Transcript Lecture 2
Supersymmetry Basics: Lecture II
SSI 2012
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 Supersymmetry breaking origin (Hidden sector) MSSM (Visible sector) • SUSY breaking occurs in hidden sector which has little to none direct couplings to visible sector • SUSY breaking mediated through shared interactions
Gravity-Mediated SUSY Breaking Supersymmetry breaking origin (Hidden sector) MSSM (Visible sector) • vev
Minimal Supergravity • Assume universal scalar and gaugino masses @ GUT scale • Terms in
L
soft determined by just 4 parameters: m A 0 1/2 = f
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 spectrum @ EW scale w/ Bino as LSP • M 3 : M 2 g 3 2 yields M 3 : M 2 : M : g 2 : M 1 1 2 = : (5/3)g Y 2 | = 7 : 2 : 1 | GUT EW
Gauge-Mediated SUSY Breaking
Supersymmetry breaking origin (Hidden sector) messengers MSSM (Visible sector) • vev
Minimal Gauge Mediation
• Messenger supermultiplets split by SUSY breaking in hidden sector • Communicated to MSSM through radiative corrections – Gaugino masses arise from 1 loop diagrams involving messenger particles – Scalar masses arise from 2-loop diagrams
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 Q1 , m Q3 , m u1 , m d1 , m u3 , m d3 , m L1 , m L3 , m e1 , m e3 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 mediated Gauge 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 M Stop Haber, Hempfling A heavy h 0 needs a heavy stop-squark t 1
Predictions for Lightest Higgs Mass in the CMSSM
• Χ 2 set fit to EW, Flavor, Collider, Cosmology global data Ellis etal arXiv:0706.0652
Predictions for Lightest Higgs Mass in the pMSSM Models consistent with EW Precision, B Physics, Cosmology, and Collider data Neutralino LSP Gravitino LSP Cahill-Rowley, JLH, Ismail, Rizzo
125 GeV Higgs Constraints Maximum mass for h 0 in various SUSY breaking scenarios Simplest versions of GMSB, AMSB, etc are ruled out!!
1112.3028
Supersymmetry and Naturalness The hierarchy problem needs a light stop-squark t 1
Tension???
Naturalness Criterion Standard prescription to compute fine-tuning: • Take mass relation w/ radiative corrections + higher order • Compute dependence on each SUSY parameter, p i • Overall fine-tuning of model given by Δ = max|Z i | Barbieri, Giudice Kasahara, Freese, Gondolo
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 50 GeV m sfermions |M 1 , M 2 , | 4 TeV 4 TeV 400 GeV 100 GeV 1 tan M 3 M A 60 4 TeV 4 TeV |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 Gravitino LSP LSP m h = 125 ± 2 GeV
Fine-Tuning in the pMSSM Neutralino Gravitino LSP LSP m h = 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