NLO corrections to h WW/ZZ 4 fermions in a Singlet Extension of the Standard Model

Transcription

1 NLO corrections to h WW/ZZ 4 fermions in a Singlet Extension of the Standard Model Michele Boggia in collaboration with L. Altenkamp and S. Dittmaier Albert-Ludwigs-Universität, Freiburg November 8, 2017

2 Overview 1 Introduction 2 SESM basics 3 Renormalization of SESM 4 The decay h WW/ZZ 4 fermions 5 Numerical analysis Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

3 Introduction Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

4 Intro Higgs measurements are compatible with SM predictions h f f µ = Γ exp Γ SM κ f h V V κ V but baryon asymmetry dark matter neutrino masses... SM cannot be the ultimate theory BSM precise predictions are required Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

5 Intro the SM Higgs sector is working well, we consider L Higgs = L SM Higgs +real singlet used in the literature for dark matter extra symmetry vanishing singlet VEV hidden sector SB extra symmetry non-vanishing VEVs baryon asymmetry [Silveira, Zee, 1985] [McDonald, 1994] [Burgess et al., 2001] [Davoudiasl et al., 2005] [Barger et al., 2008] [Fischer, Van der Bij, 2014] [Datta, Raychaudhuri, 1997] [Patt, Wilczek, 2008] [Pruna, Robens, 2013] [Profumo et al., 2007] [Barger et al., 2007] Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

6 SESM in a nutshell Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

7 SESM in a nutshell recipe: most general Z 2 - and gauge-invariant scalar Lagrangian L Higgs =(D µ Φ) (D µ Φ)+ 1 2 ( µσ)( µ σ) V(Φ,σ) V(Φ,σ) = µ 2 2Φ Φ+ λ 2 4 (Φ Φ) 2 +λ 12 σ 2 Φ Φ µ 2 1σ 2 +λ 1 σ 4 EWSB on both scalar fields ( ) φ + Φ = 1 2 [v 2 +h 2 +iφ 0, σ = v ] 1 +h 1 covariant derivative D µ = µ ig 2 I a w Wa µ +ig 1Y w 2 B µ Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

8 SESM in a nutshell after EWSB V = t 2 h 2 t 1 h with non-diagonal mass matrix M Higgs M Higgs = ( ( ) ( ) h2 h2,h 1 MHiggs +... h 1 ) v1 2λ v2 2 λ 2 µ v 1 v 2 λ 12 2v 1 v 2 λ 12 v2 2λ v1 2λ 1 2µ 2 1 rotation about an angle α to get mass-basis h,h ( ) ( )( ) h cosα sinα h2 = H sinα cosα diagonal Higgs propagators required h h = i k 2 Mh 2, H H = h 1 i k 2 MH 2, h H = 0 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

9 SESM in a nutshell gauge- and fermion-scalar interactions light Higgs heavy Higgs h f f, h V V c α H f f, H V V s α multi-scalar interactions V c hhh h 3 +c hhh h 2 H +c hhh hh 2 +c HHH H 3 +c φφφφ ( 2φ + φ + ( φ 0) 2 ) 2 +c hhhh h 4 +c hhhh h 3 H +c hhhh h 2 H 2 +c hhhh hh 3 +c HHHH H 4 + [ c hφφ h+c Hφφ H +c hhφφ h 2 +c hhφφ hh +c HHφφ H 2]( 2φ + φ + ( φ 0) 2 ) SESM parameters {M h,m H,M W,M Z,e,λ 12,α,m f,t h,t H } Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

10 Renormalization of SESM Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

11 Renormalization bare parameters do not have physical meaning as far as possible, make use of OS renormalization conditions M h,m H,M W,M Z,m f are the physical (OS) masses OS renormalization not always possible! no natural choice for α,λ 12 our choice MS conditions for α and λ 12 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

12 Tadpole renormalization two schemes considered renorm. tadpoles t h = t H = 0 ignore explicit tadpoles gauge-dependent δt h,δt H in counterterms bare parameters potentially gauge-dependent gauge-dependent contributions cancel in OS scheme bare tadpoles t h,0 = t H,0 = 0 [Fleischer, Jegerlehner, 1980] [Actis et al., 2006] include everywhere technical variants can be used (e.g. shift VEVs) gauge-independent relations between ren. parameters and observables Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

13 h WW/ZZ 4 fermions Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

14 h WW/ZZ 4 fermions leading contribution h V V most promising channel for precise Higgs implemented in SM [Bredenstein et al., 2006] THDM [Altenkamp et al., 2017] see talk by S. Dittmaier object of this talk SESM Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

15 NLO corrections EW QCD M LO 2, QCD and real emission rescaled by c 2 α wrt SM singlet changes EW loops CTs are consistently taken into account Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

16 Automation loop corrections FeynRules LSESM SESM.gen FeynArts h V SESM.mod V FormCalc + complex mass scheme for vector bosons [Denner et al., 2005] real corrections dipole subtraction for IR singularities [Catani, Seymour, 1996] [Dittmaier, 1999] [Dittmaier et al., 2008] multi-channel MC integration within Prophecy4f Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

17 Numerical analysis Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

18 Input parameters SM parameters {M h,m H,M W,M Z,e,λ 12,α,m i } [ATLAS, CMS, 2015] M h [HXSWG, 2016] M OS W,MOS Z,ΓOS W,ΓOS Z,m f,g µ,α s BSM parameters restricted by perturbativity 4 λ 1 4π, vacuum stability µ 2 2,µ2 1 > 0 λ 2 4 4π, 2 λ12 4π c2 αm 2 H +M 2 hs 2 α 2v 2 2 < λ 12 < c2 αs 2 α(m 2 H M 2 h) 2 2v 2 2 (c2 αm 2 h +M2 H s2 α) or λ 12 > 0 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

19 Input parameters Perturbativity and vacuum stability constraints λ12 λ MH = 200 Î λ1 > π ÙÒ Ø Ð Ú º λ12 > 2π s α MH = 600 Î λ1 > π ÙÒ Ø Ð Ú º λ12 > 2π λ12 λ MH = 400 Î λ1 > π ÙÒ Ø Ð Ú º λ12 > 2π s α MH = 800 Î λ1 > π ÙÒ Ø Ð Ú º λ12 > 2π perturbativity matters for small M H vacuum stab. important for higher M H λ 12 < 0 mostly excluded s α considered 4 scenarios from [HXSWG, 2016] [Robens, Stefaniak 2016] s α Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

20 Input parameters Scheme conversion in order to compare results in different renormalization schemes p 0 = p MS +δp MS (p MS ) = p FJ +δp FJ (p FJ ) example for M H = 600GeV, λ 12 = MS FJ µ = Î ÀÅ ¼¼ ÒÙÑ Ö Ð Ð Ò Ö FJ MS µ = Î ÀÅ ¼¼ sα FJ 0 sα MS s α MS s α FJ Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

21 Running of s α M H = 200GeV, λ 12 = 0.07 s α µ 0 s α(µ 0) = 0.29 MS ¼º Àž¼¼ FJ ¼º¾ M H = 600GeV, λ 12 = 0.23 µ 0 s α(µ 0) = 0.22 MS FJ s α ÀÅ ¼¼ ¼º ¼º¾ ¼º¾ ½¼¼ ¼¼ ½¼¼ µ r Î µ r Î explains LO behavior of Γ h 4f scale dependence for consistency, running of λ 12 taken into account ¾¼¼ Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

22 Scale dependence of Γ h 4f LO (dashed) vs. NLO (solid) M H = 200GeV, s α = 0.29, λ 12 = 0.07 Γ h 4f [MeV] µ s α MS (µ 0) = 0.29 MS BHM200 FJ M H = 600GeV, s α = 0.22, λ 12 = 0.23 Γ h 4f [MeV] µ s α MS (µ 0) = 0.22 MS BHM600 FJ µ r [GeV] µ r [GeV] more pronounced scale and scheme dependence at LO µ r = M h appropriate renormalization scale Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

23 Mixing angle dependence of Γ h 4f LO (dashed) vs. NLO (solid) M H = 200GeV, λ 12 = 0.07 Γ h 4f [MeV] µ 0 = Î Àž¼¼ MS FJ ËÅ M H = 600GeV, λ 12 = 0.23 Γ h 4f [MeV] µ 0 = Î ÀÅ ¼¼ MS FJ ËÅ s α MS behavior mostly driven by c 2 α factor SM typically reduced by NLO contributions SM 5%(10%) for s α < 0.2(0.3) s α MS * spurious effects in LO driven by NLO parameter conversion Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

24 Differential distributions possible generation of distributions for invariant masses angles for all four-light-fermion final states cosθ Zµ = ( k2,z k3,z + ) k 4,Z k 2,Z k3,z + k 4,Z cosφ µe,t = k 2,T k 3,T k 2,T k3,t Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

25 NLO leptonic distributions dγ dmµµ h µ µ + e e + ËÅ Ë ËÅ Àž¼¼ [ ] dγ dφ 10 7MeV deg h µ µ + e e + ËÅ Ë ËÅ Àž¼¼ 10 7 δ NLO [%] M µµ Î δ NLO [%] constant offset in δ NLO wrt SM distributions similar behavior and magnitude in the FJ scheme φ Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

26 NLO leptonic distributions dγ dmνµµ h ν µ µ + e ν e ËÅ Ë ËÅ Àž¼¼ dγ dφµe,t [ ] 10 5MeV deg 5 4 h ν µµ + e ν e ËÅ Ë ËÅ Àž¼¼ δ NLO [%] M νµµ Î 1 δ NLO[%] constant offset in δ NLO wrt SM distributions similar behavior and magnitude in the FJ scheme φ µe,t Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

27 Conclusions SESM renormalization performed treating tadpoles within two schemes FeynArts model file for one-loop calculations produced computed matrix elements for the decay h WW/ZZ 4f h WW/ZZ 4f results scheme conversion: sizable effects, become larger approaching non-perturbative regions renormalization group equations solved for MS parameters scale and scheme dependence reduced in NLO results SM 10% for the decay width in the proposed scenarios no further distortion wrt SM in differential distributions coming soon Prophecy4f version including SESM implementation paper in preparation Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 21

28 Backup Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

29 SESM in a nutshell after EWSB V = t 2 h 2 t 1 h with non-diagonal mass matrix M Higgs M Higgs = ( ( ) ( ) h2 h2,h 1 MHiggs +... h 1 ) v1 2λ v2 2 λ 2 µ v 1 v 2 λ 12 2v 1 v 2 λ 12 v2 2λ v1 2λ 1 2µ 2 1 h 2,h 1 have non-diagonal propagators! h 2 h 2 = i k 2 M22 2, h 1 h 1 = i k 2 M11 2, h 2 h1 0 rotate about an angle α to get mass-basis h,h ( ) ( )( ) h cosα sinα h2 = H sinα cosα h 1 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

30 SESM in a nutshell requiring diagonal Higgs propagators h h = i k 2 Mh 2, H H = i k 2 MH 2, h H = 0 inversion relations µ 2 2 = 1 2v 2 [3c αt h +3t H s α +c αm 2 h (v 2c α v 1 s α)+m 2 H sα(v 1c α +v 2 s α)] µ 2 1 = 1 4v 1 [M 2 h sα(v 1s α v 2 c α)+c αm 2 H (v 1c α +v 2 s α)+3c αt H 3t h s α] λ 2 = 2 ( v2 3 [v 2 c 2 α Mh 2 +M2 H α) s2 +cαt h +t H s α] λ 1 = 1 ( 8v1 3 [v 1 c 2 α MH 2 +M2 h α) s2 +cαt H t h s α] v 1 = cαsα (MH 2 2λ 12 v M2 h ) 2 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

31 SESM in a nutshell requiring diagonal Higgs propagators h h = i k 2 Mh 2, H H = i k 2 MH 2, h H = 0 mass terms Mh 2 = 1 4 v2 2λ 2 +4v1λ 2 1 ± (2v 1 v 2 λ 12 ) ( 16v λ 1 v2 2λ 2 2) MH 2 = 1 4 v2 2λ 2 +4v1λ 2 1 (2v 1 v 2 λ 12 ) ( 16v λ 1 v2 2λ 2 2) sign choice such that M 2 H > M2 h Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

32 NLO semileptonic distributions 10 4 dγ dmq q h d de e + ËÅ Ë ËÅ Àž¼¼ dγ d cosφ [Å Î] 0.01 h d de e + ËÅ Ë ËÅ Àž¼¼ δ NLO [%] M q q Î δ NLO [%] cosφ Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

33 NLO semileptonic distributions 10 2 dγ dmq q h ν e e + dū ËÅ Ë ËÅ Àž¼¼ dγ [Å Î] h ν e e + dū dcosφew 0.06 ËÅ Ë ËÅ Àž¼¼ δ NLO [%] M q q Î 0 δ NLO [%] cosφ ew Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

34 Input parameters SM parameters [ATLAS, CMS, 2015] M h = ±0.21(stat.)±0.11(syst.)GeV 125.1GeV [HXSWG, 2016] M OS W = GeV M OS Z = GeV Γ OS W = 2.085GeV Γ OS Z = GeV m e = MeV m µ = MeV m τ = MeV m u = 0.1GeV m c = 1.51GeV m t = 172.5GeV m d = 0.1GeV m s = 0.1GeV m b = 4.92GeV G µ = GeV 2 α s = Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

35 Input parameters internally pole masses from M V = M OS V 1+ ( Γ OS V /MOS V ) 2 pole decay widths Γ W and Γ Z calculated from the experimental input, taking into account O(α em ) corrections and using real masses G µ -scheme (large corrections shifted to lowest order) α em = 2Gµ M 2 W π ( ) 1 M2 W MZ 2 Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

36 Input parameters Benchmark scenarios scenarios taken from [HXSWG, 2016] [Robens, Stefaniak 2016] Scenario M H [GeV] sinα λ 12 BHM BHM BHM BHM Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

37 Baryon asymmetry of the universe three basic ingredients CP violation baryon number violation departure from thermal equilibrium (otherwise CPT would assure compensation between processes increasing and decreasing baryon number) SM SESM CP violation B violation 1 first order EWPT 1 non-perturbative effect Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

38 Scale choice BHM400 Γ h 4f [MeV] s MR α (µ0) = 0.26 BHM400 µ0 MR FJ Γ h 4f [MeV] s FJ α (µ0) = 0.26 BHM400 µ0 MR FJ µ 0 = M h +M H µ r [GeV] Γ h 4f [MeV] µ0 0.9 s MR α (µ0) = 0.26 BHM400 MR FJ µ r [GeV] Γ h 4f [MeV] µ0 0.9 s FJ α (µ0) = 0.26 BHM400 MR FJ µ 0 = M h µ r [GeV] µ r [GeV] Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

39 Scale choice BHM600 Γ h 4f [MeV] s MR α (µ0) = 0.22 BHM600 µ0 MR FJ Γ h 4f [MeV] s FJ α (µ0) = 0.22 BHM600 µ0 MR FJ Γ h 4f [MeV] s MR α (µ0) = 0.22 BHM µ r [GeV] µ0 MR FJ Γ h 4f [MeV] s FJ α (µ0) = 0.22 BHM µ r [GeV] µ0 MR FJ µ 0 = M h +M H 2 µ 0 = M h µ r [GeV] µ r [GeV] Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11

40 Scale choice BHM800 Γ h 4f [MeV] 0.94 s MR α (µ0) = 0.2 BHM800 µ0 MR FJ Γ h 4f [MeV] 0.94 s FJ α (µ0) = 0.2 BHM800 µ0 MR FJ µ 0 = M h +M H 2 Γ h 4f [MeV] s MR α (µ0) = 0.2 BHM µ r [GeV] µ0 MR FJ Γ h 4f [MeV] s FJ α (µ0) = 0.2 BHM µ r [GeV] µ0 MR FJ µ 0 = M h µ r [GeV] µ r [GeV] Michele Boggia NLO SESM, h WW/ZZ 4 fermions November 8, / 11