Baryogenesis and dark matter in the nMSSM

C.Balázs, M.Carena, A. Freitas, C.Wagner

Phenomenology of the nMSSM from colliders to cosmology

arXiv:0705431

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 1/18

Minimal Supersymmetric Standard Model

Explains the origin of

è mass: radiative dynamics Ø

electroweak symmetry breaking

è dark matter: R-parity Ø

stable, neutral WIMP LSP

è baryons: lepto-, baryogenesis Ø

baryon-antibaryon asymmetry

è ...

But the Higgs sector of the MSSM is problematic

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 2/18

Problems with the Higgs sector of the SSM

è the m problem:

W   m H`

1.H`

2 in not natural

è the fine-tuning problem:

tension between mh > 114 GeV and ... stops

è the baryogenesis problem:

electroweak baryogenesis demands mh d 120 GeV

è ... put your own problem here ...

...

Fortunately, it's is easy to fix these problems while

keeping radiative EWSB intact

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 3/18

nMSSM: nearly MSSM

— Discreet symmetries of super- & Kahler potentials

Z5R, Z7

R Õ U 1 R' where R' = 3R + "PQ"

to prevent domain walls and large tadpoles

è Superpotential

W = WMSSM + m122

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄl

S`

+ l S`

H`

1.H`

2

è Scalar potential

V = VMSSM + tS S + h.c. + mS2 S 2 + al S H1.H2 + h.c.

è New parameters

vS, l, al , m12, mS, tS

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 4/18

Positive features of the nMSSM

— Solves m problem naturally

W = WMSSM + m122

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄl

S`

+ l S`

H`

1.H`

2

è m = l S = l vS set by EW scale

— Alleviates fine tuning in Higgs/stop sector

mh2 § mZ

2 cos2 2 b + 2 l2ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄgèèè2 sin2 2 b

è tree level lightest Higgs mass limit relaxed

— Tree level cubic term of scalar potential

V = VMSSM + tS S + h.c. + mS2 S 2 + al S H1.H2 + h.c.

è assists a strongly 1st order EW phase transition

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 5/18

Electroweak baryogenesis in the nMSSM

— Measured hB ¨ strongly 1st order EWPT ¨ large OP

fC/TC t 1

è strength of EWPT ¨ minimum of finite T eff. potential

Veff(f,T) = (— m2+aT2)f2 — g T f3+ lÅÅÅÅÅ4 f4+ ...

è V eff minimal for 0 < f if

l fCÅÅÅÅÅÅÅÅTC~ gÅÅÅÅÅl Ø g affects OP

è g generated byl SM : bosonic loops Ø g ~g 3

l MSSM : sc. loops Ø g ~ y 3

l nMSSM : tree level Ø g ~al

è MSSM: light stop induces strongly 1st order EWPT

nMSSM: tree level al S H1.H2 coupling does the same

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 6/18

Dark matter in nMSSM

— Neutralinos

Zé =

M1 . . . .

0 M2 . . .

-cb sw mZ cb sw mZ 0 . .

sb cw mZ -sb cw mZ l vS 0 .

0 0 l v2 l v1 0

è unification assumption: |M2|= a2/a1|M1|

è EWBG Ø low tanb &

Arg(M1) = Arg(M2) = fM ~ 0.1

è typical lightest neutralino (Zè

1): mostly singlino

mZé

1~ 2lv1v2vS/(v1

2 +v22+vS

2) d 60 GeV

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 7/18

All matter in nMSSM

— Neutralino relic density

è Zè

1 light Ø no coannihilations

dominant annihilation channel: Zè

1 Zè

1 Ø Z* Ø SM

Menon, Morrissey, Wagner 2004

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 8/18

Can we "measure" WZè

1 at colliders?

— WZè

1(mZ

è1, sv ) under standard thermal assumptions

— nMSSM benchmark: point "A"

tanb l vS al ma M2 fM

1.70 0.619 –384 373 923 245 0.14

GeV GeV GeV GeV

— Extracting physical parameters from cross sections

è generate LHC & ILC events (tree & parton level w/

BGs, jet broadening, ...)

è construct appropriate invariant mass distributions

è reconstruct masses (couplings) from distributions

è determine central values and precision

è scan around the central value in a precision window

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 9/18

Mass determination at the LHC

— Typical production/decay chain:

squarks/gluinos Ø

charginos/neutralinos Ø

leptons/jets

è typical invariant mass spectra (lumi 300 fb-1)

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 10/18

Mass determination at the LHC

è four kinematic (mass) edges Ø four mass parameters

mll,max = mZé

2–mZ

é1= 73.5±0.6 GeV

m jll,max,22 = (mZ

é2

2 –mZé

1

2 )(mb1é2 –mZ

é2

2 )/mZé

2

2 = 447.0±20.0 GeV

m jll,min,32 = f1(mZ

é1,mZ

é3,mZ

é2,mb

é1)= 256.2±7.0 GeV

m jll,max,32 = f2(mZ

é1,mZ

é3,mZ

é2,mb

é1)= 463.5±9.0 GeV

è results for individual masses

mZé

1= 33-18

+32 GeV mZé

2= 107-18

+33 GeV

mZé

3= 181-10

+20 GeV mbé

1= 499-17

+30 GeV

è absolute precision is reasonable but Zè

1 is very light!

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 11/18

LHC "precision"

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 12/18

Mass determination at the ILC

— Processes utilized at ILC (lumi 500 fb-1)

e+ e- Ø Wè1+ Wè

1- e+ e- Ø Zè 2 Zè 4 e+ e- Ø Zè 3 Zè 4

è results for individual masses

mZé

1= 33.3±1.1 GeV mZ

é2= 106.6-1.7

+1.4 GeV

mZé

3= 181.5±5.2 GeV mWè

1+= 165 ± 0.3 GeV

è after inclusion of e+ e- Ø Wè1+ Wè

1- threshold scan

mZé

1= 33.3-0.3

+0.4 GeV

è resulting precision of WZé

1 is comparable to WMAP!

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 13/18

ILC precision

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 14/18

ILC precision

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 15/18

Dark matter direct detection

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 16/18

Dark matter indirect detection

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 17/18

Conclusions

nMSSM improves on MSSM: no m problem, less

fine-tuning, looser constraints on EWBG

All matter in the Universe can be simultaneously

generated in the nMSSM

Model can be discovered at LHC, direct detection,

and low energy experiments (e-EDM)

ILC precision is critical for determining astrophysical

parameters: relic density, WIMP-nucleon scattering, ...

C. Balázs, Monash U Melbourne BG & DM in the nMSSM DSU, June 6, 2007 18/18