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Supersymmetric Higgs Supersymmetric Higgs Marcela Carena Theoretical Physics Department, Fermilab Enrico Fermi Institute, University of Chicago Searching for New Physics at the LHC The Galileo Galilei Institute for Theoretical Physics October 30, 2009, Florence Outline • The SM-like Higgs Boson: state of the art • The MSSM Higgs Bosons -- Basics -- The impact of radiative corrections on masses & couplings -- Collider searches • MSSM Higgs Extensions: A model-independent approach -- The EFT at NLO -- Masses and Couplings -- Comments on collider phenomenology The Standard Model Higgs Mechanism • One physical state -- the Higgs Boson -- left in the spectrum First evidence of EWSB ==> masses of gauge bosons Measuring the WWH and ZZH couplings is essential to identify the Higgs as the agent of EWSB: without a v.e.v, no such trilinear coupling at tree level ==> we need to detect the Higgs in association with gauge bosons ==> if the theory remains perturbative, the top mass will mainly come from a Higgs with SM-like couplings to W and Z The search for the SM Higgs: state of the art + ! Z * + # e e "" # HSM Z with H SM ! bb," " Gluon-gluon fusionwith H WW ! Constraints on m H from 2 isolated leptons + missing Energy precision tests of the SM SM Higgs production processes at hadron colliders Much progress recently in computing NLO and NNLO QCD and EW corrections with H WW(*). with H bb, WW* The Tevatron Projections based on improvements already achieved for some analysis, extending them to the rest- 95 95 SM R i= S i/Si The SM Higgs LHC potential Talk by A. Nisati Tevatron excl. LEP excl. ! L E P -1 With 10 fb , discovery for mh [~125,~500] GeV range; -1 -1 With 1-2 fb , some reach in the H to WW channel (2 fb :exclusion for all mh) What can the LHC do with 10 TeV and 1fb-1? Looking at the golden channel H WW/ZZ Main Backgrounds increase relative to the signal Comparable to Tevatron reach with 10 fb-1 and 1.5 efficiency factor improvement Supersymmetric Higgs ? The Higgs Sector in the Minimal Supersymmetric SM 2 Higgs SU(2) doublets ! 1 and ! 2 : after Higgs Mechanism 2 CP-even h, H with mixing angle ! tan! = v2 v1 ± 1 CP-odd A and a charged pair H 2 2 ! v= v1 +v2 = 246 GeV At tree level, one Higgs doublet couples only to down quarks, the other couples only to up quarks + + !L =" i hˆ ij # d j + hˆ ij # u j + h.c. L ( d 1 R u 2 R ) Since the up and down sectors are diagonalized independently, the Higgs interactions remain flavor diagonal at tree level. Couplings to gauge bosons & fermions (SM normalized) Decoupling limit mA >> mZ Lightest (SM-like) Higgs , others heavy and roughly degenerate mh ! mZ Radiative Corrections to Higgs Boson Masses Important quantum corrections due to incomplete cancellation of particles and superparticles in the loops Main effects: stops; and sbottoms at large tan beta 4 • m t enhancement • log sensitivity to stop masses M S • depend. on stop mass mixing X t 2 -loop corrections: mh !135GeV Brignole, M.C., Degrassi, Ellis, Haber, Hempfling, Heinemeyer, Hollik, Espinosa, Martin, Quiros, Ridolfi, Slavich, Wagner, Weiglein, Zhang, Zwirner, … • If 3rd gen. scalar masses > tens of TeV need to resum large logs for reliable mh calc. Radiative Corrections to the Higgs Couplings 2 1) Important effects through radiative corrections to the CP-even mass matrix ! M ij , which defines the mixing angle ! 2 2 2 2 sin! cos! = M12 / (Tr M ) " 4 det M The off diagonal elements are prop. to 4 2 m µX % X ( M 2 ! " m2 + m2 cos # sin # + t t t " 6 M.C. Mrenna, Wagner 12 ( A Z ) 2 2 2 ' 2 * 16$ v M S & M S ) Important effects of rad. correc. on sin ! or cos ! depending on the sign of µXt µ / M and the magnitude of X t / M S and S ===> govern couplings of Higgs to fermions and vector bosons When off-diagonal elements vanish, either sin ! or cos ! vanish ===> strong suppression of the SM-like Higgs boson coupling to b-quarks and taus !! Enhancement of BR (h/H --> WW/ ) for mh/H < 135 GeV 2) Important Vertex corrections to Higgs-fermion couplings from SUSY loops - relevant for sizeable tan ! - Can induce Flavor changing neutral and charged current effects * * !L = d 0hˆ " 0 + " 0 #ˆ + #ˆ hˆ +hˆ d o + " 0u 0hˆ u0 + h.c. eff . R d [ 1 2 ( 0 Y u u)] L 2 R u L + ! loop factors intimately hd h u connected to the structure of the squark mass matrices. hu hd • In terms of the quark mass eigenstates L 1 tan 0* 0* d M $V+ R-1V &d h.c. ... Dedes, Pilaftsis ! = ( " #1 ! #2 ) R d % CKM CKM ' L + + eff v2 2 and R = 1 + !0 tan" + !Y tan" hu R diagonal * * * * µ At 2# µ Mg˜ Dependence i s !Y " ! " 2 2 2 2 0 2 2 2 16 max m ,m , on SUSY param. 3$ # t˜ t˜ µ max md˜ i ,md˜ i ,Mg˜ [ 1 2 ] [ 1 2 ] Higgs Physics strongly connected to flavor physics and to the SUSY mechanism Looking at VCKM ! I " Flavor Conserving Higgs-fermion couplings 1 $ 0* 0* ' 1 1 0* !L = & tan " #1 ! #2 ) b RM b 33 bL + #2 b RM d bL + h.c. eff v2 % ( R v2 33 3 2 R =1+ (!0 + !Y ht )tan" #1+ $ b 0 In terms of h,H and A: !1 = "sin# h +cos# H +i sin$ A 0 !2 = cos# h +sin# H - i cos$ A Hence: "mb sin# ghbb ! (1" $b /tan# tan %) destroy basic relation (1+ $b ) v cos% gh,H,Abb gh,H,A !! " mb m! mb cos" g Hbb ! (1% #b tan" /tan $) (1+ #b ) v cos$ mb tan " At large tan ! " g Hbb # gAbb gAbb ! (1+ #b )v M.C. Mrenna, Wagner; Haber,Herrero, Logan, Penaranda, Rigolin, Temes Noth, Spira: Muhlleitner, Rzehak, Spira Strong suppression of h(H) -bottom coupling tan! ! "b / tan# $ ghbb ! 0; gh%% ! "bm% / v (Similar for H) Radiative corrections main decay modes of the SM-like MSSM Higgs into b- and tau-pairs can be drastically changed What can the Tevatron say about an SM-like MSSM Higgs? Different SUSY benchmark scenarios will yield very different results M.C.,Heinemeyer, Wagner,Weiglein max • The mh scenario: [Maximizes mh] M S = 1 TeV ; Xt = 2.4 MS ; mg˜ = 0.8 MS ; M 2 = !µ = 200GeV; At = Ab g hbb , g h !! due to factor for low m and intermediate enhanced sin!eff , /cos " A max to large tan beta (analogous for H if mA> mh ) hence, strong suppression of BR( h ! " " ) and BR(h WW) with respect to SM min • The mh scenario: [zero mixing in the stop sector] max Similar coupling’s behaviour as mh , but minimizes mh. • The small sin ! eff . scenario: M S = 800 GeV ; Xt = - 1.2 TeV ; µ = 2.5 M s ; mg˜ = M 2 = 500GeV; At = Ab g hbb , g h !! importantly suppressed for large tan beta and small mA, and in different ways due to ! b corrections hence, BR( h ! " " ) and BR(h WW) enhanced with respect to SM Tevatron reach for the MSSM SM-like Higgs All channels included in CDF/DO combination. 95% C.L. Exclusion- 10 fb-1. max The m min scenario: m < 120 GeV The mh scenario: mh ~ 125 GeV h h No reach at present BUT with the expected improvement factor of 1.5 assumed good/full coverage Draper, Liu, Wagner An interesting case: The small sin ! eff .scenario CDF/DO combination: 95% C.L. Exclusion- 10 fb-1. Draper, Liu, Wagner H/h bb final channel only H/h bb + WW channels • Useful h WW Tevatron search for a low mass MSSM SM-like Higgs • Full coverage of the MSSM plane once the tan beta enhanced channels !! inclusive, b!!, and bbb, with present efficiency and 10fb-1, are included Non-Standard Higgs Production at the Tevatron and LHC • Enhanced couplings to b quarks and tau-leptons • Considering value of running bottom mass and 3 quark colors 9 2 + # (1+ % b ) BR(A ! bb ) " 2 BR(A ! " " ) $ 2 9 + (1+ # b ) 9 + (1+ % b ) tan% 2 9 Strong dependence on the ! bb A " BR A # bb $ ! bb A " " ( ) ( ) ( )SM 2 2 SUSY parameters (1+ & b ) (1+ & b ) + 9 in the bb channel. tan& 2 ! bb ,gg " A # BR A " $$ % ! bb ,gg " A # Robust predictions ( ) ( ) ( )SM 2 (1+ ' b ) + 9 in the tau-tau channel Excellent coverage at both colliders in the di-tau inclusive channel M.C, Heinemeyer, Weiglein, Wagner MSSM Higgs at the Tevatron . H/A tau pairs, with both exp. and for 10 fb-1 Draper, Liu, Wagner max Small scenario Mh . Scenario sin!eff . Limits are robust under variation of SUSY parameters MSSM Higgs at the Tevatron . All channels combined both exp. and for 10 fb-1 Draper, Liu, Wagner max M min scenario Mh scenario h Extensions of the MSSM Higgs Sector • MSSM with Explicit CP violation • Additional SM singlets • Additional gauged U(1)’s • Models with enhanced weak gauge symmetries • Effective field theory with higher dimensional operators: A more model-independent approach More general MSSM Higgs extensions: EFT approach • The non-minimal part of Higgs sector is parametrically heavier than the weak scale (understood as v = 174 GeV) • SUSY breaking is of order v, hence heavy masses nearly supersymmetric : overall ``heavy” scale SUSY breaking mass splittings In practice: formalism applies for e.g. Low energy superpotential: at leading order in 1/M 2 ! • can include SUSY breaking via a spurion X= mS ! 1 M.C, Kong, Ponton, Zurita and Only two new parameters: see also Dine, Seiberg, Thomas; Antoniadis, Dudas, Ghilencea, Tziveloglou • At NLO, Kähler potential only: Custodially violating (treel level) : Custodially preserving (tree level) : Plus SUSY breaking terms obtained by multiplication by spurion, with new coefficients • EFT coefficients can be essentially arbitrary, if UV theory complicated enough Examples Example 1: singlets Integrating out the singlet: Example 2: triplets with Integrating out the triplets: Induce custodially violating ops.
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