Supersymmetry Basics: Lecture II J. HewettSSI 2012 J. Hewett

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 Supersymmetry breaking origin (Hidden sector) MSSM (Visible sector)

Gravity-Mediated SUSY Breaking vev in hidden sector breaks SUSY Communicated to visible sector by gravitational interactions m soft ~ /M Pl m soft ~ 100 GeV if √ ~ GeV Supersymmetry breaking origin (Hidden sector) MSSM (Visible sector)

Minimal Supergravity Assume universal scalar and gaugino GUT scale Terms in L soft determined by just 4 parameters: m 1/2 = f /M Pl, m 0 2 = (k+n 2 )| | 2 /M Pl 2, A 0 = (α+3n) /M Pl, B 0 = (β+2n) /M Pl, (α,β,f,k,n dimensionless parameters of order 1, determined by full underlying theory) Eliminate B 0 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! m 1/2, m 0, A 0, 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 EW scale w/ Bino as LSP M 3 : M 2 : M 1 = g 3 2 : g 2 2 : (5/3)g Y 2 | GUT yields M 3 : M 2 : M 1 = 7 : 2 : 1 | EW

Gauge-Mediated SUSY Breaking vev in hidden sector breaks SUSY Communicated to visible sector by SM gauge interactions m soft arise from loop diagrams containing messenger particles (new chiral supermultiplets) m soft ~ α a /4πM messenger m soft ~ 100 GeV if √ ~ M mess ~ 10 4 GeV Supersymmetry breaking 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 N 5 >1) If N 5 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: m Q 1, m Q 3, m u 1, m d 1, m u 3, m d 3, m L 1, m L 3, m e 1, m e 3 gauginos: M 1, M 2, M 3 tri-linear couplings: A b, A t, A τ Higgs/Higgsino: μ, M A, 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 mediatedGauge mediated

The SUSY Higgs Sector SUSY Higgs sector: h 0, H 0, H ±, A 0 2 free parameters in the Higgs potential: very predictive at tree-level! Radiative corrections are important! Higgs mass is very senistive in particular to the lightest stop mass

The SUSY Higgs Sector Haber, HempflingM Stop A heavy h 0 needs a heavy stop-squark t 1 ~

Predictions for Lightest Higgs Mass in the CMSSM Χ 2 fit to EW, Flavor, Collider, Cosmology global data set Ellis etal arXiv:

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 LSP Gravitino LSP

125 GeV Higgs Constraints Maximum mass for h 0 in various SUSY breaking scenarios Simplest versions of GMSB, AMSB, etc are ruled out!!

Supersymmetry and Naturalness The hierarchy problem needs a light stop-squark t 1 ~

Tension???

Naturalness Criterion Barbieri, Giudice Kasahara, Freese, Gondolo Standard prescription to compute fine-tuning: Take mass relation w/ radiative corrections Compute dependence on each SUSY parameter, p i Overall fine-tuning of model given by Δ = max|Z i | + higher order

Naturalness and the CMSSM CMSSM global fit to the data before LHC SUSY search results

Naturalness and the CMSSM CMSSM global fit to the data AFTER LHC SUSY search results

Naturalness and the CMSSM Fine-tuning parameter Δ > 500 – 1000 in the CMSSM The CMSSM is untenable at this time Report 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  m sfermions  4 TeV 50 GeV  |M 1, M 2,  |  4 TeV 400 GeV  M 3  4 TeV 100 GeV  M A  4 TeV 1  tan   60 |A t,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 squarks Gluinos Stop Sparticle distributions: Before LHC 7 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! B s  μ

Fine-Tuning in the pMSSM Neutralino LSP Gravitino LSP m h = 125 ± 2 GeV

Fine-Tuning in the pMSSM Neutralino LSP Gravitino LSP m h = 125 ± 2 GeV models with Δ < 100

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