Timothy Cohen (SLAC) Timothy Cohen (SLAC) 1/46 Here Be Dragons: T HE U NEXPLORED C ONTINENTS OF THE CMSSM Timothy Cohen (SLAC) with Jay Wacker arXiv:1305.2914 GGI workshop: Beyond the Standard Model after the first run of the LHC July 5, 2013
Timothy Cohen (SLAC) 2/46 Outline I) Motivation II) CMSSM Cartography III) Circumnavigating the CMSSM IV) Conclusions
Timothy Cohen (SLAC) 3/46 M OTIVATION
Timothy Cohen (SLAC) 4 /46 The MSSM in the Era of Higgs Discovery • A SM-like Higgs has been discovered at 125 GeV. ATLAS [arXiv:1207.7214]; CMS [arXiv:1207.7235] • “Consistent” with the MSSM (and its extensions). ✓ e ◆ ✓ ◆� Z cos 2 2 β + 3 g 2 m 4 A 2 A 2 m t 1 e m t 2 t t t m 2 h ' m 2 log + 1 � 8 π 2 m 2 m 2 m t 1 e e m t 2 12 e m t 1 e m t 2 t W • Stops from O(100 GeV) to O(100 TeV) 4x heavier than pre discovery: 3 g 2 m 4 log e m t 0 1 e m t 0 ∆ mh t m h 0 � m h ' 2 = m t 0 e 1 e m t 0 2 ' e m t 1 e m t 2 2 ) 5 . 6 GeV 16 π 2 m h m 2 m t 1 e e m t 2 W • The motivation for weak-scale superpartners still stands: • Solves the hierarchy problem; • Explains the dark matter; • Predicts gauge coupling unification.
Timothy Cohen (SLAC) 5 /46 The MSSM in the Era of Higgs Discovery • The parameter space of the MSSM is enormous. • The soft supersymmetry breaking Lagrangian includes more than 120 new dimensionful terms. • How can we map out all possible signatures? • Simplified models: isolate particles for specific signature. Parameter space is tractable; only a few masses and branching ratios. Alwall, Le, Listanti, Wacker [arXiv:0809.3264]; Alwall, Schuster, Toro [arXiv:0810.3921]; LHC New Physics Working Group [arXiv:1105.2838] • pMSSM: phenomenologically motivated reduction to 19 parameters. Berger, Gainer, Hewett, Rizzo [arXiv:0812.0980] • CMSSM/mSUGRA: 4 parameters. Chamseddine, Arnowitt, Nath [PRL 49 (1982)]; Barbieri, Ferrara, Savoy [PLB (1982)]; Hall, Lykken, Weinberg [PRD (1983)] • 4 parameters is potentially tractable. • Can we understand all predictions of the CMSSM ansatz?
Timothy Cohen (SLAC) 6 /46 A Simple Ansatz - a wide range of dynamics • The CMSSM is a four dimensional subspace of the R -parity conserving MSSM. • It is defined at the GUT scale by the following (real) inputs: • The unified scalar soft mass, . M 0 • The unified gaugino mass: . M 1 / 2 • The unified A -term: . A 0 • The ratio of the Higgs vevs: (traded for the term). tan β B µ • Parameters are evolved to weak scale using RGEs. • -term is determined by requiring . m Z = 91 GeV µ • 19 coupled RGEs integrated over 32 e-folds: relation between the inputs & low energy parameters is highly non-linear.
Timothy Cohen (SLAC) 6 /46 A Simple Ansatz - a wide range of dynamics • The CMSSM is a four dimensional subspace of the R -parity conserving MSSM. • It is defined at the GUT scale by the following (real) inputs: • The unified scalar soft mass, . M 0 • The unified gaugino mass: . M 1 / 2 • The unified A -term: . A 0 • The ratio of the Higgs vevs: (traded for the term). tan β B µ • Parameters are evolved to weak scale using RGEs. • -term is determined by requiring . m Z = 91 GeV µ • 19 coupled RGEs integrated over 32 e-folds: relation between the inputs & low energy parameters is highly non-linear.
Timothy Cohen (SLAC) 7 /46 State of the Art: The LHC • Both ATLAS and CMS put limits on the CMSSM: 1000 CMS -1 L = 4.98 fb , s = 7 TeV int. (GeV) m( m ~ P q ( ~ ) = 2000 tan( β )=10 q S ) 900 = A = 0 GeV L 0 2 ~ 5 m ( g ) = > 0 2 0 0 0 = µ 0 0 ∼ m = 173.2 GeV τ t 800 1/2 m( ~ q ) = 1500 m 700 ~ m g ( ) = 1 5 0 0 600 Observed Limit (NLO+NLL with uncertainties) Expected Limit (NLO+NLL) 500 m( ~ -1 NLO Obs. Limit (L = 35 pb ) q ) = 1000 int ~ m g ( ) = 1 400 0 0 0 ~ ± LEP2 l 300 ∼ ± LEP2 χ 1 ~ Non-Convergent RGE's 200 m ( g ) = 5 0 0 B S W E o N 100 500 1000 1500 2000 2500 m (GeV) 0 CMS [arXiv:1205.6615] ATLAS-CONF-2012-109 • Exclusions for a region of the versus plane at a M 0 M 1 / 2 fixed and . A 0 tan β • What is the Higgs mass? • Does the neutralino overclose the Universe?
Timothy Cohen (SLAC) 7 /46 State of the Art: The LHC • Both ATLAS and CMS put limits on the CMSSM: 1000 CMS -1 L = 4.98 fb , s = 7 TeV int. (GeV) m( m ~ P q ( ~ ) = 2000 tan( β )=10 q S ) 900 = A = 0 GeV L 0 2 ~ 5 m ( g ) = > 0 2 0 0 0 = µ 0 0 ∼ m = 173.2 GeV τ t 800 1/2 m( ~ q ) = 1500 m 700 ~ m g ( ) = 1 5 0 0 600 Observed Limit (NLO+NLL with uncertainties) Expected Limit (NLO+NLL) 500 m( ~ -1 NLO Obs. Limit (L = 35 pb ) q ) = 1000 int ~ m g ( ) = 1 400 0 0 0 ~ ± LEP2 l 300 ∼ ± LEP2 χ 1 ~ Non-Convergent RGE's 200 m ( g ) = 5 0 0 B S W E o N 100 500 1000 1500 2000 2500 m (GeV) 0 CMS [arXiv:1205.6615] ATLAS-CONF-2012-109 • Exclusions for a region of the versus plane at a M 0 M 1 / 2 fixed and . A 0 tan β • What is the Higgs mass? • Does the neutralino overclose the Universe?
Timothy Cohen (SLAC) 8 /46 State of the Art: Theory • Many groups approach CMSSM (and other models) from statistical point of view. Baltz, Gondolo [arXiv:hep-ph/0407039]; Allanach, Lester [arXiv:hep-ph/0507283]; de Austri, Trotta, Roszkowski [arXiv:hep-ph/0602028]; Akrami, Scott, Edsjo, Conrad, Bergstrom [arXiv:0910.3950]; Buchmueller et. al [arXiv:0907.5568] • Techniques are very powerful. • Allow inclusion of many experimental inputs (with errors). • Assign likelihood to all points in parameter space. • Not obvious what drives boundaries. • For example: claims that stop coannihilation largely excluded. Allanach, Lester [arXiv:hep-ph/0507283]
Timothy Cohen (SLAC) 9 /46 Classification • We will require that the Higgs mass is ~125 GeV and the neutralino comprises all of the dark matter. • “Quadrants” are defined by the and the . sign( A 0 ) sign( µ ) • Schematically, the RGEs for A and B terms are given by 16 π 2 d + y g 2 M, | y | 2 � g 2 � � dtA = A 16 π 2 d A y † + g 2 M | y | 2 � g 2 � � � � dtB = B + µ , • The low energy behavior can be very different depending on these signs.
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation”
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” χ 0 f e Z 0 χ 0 e f
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” χ 0 W + e χ + e χ 0 e W −
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” b χ 0 e A 0 χ 0 e b
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” τ ± χ 0 e τ ± e τ ± e Z 0
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” χ 0 e t e t e t g
Timothy Cohen (SLAC) 10 /46 Classification • What process determines the relic abundance? χ 0 e Z 0 • “light a”: annihilation is dominated by the and h poles. W + W − • “well-tempered”: annihilation via Higgsino/bino mixing to . A 0 • “ pole”: annihilation is dominated by an s -channel resonance. A 0 • “stau coannihilation” • “stop coannihilation” χ 0 e t e g s t e t g
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