Constraints on Supersymmetry using the latest data from cosmology, DM searches and LHC

KIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft

Institut für Experimentelle Kernphysik

www.kit.edu

Constraints on Supersymmetry using the latest data from cosmology, DM searches and LHC

C. Beskidt, W. de Boer, D. Kazakov, F. Ratnikov

2Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012

Introduction to Supersymmetry (SUSY)

Predictions of SM of particle physics in good agreement with experimental results

BUT: still good arguments for physics beyond the SM

No dark matter candidate, that can give the right amount of DMQuadratic divergences on the Higgs massHiggs mechanism has to be introduced ad hocGravitation cannot be included within QFTetc.

→ need a theory beyond the SM

Supersymmetry,…


Introduction to SUSY

SUSY = symmetry between fermions and bosons Minimal supersymmetric SM (MSSM): SM particles + SUSY partners + 2 Higgs Doublets (h,H,A,H±)

SUSY leads to equal masses of superpartners → broken symmetrySoft Breaking would lead to over 100 free parameters → no prediction possible

R Parity +1 R Parity -1


Introduction to SUSY – Constrained MSSM

Assuming unified SUSY masses and couplings at the GUT (~ 1016 GeV) scale → 4 free parameters and one free sign

m0: common spin 0 mass

m1/2: common spin ½ mass

tanβ: ratio between the vev’s of the two Higgs fieldsA0: trilinear coupling

sign(μ): sign of higgs mixing parameter

Which combination of 4 free parameters are allowed?


Outline

Find allowed parameter space in CMSSM using a 2 method based on LHC SUSY searches, Higgs discovery, relic density, flavour constraints, electroweak constraints, direct DM searches

Problem 1: Free CMSSM parameters are highly correlated Solution 1: Multi-step fitting approach → highly correlated parameters are fitted first for fixed other CMSSM parameters

Problem 2: Higgs of 125 GeV and large BR hard to accommodate in CMSSMSolution 2: go to NMSSM


Constraints used for the 2-function

Relic Density h2 = 0.1131 ± 0.0034B → BRexp(B→) = (1.68 ± 0.31)·10-4

Myon g-2 Δa=(30.2 ± 6.3 ± 6.1) ·10-11

b →s BRexp(b→s) = (3.55 ± 0.24)·10-4

Bs→ BRexp(Bs→) < 4.5·10-9

Higgs Mass mh mh > 114.4 GeV

LHC direct searches had < 0.001 – 0.03 pb

XENON100 N < 1.8·10-45 - 6·10-45 cm2

Pseudo-scalar Higgs mA mA > 510 GeV for tanβ ~ 50

For more details see CB et al., EPJ C


Combination of all constraints

2 = 2 – min2

For each 95% CL exclusion contour 2 = 5.99

Best fit point χmin2 = 4.3

95% CL → Δχ2 < 5.99

Contour

1 2 3 4 5

68% CL → Δχ2 < 2.3

~LSP

For more details see CB et al., EPJ C or backup slides

LHC direct searches Bs→ mh > 114.4 GeV mA XENON100


Influence of g-2

Preferred region by g-2 if the errors are added quadratically or linearly

g-2 gives a light preference for light SUSY masses but light SUSY masses are already excluded by the LHC direct searches → errors underestimated or additional loop contribution

tan10010132

10

SUSY

SUSY

mGeVa

52

2

TDDeviation from SM 2-3: for heavy mSUSY


(SM?) - Higgs found at the LHC

Both the CMS and ATLAS experiment measured a Higgs within the errors of about 126 GeV

What does this mean for the allowed CMSSM parameter space?

CMS (CMS-PAS-HIG-12-020) ATLAS (ATLAS-CONF-2012-093)

(125.3 ± 0.4 (stat) ± 0.5 (syst)) GeV (126.5 ± 0.6 (stat) ± 0.6 (syst)) GeV


125 GeV Higgs within the CMSSM

A 125 GeV light Higgs is possible within the CMSSM if the SUSY masses are heavy enough and if the trilinear coupling A0 is negative

The allowed parameter space is largely determined by the assigned error → strong dependence on the theoretical errorExp. ~ 2GeV, theo. ~ 3GeV, non-Gaussian → lin. addition → 5GeV

best fit points for different errors

(2=5.99) 95% C.L. contour

125123

121

119

Higgs mass contours


Summary so far

125 GeV Higgs hard to accomodate in CMSSM (unless one stretches the errors)

In addition, couplings have tendency to deviate from SM (see next slides)

Heavier Higgs and non-SM couplings easy to accomodate if mixing between Higgs doublet and additionally singlet, as proposed in NMSSM to solve -problem (Kim, Nilles Phys. Lett. B 138, 150 (1984))


NMSSM versus MSSMNMSSM (Next to MSSM):

Mixing: larger Higgs mass couplings to up and down type fermions can be different

new free parameters: couplings , trilinear couplings A, A mixing parameter eff = <S> (in addition to m0, m1/2, A0, tan)

...ˆ3

ˆˆˆ 3

,3,3,33

,2,2,22

,1,1,11

SHHSW

SSHSHSH

SSHSHSH

SSHSHSH

duNMSSM

suudd

suudd

suudd

MSSM

NMSSM

Higgs content

3 CP even 2 CP odd 1 singlet


Fit to SM couplings (scale factors)

CF = scale factor for coupling to fermions

CV = scale factor for coupling to vector bosons

Best fit point: CF ≈ 0.5 CV ≈ 1.0

SM: CF = CV = 1

(CMS-PAS-HIG-12-020)

SM

Best fit point


Higgs mass

MSSM

NMSSM: Mixing with singlet

Hall, Pinner, Ruderman,arXiv 1112.2703

loop corrections

2

~

2

2~

2

2

2~

2

4

2222

121ln

432cos

t

t

t

t

t

ttZh m

XmX

mm

vmmm

Increases Higgs mass for large

2

222222

,,,,2cos2sin

SS

SZ

mAMvAMvMv

M

2Zm 2130GeV

cot ttt AmX


Benchmark points in NMSSM

Analyses have been done e.g. Ellwanger, Hugonie (arXiv:1203.5048 using GUT scale parameters), Mühlleitner et al. (arXiv:1201.2671 using low energy values of parameters)Benchmark points fulfill Higgs mass and couplings, but one needs very specific singlet mixing to obtain simultaneously mH=125 GeV, large branching into , small branching into

M0 m1/2 A0 A A tan eff

600 600 -1550 -275 -625 2.40 0.545 0.253 120

960 525 -1140 -360 -575 2.29 0.600 0.321 122

E.g. Benchmark points from Ellwanger, Hugonie, arXiv:1203.5048

Input at MSUSY

Input at MGUT

BM I

BM II


Typical Higgs masses and couplings

126 126

Components of H2

Hd 0.26 0.04

Hu 0.85 -0.54

S -0.45 0.84

2HM

BM I II

100 121

Components of H1

Hd 0.39 0.50

Hu 0.34 0.74

S 0.86 0.45

1HM

BM I II

Strong mixing with singlet → R can be enchanced

It is possible that 126 GeV is not the lightest Higgs

Lightest Higgs H1 Second lightest Higgs H2


2 including R, Mh and h2 constraint

Allowed region in -plane for BM I

Parameters strongly constrained by Mh=125, R=1.7, h2=0.11(all other parameters fixed)

2 including R and Mh constraint


2 including R, Mh and h2 constraints. Parameters , and eff have been varied, A0, A and A fixed large allowed region within m0m1/2-plane

Allowed region in m0m1/2-plane

02~ fm

ex. by h2

excluded by R


Allowed region in m0m1/2-plane

Even though other constraints have not been included to the previous fit, the result is in good agreement with b s, Bs, B and g-2

g-2

Bs b s

B

Similar to CMSSM:Including g-2 to 2 constantoffset at largeMsusy


Summary

125 GeV Higgs within CMSSM only possible for high SUSY massesAllowed CMSSM parameter space depends on total error of the Higgs massWithin NMSSM one can get a 125 GeV Higgs and in addition an enhancement/reduction in Rγγ/ττ “naturally” because of large mixing with additional Higgs singletOther constraints fulfilled like in CMSSM, e.g. h2 ,b →s, Bs→, B →, and g-2 → good starting point to do same minimization as in CMSSM → work in progress…


BACKUP


Details on χ2-function

Relic Density B →τνMyon g-2b →sγ

Bs→μμ BRexp(Bs→μμ) < 4.5·10-9


LHC direct searches σhad < 0.003 – 0.03 pb

DDMS σχN < 8·10-45 - 2·10-44 cm2


Experimental Values

Defined in a straight forward way:

2

2exp2

XX SUSY


Details on χ2-function?

Relic Density Ωh2 = 0.1131 ± 0.0034B →τν BRexp(B→τν) = (1.68 ± 0.31)·10-4

Myon g-2 Δaμ=(30.2 ± 6.3 ± 6.1) ·10-11

b →sγ BRexp(b→sγ) = (3.55 ± 0.24)·10-4

Bs→μμ

Higgs Mass mh

LHC direct searches σhad < 0.003 – 0.03 pb

DDMS σχN < 8·10-45 - 2·10-44 cm2


95% CL only added if XSUSY > X95% XSUSY

= model value of BR(Bs→μμ) or mh X95% can be determined from requirement Δχ2=5.99 at 95% CL exclusion limit


Details on χ2-function?

Relic Density Ωh2 = 0.1131 ± 0.0034B →τν BRexp(B→τν) = (1.68 ± 0.31)·10-4

Myon g-2 Δaμ=(30.2 ± 6.3 ± 6.1) ·10-11

b →sγ BRexp(b→sγ) = (3.55 ± 0.24)·10-4

Bs→μμ BRexp(Bs→μμ) < 4.5·10-9


LHC direct searches DDMS Pseudo-scalar Higgs mA

95% CL exclusion contours Define χ2=(XSUSY - X95%)2/σ95%

2 XSUSY = model value of mA or hadronic cross section or χN elastic scattering cross section σ95% can be determined from 1σ band given by experiments X95% determined from requirement Δχ2=5.99 at 95% CL exclusion contour


Typical Sparticle masses and LSP mixing (NMSSM)

Components of

0.20 0.25

-0.16 -0.20

0.48 0.52

-0.70 -0.70

0.46 0.37

0.10 0.10

01

BM I II

Sparticle masses

1388 1254

1318 1397

359 463

1001 1060

528 900

108 108

77 78

BM I II

gm~

qm~

1~tm

1~bm

1~m

1

m

01

m

B~

W~

dH~

uH~

S~

2h


Start with Relic Density Constraint

2/12 mmmA

f

f

A

χ

χ

~

~

tan(β)·mfd

mW

8

N1N3(4)

tan(β)·mfd ↔ tan(β)mfu

f

f

A

χ

χ

~

~

tan(β)·mfd

mWmW

88

N1N3(4)

tan(β)·mfd ↔ tan(β)mfu

1+( /mχ )2 – (mW/mχ )2

8

W

W+

χi+

χ

χ

~

~

~

Z

Z

χi

χ

χ

~

~

~

1mχ+

i 1+( /mχ )2 – (mW/mχ )2

88

W

W+

χi+

χ

χ

~

~

~

W

W+

χi+

χ

χ

~

~

~

Z

Z

χi

χ

χ

~

~

~

Z

Z

χi

χ

χ

~

~

~

1mχ+

i mχ+

i

f

f

Z

χ

χ

~

~

mχ mf

mZ2

8

(N3(4))2

_

f

f

Z

χ

χ

~

~

mχ mf

mZ2mZ2

88

(N3(4))2

_

f

f

f

χ

χ

~

~

~

mχmf

mf2~

8

_

f

f

f

χ

χ

~

~

~

mχmf

mf2~

8

f

f

f

χ

χ

~

~

~

mχmf

mf2~ mf2~

88

_

4

2tan

Am

Problem: for excluded first diagram too small. Last diagram also small → can get correct relic density by mA s-channel annihilation

qm~

mA can be tuned with tanβ for any m1/2 → tanβ ≈ 50 (see next slide)


tan 50

Co-annihilation

Relic Density Constraint – Dependence on tanβ

22

21

2 mmmA

arXiv:1008.2150

(Tree Level)

bh

2

21

2222

21

22

2123

222

21

2121 28

..,2

HHgHHggchHHmHmHmHHVtree

th

running < 0 → if ht and hb similar → small mA for tan= mt/mb 50

Fit of Ωh2 determines mA and tanβ

m1 runningm2 running

mAm1/2


tanβ ≈ 50

(CMS PAS HIG-11-009)Atlas similar

For tanβ ≈ 50mA > 440 GeV

What about Higgs mA limit?


Examples for high correlation

χ2 for Bs → μμ and Ωh2

co-annihilation region

mA exchange

focus point region

Origin of correlation:Both strongly dependent ontanβ

Bs → μμ Ωh2

For given m0 only very specific values of tan

For given tan only very specific values of A0


Origin of correlation

Upper Limit for Bs → μμ (LHCb, CMS)

exp. Value Ωh2

Upper limit for tanβ for upper limit on Bs → μμ

Best tanβ for Ωh2

A0=0


Origin of correlationUpper Limit for Bs → μμ exp. Value Ωh2

A0=1580 GeV

Best tanβ for Bs → μμ and Ωh2 simultaneously

Common tanβ can only be found for specific A0 value


Reason for strong A0 dependence of Bs → μμ

Becomes small, ifcan be achieved by adjusting At, till mixing term ~ (At – μ/tanβ) becomes small.Important only for light SUSY masses (see blue region)

arXiv:hep-ph/0203069v2

21~~ tt

Stop mass difference


Combination of Bs → μμ and Ωh2

Tension at large tan from Bs can be removed by large A0

Tension can’t be removed by varying A0 because A0 < 3m0, A0 not high enough to get small BR

Tension still there although A0 large enough to get small BR


Why there‘s still a tension for large m0?

Small Stau masscontribute to Ωh2

Bs →μμ needs large A0 for large tanβ

Ωh2 too high for large A0

mA high → small cross section

Bs →μμ smaller than SM value, even at large tanβ

m0=1000 m1/2=250 SM value


How to treat theoretical errors?• Theoretical errors can be treated as nuisance parameters and

integrated over in the probability distribution (=convolution for symm. distr.)

• If errors Gaussian, this corresponds to adding the experimental and theoretical errors in quadrature

• Assume σtheo ~ σexp (only then important)

Convolution of 2 GaussiansConvolution of Gaussian + “flat top Gaussian” (expected if theory errors indicate a range)

Adding errors linearly more conservative approach for theory errors.

2exp

22 theo exp~ theo


SUSY particles can be produced in pp collisions at the LHC

Combination of the different cross sections of

Direct searches for SUSY particles

qqqgggpp ~~,~~,~~

qq~~

qg~~gg~~

95% CL exclusion by CMS + Atlas (Jets+MET)CMS PAS SUS-11-003

arXiv:1109.6572

Contribution to σtot=0,1pb

Parametrization of with σeff

2 that Δχ2 = χ2 – χ2

min = 5,99

222efftot


Direct search for dark matter (DDMS)

Assume Neutralino is LSP and therefore perfect WIMP candidateDirect detection of WIMPs through elastic scattering on heavy nuclei

Coherent scattering: σ ~ N2 and effective coupling on proton/neutron fp/fn

Effective coupling includes couplings of WIMPs on quarks fq

n/fqp

90% CL → Δχ2 = 4,21(arXiv:1005.0380)


Including DDMS constraint into χ2

UncertaintiesLocal DM density (0,3/1,3 GeV/cm³)Effective coupling (especially s-quark) because of different calculations

;02.0

;026.0

;02.0

ps

pd

pu

f

f

f

;02.0

;036.0

;014.0

ps

pd

nu

f

f

f

;26.0

;033.0

;023.0

ps

pd

pu

f

f

f

;26.0

;042.0

;018.0

ps

pd

nu

f

f

f

lattice πN

conservative


Excluded parameter space by XENON100

Scattering cross section is proportional to the product of gaugino und higgsino component → Increase of the cross section if higgsino component is increasingHiggsino component increases for high values of m0 → DDMS is sensitive for high m0 in contrast to the direct searches at the LHC


Comparison to other groups

Strong correlation between A0 and tanβ

Buchmueller et al. arXiv: 1110.3568

If one include the exclusion limit of the LHC, the difference between the 95% CL contour of the quadratic and linear addition of the errors vanishes.


Exclusion because of Ωh2 for large values of m1/2

Excluded region for large values of m1/2 and small m0 because of the relic densityFor this combination of m0 and m1/2 one needs a high value of tanβ for the correct relic densityFor such high values of tanβ the Neutralino is not the LSP anymore

Χ2 contribution of Ωh2

m0=500 GeV m1/2=1300 GeV

LSP~

Contributors to CF and CV

Constraints on Supersymmetry using the latest data from cosmology, DM searches and LHC

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