LHC Higgs Cross Section WG: Branching Ratios – MSSM Sven Heinemeyer, IFCA (CSIC, Santander) Freiburg, 04/2010 co-contacts: Ansgar Denner, Ivica Puljak, Daniela Rebuzzi 1. Introduction 2. MSSM issues 3. What has been done (few) 4. What has to be done (a lot) 5. Discussion points / future plans Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 1
1. Introduction Supersymmetry (SUSY) : Symmetry between Bosons ↔ Fermions Q | Fermion � → | Boson � Q | Boson � → | Fermion � Simplified examples: | scalar top , ˜ Q | top , t � → t � Q | gluon , g � → | gluino , ˜ g � ⇒ each SM multiplet is enlarged to its double size Unbroken SUSY: All particles in a multiplet have the same mass Reality: m e � = m ˜ e ⇒ SUSY is broken . . . . . . via soft SUSY-breaking terms in the Lagrangian (added by hand) SUSY particles are made heavy: M SUSY = O (1 TeV) Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 2
The Minimal Supersymmetric Standard Model (MSSM) Superpartners for Standard Model particles � � � � � � Spin 1 u, d, c, s, t, b e, µ, τ ν e,µ,τ 2 L,R L,R L � � � � � � u, ˜ t, ˜ s, ˜ ˜ d, ˜ c, ˜ b ˜ e, ˜ µ, ˜ τ ν e,µ,τ ˜ Spin 0 L,R L,R L W ± , H ± γ, Z, H 0 1 , H 0 g Spin 1 / Spin 0 2 � �� � � �� � Spin 1 χ ± χ 0 ˜ ˜ ˜ g 1 , 2 1 , 2 , 3 , 4 2 Enlarged Higgs sector: Two Higgs doublets ⇐ focus here! Problem in the MSSM: many scales Problem in the MSSM: complex phases Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 3
Enlarged Higgs sector: Two Higgs doublets √ H 1 v 1 + ( φ 1 + iχ 1 ) / 2 1 = = H 1 φ − H 2 1 1 φ + H 1 2 2 = = H 2 √ H 2 v 2 + ( φ 2 + iχ 2 ) / 2 2 m 2 H 1 + m 2 H 2 − m 2 12 ( ǫ ab H a 1 H b 1 H 1 ¯ 2 H 2 ¯ V = 2 + h.c.) + g ′ 2 + g 2 H 2 ) 2 + g 2 H 2 | 2 ( H 1 ¯ H 1 − H 2 ¯ | H 1 ¯ 8 2 � �� � ���� gauge couplings, in contrast to SM physical states: h 0 , H 0 , A 0 , H ± Goldstone bosons: G 0 , G ± Input parameters: (to be determined experimentally) tan β = v 2 M 2 A = − m 2 , 12 (tan β + cot β ) v 1 Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 4
Enlarged Higgs sector: Two Higgs doublets with CP violation √ H 1 v 1 + ( φ 1 + iχ 1 ) / 2 1 = = H 1 φ − H 2 1 1 φ + H 1 2 2 e iξ = = H 2 √ H 2 v 2 + ( φ 2 + iχ 2 ) / 2 2 m 2 H 1 + m 2 H 2 − m 2 12 ( ǫ ab H a 1 H b 1 H 1 ¯ 2 H 2 ¯ V = 2 + h.c.) + g ′ 2 + g 2 H 2 ) 2 + g 2 H 2 | 2 ( H 1 ¯ H 1 − H 2 ¯ | H 1 ¯ 8 2 � �� � ���� gauge couplings, in contrast to SM physical states: h 0 , H 0 , A 0 , H ± 2 CP -violating phases: ξ , arg( m 12 ) ⇒ can be set/rotated to zero Input parameters: (to be determined experimentally) tan β = v 2 M 2 , H ± v 1 Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 5
t/ ˜ ˜ b sector of the MSSM: (scalar partner of the top/bottom quark) Stop, sbottom mass matrices ( X t = A t − µ ∗ / tan β , X b = A b − µ ∗ tan β ): M 2 t L + m 2 m t X ∗ m 2 t + DT t 1 0 θ ˜ t ˜ ˜ M 2 t 1 t t = − → ˜ M 2 t R + m 2 m 2 m t X t t + DT t 2 0 ˜ ˜ t 2 M 2 b L + m 2 m b X ∗ m 2 b + DT b 1 0 θ ˜ ˜ b ˜ M 2 b 1 b b = − → ˜ M 2 b R + m 2 m 2 m b X b b + DT b 2 0 ˜ ˜ b 2 mixing important in stop sector (also in sbottom sector for large tan β ) t/ ˜ soft SUSY-breaking parameters A t , A b also appear in φ -˜ b couplings SU (2) relation ⇒ M ˜ t L = M ˜ b L ⇒ relation between m ˜ t 1 , m ˜ t 2 , θ ˜ t , m ˜ b 1 , m ˜ b 2 , θ ˜ b Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 6
The BR subgroup: contacts: Ansgar Denner, S.H., Ivica Puljak, Daniela Rebuzzi other members/contributors: Michael Spira, Georg Weiglein (and as ‘everywhere’: Chiara Mariotti, Reisaburo Tanaka) MSSM part: strong overlap with MSSM subgroup ⇒ more MSSM experimentalists needed! ⇒ more MSSM theorists needed? Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 7
2. MSSM issues: Example: h → γγ : γ γ t W + + . . . H t H W t W γ γ SM: input: − SM Higgs mass (free parameter) − SM (fermion) masses − SM couplings (at the appropriate scale) output: − SM amplitude, branching ratio Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 8
Now for the MSSM: Input parameters: M A and tan β ⇒ all other masses and mixing angles are predicted! Tree-level result for m h , m H : m 2 H,h = � � 1 � A cos 2 2 β Z ) 2 − 4 M 2 M 2 A + M 2 ( M 2 A + M 2 Z M 2 Z ± 2 ⇒ m h ≤ M Z at tree level Huge higher-order corrections: [ G. Degrassi, S.H., W. Hollik, P. Slavich, G. Weiglein ’02 ] M h < ∼ 135 GeV ⇒ (most) Higgs masses and couplings are not free parameters Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 9
Propagator/Mass matrix at tree-level: q 2 − m 2 0 0 A q 2 − m 2 0 0 H q 2 − m 2 0 0 h Propagator / mass matrix with higher-order corrections ( → Feynman-diagrammatic approach): q 2 − m 2 A + ˆ Σ AA ( q 2 ) Σ AH ( q 2 ) ˆ Σ Ah ( q 2 ) ˆ q 2 − m 2 M 2 hHA ( q 2 ) = Σ HA ( q 2 ) ˆ H + ˆ Σ HH ( q 2 ) Σ Hh ( q 2 ) ˆ q 2 − m 2 ˆ ˆ h + ˆ Σ hA ( q 2 ) Σ hH ( q 2 ) Σ hh ( q 2 ) Σ ij ( q 2 ) ( i, j = h, H, A ) : renormalized Higgs self-energies ˆ Σ Ah , ˆ ˆ Σ AH � = 0 ⇒ CP V, CP -even and CP -odd fields can mix h i ( i = 1 , 2 , 3) : M 2 = M 2 − iM Γ complex roots of det( M 2 hHA ( q 2 )): M 2 Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 10
Higgs couplings, tree level: sin( β − α ) g SM V = W ± , Z = g hV V HV V , cos( β − α ) g SM g HV V = HV V g ′ g hAZ = cos( β − α ) 2 cos θ W − sin α cos β g SM g hb ¯ b , g hτ + τ − = Hb ¯ b,Hτ + τ − cos α sin β g SM g ht ¯ = t Ht ¯ t γ 5 tan β g SM = g Ab ¯ b , g Aτ + τ − Hb ¯ b ⇒ g hb ¯ b , g hτ + τ − : significant suppression or enhancement w.r.t. SM coupling possible ⇒ also here: large higher-order corrections! Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 11
Important higher-order corrections in the MSSM: ∆ b Additional enhancement factors compared to the SM case: b tan β y b → y b A 1 + ∆ b ¯ b At large tan β : either H ≈ A or h ≈ A t tan β y b H + 1 + ∆ b ¯ b 2 α s ∆ b = g µ tan β × I ( m ˜ g ) 3 π m ˜ b 1 , m ˜ b 2 , m ˜ α t + 4 π A t µ tan β × I ( m ˜ t 1 , m ˜ t 2 , µ ) ⇒ other parameters enter ⇒ strong µ dependence Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 12
b → H/A → τ + τ − → 2 jets on µ : Dependence of LHC wedge from b ¯ [ S.H., A. Nikitenko, G. Weiglein et al. ’06 ] β β 2 2 = -1000 GeV/c = -1000 GeV/c µ µ tan tan 50 50 2 2 µ = -200 GeV/c µ = -200 GeV/c 2 2 = 200 GeV/c = 200 GeV/c µ µ 40 40 2 2 = 1000 GeV/c = 1000 GeV/c µ µ 30 30 -1 -1 CMS, 60 fb CMS, 60 fb pp bb j+j pp bb j+j → φ → τ τ → → φ → τ τ → 20 20 m scenario max no mixing scenario h 2 2 M = 2 TeV/c M = 1 TeV/c SUSY SUSY 2 2 M = 200 GeV/c M = 200 GeV/c 10 10 2 2 m = 0.8 M m = 0.8 M SUSY SUSY gluino gluino Stop mix: X = 2 M Stop mix: X = 0 t SUSY t 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 2 2 M ,GeV/c M ,GeV/c A A ⇒ non-negligible variation with the sign and absolute value of µ (despite numerical compensations in production and decay) Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 13
Another issue: external (on-shell) Higgs bosons Examples for external (on-shell) Higgs bosons ( φ = h 1 , h 2 , h 3 ): Higgs production: q ′ q g t W t φ φ W t g q q ′ Higgs decays: γ b W φ W φ W γ ¯ b ⇒ important to ensure on-shell properties of external Higgs boson Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 14
Correct on-shell amplitude with external Higgs h i : [ M. Frank, T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein, K. Williams ’06 ] � � � A ( h i ) = Γ h i + Z ij Γ h j + Z ik Γ h k Z i √ Z i : ensures that the residuum of the external Higgs boson is set to 1 Z ij : describes the transition from i → j ¯ f h i h i,j,k f Written more compact with the Z matrix : Z ij = √ Z i Z ij Sven Heinemeyer, LHC-Higgs-XS inauguration workshop, Freiburg, 13.04.2010 15
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