The MSSM after two years of LHC running Felix Brümmer DESY Felix Brümmer MSSM status 1 / 14
The Standard Model Felix Brümmer MSSM status 2 / 14
Beyond the Standard Model: The MSSM Felix Brümmer MSSM status 3 / 14
Beyond the Standard Model: The MSSM minimal SUSY extension of Standard Model two Higgs doublets a scalar s-particle for every SM fermion: squarks, sleptons a fermionic particl-ino for every SM boson: gauginos, higgsinos → charginos χ ± , neutralinos χ 0 O ( 100 ) parameters Felix Brümmer MSSM status 3 / 14
Restricting the parameter space � SUSY = − 1 M a λ a λ a + h.c. − m 2 H u h † u h u − m 2 H d h † L ✘✘ d h d ✘ 2 a Q † � U † � D † � E † � Q � U � D � L � L † � E � − m 2 Q − m 2 U − m 2 D − m 2 L − m 2 E � � A U y u � Q � Uh u + A D y d � Q � Dh d + A E y e � L � − Eh d + B µ h u h d + h.c. Felix Brümmer MSSM status 4 / 14
Restricting the parameter space � SUSY = − 1 M a λ a λ a + h.c. − m 2 H u h † u h u − m 2 H d h † L ✘✘ d h d ✘ 2 a Q † � U † � D † � E † � Q � U � D � L � L † � E � − m 2 Q − m 2 U − m 2 D − m 2 L − m 2 E � � A U y u � Q � Uh u + A D y d � Q � Dh d + A E y e � L � − Eh d + B µ h u h d + h.c. Benchmark scenarios: e.g. CMSSM: M 1 / 2 , m 0 , A 0 , tan β, sgn ( µ ) Convenient; self-consistent; not well motivated theoretically Do not expect the world to be anywhere close to mSUGRA Felix Brümmer MSSM status 4 / 14
Restricting the parameter space � SUSY = − 1 M a λ a λ a + h.c. − m 2 H u h † u h u − m 2 H d h † L ✘✘ d h d ✘ 2 a Q † � U † � D † � E † � Q � U � D � L � L † � E � − m 2 Q − m 2 U − m 2 D − m 2 L − m 2 E � � A U y u � Q � Uh u + A D y d � Q � Dh d + A E y e � L � − Eh d + B µ h u h d + h.c. Benchmark scenarios: e.g. CMSSM: M 1 / 2 , m 0 , A 0 , tan β, sgn ( µ ) Convenient; self-consistent; not well motivated theoretically Do not expect the world to be anywhere close to mSUGRA Simplified models: truncate to a few states relevant for specific signatures good starting point for phenomenology; exclusion bounds often too strong related: pMSSM, 19 TeV-scale parameters Felix Brümmer MSSM status 4 / 14
Restricting the parameter space � SUSY = − 1 M a λ a λ a + h.c. − m 2 H u h † u h u − m 2 H d h † L ✘✘ d h d ✘ 2 a Q † � U † � D † � E † � Q � U � D � L � L † � E � − m 2 Q − m 2 U − m 2 D − m 2 L − m 2 E � � A U y u � Q � Uh u + A D y d � Q � Dh d + A E y e � L � − Eh d + B µ h u h d + h.c. Benchmark scenarios: e.g. CMSSM: M 1 / 2 , m 0 , A 0 , tan β, sgn ( µ ) Convenient; self-consistent; not well motivated theoretically Do not expect the world to be anywhere close to mSUGRA Simplified models: truncate to a few states relevant for specific signatures good starting point for phenomenology; exclusion bounds often too strong related: pMSSM, 19 TeV-scale parameters Full models: Where to start? Realistic, but usually more intricate than needed for LHC Exclusion bounds not easily transferrable Felix Brümmer MSSM status 4 / 14
Sparticle production and decays R-parity ⇒ sparticles produced pairwise at hadron collider: mainly ˜ q ˜ g , ˜ q ˜ q , ˜ q ˜ q ∗ , ˜ g ˜ g typical decay signature: cascade decays into lightest SUSY particle ⇒ MET + jets (+ leptons) q q q ~ ~ g 0 χ q ~ q + 0 χ χ ~ q + g W ν q e Felix Brümmer MSSM status 5 / 14
Constraints I: Direct sparticle searches Stringent limits on first-generation squark and gluino masses: At m ˜ u 1 ≈ m ˜ d 1 ≈ M ˜ g : all � 1 . 4 TeV Beware: model dependence! more general pMSSM analysis: → Sekmen et al. ’11 @ 1 fb − 1 → ATLAS-CONF-2012-037 Felix Brümmer MSSM status 6 / 14
Constraints II: A 125 GeV Higgs Further constraints on stop sector: Suppose a SM-like Higgs is at m h 0 = 125 ± 2 GeV m h 0 > m Z needs large loop contributions (from large stop masses/mixings) � � �� m 2 + A 2 A 2 3 ˜ m 2 h 0 = m 2 4 π 2 y 4 t v 2 t t t Z + log 1 − + . . . m 2 m 2 12 m 2 t ˜ ˜ t t 125 2 = 91 2 + 86 2 Needs m ˜ t � 2 TeV, heavy stops or large | A t / m ˜ t | ≈ 2, “maximal stop mixing” Felix Brümmer MSSM status 7 / 14 → FB/Kraml/Kulkarni, in progress
Fine-tuning I: The Little Hierarchy m 2 Z = − 2 ( m 2 H u + | µ | 2 ) µ = Higgsino mass, m 2 H u = up-type Higgs soft mass ( < 0 by EWSB) m H u , m ˜ t , M ˜ g generically of similar magnitude m ✘✘ SUSY ✘ therefore m Z ∼ m ✘✘ SUSY unless ✘ large cancellation between | µ | 2 and m 2 H u , or | m H u | ≪ m ✘ SUSY accidentally at the weak scale (and µ small) ✘ Either way: fine-tuning of parameters needed for m Z ≪ m ✘✘ SUSY ✘ Generic: m Z ∼ m ✘✘ SUSY ✘ Fine-tuned: m Z ≪ m ✘✘ SUSY ✘ Felix Brümmer MSSM status 8 / 14
Fine-tuning II: Neutralino dark matter Bino relic density too large: need τ or ˜ ˜ t coannihilation resonant h 0 or A 0 exchange some higgsino admixture (focus point) 0 < m 0 < 5 TeV, 5 < m 0 < 20 TeV → Baer, Barger, Mustafayev ’12 Felix Brümmer MSSM status 9 / 14
Fine-tuning II: Neutralino dark matter Bino relic density too large: need ✭✭✭✭✭✭✭✭✭ τ or ˜ ˜ t coannihilation ✭ ✭✭✭✭✭✭✭✭✭✭✭✭ resonant h 0 or A 0 exchange some higgsino admixture (focus point) (?) 0 < m 0 < 5 TeV, 5 < m 0 < 20 TeV → Baer, Barger, Mustafayev ’12 Felix Brümmer MSSM status 9 / 14
Fine-tuning II: Neutralino dark matter Bino relic density too large: need ✭✭✭✭✭✭✭✭✭ τ or ˜ ˜ t coannihilation ✭ ✭✭✭✭✭✭✭✭✭✭✭✭ resonant h 0 or A 0 exchange some higgsino admixture (focus point) (?) 0 < m 0 < 5 TeV, 5 < m 0 < 20 TeV → Baer, Barger, Mustafayev ’12 Caution: this is just for CMSSM Still “WIMP miracle” losing some of its appeal (SUSY doesn’t need thermal WIMPs. Gravitinos, axinos, nonthermally produced higgsinos? . . . ) Felix Brümmer MSSM status 9 / 14
Natural SUSY Idea: keep states related to naturalness “light” → Papucci/Ruderman/Weiler ’11 µ, m H u , m ˜ t 1 , m ˜ t 2 , m ˜ b L , ( M ˜ g ) � 1 TeV first-generation squarks ≫ 1 TeV everything else B -like χ ± , χ 0 undetermined � W - and � ~ g direct ˜ q , ˜ g search bounds evaded ~ ~ t t L R Higgs mass still problematic ~ b L LHC should find higgsinos, ˜ t , ˜ b , ( ˜ g ) ~ H Felix Brümmer MSSM status 10 / 14
Natural SUSY Idea: keep states related to naturalness “light” → Papucci/Ruderman/Weiler ’11 µ, m H u , m ˜ t 1 , m ˜ t 2 , m ˜ b L , ( M ˜ g ) � 1 TeV first-generation squarks ≫ 1 TeV everything else B -like χ ± , χ 0 undetermined W - and � � ~ g direct ˜ q , ˜ g search bounds evaded ~ ~ t t L R Higgs mass still problematic ~ b L LHC should find higgsinos, ˜ t , ˜ b , ( ˜ g ) ~ H Comments: Phenomenological ansatz: soft terms prescribed at TeV scale Not clear a priori if realizable in a UV-scale model Some proposals: → Craig/McCullough/Thaler, Craig/Dimopoulos/Gherghetta, Krippendorf/Nilles/Ratz/Winkler, Csaki/Randall/Terning, Larsen/Nomura/Roberts. . . Felix Brümmer MSSM status 10 / 14
Heavy stops Idea: Maybe heavy stops can be reconciled with naturalness m Z ≪ m ✘✘ SUSY due to model relations between soft terms ✘ Prototype: Focus point → Chan/Chattopadhyay/Nath ’97, Feng/Matchev/Moroi ’99 Natural to have m 0 ≫ TeV in CMSSM Nice explanation for dark matter relic density Felix Brümmer MSSM status 11 / 14
Heavy stops Idea: Maybe heavy stops can be reconciled with naturalness m Z ≪ m ✘✘ SUSY due to model relations between soft terms ✘ Prototype: Focus point → Chan/Chattopadhyay/Nath ’97, Feng/Matchev/Moroi ’99 Natural to have m 0 ≫ TeV in CMSSM Nice explanation for dark matter relic density (?) ·· g � 1 TeV � Experiment now requires M ˜ ⌢ Felix Brümmer MSSM status 11 / 14
Heavy stops Idea: Maybe heavy stops can be reconciled with naturalness m Z ≪ m ✘✘ SUSY due to model relations between soft terms ✘ Prototype: Focus point → Chan/Chattopadhyay/Nath ’97, Feng/Matchev/Moroi ’99 Natural to have m 0 ≫ TeV in CMSSM Nice explanation for dark matter relic density ·· g � 1 TeV � Experiment now requires M ˜ ⌢ Variations: non-universal gaugino masses contributing to m Z ≪ m ✘✘ SUSY ✘ → Abe/Kobayashi/Omura ’07, Horton/Ross ’09, FB/Buchmüller ’11, ’12, Younkin/Martin ’12 everything else Potentially all superparticles heavy (except higgsinos?) ~ H Difficult to test at LHC Criticism: high sensitivity to dimensionless (Yukawa, gauge) couplings → Romanino/Strumia ’99 Felix Brümmer MSSM status 11 / 14
Large stop mixing SUSY = − A t y t ˜ t L ˜ L ✘✘ t R h u + h.c. + . . . ✘ X t = A t − µ cot β : stop mixing parameter | X t / m ˜ t | ≈ 2 at TeV scale ⇒ large m h 0 possible Non-trivial to get this from a model → Draper et al. ’11, Aparicio/Cerdeño/Ibañez ’12, FB/Kraml/Kulkarni, in progress, . . . e.g. gauge mediation or AMSB: → Arbey/Battaglia/Djouadi/Mahmoudi/Quevillon no way (so far) Felix Brümmer MSSM status 12 / 14
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