Supersymmetry Basics: Lecture II
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Transcript of Supersymmetry Basics: Lecture II
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