and Neutralino Sectors

VF = |hsHu · Hd+ξFM2n+κS2|2+|hsS|2

(|Hd|2 + |Hu|2

)VD =

G2

8

(|Hd|2 − |Hu|2

)2+

g22

2

(|Hd|2|Hu|2 − |Hu · Hd|2

)+

g1′2

2

(QHd|Hd|2 + QHu|Hu|2 + QS|S|2

)2Vsoft = m2

d|Hd|2 + m2u|Hu|2 + m2

s|S|2

+(

AshsSHu · Hd+κ

3AκS

3+ξSM3nS + h.c.

)black = MSSM (with µ = hs〈S〉); blue= extensions;

cyan = NMSSM; magenta = UMSSM; red= n/sMSSM


Mass matrices in {Hd, Hu, S} basis

• CP-even (tree level) (〈H0u,d〉 ≡ vu,d/

√2, 〈S〉 ≡ s/

√2)

(M0+)dd =

"G2

4+Q

2Hdg

21′

#v

2d + (

hsAs√2

+hsκs

2+hsξFM

2n

s)vus

vd

(M0+)du =

"−G2

4+ h

2s +QHd

QHug21′

#vdvu − (

hsAs√2

+hsκs

2+hsξFM

2n

s)s

(M0+)ds =

hh

2s +QHd

QSg21′

ivds− (

hsAs√2

+ hsκs)vu

(M0+)uu =

"G2

4+Q

2Hug

21′

#v

2u + (

hsAs√2

+hsκs

2+hsξFM

2n

s)vds

vu

(M0+)us =

hh

2s +QHuQSg

21′

ivus− (

hsAs√2

+ hsκs)vd

(M0+)ss =

hQ

2Sg

21′ + 2κ2

is

2 + (hsAs√

2−

√2ξSM3

n

vdvu)vdvu

s+κAκ√

2s


• Also CP-odd and charged Higgs (CP breaking ignored)

• Leading loop corrections (top-stop loops) are common

• Theoretical upper limits on H01 relaxed (→ smaller tanβ allowed)

– MSSMM

2H0

1≤ M

2Z cos2 2β + M(1)

M(1) = (M(1)+ )dd cos2

β + (M(1)+ )uu sin2

β + (M(1)+ )du sin 2β

– NMSSM, n/sMSSM, and Peccei-Quinn limits

M2H0

1≤ M

2Z cos2 2β +

12h

2sv

2 sin2 2β + M(1)

– UMSSM

M2H0

1≤ M

2Z cos2 2β+

12h

2sv

2 sin2 2β+g2Z′v

2(QHdcos2

β+QHu sin2β)2+M(1)


• Experimental LEP SM and MSSM bounds may be relaxed bysinglet-doublet mixing

0 50 100 150MH1

(GeV)0.001

0.01

0.1

1

ξ ZZH

1

MSSMNMSSMn/sMSSMUMSSMLEP limit 95% C.L.

60 80 100 120 140 160 180 200MA2

(GeV)0

0.2

0.4

0.6

0.8

1

cos2 (β

−α)

MSSM

(a) (b)

FIG. 3: (a) LEP limit [34] on ξZZHi =(gZZHi/g

SMZZh

)2= ΓZ→ZHi/Γ

SMZ→Zh, the scaled ZZHi

coupling in new physics, versus the light Higgs mass. The solid black curve is the observed limit

with a 95% C. L. Points falling below this curve pass the ZZHi constraint. (b) cos2(β −α) versus

MA2in the MSSM. The hard cutoff shown by the solid green line at MA2

= 93.4 GeV is due to

the constraint on σ(e+e− → AiH1) discussed in Section IIIA.

state due to global U(1) symmetries discussed in Section VA. In these models, the CP-odd

masses extend to zero since the mixing of two CP-odd states allow one CP-odd Higgs to be

completely singlet and avoid the constraints discussed above.

d. Higgs Boson Searches

The focus of Higgs searches is most commonly the lightest CP-even Higgs boson. In the

models that we consider, the lightest CP-even Higgs boson can have different couplings than

in the SM. In Fig. 3a, we show the present limits from LEP on the scaled ZZHi coupling.6

Mixing effects can lower the ZZHi coupling and, in the MSSM, this occurs if MA2is low,

as seen in Fig. 3b where the ZZHi coupling is lowest for cos2(β − α) = 1. However, an

additional limit is placed on the mixing via the e+e− → AiH1 cross section discussed in

Section IIIA, eliminating low mass CP-even Higgs bosons in the MSSM, as seen in Fig. 3b.

In extended-MSSM models, additional mixing may occur with the singlet fields. Due to this

mixing and the subsequent evasion of the LEP limit on the ZZHi coupling, the lightest CP-

even Higgs may then have a mass smaller than the SM Higgs mass limit. Indeed, attempts

6 For clarity, in all the plots that follow we sample the passed points in the results from the random scans.

22

• Reduced ZZHi coupling

ξZZHi = (Ri1+ cos β+Ri2

+ sin β)2

• Also, Z→HA, Z width, χ±

mass, Z − Z′ mixing,V minimum, RGE


Limiting Cases

• MSSM limit (s→∞ with µeff = hss/√

2 fixed) → two MSSM-likeCP-even Higgs and one largely singlet (heavy in UMSSM, light in

n/sMSSM, depends on κ in NMSSM)

• PQ and R limits (massless pseudoscalar)

Model Limits Symmetry EffectsMSSM B → 0 U(1)PQ MA1 → 0

NMSSM κ, Aκ → 0 U(1)PQ MA1 → 0NMSSM As, Aκ → 0 U(1)R MA1 → 0

n/sMSSM ξF , ξS → 0 U(1)PQ MA1 → 0UMSSM g1′ → 0 U(1) MZ′, MA1 → 0


1 10tan β

0

50

100

150

200

Hig

gs M

ass (

GeV

)

MSSMNMSSMn/sMSSMUMSSMPQ Limit

CP Even

s = 500 GeV

1 10tan β

0

500

1000

1500

2000

Hig

gs M

ass (

GeV

)


CP Odd

s = 500 GeV

(a) (b)

100 1000s (GeV)

0

50

100

150

200

Hig

gs M

ass (

GeV

)


CP Even

tan β = 2

100 1000s (GeV)

0

200

400

600

800

1000

Hig

gs M

ass (

GeV

)


CP Odd

tan β = 2

(c) (d)

FIG. 1: Lightest CP-even and lightest CP-odd Higgs masses vs. tan β and s for the MSSM,

NMSSM, n/sMSSM, UMSSM, and the PQ limits. Only the theoretical constraints are applied

with s = 500 GeV (for tan β-varying curves), tan β = 2 (for s-varying curves). Input parameters

of As = 500 GeV, At = 1 TeV, MQ = MU = 1 TeV, κ = 0.5, Aκ = −250 GeV, Mn = 500 GeV,

ξF = −0.1, ξS = −0.1, hs = 0.5, θE6 = − tan−1√

53 , and Q = 300 GeV, the renormalization scale,

are taken. The U(1)PQ limit allows one massive CP-odd Higgs whose mass is equivalent to that

of the UMSSM CP-odd Higgs.

tree-level dependence on s prevents a level crossing between the H1 and H2 states. However,

in the extended models there are three CP-even Higgs bosons. Level crossings are possible

here as there is a Higgs boson of intermediate mass: see Fig. 1(c). We also see a significant

19

(As = Mn = 500 GeV, Aκ = −250 GeV, hs = κ = 0.5, ξF,S = −0.1)


100 1000Higgs Mass (GeV)

0

0.2

0.4

0.6

0.8

1

ξ MSS

M

H1H2H3A1A2

NMSSM


0

0.2

0.4

0.6

0.8

1

ξ MSS

M

H1H2H3A1A2

n/sMSSM

(a) (b)


0

0.2

0.4

0.6

0.8

1

ξ MSS

M

H1H2H3A2

UMSSM

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0

0.2

0.4

0.6

0.8

1

ξ MSS

M

NMSSMn/sMSSMUMSSM

Lightest Higgs

(c) (d)

FIG. 4: Higgs masses vs. ξMSSM in the (a) NMSSM, (b) n/sMSSM, (c) UMSSM and (d) the

lightest CP-even Higgs of all extended models. The vertical line is the LEP lower bound on the

MSSM (SM-like) Higgs mass.

to explain the the 2.3σ and 1.7σ excess of Higgs events at LEP for masses of 91 GeV and

114 GeV, respectively, with light CP-even Higgs bosons in the UMSSM has been explored

[47]. This slight excess has also been studied in the NMSSM where a light Higgs with a SM

coupling to ZZ decays to CP-odd pairs [48].

The reduction in the CP-even Higgs mass in extended models can be seen in Fig. 4,

where we plot the MSSM fraction versus the Higgs boson mass. When there is little mixing

between the singlet and doublet Higgs fields, the MSSM limit is reached and the LEP bound

applies, as seen by the MSSM cutoffs at ξMSSM = 1 and MHi= 114 GeV. A common feature

23

(MSSM fraction ξHiMSSM =

Puj=d(R

ij+ )2)


0 50 100 150 200Higgs Mass (GeV)

0

CP-Even Higgs Mass Range

90

13592

173

170

1642

2

MSSM

NMSSM

n/sMSSM

UMSSM

Th.

Th.

Th.

Th.

LEP

LEP & αZZ’

Scan

Scan

0 2000 4000 6000Higgs Mass (GeV)

0

CP-Odd Higgs Mass Range

93

685094

3617

701

16320

0

MSSM

NMSSM

n/sMSSM

UMSSM

State Crossing

LEP

LEP & αZZ’

Scan

State Crossing

Scan

Th.

Th.

0 2000 4000 6000Higgs Mass (GeV)

0

Charged Higgs Mass Range

80

687379

3590

4080

684183

80

MSSM

NMSSM

n/sMSSM

UMSSM

Scan

LEP

LEP

Scan

Scan

Scan

LEP

LEP

FIG. 2: Mass ranges of the lightest CP-even and CP-odd and the charged Higgs bosons in each

extended-MSSM model from the grid and random scans. Explanation of extremal bounds and

their values are provided for each model. Explanations are Th. - theoretical bound met, value not

sensitive to limits of the scan parameters; Scan - value sensitive to limits of the scan parameters;

State Crossing - value has maximum when crossing of states occurs (specifically for A1 and A2

in the NMSSM and n/sMSSM); LEP - experimental constraints from LEP; αZZ′ - experimental

constraints in the UMSSM on the Z − Z ′ mixing angle.

the charged Higgs is often the lightest member of the Higgs spectrum. However, these cases

require fine tuning to obtain values of µeff > 100 GeV [9]. The upper limit of the charged

Higgs mass is dependent on the range of the scan parameters as seen in Eq. (45). The

discrepancy in the upper limit of the charged and CP-odd Higgs mass between the UMSSM

and MSSM is a consequence of a lower µeff in the UMSSM, resulting in a lower MY . Large

values of µeff are more fine-tuned in the UMSSM than the MSSM since the additional gauge,

23


Lightest Higgs Decays

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

10

Parti

al W

idth

(MeV

)

SMH1 MSSMH1 NMSSMH1 n/sMSSMH2 n/sMSSMH1 UMSSM

W W*W W*W W*W W*W W*

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

10

Parti

al W

idth

(MeV

)

Z Z*Z Z*Z Z*

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

10

Parti

al W

idth

(MeV

)

g gg gg gg gg g

FIG. 9: Decay widths for WW ∗, ZZ∗, and gg in the MSSM and extended-MSSM models. Lines

denote the corresponding SM width. For clarity, not all points generated are shown.

extensions7. For the decays of the very light Higgs boson to occur in the n/sMSSM two

off-shell gauge bosons are involved, resulting in high kinematic suppression of decay rates.

In all the models considered, the WW ∗ and ZZ∗ partial widths are bounded above by those

of the SM. This is a consequence of the complementarity of the couplings of H1 and H2 to

gauge fields in the MSSM. The gauge couplings in the MSSM follow the relation

(gSMV V h)

2 = (gMSSMV V H1

)2 + (gMSSMV V H2

)2 (71)

More sum rules exist in the MSSM and can be found in [56]. In extended-MSSM models

7 In this case the decay width cannot be translated directly into a production rate since they require

transverse and longitudinal polarizations of the W -bosons to be treated separately. However, the gauge

coupling is equivalent in either case, and its scaling contains the suppression of the production rate.

30


Invisible Decays

n/sMSSM [7, 41]. However, in the n/sMSSM most of the kinematic region is disfavored due

to a large χ01 relic density [7]. This is indicated in Fig. 11a below the red horizontal line

at Mχ01

= 30 GeV. However, this region is not excluded since the relic density calculation

includes only the Z pole. In principle, other annihilation channels may decrease the relic

density to the preferred range.

0 50 100 150Lightest Higgs Mass (GeV)

0

20

40

60

80

100

Ligh

test

Neu

tralin

o M

ass (

GeV

) H1 MSSMH1 NMSSMH1 n/sMSSMH2 n/sMSSMH1 UMSSM

M H 1=2 M χ 1

0

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

χ01χ0

1

(a) (b)

FIG. 11: (a) MH1vs. Mχ0

1in all the models considered. Points falling below the blue line allow

the decay of the lightest CP-even Higgs to two χ01. (b) Branching fraction to χ0

1χ01

The χ01χ

01 partial decay width is given by

ΓHi→χ01χ0

1=

1

16πMHi

λ1/2(M2

χ01

/M2Hi

, M2χ0

1

/M2Hi

)(M2

Hi− 4M2

χ01

)|CHiχ0

1χ0

1|2 (75)

where the H1χ01χ

01 coupling is

CHiχ01χ0

1=

[(g2N12 − g1N11 + g1′QH1

N16)Ri1+ −

√2hsN15R

i2+

](N13 sin β + N14 cos β)

+[(g1N11 − g2N12 + g1′QH2

N16)Ri2+ +

√2hsN15R

i1+

](N13 cos β − N14 sin β)

+√

2 [hsN13N14 + g1′QSN16N15 − κN15N15] Ri3+ . (76)

For a particular model, the irrelevant parameters are understood to be set to zero as in

Eq. (6). The lightest Higgs boson in the MSSM, NMSSM and n/sMSSM can have a high

branching fraction to the lightest neutralino as seen in Figs. 11b. In fact in these models,

the χ01χ

01 branching fraction can be near 100%.8 This decay is seen as missing energy and

8 If we do not assume gaugino mass unification and that µeff is light and M1′ is heavy, then χ01 is light and

34


H1,2→A1A1

0 50 100 150MH1

(GeV)0

50

100

150

200

MA

1 (GeV

)

H1 MSSMH1 NMSSMH1 n/sMSSMH2 n/sMSSM

MH 1=2M A 1

MZ =M

H1

+MA

1

20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

A1 A1

(a) (b)

FIG. 12: (a) MH vs. MA1showing the kinematics for decays in extended-MSSM models. H →

A1A1 decays are allowed for regions below the blue-dashed line. Decays of Z → H1A1 are allowed

to the left of the green dark line. (b) H → A1A1 branching fraction versus Higgs mass. The

n/sMSSM parameter ξS is scanned with a higher density at low ξS to allow low Higgs masses.

makes Higgs searches difficult at the Tevatron or LHC and has been explored in the MSSM

[62].

In addition to decays to neutralino pairs, decays involving the lightest CP-odd Higgs

boson are allowed. In Fig. 12a we show the possibilities for decays involving both A1 and

H1. The kinematic regions where Z → A1H1 and H1 → A1A1 are given. Even though

the Z decay is possible in the n/sMSSM and NMSSM, it is suppressed due to the low

MSSM fraction of both A1 and H1 seen in Fig. 4b. Also shown is the crossing of states

in the n/sMSSM where H2 and H1 switch content and hence their variation with MA1.

The lightest CP-even and CP-odd Higgs masses in both the MSSM and n/sMSSM show a

strong correlation below the LEP limit. In the MSSM, this is evident from Fig. 3b where

the reduced ZZh coupling occurs when cos2(β − α) does not vanish, resulting in a lower

CP-even Higgs mass. The n/sMSSM correlation is more clearly shown in Fig. 5 where the

crossing of states at ξS ∼ −0.1 is discussed.

The H → A1A1 mode can be significant if allowed kinematically [6] and has been studied

large χ01χ

01 branching fractions are possible in the UMSSM, similar to those found in the n/sMSSM. For

constraints on Mχ0

1in the MSSM from supernova data see [61].

35


Total Width

0 50 100 150Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

1e+05To

tal W

idth

(MeV

)


FIG. 14: Total decay width for each model. Large enhancements with respect to the SM are largely

due to the decays to A1A1 and χ01χ

01.

VII. CONCLUSIONS

Extensions of the MSSM that include a singlet scalar field provide a natural solution

to the undesirable fine-tuning of the µ-parameter needed in the MSSM. After symmetry

breaking, the singlet Higgs obtains a VEV, generating an effective µ-parameter naturally

at the EW/TeV scale. While the extensions to the MSSM that we consider each contain

at least one additional singlet field, S, the symmetries that distinguish each model and

their resulting superpotential terms provide phenomenologically distinct consequences. We

made grid and random scans over the parameter space of each model and imposed the LEP

experimental bounds on the lightest CP-even ZZHi couplings. The limits on MA2and

MH1in the MSSM were converted to associated AiHj production cross section limits and

imposed. We also imposed constraints from the LEP chargino mass limit and the allowed

contribution of the invisible Z decay to neutralino pairs. Within the UMSSM, we enforced

an additional constraint on the Z ′ boson mixing with the SM Z.

We found the following interesting properties of the considered models:

(i) The lightest Higgs boson can have a considerable singlet fraction in the n/sMSSM

and NMSSM. Since the singlet field does not couple to SM fields, the couplings of the

lightest Higgs to MSSM particles are reduced due to the mixing of the singlet field

with the doublet Higgs bosons, resulting in the e+e− production cross sections being

significantly smaller. Therefore, in the n/sMSSM and NMSSM, Higgs boson masses

38


Lightest Neutralino

Mass matrix (Mχ0) in basis {B, W3, H01 , H0

2 , S, Z′}:M1 0 −g1v1/2 g1v2/2 0 00 M2 g2v1/2 −g2v2/2 0 0

−g1v1/2 g2v1/2 0 −µeff −µeffv2/s gZ′Q′H1v1

g1v2/2 −g2v2/2 −µeff 0 −µeffv1/s gZ′Q′H2v2

0 0 −µeffv2/s −µeffv1/s√

2κs gZ′Q′Ss

0 0 gZ′Q′H1v1 gZ′Q′

H2v2 gZ′Q′

Ss M1′

(〈S〉 ≡ s√

2, 〈H0

i 〉 ≡ vi√2,

pv2

1 + v22 ≡ v ' 246 GeV, Q′

φ = φ U(1)′ charge)

(black = MSSM; blue= extensions; cyan = NMSSM; magenta = UMSSM)


0 100 200 300M

χ0

1 (GeV)

0

0.2

0.4

0.6

0.8

1|N

15|2

(Sin

glin

o in

χ0 1)

NMSSMnMSSMUMSSM|N16|2 in UMSSM

0 10 20 30 40 50 60 70 80M

!!" (GeV)

0.0001

0.001

0.01

0.1

1

10

100

1000

"!! h

2

nMSSMnMSSMWMAP+SDSS (3##

(Relic density in nMSSM from

χ01χ

01→ Z only; may be χ0

1→secluded in sMSSM)


-400 -200 0 200 400M2 (GeV)

0

100

200

300

400

500

µ (G

eV)

hs = 0.1

hs = 0.75

Mχ± < 104 GeV ΓZ-->χχ > 2.3 MeV

7.9 < Δaµ×10

10 < 39.9

Ωχh2 < 0.09

0.09 < Ωχh2 < 0.15

tanβ = 2 s = 500 GeV

(Relic density and gµ − 2 in n/sMSSM)


0 100 200 300M

χ0

2 (GeV)

0

100

200

300

400

500

Mχ+

1 (GeV

)

NMSSMnMSSMUMSSMMSSM

Masses of χ+

1 vs χ0

2

M χ+ 1 =

2Mχ

0 2

M χ+

1 = M χ

02

Mχ+

1 < 104 GeV

Mχ0

2 > Μχ

01 + MZ0

Mχ+

1 > Μχ

01 + MW+

0 100 200 300M

χ0

2 (GeV)

0

100

200

300

400

500

Mχ+

1 (GeV

)

NMSSMnMSSMUMSSMMSSM

Masses of χ+

1 vs χ0

2

M χ+ 1 =

2Mχ

0 2

M χ+

1 = M χ

02

Mχ+

1 < 104 GeV

Mχ0

2 > Μχ

01 + Mh0 (120)

Mχ+

1 > Μχ

01 + MW+

• Often χ02 · · ·χ0

5 are MSSM-like with light singlino-dominated χ01

• MSSM-like cascades with extra χ02→χ0

1 + (ll, qq, Z, h)• Often χ0

2→χ01 + (Z, h); χ+

1 →χ01 + (W+,H+) are open

(e.g., χ+1 χ

02→W+ h + 6ET→l+ b b + 6ET )


Quasi-Chiral Exotics

(J. Kang, PL, B. Nelson, in progress)

• Often find exotic (wrt SU(2)×U(1)) quarks or leptons at TeVscale

– Assume non-chiral wrt SM gauge group (strong constraints from

precision EW, expecially on extra or mirror families)

– Can be chiral wrt extra U(1)′s or other extended gauge

– Usually needed for U(1)′ anomaly cancellation

– Modify gauge unification unless in complete GUT multiplets

– Can also be more extreme exotics (e.g., adjoints, symmetric, fractional

charge, mixed quasi-hidden)

– Experimental limits relatively weak


• Examples in 27-plet of E6

– DL + DR (SU(2) singlets, chiral wrt U(1)′)

–

(E0

E−

)L

+

(E0

E−

)R

(SU(2) doublets, chiral wrt U(1)′)

• Pair produce D + D by QCD processes (smaller rate for exotic leptons)

• D or D decay by

– D→uiW−, D→diZ, D→diH

0 if driven by D − d mixing (not

in minimal E6; FCNC)→ mD>∼ 200 GeV (future: ∼ 1 TeV)

– D → quark jets if driven by diquark operator uuD, or quark jet+ lepton for leptoquark operator lqD (still have stable LSP)

– May be stable at renormalizable level due to accidental symmetry(e.g., from extended gauge group) → hadronizes and escapes orstops in detector (Quasi-stable from HDO → τ < 1/10 yr)


Neutrino Mass

• Nonzero mass may be first break with standard model

• Enormous theoretical effort: GUT, family symmetries, bottom up

– Majorana masses may be favored because not forbidden by SMgauge symmetries

– GUT (+ family symmetry) seesaw (heavy Majorana singlet).Usually ordinary hierarchy.


• Very little work from string constructions, even though may bePlanck scale effect (Witten; Coriano, Faraggi, Thormeier; Ellis, Leontaris,

Lola, Nanopoulos; Ibanez, Marchesano, Rabadan)

• Key ingredients of most bottom up models forbiddenin known constructions (heterotic or intersecting brane)

(Due to string symmetries or constraints, not simplicity or elegance)

– “Right-handed” neutrinos may not be gauge singlets

– Large representations difficult to achieve (bifundamentals,singlets, or adjoints)

– GUT Yukawa relations broken

– String symmetries/constraints severely restrict couplings, e.g.,Majorana masses, or simultaneous Dirac and Majorana masses


Neutrino Mass in Strings

• Dirac masses

– Can achieve small Dirac masses (neutrino or other) by higherdimensional operators or by large intersection areas

Lν ∼(

S

MPl

)pLNc

LH2, 〈S〉 � MPl

⇒ mD ∼( 〈S〉

MPl

)p〈H2〉

– Large p⇒〈S〉 close to MPl (e.g., anomalous U(1)A)

– Small p⇒ intermediate scale � MPl

– Similar HDO may give light steriles and ordinary/sterile mixing


• Majorana masses

– Existing intersecting brane models: conserved L; no diagonal(Majorana) triangles

– Heterotic: can one generate large effective mS from

Wν ∼ cijSq+1

MqP l

NiNj ⇒ (mS)ij ∼ cij〈S〉q+1

MqP l

,

consistent with D and F flatness?

– Can one have such terms simultaneously with Dirac couplings,consistent with flatness and other constraints?

– Are bottom-up model assumptions for relations to quark, chargedlepton masses maintained?


• The Z3 Heterotic Orbifold (Giedt, Kane, PL, Nelson, hep-th/0502032)

– Systematically studied large class of vacua

∗ Is minimal seesaw common?

∗ If rare, possibly guidance to model building

∗ Clues to textures, etc.

– Several models from each of 20 patterns; superpotential throughdegree 9; huge number of D flat directions reduced greatly byF -flatness

– Only two patterns had Majorana mass operators〈S1 · · · Sn−2〉NN/Mn−3

PL

– None had simultaneous Dirac operators 〈S′1 · · · S′

d−3〉NLHu/Md−3PL

leading to ∆m2 > 10−10 eV2 (one apparent model ruined by off-

diagonal Majorana)


– Feature of Z3 orbifold? Or more general?

– Systematic searches in other constructions important (Is seesaw

generic? Rare? Alternatives?)

– Alternatives:

∗ Small Dirac? (by HDO (common in constructions) or LED)

∗ Extended seesaw? mν ∼ m2+kD /M1+k, with k ≥ 1 (TeV scale

physics?)

∗ Loops, RP breaking? (TeV physics)

∗ Higgs triplet? (higher Kac-Moody or intersecting brane)

· Higher Kac-Moody embedding in heterotic string (PL, B.

Nelson, hep-ph/0507063)

· Inverted hierarchy with bimaximal mixing

· Solar mixing non-maximal → small (Cabibbo-like) chargedlepton mixing

· Ue3 close to Chooz limit


Conclusions

• Combination of theoretical ideas and new experimental facilitiesmay allow testable theory to Planck scale

• From the bottom up: there may be more at TeV scale than(minimal SUGRA) MSSM (e.g., Z′, extended Higgs/neutralino, quasi-

chiral exotics)

• From the top down: there may be more at TeV scale than (minimalSUGRA) MSSM

• Dynamical µ term leads to very rich Higgs/neutralino physics atcolliders and for cosmology

• Consider alternatives to the minimal seesaw


The µ problem

Superpotential: W = µ HuHd︸︷︷︸superfields

+ht QHudc︸︷︷︸superfields

⇒

Lfermion = µ HuHd︸︷︷︸Higgsino mass

+ht( QHudc︸︷︷︸top Yukawa

+ QHudc + QHudc︸︷︷︸Higgsino−quark−squark

)

−LWscalar =∑φ

∣∣∣δWδφ ∣∣∣2 = µ2(|Hu|2 + |Hd|2

)︸︷︷︸Higgs masses

+ht terms

−LD = g2+g′2

8

(|Hu|2 − |Hd|2

)2+ charged Higgs, squark, slepton

−Lsoft = m2u |Hu|2 + m2

d |Hd|2 + (m23 HuHd + h.c.)

+ squark/slepton + M3 gg︸︷︷︸gluino

+ M2 ww︸︷︷︸wino

+ M1 bb︸︷︷︸bino


• Soft terms set ew scale, e.g., msoft ∼ F 2/Mpl, F ∼ 1011 GeV,Mpl ∼ 1019 GeV

• µ problem: µ is supersymmetric ⇒ could be very large (or exactlyzero in string theory), but need µ ∼ msoft

<∼ 1 TeV

• Two classes of solutions

– Generate µ in hidden sector along with msoft

– Dynamical: µ ≡ 0 by symmetry or string, but

W = hs S︸︷︷︸SM singlet

HuHd⇒µeff = hs〈S〉, 〈S〉 ∼ msoft

(Examples: Z′ models, NMSSM, nMSSM)


0 500 1000 1500 2000s (GeV)

10

100

1000H

iggs

Mas

s (G

eV)

H1H2H3A1A2

H+/-

NMSSM

0 500 1000 1500 2000s (GeV)

1

10

100

1000

Hig

gs M

ass (

GeV

)

H1H2H3A1A2

H+/-

n/sMSSM

(a) (b)

0 500 1000 1500 2000s (GeV)

100

1000

Hig

gs M

ass (

GeV

)

H1H2H3A2

H+/-

UMSSM

0 500 1000 1500 2000s (GeV)

0

20

40

60

80

100

120

140

Hig

gs M

ass (

GeV

)NMSSMn/sMSSMUMSSM

Lightest Higgs

(c) (d)

FIG. 6: Higgs masses vs. s in the (a) NMSSM, (b) n/sMSSM, (c) UMSSM and (d) the lightest

CP-even Higgs of all extended models. The vertical line is the LEP lower bound on the mass of

the SM Higgs.

CP-even Higgs boson can have a mass lower than the LEP limit if

−ξS <(114 GeV)2s√

2M3n

∼ 0.1 (65)

In Fig. 5, we show the Higgs mass dependence on this parameter, which exhibits the crossing

of states at ξS = −0.1.

In the UMSSM, the lightest Higgs mass is concentrated near the LEP limit with ξMSSM

near one, which is a direct consequence of the high s constraint placed by the strict αZZ′

limit. This is also seen in Fig 6, where we plot the Higgs masses versus the singlet VEV. The

25


1 10tan β

10

100

1000H

iggs

mas

s (G

eV)

H1H2H3A1A2

H+/-

NMSSM

1 10tan β

10

100

1000

Hig

gs m

ass (

GeV

)

H1H2H3A1A2

H+/-

n/sMSSM

(a) (b)

1 10tan β

10

100

1000

Hig

gs m

ass (

GeV

)

H1H2H3A2

H+/-

UMSSM

1 10tan β

0

50

100

150

Hig

gs m

ass (

GeV

)

NMSSMn/sMSSMUMSSM

Lightest Higgs

(c) (d)

FIG. 7: Higgs masses vs. tan β in the (a) NMSSM, (b) n/sMSSM, (c) UMSSM and (d) the lightest

CP-even Higgs of all extended models.

lowest allowed point in the UMSSM has s above 800 GeV, compared to the other models

which allow s to be as low as a few hundred GeV. By examining Fig. 4c and 6c we see that

MH2varies linearly with s and is characteristically dominantly singlet. Without the αZZ′

constraint, the H1 and H2 states cross near s ∼ 400 GeV. This constraint may be evaded by

the fine tuning cases discussed in Section VB2. At this point, the mass eigenstates switch

content, below which the lightest Higgs is dominantly singlet, has a mass below the LEP

bound, and evades the ZZHi coupling constraint.

The Higgs mass dependence on tan β has some interesting features, specifically that of

the lightest Higgs. We show this dependence in Fig. 7 for the all Higgs bosons of each

26


10 100 1000 10000Higgs Mass (GeV)

-1

-0.8

-0.6

-0.4

-0.2

0ξ S H1

H2H3A1A2

H+/-

n/sMSSM, Mn = 500 GeV

FIG. 5: Higgs mass dependence on ξS in the n/sMSSM. When ξS ∼ −0.1, H2 and H1 switch

content, allowing a light CP-even Higgs below the LEP limit.

of each model is a CP-even Higgs boson with a mass range concentrated just above the

LEP SM mass limit shown by the dark-green vertical line. These Higgs bosons have a large

MSSM fraction, for which the ZZHi coupling limit is effective in elimination of the generated

points. We note that there are cases where a Higgs boson mass below 114 GeV but with

relatively high MSSM fraction is allowed due to cancellation between the rotation matrices

in Eq. (44). This cancellation permits the lightest MSSM Higgs boson to be below the SM

limit, and has been taken as a possible explanation of the Higgs signal excess [49].

By measuring the lightest Higgs boson couplings to MSSM fields, an estimation of the

MSSM fraction may be obtained, providing important information on the singlet content.

In the NMSSM and especially the n/sMSSM the lightest CP-even Higgs boson may have

both low MSSM fraction and low mass as seen in Fig. 4d. Since µeff is fixed at the EW

scale, the matrix elements (M+)i3 are suppressed in the n/sMSSM at large s. This results

in a low mass CP-even Higgs boson with high singlet composition; the other Higgs states

have a high MSSM fraction due to the sum rule in Eq. (54). However in the n/sMSSM, the

existence of a low mass CP-even Higgs boson depends on the value of ξS. In appendix D 2 g,

we show that the tree-level mass-squares of the singlet dominated CP-even and odd Higgs

bosons in the n/sMSSM at large s are

M2H1

∼ M2A1

∼ −√

2ξSM3n

s, (64)

which forces the parameter ξS to be negative in this limit. Therefore, a largely singlet

24


1 10tan β

100

1000

Hig

gs M

ass (

GeV

)

H1H2A2

H+/-

MSSM

s = 500 GeV

1 10tan β

10

100

1000

10000

Hig

gs M

ass (

GeV

)

H1H2H3A1A2

H+/-

NMSSM

s = 500 GeV

1 10tan β

100

1000

Hig

gs M

ass (

GeV

)

H1H2H3A1A2

H+/-

n/sMSSM

s = 500 GeV

1 10tan β

10

100

1000

10000

Hig

gs M

ass (

GeV

)

H1H2H3A2

H+/-

UMSSM

s = 500 GeV

1 2 3 4tan β

0100200300400500600700800900

1000

Hig

gs M

ass (

GeV

)

H1H2H3A2

H+/-

All models, PQ limit

s = 500 GeV

100 1000s (GeV)

100

1000

Hig

gs M

ass (

GeV

)

H1H2A1

H+/-

MSSM

tan β = 2

1000s (GeV)

0

500

1000

1500

Hig

gs M

ass (

GeV

)

H1H2H3A1A2

H+/-

NMSSM

tan β = 2

100 1000s (GeV)

0

100

200

300

400

500

600

700

Hig

gs M

ass (

GeV

)

H1H2H3A1A2

H+/-

n/sMSSM

tan β = 2

1000s (GeV)

0

200

400

600

800

1000

Hig

gs M

ass (

GeV

)

H1H2H3A2

H+/-

UMSSM

tan β = 2

400 500 600 700 800s (GeV)

0

100

200

300

400

500

600

700

800

Hig

gs M

ass (

GeV

)

H1H2H3A2

H+/-

All Models, PQ Limit

tan β = 2

FIG. 15: Higgs masses vs. tan β and s for the NMSSM, n/sMSSM, UMSSM, and the PQ limit for

the extended models. Only the theoretical constraints are applied. Input parameters of As = 500

GeV, At = 1 TeV, MQ = MU = 1 TeV, κ = 0.5, Aκ = −250 GeV, Mn = 500 GeV, ξF = −0.1,

ξS = −0.1, hs = 0.5, θE6 = − tan−1√

53 , and the renormalization scale Q = 300 GeV are used.

Note that the U(1)PQ symmetry allows only one CP-odd Higgs boson to be massive.

in mass signify a model dependence in MH± and MA2. For large s, the behavior of the

charged Higgs boson is effectively the same among the models as its mass scales with s,

see ,e.g., Eq. 43. The heaviest CP-even and CP-odd Higgs bosons masses also scale with

increasing s for most of the models in this parameter range. However, the corresponding

53


0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n


W W*

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

Z Z*Z Z*Z Z*

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

b b

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

τ τ τ τ τ τ τ τ τ τ

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

n

γ γ γ γ

0 20 40 60 80 100 120 140Higgs Mass (GeV)

0.0001

0.001

0.01

0.1

1

Bran

chin

g Fr

actio

nZ γZ γZ γ

FIG. 10: Branching fractions for various modes in the MSSM and extended-MSSM models. Lines

denote SM branching fractions.

γγ, and Zγ are presented in Fig. 10 for the lightest CP-even Higgs boson in the MSSM,

and NMSSM, both H1 and H2 in the n/sMSSM, and h in the SM.

Note that the branching fractions may be larger in the SUSY models than in the SM.

For instance, in the NMSSM the branching fractions to WW ∗ and ZZ∗ can be larger than

the corresponding SM branching fractions, as seen in Fig 10. These enhancements are due

32


0 100 200 300M

χ0

1 (GeV)

0

100

200

300

400

500M

χ02 (G

eV)

MSSMNMSSMnMSSMUMSSM

Masses of χ02 vs χ0

1

M χ0

2 = M χ

01

M χ0 2 =

2Mχ0 1

+ MZ

+ Mh0 (120)+ Mh0 (150)

0 100 200 300M

χ0

1 (GeV)

0

100

200

300

400

500

Mχ+

1 (GeV

)

MSSMNMSSMnMSSMUMSSM

Masses of χ+1 vs χ0

1

M χ+

1 = M χ

01

+ MW

Mχ02

= 2Mχ01

Mχ+

1 < 104 GeV

+ MH+ (100)

+ MH+ (200)

+ M H+ (3

00)

• Often χ02→χ0

1 + (Z, h); χ+1 →χ0

1 + (W+,H+) open w. fairly light χ+1 , χ0

2(e.g., χ+

1 χ02→W+ h + 6ET→l+ b b + 6ET ,

or χ+1 χ

02→W+ Z + 6ET→l+ l′ l′ + 6ET )


Beyond the MSSMpgl/talks/nyu_2006.pdf · 2009. 1. 28. · NMSSM nMSSM UMSSM |N 16 |2 in UMSSM •...

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Transcript of Beyond the MSSMpgl/talks/nyu_2006.pdf · 2009. 1. 28. · NMSSM nMSSM UMSSM |N 16 |2 in UMSSM •...