Precise Predictions for Higgs Production in Neutralino Decays - PowerPoint PPT Presentation

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Precise Predictions for Higgs Production in Neutralino Decays Alison Fowler Supervisor: G. Weiglein IPPP Seminar, Friday 19th June

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Outline CP-violating MSSM 1 Higgs sector in the CP-violating MSSM Higgs production in CPX scenario χ 0 χ 0 Higher Order Corrections to ˜ i ˜ j h k vertex 2 Improved Born Approximation Renormalisation Full 1-loop vertex correction Numerical Results 3 χ 0 ˜ 2 Decay Width χ 0 ˜ 2 Branching Ratio Summary 4

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary The CP-violating MSSM Every SM particle gets supersymmetric partner 2 Higgs doublets ⇒ 5 physical Higgs bosons Rich mixing structure: � f L , R mix ⇒ sfermions � f 1 , 2 W ± mix ⇒ charginos ˜ � u , d , � h ± χ ± 1 , 2 W 3 mix ⇒ neutralinos ˜ � u , � d , � B, � h 0 h 0 χ 0 1 , 2 , 3 , 4 New source of CP-violation: A f , µ , M 1 , 2 , 3 May help explain matter-antimatter asymmetry of the universe

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary The Higgs Sector Higgs sector at tree-level: Higgs sector is CP-conserving: h , H (CP-even), A (CP-odd), H + , H − Beyond tree-level: Loop corrections can be large CP-violating phases φ A t , b ,τ , φ µ , φ M 1 , 3 enter via loops Mixing between h,H,A → h 1 , h 2 , h 3 t, ˜ t 1 , ˜ ˜ t 1 , ˜ t 2 t 2 h, H, A h, H, A h, H, A h, H, A t, ˜ t 1 , ˜ t 2 Higgs sector is CP-violating at 1-loop level CP-violating mixing ∝ Im ( A t µ ) / M 2 SUSY

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX Scenario at LEP Extreme CP violating scenario with large h-H-A mixing. µ M SUSY | M 3 | | A t , b ,τ | φ M 3 φ A t , b ,τ [Carena et al. hep-ph/0009212] 2000 500 1000 900 GeV π/ 2 π/ 2 h 1 mostly CP-odd A LEP: e + e − → Z ∗ → Zh , hA Suppression of ZZh 1 coupling Suppression of h 1 production h 2 may be within LEP reach But h 2 → h 1 h 1 : difficult final state Light Higgs not excluded! “CPX hole” at t β ≈ 7, M h 1 ≈ 40GeV Genuine vertex corrections to [LEP Higgs Working Group ’06] h 2 → h 1 h 1 very important

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX scenario at LHC [M. Schumacher, ATLAS ’07] CPX holes not covered by conventional channels at LHC Need to consider other production methods Perhaps involve SUSY particles themselves See eg. H + → W + h 1 : [Ghosh, Godbole and Roy hep-ph/0412193] and ˜ t ˜ th 1 : [Bandyopadhyay, Datta et al. arXiv:0710.3016]

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Higgs in SUSY cascade decays SUSY cascade decays: another source of light Higgs χ 0 χ + χ 0 χ + j + X + h , H , A , H ± pp → � g � g , � q � q , � g � q → � i , � i + X → � j , � May complement Higgs searches in conventional channels Also a probe to determine parameters of EWSB Applicable to both CP-conserving and CP-violating MSSM Recent interest in SUSY cascade Higgs production: CP-conserving MSSM [Datta and Djouadi et al. hep-ph/0303095] χ 0 χ 0 Experimental analyses of ˜ 2 → ˜ 1 h [CMS TDR ’07] MSSM with non-universal gaugino masses [Banyopadhyay et al. arXiv:0806.2367, Huitu et al. arXiv:0808.3094] NMSSM with light Higgs [Djouadi ’08, Cheung and Hou arXiv:0809.1122]

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX Cascades CPX with M 2 = 200 GeV, tan β = 5 . 5: Masses in GeV: M e M e M e M e M e M e M e χ + χ + χ 0 g u , e χ 0 χ 0 3 , 4 , e d , e c , e 2 , e s t 1 , 2 b 1 , 2 2 1 1 ≃ 2000 1000 ≃ 500 332,667 471,531 198.5 95.1 χ 0 ˜ q ¯ q 1 b , τ − χ 0 ˜ g ˜ q 1 , 2 ˜ h 1 2 b , τ + ¯ ∼ 100% ∼ 0 − 42% χ 0 Total: 18 % of all gluinos decay to � 2 , which may decay to h 1 . χ 0 χ 0 What is branching ratio for ˜ 2 → ˜ 1 h 1 ?

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX Cascades CPX with M 2 = 200 GeV, tan β = 5 . 5: Masses in GeV: M e M e M e M e M e M e M e χ + χ + χ 0 g u , e χ 0 χ 0 3 , 4 , e d , e c , e 2 , e s t 1 , 2 b 1 , 2 2 1 1 ≃ 2000 1000 ≃ 500 332,667 471,531 198.5 95.1 χ 0 ˜ q ¯ q 1 b , τ − χ 0 ˜ g ˜ ˜ q 1 , 2 2 ¯ b , τ + ∼ 100% ∼ 0 − 42% χ 0 Total: 18 % of all gluinos decay to � 2 , which may decay to h 1 . χ 0 χ 0 What is branching ratio for ˜ 2 → ˜ 1 h 1 ?

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX Cascades CPX with M 2 = 200 GeV, tan β = 5 . 5: Masses in GeV: M e M e M e M e M e M e M e χ + χ + χ 0 g u , e χ 0 χ 0 3 , 4 , e d , e c , e 2 , e s t 1 , 2 b 1 , 2 2 1 1 ≃ 2000 1000 ≃ 500 332,667 471,531 198.5 95.1 χ 0 ˜ q ¯ q 1 b , τ − χ 0 ˜ g ˜ q 1 , 2 ˜ h 1 2 ∼ 91% , 9% b , τ + ¯ ∼ 100% ∼ 0 − 42% χ 0 Total: 18 % of all gluinos decay to � 2 , which may decay to h 1 . χ 0 χ 0 What is branching ratio for ˜ 2 → ˜ 1 h 1 ?

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary CPX Cascades CPX with M 2 = 200 GeV, tan β = 5 . 5: Masses in GeV: M e M e M e M e M e M e M e χ + χ + χ 0 g u , e χ 0 χ 0 3 , 4 , e d , e c , e 2 , e s t 1 , 2 b 1 , 2 2 1 1 ≃ 2000 1000 ≃ 500 332,667 471,531 198.5 95.1 χ 0 ˜ q ¯ q 1 b , τ − χ 0 ˜ g ˜ q 1 , 2 ˜ h 1 2 ? b , τ + ¯ ∼ 100% ∼ 0 − 42% χ 0 Total: 18 % of all gluinos decay to � 2 , which may decay to h 1 . χ 0 χ 0 What is branching ratio for ˜ 2 → ˜ 1 h 1 ?

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary χ 0 χ 0 ˜ i ˜ j h k vertex: Why study? χ 0 χ 0 ˜ ˜ i j h k Higgs propagator corrections already known to be large Vertex corrections to Γ( h 2 → h 1 h 1 ) were O ( 400 %) for CPX [Williams and Weiglein arXiv:0710.5320] Large µ , A t may also enhance loop contributions Already available: χ 0 χ 0 1-loop (s)fermion corrections to h , H , A → ˜ i ˜ j in rMSSM [Eberl et al. hep-ph/0111303, Ren-You et al. hep-ph/0201132] χ 0 χ 0 1-loop effective Lagrangian for h k → ˜ i ˜ j in cMSSM [Ibrahim arXiv:0803.4134] 2-loop Higgs propagator corrections in FeynHiggs at O ( α s α t ) in cMSSM [Heinemeyer et al. arXiv:0705.0746]

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Loop Corrections in the Higgs Sector Step 1: Improved Born Approximation incorporating existing 2-loop Higgs propagator corrections χ 0 ˜ χ 0 1 ˜ + Z hA + Z hH 2 Z hh ∼ ∼ h 1 h H A h, H, A h Finite wavefunction normalisation factors Z ij include mixing between h , H , A (i.e. h-H-A self-energy diagrams). We evaluate M h i , Z ij using FeynHiggs2.6.5 , which contains the leading 2-loop corrections.

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Genuine vertex corrections in Higgs/Neutralino sectors Step 2: Full 1-loop vertex correction We evaluate triangle and self-energy diagrams: eg. χ 0 χ 0 χ 0 χ 0 χ 0 ˜ ˜ ˜ ˜ ˜ 1 1 1 1 1 t, ˜ ˜ ˜ χ b φ χ 0 χ 0 χ 0 χ 0 ˜ ˜ ˜ ˜ 2 2 2 2 t, ˜ ˜ ˜ t, b χ b V φ ˜ G , Z χ t, b h h h t, ˜ ˜ b h We implement our own renormalisation scheme into FeynArts and also use FormCalc/LoopTools

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Renormalisation in the Higgs Sector We implement the same scheme used in FeynHiggs : See [Frank et al. hep-ph/0611326] and [Williams and Weiglein arXiv:0710.5320] for details Charged Higgs boson mass, M H ± , is fixed on-shell M h 1 , M h 2 , M h 3 derived from poles of loop-corrected 3x3 propagator matrix ∆ hHA ( p 2 ) DR renormalisation for tan β DR renormalisation for fields: δ Z DR H 1 , 2 To obtain correct on-shell properties of neutral Higgs bosons, we then introduce finite normalisation factors Z ij Convenient for including CP-violating mixing effects beyond one-loop order

χ 0 χ 0 CP-violating MSSM Higher Order Corrections to ˜ i ˜ j h k vertex Numerical Results Summary Renormalisation in the Neutralino/Chargino Sector √ � � M 2 2 M W sin β √ X = 2 M W cos β µ   M 1 0 − M Z c β s W M Z s β s W   0 M 2 M Z c β c W − M Z s β c W   Y =   − M Z c β s W M Z c β c W 0 − µ M Z s β s W − M Z s β c W − µ 0 We renormalise the 3 independent parameters: M 1 , M 2 , µ χ 0 χ + We fix masses of ˜ 1 , 2 , ˜ 2 on-shell ⇒ δ M 1 , δ M 2 , δµ χ 0 χ + Other 3 masses of ˜ 3 , 4 , ˜ 1 receive loop corrections χ 0 χ 0 Convenient for ˜ 2 → ˜ 1 h k with M 1 < M 2 ≪ µ For other processes and parameters we found different choices can be more convenient and numerically stable.