Supersymmetry Basics:Lecture II

J. Hewett SSI 2012J. Hewett

Implications of LHC Results

Implications of LHC Results

Soft SUSY Breaking Mechanisms

• Spontaneous SUSY breaking (vev w/ tree-level couplings)– Requires a gauge extension to the MSSM – Tends to yield unacceptably small sparticle masses

Assume MSSM soft terms arise radiatively

• SUSY breaking occurs in hidden sector which has little to none direct couplings to visible sector

• SUSY breaking mediated through shared interactions

Supersymmetrybreaking origin(Hidden sector)

MSSM(Visible sector)

Gravity-Mediated SUSY Breaking

• vev <F> in hidden sector breaks SUSY• Communicated to visible sector by gravitational interactions

• msoft ~ <F>/MPl

• msoft ~ 100 GeV if √<F> ~ 1010-11 GeV

Supersymmetrybreaking origin(Hidden sector)

MSSM(Visible sector)

Minimal Supergravity

• Assume universal scalar and gaugino masses @ GUT scale

• Terms in Lsoft determined by just 4 parameters:

m1/2 = f<F>/MPl , m02 = (k+n2)|<F>|2/MPl

2 ,

A0 = (α+3n)<F>/MPl , B0 = (β+2n)<F>/MPl ,

(α,β,f,k,n dimensionless parameters of order 1, determined by full underlying theory)

• Eliminate B0 in favor of tanβ, and include sign of μ (value of μ fixed by requiring correct Z mass in Higgs potential)

4 parameters describe the complete theory! m1/2 , m0 , A0 , tanβ, sgn μ

known as mSUGRA or Constrained MSSM

Evolution of Scalar/Gaugino Masses

• Evolve common scalar/gaugino masses from

GUT scale via RGE’s

• Gauge couplings increase mass, Yukawa couplings decrease mass

• Results in predictive SUSY spectrum @ EW scale w/ Bino as LSP

• M3 : M2 : M1 =

g32 : g2

2 : (5/3)gY2

|GUT

yields M3 : M2 : M1 = 7 : 2 : 1 |

EW

Gauge-Mediated SUSY Breaking

• vev <F> in hidden sector breaks SUSY• Communicated to visible sector by SM gauge interactions

• msoft arise from loop diagrams containing messenger particles (new chiral supermultiplets)

• msoft ~ αa<F>/4πMmessenger

• msoft ~ 100 GeV if √<F> ~ Mmess ~ 104 GeV

Supersymmetrybreaking origin(Hidden sector)

MSSM(Visible sector)

messengers

Minimal Gauge Mediation

• Communicated to MSSM through radiative corrections – Gaugino masses arise from 1-loop diagrams involving messenger particles

– Scalar masses arise from 2-loop diagrams

• Messenger supermultiplets split by SUSY breaking in hidden sector

Minimal Gauge Mediation

• Masses depend on – Messenger scale – Number of SU(5) 5+5-bar messenger representations

– Number and strength of gauge interactions

• Gauginos tend to be heavier than scalars (for N5 >1)

• If N5 is too large, there is no unification

• Gravitino is the LSP strikingly different phenomenology!

phenomenological MSSM

• Most general CP-conserving MSSM– Minimal Flavor Violation– Lightest neutralino is the LSP– First 2 sfermion generations are degenerate w/ negligible Yukawas

– No GUT, SUSY-breaking assumptions!

• ⇒19(20) real, weak-scale parameters scalars:

mQ1, mQ3

, mu1, md1

, mu3, md3

, mL1, mL3

, me1, me3

gauginos: M1, M2, M3

tri-linear couplings: Ab, At, Aτ

Higgs/Higgsino: μ, MA, tanβ (Gravitino mass, if Gravitino LSP)

SUSY Spectrum

• Details of the sparticle spectrum depend on the soft SUSY breaking mechanism!

• Precision measurements of the sparticle masses can reveal insight into the soft SUSY breaking mechanism!

Sample Sparticle Spectra: CMSSM and GMSB

Gravity mediated Gauge mediated

The SUSY Higgs Sector

• SUSY Higgs sector: h0, H0, H±, A0

• 2 free parameters in the Higgs potential: very predictive at tree-level!

• Radiative corrections are important!Higgs massis very senistivein particular tothe lighteststop mass

The SUSY Higgs Sector

Haber, HempflingMStop

A heavy h0 needs a heavy stop-squark t1

~

Predictions for Lightest Higgs Mass in the CMSSM

• Χ2 fit to EW, Flavor, Collider, Cosmology global data set

Ellis etal arXiv:0706.0652

Predictions for Lightest Higgs Mass in the pMSSM

Cahill-Rowley, JLH, Ismail, Rizzo

Models consistent with EW Precision, B Physics, Cosmology,and Collider data

Neutralino LSPGravitino LSP

125 GeV Higgs Constraints

1112.3028

Maximum mass for h0 in various SUSY breaking scenarios

Simplest versionsof GMSB, AMSB,etc are ruled out!!

Supersymmetry and Naturalness

The hierarchy problem needs a light stop-squark t1

~

Tension???

Naturalness Criterion

Barbieri, GiudiceKasahara, Freese, Gondolo

Standard prescription to compute fine-tuning:

•Take mass relation w/ radiative corrections

•Compute dependence on each SUSY parameter, pi

•Overall fine-tuning of model given by

Δ = max|Zi|

+ higher order

Naturalness and the CMSSM

CMSSM global fit tothe data before LHCSUSY search results

Naturalness and the CMSSM

CMSSM global fit tothe data AFTER LHCSUSY search results

Naturalness and the CMSSM

Fine-tuning parameter Δ > 500 – 1000 in the CMSSM

The CMSSM is untenable at this timeReport submitted to European Strategy

A Natural Spectrum

Barbieri

Future Searches

• “Naturalness” dictates:– Stop < 700 GeV– Gluino < 1500 GeV

• Dedicated searches for direct stop/sbottom and

EW gaugino production will be a focus for the rest of

the 8 TeV run

• Can more complex models accommodate Naturalness?

Study of the pMSSM

Linear Priors

Perform large scan over Parameters

100 GeV msfermions 4 TeV

50 GeV |M1, M2, | 4 TeV

400 GeV M3 4 TeV 100 GeV MA 4 TeV 1 tan 60|At,b,| 4 TeV

Subject these points to Constraints from:

•Flavor physics•EW precision measurements•Collider searches•Cosmology

~225,000 viable models survive constraints! Cahill-Rowley, JLH, Ismail, Rizzo

Subject these Models to LHC Searches

Light squarksGluinos

Stop

Sparticle distributions:Before LHC7 TeV 1 fb-1

7 TeV 5 fb-1

8 TeV 5 fb-1

5 TeV 20 fb-1

Non-MET Searches

• Non-MET searches are also important!

Bs μ

Fine-Tuning in the pMSSM

Neutralino LSPGravitino LSP

mh = 125 ± 2 GeV

Fine-Tuning in the pMSSM

Neutralino LSPGravitino LSP

mh = 125 ± 2 GeV

13 + 1 models with Δ < 100

Sample Spectra w/ low FT

Sample Spectra w/ low FT

Light Stop Decay Channels

Dark Matter Direct Detection

Summary

• Weak-scale Supersymmetry extremely well motivated

• Simplest models (CMSSM) in tension with LHC searches

• Some minimal models excluded by 125 GeV Higgs (GMSB, AMSB)

• More complex scenarios (pMSSM) are still robust

• Don’t give up on Weak-scale SUSY until 14 TeV with 300 fb-1 !

The theory community is presently working hard in light of the LHC results!

A. Pomarol, ICHEP 2012