Alessandro Vicini University of Milano, INFN Milano

Transcription

1 Higgs production via gluon fusion in the POWHEG approach in the SM and in the MSSM Alessandro Vicini University of Milano, INFN Milano Padova, 15 febbraio 12 in collaboration with: E. Bagnaschi, G. Degrassi, P. Slavich arxiv: , to appear on JHEP

2 Introductory remarks searches for the Higgs boson need for accurate predictions of the total production rate and of the branching ratios i.e. need for (NNLO-QCD total cross sections experimental searches classify candidate events according to the number of jets associated to each relevant signature the Higgs boson recoils against QCD radiation need for differential (NNLO-QCD distributions important role of initial state multiple gluon radiation searches for BSM Higgs bosons need for observables that allow to disentangle between SM and BSM POWHEG with exact NLO matrix elements in the SM and in the MSSM

3 Outline Recent results of the searches at LEP, Tevatron and LHC Status of the total cross section predictions The POWHEG method: interfacing NLO corrections with Parton Shower The gluon fusion process in POWHEG in the SM: finite quark mass effects The gluon fusion process in POWHEG in the MSSM

4 The total production cross section g t, b H g the gluon fusion process dominates but weak-boson fusion has a very good signal/background ratio the uncertainty bands include: PDF+alphas uncertainty, scale uncertainty

5 LEP and Tevatron results

6 The Higgsstrahlung process NLO-QCD Han, Willenbrock 1990 NNLO-QCD Hamberg, van Neerven, Matsuura 1991 NNLO-QCD Brein, Djouadi, Harlander 03 NLO-EW Ciccolini, Dittmaier, Kraemer 03 NLO-(EW+QCD+4f decay Denner, Dittmaier, Kallweit, Mueck 11 (HAWK Denner et al.

7 The weak-boson fusion process Bolzoni et al. NLO-QCD Figy, Oleari, Zeppenfeld 03 (VBFNLO NLO-(QCD+EW Ciccolini, Denner, Dittmaier 08 (HAWK EW+SUSY Figy, Palmer, Weiglein 10 gluon fusion-wbf interference Andersen et al. 07, Bredenstein et al. 08 gluon induced WBF Harlander, Vollinga, Weber 08 DIS-like NNLO-QCD Bolzoni, Maltoni, Moch, Zaro 11 Ciccolini et al.

8 The gluon fusion process: search channels

9 The gluon fusion process: decay channel H ZZ* 4l

10 The gluon fusion process: decay channel H γ γ

11 The gluon fusion process: existing literature for the total cross section

12 The gluon fusion process: existing literature for the total cross section g t, b H LO-QCD Georgi Glashow Machacek Nanopoulos 1978 g

13 The gluon fusion process: existing literature for the total cross section g t, b H LO-QCD Georgi Glashow Machacek Nanopoulos 1978 g g t, b H Effective theory (HQET mtop infinity H g g t, b

14 The gluon fusion process: existing literature for the total cross section g t, b H LO-QCD Georgi Glashow Machacek Nanopoulos 1978 g g t, b H Effective theory (HQET mtop infinity H g g t, b HQET NLO-QCD HQET Dawson 1991, Djouadi Graudenz Spira Zerwas 1992 exact Spira Djouadi Graudenz Zerwas 1995 Aglietti Bonciani Degrassi AV 07 Anastasiou Beerli Bucherer Daleo Kunszt 07 exact HIGLU POWHEG FeHipro

15 The gluon fusion process: existing literature for the total cross section

16 The gluon fusion process: existing literature for the total cross section NNLO-QCD HQET Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03 ihixs, HNNLO

17 The gluon fusion process: existing literature for the total cross section NNLO-QCD HQET Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03 ihixs, HNNLO... g t, b H NNLO-QCD + soft gluon resummation NNLL-QCD HQET Catani De Florian Grazzini Nason 03 Moch Vogt 05 Idilbi Ji Yuan 06 Ravindran Smith van Neerven 07 HqT

18 The gluon fusion process: existing literature for the total cross section NNLO-QCD HQET Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03 ihixs, HNNLO... g t, b H NNLO-QCD + soft gluon resummation NNLL-QCD HQET Catani De Florian Grazzini Nason 03 Moch Vogt 05 Idilbi Ji Yuan 06 Ravindran Smith van Neerven 07 HqT NNLO-QCD + finite top mass effects Marzani Ball Del Duca Forte AV 08 Harlander Ozeren 09 Pak Rogal Steinhauser 09 Harlander Mantler Marzani Ozeren 09

19 The gluon fusion process: existing literature for the total cross section NNLO-QCD HQET Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03 ihixs, HNNLO... g t, b H NNLO-QCD + soft gluon resummation NNLL-QCD HQET Catani De Florian Grazzini Nason 03 Moch Vogt 05 Idilbi Ji Yuan 06 Ravindran Smith van Neerven 07 HqT NNLO-QCD + finite top mass effects Marzani Ball Del Duca Forte AV 08 Harlander Ozeren 09 Pak Rogal Steinhauser 09 Harlander Mantler Marzani Ozeren 09 NLO-EW Djouadi Gambino 1994 Aglietti Bonciani Degrassi AV 04 Degrassi Maltoni 04 Actis Passarino Sturm Uccirati 08

20 The gluon fusion process: existing literature for the total cross section NNLO-QCD HQET Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03 ihixs, HNNLO... g t, b H NNLO-QCD + soft gluon resummation NNLL-QCD HQET Catani De Florian Grazzini Nason 03 Moch Vogt 05 Idilbi Ji Yuan 06 Ravindran Smith van Neerven 07 HqT NNLO-QCD + finite top mass effects Marzani Ball Del Duca Forte AV 08 Harlander Ozeren 09 Pak Rogal Steinhauser 09 Harlander Mantler Marzani Ozeren 09 NLO-EW Djouadi Gambino 1994 Aglietti Bonciani Degrassi AV 04 Degrassi Maltoni 04 Actis Passarino Sturm Uccirati 08 mixed NLO EWxQCD Anastasiou Boughezal Petriello 09 ihixs

21 The gluon fusion process: best available results (NNLO+NNLL-QCD + NLO-EW Yellow Report 1 of the Higgs Cross Section Working Group, arxiv: g t, b H g NLO-QCD exact results, t and b mass effects + (NNLO+NNLL-QCD results in HQET NLO-EW corrections applied in a factorized form

22 The gluon fusion process: fixed order QCD results Very large NLO-QCD K-factor HQET Dawson 1991, Djouadi Graudenz Spira Zerwas 1992 exact Spira Djouadi Graudenz Zerwas 1995 Aglietti Bonciani Degrassi AV 07 Anastasiou Beerli Bucherer Daleo Kunszt 07 Still sizeable NNLO-QCD effects Anastasiou Melnikov 02 Harlander Kilgore 02 Ravindran Smith van Neerven 03

23 The gluon fusion process: role of the soft-gluon resummation The resummation increases the cross section reduces the scale dependence

24 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10

25 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10

26 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10 the predictions of different PDF groups did not overlap at 1-sigma use of different values of alpha_s different PDF parametrization

27 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10 the predictions of different PDF groups did not overlap at 1-sigma use of different values of alpha_s different PDF parametrization the cross section strongly depends on the precise alpha_s value the dependence is milder than alpha_s^3 because of a partial anti-correlation between alpha_s and gluon density

28 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10 the predictions of different PDF groups did not overlap at 1-sigma use of different values of alpha_s different PDF parametrization the cross section strongly depends on the precise alpha_s value the dependence is milder than alpha_s^3 because of a partial anti-correlation between alpha_s and gluon density with very good approximation the pure PDF uncertainty and the the alpha_s uncertainty are uncorrelated and can be combined summing them in quadrature a more refined treatment allows to account for all the correlations, in each PDF group

29 The gluon fusion process: PDF + alpha_s uncertainties Demartin, Forte, Mariani, Rojo, AV 10 the predictions of different PDF groups did not overlap at 1-sigma use of different values of alpha_s different PDF parametrization the cross section strongly depends on the precise alpha_s value the dependence is milder than alpha_s^3 because of a partial anti-correlation between alpha_s and gluon density with very good approximation the pure PDF uncertainty and the the alpha_s uncertainty are uncorrelated and can be combined summing them in quadrature a more refined treatment allows to account for all the correlations, in each PDF group envelope of the predictions by MSTW08, CTEQ6.6, NNPDF2.0 as estimate of the PDF+alpha_s uncertainty Ansatz: the NLO-QCD enveloped as estimate of the NNLO-QCD PDF+alpha_s uncertainty

30 The gluon fusion process: HQET vs exact results at LO-QCD plot by R.Harlander The mass expansion does not reproduce the ttbar threshold for light Higgs is an excellent approximation of the full result

31 The gluon fusion process: HQET vs exact results at NLO-QCD

32 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t =

33 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t = Born-improved, only top, NLO result in the HQET σ(gg H + X =σ 0 (m t K

34 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t = Born-improved, only top, NLO result in the HQET σ(gg H + X =σ 0 (m t K

35 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t = Born-improved, only top, NLO result in the HQET σ(gg H + X =σ 0 (m t K Ansatz: Born-improved, (top+bottom, NLO result in the HQET σ(gg H + X =σ 0 (m t,m b K

36 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t = Born-improved, only top, NLO result in the HQET σ(gg H + X =σ 0 (m t K λ b = +10 λ b = +1 Ansatz: Born-improved, (top+bottom, NLO result in the HQET σ(gg H + X =σ 0 (m t,m b K differences at the few per cent level, due to the use of the approximate K-factor K(mt,mb/K Alessandro Vicini - University of Milano m H (GeV Padova, 15 febbraio 12

37 The gluon fusion process: HQET vs exact results at NLO-QCD NLO result in the HQET σ(gg H + X =σ 0 (m t = K K = σ NLO(m t = σ LO (m t = Born-improved, only top, NLO result in the HQET σ(gg H + X =σ 0 (m t K K(mt,mb/K λ b = +10 λ b = +1 Ansatz: Born-improved, (top+bottom, NLO result in the HQET σ(gg H + X =σ 0 (m t,m b K differences at the few per cent level, due to the use of the approximate K-factor the HQET K-factor can lead to sizeable inaccuracies with enhanced bottom couplings, like e.g. in the MSSM Alessandro Vicini - University of Milano m H (GeV Padova, 15 febbraio 12

38 The gluon fusion process: top mass effects at NNLO-QCD To estimate the top mass effects at NNLO-QCD (3-loop results not available, the naive expansion of NNLO amplitudes in powers of 1/mt fails Marzani Ball Del Duca Forte AV 08 In the pointlike approximation, the amplitude develops spurious logs of ŝ absent in the exact theory, where the triangle fermion loop acts as a form factor lim ˆσ ŝ α 2 s k=1 αk s log 2k 1 ( ŝ m 2 H α 2 s k=1 αk s log k 1 ( ŝ m 2 H pointlike = m t resolved : finite m t It is possible to subtract systematically all the spurious logs compute the correct coefficient of the first allowed log, using high energy resummation techniques match the improved expression valid for large ŝ, with the pointlike expression valid for small ŝ Procedure checked at NLO-QCD, where an exact analytical expression is available applied at NNLO-QCD, where only the pointlike result is known checked the impact on the hadronic cross section at NNLO-QCD

39 The gluon fusion process: top mass effects at NNLO-QCD

40 The gluon fusion process: top mass effects at NNLO-QCD NLO-QCD pointlike exact approx NNLO-QCD pointlike Anastasiou et al approx Although the rise at large ŝ of the pointlike partonic cross section is very steep, because of the spurious logs, the contribution to the total hadronic cross section is modest, when convoluted with the gluon density the improved hadronic cross section differs at the level of 1% (or less of the LO-QCD result w.r.t. the pointlike result

41 The gluon fusion process: top mass effects at NNLO-QCD NLO-QCD pointlike exact approx NNLO-QCD pointlike Anastasiou et al approx Although the rise at large ŝ of the pointlike partonic cross section is very steep, because of the spurious logs, the contribution to the total hadronic cross section is modest, when convoluted with the gluon density the improved hadronic cross section differs at the level of 1% (or less of the LO-QCD result w.r.t. the pointlike result Systematic study by R. Harlander et al, M. Steinhauser et al, including arbitrary powers of 1/mt Harlander Ozeren 09 Pak Rogal Steinhauser 09 Harlander Mantler Marzani Ozeren 09 After subtraction of the spurious terms that spoiled the convergence, the finite top mass corrections can be safely evaluated finite top mass effects on the NNLO-QCD hadronic cross section at the level of 0.5%

42 Summary on the total cross section Total cross section implemented in different public programs Exact calculation including quark mass effects up to NLO-(QCD+EW NNLO-QCD and NNLL-QCD corrections evaluated in the HQET Estimate of higher order corrections (QCD NNNLL, mixed QCDxEW available in the HQET Estimate of uncertainties: scale unc. of O( 7-10% PDF+alpha_s unc of O( 5%

43 The gluon fusion process: Higgs transverse momentum distribution the Higgs is very often produced at large transverse momentum (in association with 1 jet fixed-order results diverge in the limit pth 0 resummation of log(pth/mh is necessary to restore the correct limit pth 0 De Florian Ferrera Grazzini Tommasini 11 fixed-order results provide a correct estimate of the distribution at large pth LO-QCD with exact quark mass dependence (MCFM NLO-QCD in the infinite top mass limit (HiggsJet NLO-QCD with exact quark mass dependence (HIGLU, Petriello-Keung, FeHiPro,iHixs NNLO-QCD in the infinite top mass limit (HNNLO, FeHip including some Higgs decay channels NLO-EW with exact quark mass dependence (Petriello-Keung

44 The gluon fusion process: Higgs transverse momentum distribution the resummation of log(pth/mh can be analytical: LL, NLL, NNLL implemented via QCD Parton Shower: LL, NLL both groups of programs work in the HQET analytical resummation (NNLL+NNLO-QCD in the HQET (HqT Bozzi Catani De Florian Grazzini 03, 06 De Florian Ferrera Grazzini Tommasini 11 NLO MC matched with QCD shower NLO-QCD matched with HERWIG/PYTHIA, in the HQET POWHEG Frixione Webber 02 Nason 04 Alioli Nason Oleari Re 09 Missing: NLO-QCD matched with a QCD shower with exact quark mass effects

45 The gluon fusion process: Higgs pt distribution, perturbative uncertainties with HqT de Florian, Ferrera, Grazzini, Tommasini, arxiv: For pt<50 GeV, the best estimate of the perturbative uncertainty band (renormalization, factorization, resummation scale variations is obtained with HqT, (HQET, NNLL+NLO-QCD to be of order ±10% (for MH=165 GeV Finite quark mass effects may modify the prediction of the central value of the band Are top and bottom mass effects relevant at the 10% level?

46 The gluon fusion process: Higgs pt distribution, PDF uncertainties with HqT

47 The gluon fusion process: Higgs pt distribution, PDF uncertainties with HqT de Florian, Ferrera, Grazzini, Tommasini, arxiv: The PDF+alpha_s uncertainty band is estimated with HqT, (HQET, NNLL+NLO-QCD to be of order ±2%, around the peak of the distribution

48 The gluon fusion process: Higgs pt distribution, PDF uncertainties with HqT de Florian, Ferrera, Grazzini, Tommasini, arxiv: The PDF+alpha_s uncertainty band is estimated with HqT, (HQET, NNLL+NLO-QCD to be of order ±2%, around the peak of the distribution We decided to investigate the relevance of top and bottom mass effects by implementing them in a new release of POWHEG

49 The POWHEG method (Nason 04, Frixione Nason Oleari 07, Alioli Nason Oleari Re 09 matching NLO-QCD matrix elements with QCD Parton Shower avoiding double countings between the first emission (hard matrix element and the PS radiation generating positive weight events independent of the details of the (vetoed shower adopted

50 The POWHEG method (Nason 04, Frixione Nason Oleari 07, Alioli Nason Oleari Re 09 matching NLO-QCD matrix elements with QCD Parton Shower avoiding double countings between the first emission (hard matrix element and the PS radiation generating positive weight events independent of the details of the (vetoed shower adopted dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad, NLO-QCD accuracy of the total cross section: inclusion of virtual corrections, B( Φ 1 = B gg ( Φ 1 +V gg ( Φ integral over the whole phase space of (subtracted real matrix element 1 + { } dφ rad ˆR gg ( Φ1, Φ rad + ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad + c. r. q

51 The POWHEG method (Nason 04, Frixione Nason Oleari 07, Alioli Nason Oleari Re 09 matching NLO-QCD matrix elements with QCD Parton Shower avoiding double countings between the first emission (hard matrix element and the PS radiation generating positive weight events independent of the details of the (vetoed shower adopted dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad, NLO-QCD accuracy of the total cross section: inclusion of virtual corrections, B( Φ 1 = B gg ( Φ 1 +V gg ( Φ integral over the whole phase space of (subtracted real matrix element 1 + { } dφ rad ˆR gg ( Φ1, Φ rad + ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad + c. r. q NLO-QCD accuracy of the real emission probability: exact real matrix elements, are used also in the Sudakov form factor (instead of the collinear splitting function ( Φ 1,p T = exp { dφ rad R( Φ 1, Φ rad B( Φ 1 } θ(k T p T

52 The POWHEG method (Nason 04, Frixione Nason Oleari 07, Alioli Nason Oleari Re 09 matching NLO-QCD matrix elements with QCD Parton Shower avoiding double countings between the first emission (hard matrix element and the PS radiation generating positive weight events independent of the details of the (vetoed shower adopted dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad, NLO-QCD accuracy of the total cross section: inclusion of virtual corrections, B( Φ 1 = B gg ( Φ 1 +V gg ( Φ integral over the whole phase space of (subtracted real matrix element 1 + { } dφ rad ˆR gg ( Φ1, Φ rad + ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad + c. r. q NLO-QCD accuracy of the real emission probability: exact real matrix elements, are used also in the Sudakov form factor (instead of the collinear splitting function ( Φ 1,p T = exp { dφ rad R( Φ 1, Φ rad B( Φ 1 } θ(k T p T The curly bracket, integrated over the whole phase space, is equal to 1 : the NLO-QCD accuracy of the total cross section is preserved

53 The POWHEG method (Nason 04, Frixione Nason Oleari 07, Alioli Nason Oleari Re 09 matching NLO-QCD matrix elements with QCD Parton Shower avoiding double countings between the first emission (hard matrix element and the PS radiation generating positive weight events independent of the details of the (vetoed shower adopted dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad, NLO-QCD accuracy of the total cross section: inclusion of virtual corrections, B( Φ 1 = B gg ( Φ 1 +V gg ( Φ integral over the whole phase space of (subtracted real matrix element 1 + { } dφ rad ˆR gg ( Φ1, Φ rad + ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad + c. r. q NLO-QCD accuracy of the real emission probability: exact real matrix elements, are used also in the Sudakov form factor (instead of the collinear splitting function ( Φ 1,p T = exp { dφ rad R( Φ 1, Φ rad B( Φ 1 } θ(k T p T The curly bracket, integrated over the whole phase space, is equal to 1 : the NLO-QCD accuracy of the total cross section is preserved The POWHEG (first emission is by construction the hardest: HERWIG/PYTHIA are bound to radiate partons with lower virtuality (transverse momentum

54 SM: old and new POWHEG implementations, QCD corrections dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T B( Φ 1 = B gg ( Φ 1 + V gg ( Φ 1 + LO and NLO-QCD virtual corrections + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad { ˆR gg ( Φ1, Φ rad + g q dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad } + c. r. old = Alioli, Nason, Oleari, Re 09 new = Bagnaschi, Degrassi, Slavich, AV 11 old new H t, b H g t, b g

55 SM: old and new POWHEG implementations, QCD corrections dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T B( Φ 1 = B gg ( Φ 1 +V gg ( Φ 1 + LO and NLO-QCD virtual corrections old + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad { ˆR gg ( Φ1, Φ rad + new g q dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad } + c. r. old = Alioli, Nason, Oleari, Re 09 new = Bagnaschi, Degrassi, Slavich, AV 11 H t, b H g t, b g NLO-QCD real corrections old new

56 UV, soft and collinear divergences in POWHEG UV renormalization the renormalization scheme affects the finite part of the virtual corrections in the new POWHEG implementation the quark masses can be renormalized in OS, MSbar, DRbar schemes IR soft and collinear divergences IR soft divergences cancel between real and virtual contributions factorize with respect to the LO cross section initial state collinear divergences are universal factorize with respect to the LO cross section the structure of the subtraction terms is universal, independent of the hard LO squared matrix element it depends only on the flavor of the incoming partons on the color structure of the final state in POWHEG the cancelation of the IR divergences is guaranteed, provided that Born and real emission amplitudes are computed consistently in the same mass approximation

57 SM: Numerical results mt=172.5 GeV mb=4.75 GeV MW= GeV MZ= GeV MSTW08nlo no acceptance cuts results for on-shell Higgs all the decay channels are available and are activated in HERWIG/PYTHIA the final state is obtained as a convolution of Higgs production (POWHEG Breit-Wigner distribution of intermediate Higgs virtualities decay in a given channel (HERWIG/PYTHIA preliminary studies for the H γ γ (with selection cuts comparison of NLO-QCD fixed order basic POWHEG formula (including Sudakov form factor effects abbreviated LHEF POWHEG + PYTHIA inclusion of NLO-EW checks: NLO-QCD total cross sections checked against HIGLU, HNNLO, FeHip-Pro NLO-QCD distributions checked against FeHiPro the input file is like in the old POWHEG implementation, with a few extra flags

58 SM: Higgs transverse momentum fixed-order vs resummed distributions 1 Bagnaschi Degrassi Slavich AV, arxiv: LHC 7 TeV SM - m H = 1 GeV 0.1 (d!/dp t H (pb/gev NLO LHEF POWHEG+PYTHIA PS p t H (GeV NLO-QCD fixed order diverges for pt 0 basic POWHEG formula (LHEF and POWHEG+PYTHIA vanish for pt 0

59 SM: Higgs transverse momentum LHC 7 TeV SM - m H = 1 GeV NLO-QCD, no EW old vs new POWHEG NLO-QCD finite quark mass effects at NLO-QCD sizeable perfect agreement with FeHiPro R m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV

60 SM: Higgs transverse momentum R LHC 7 TeV SM - m H = 1 GeV NLO-QCD, no EW m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling old vs new POWHEG NLO-QCD finite quark mass effects at NLO-QCD sizeable perfect agreement with FeHiPro The positive correction for pt < 0 GeV yields a stronger Sudakov suppression for pt 0 ( Φ 1,p T = exp R(t, b, exact B(t, b, exact { > R(t, B(t, } R( Φ 1, Φ rad dφ rad θ(k T p T B( Φ 1 (t, b, exact < (t, p t H (GeV LHC 7 TeV SM - m H = 1 GeV LHEF, no EW basic POWHEG: LHEF R m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV

61 SM: Higgs transverse momentum R LHC 7 TeV SM - m H = 1 GeV NLO-QCD, no EW m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV old vs new POWHEG NLO-QCD finite quark mass effects at NLO-QCD sizeable perfect agreement with FeHiPro The positive correction for pt < 0 GeV yields a stronger Sudakov suppression for pt 0 ( Φ 1,p T = exp R(t, b, exact B(t, b, exact { R(t, > B(t, } R( Φ 1, Φ rad dφ rad θ(k T p T B( Φ 1 (t, b, exact < (t, at intermediate pt, the real emission enhancement dominates over the Sudakov suppression LHC 7 TeV SM - m H = 1 GeV LHEF, no EW basic POWHEG: LHEF R m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV

62 SM: Higgs transverse momentum R LHC 7 TeV SM - m H = 1 GeV NLO-QCD, no EW LHC 7 TeV SM - m H = 1 GeV LHEF, no EW m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV old vs new POWHEG NLO-QCD basic POWHEG: LHEF 300 finite quark mass effects at NLO-QCD sizeable perfect agreement with FeHip The positive correction for pt < 0 GeV yields a stronger Sudakov suppression for pt ( Φ 1,p T = exp R(t, b, exact B(t, b, exact LHC 7 TeV SM - m H = 1 GeV PYTHIA, no EW { R(t, > B(t, } R( Φ 1, Φ rad dφ rad θ(k T p T B( Φ 1 (t, b, exact < (t, at intermediate pt, the real emission enhancement dominates over the Sudakov suppression The PYTHIA QCD-PS marginally modifies this effect (no acceptance cuts POWHEG + PYTHIA R m top!!" with LO rescaling exact m t m b dependence 0.8 R=(exact m t, m b dependence/(m top!!" with LO rescaling R m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling p t H (GeV p t H (GeV

63 SM: Higgs transverse momentum role of the bottom quark comparison of shapes (normalized distributions Bagnaschi Degrassi Slavich AV, arxiv: LHC 7 TeV SM - m h = 1 GeV NLO+PYTHIA R m top!!" with LO rescaling m top exact mass dependence m top, m bot exact mass dependence R=ratio to (m top!!" with LO rescaling p t H (GeV only top: the ratio R/B in the exact case is very close to the infinite top mass limit at small pt, old and new POWHEG are very close at large pt, the finite top mass yields a negative correction top+bot: important bottom NLO-QCD correction Sudakov suppression the size of the finite quark mass effects is comparable to the HqT estimate of the perturbative uncertainty

64 SM: Higgs transverse momentum.3.2 LHC 7 TeV SM - m H = 1 GeV NLO-QCD, no EW MH=1 GeV light vs heavy Higgs NLO-QCD LHC 7 TeV SM - m H = 500 GeV NLO-QCD, no EW m top!!" with LO rescaling exact m t m b dependence MH=500 GeV R=(exact m t, m b dependence/(m top!!" with LO rescaling m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling LHC 7 TeV SM - m H = 1 GeV PYTHIA, no EW LHC 7 TeV SM - m H = 500 GeV PYTHIA, no EW m top!!" with LO rescaling exact m t m b dependence R=(exact m t, m b dependence/(m top!!" with LO rescaling 1 R m top!!" with LO rescaling exact m t m b dependence 0.8 R=(exact m t, m b dependence/(m top!!" with LO rescaling R p t H (GeV p t H (GeV POWHEG+PYTHIA p t H (GeV p t H (GeV light Higgs: important bottom role, stronger Sudakov suppression at small pt heavy Higgs: finite mass effects dominated by the top quark, always negative, harder distribution at small pt

65 SM: open questions about the Higgs transverse momentum distribution POWHEG has a strong enhancement of the shape at large pt (due to the large K-factor which brings it accidentally very close to HNNLO Alioli Nason Oleari Re, 09 comparison PYTHIA vs HERWIG non perturbative parameter have a strong impact on the low pth tail of the distribution LHC 7 TeV SM - m H = 1 GeV NLO-QCD-PS need to perform a tuning of the non-perturbative parameters using the NLO-SMC to compare with the data R PYTHIA HERWIG Bagnaschi Degrassi Slavich AV, arxiv: p t H (GeV

66 SM: NLO-EW corrections to the gluon fusion they are an overall rescaling factor (complete factorization Ansatz light-fermions contribution Aglietti Bonciani Degrassi AV 04 exact results expressed in terms of HPL top-bottom contribution Degrassi Maltoni 04 Taylor expansion valid up to mh ~ 2 mw full result valid for arbitrary mh, including systematic use of complex masses Actis Passarino Sturm Uccirati 08

67 SM: inclusion of NLO-EW corrections (Actis et al. (complete factorization LHC 7 TeV SM NLO-(QCD+EW m top "!# with LO rescaling exact m t m b dependence exact m t m b dependence, EW corrections LHC 7 TeV SM NLO-(QCD+EW m top "!# with LO rescaling exact m t m b dependence exact m t m b dependence, EW corrections ! H 10! H m H (GeV m H (GeV LHC 7 TeV SM - m H = 1 GeV LHEF + NLO-EW LHC 7 TeV SM - m H = 1 GeV LHEF + NLO-EW R m top "!# with LO rescaling exact m t m b dependence exact m t m b dependence, EW corrections 0.8 m top!!" with LO rescaling exact m t m b dependence exact m t m b dependence, EW corrections R=(exact m t, m b dependence/(m top!!" with LO rescaling H

68 Summary on the SM section the release of the gluon fusion process, in the SM, including quark mass effects, is public and available in the POWHEG-BOX the effects of distorsion of the shape of the Higgs transverse momentum distribution stem from the interference of the top and bottom loops in the real radiation amplitude and are enhanced (for light Higgs mass by the light bottom mass the final shape depends on the role of the POWHEG Sudakov form factor the effects are comparable with the theoretical uncertainty estimated with HqT Gluon fusion in the MSSM In the MSSM, the role of the bottom quark can be further enhanced by tanβ The role of the squarks, including their mass effects, and their interplay with the bottom quark should be investigated in a realistic setup

69 Existing literature and motivations: MSSM Total cross section results NLO-QCD with exact quark/squark mass dependence and gluino effects via effective couplings (HIGLU Spira Muhlleitner 08 NLO with quarks, squarks and gluinos in heavy mass limit (Harlander Steinhauser 04, Degrassi Slavich NLO with exact mass dependence (Anastasiou Beerli Daleo 08, Spira Muehlleitner Rzehak 11 NNLO heavy top/stop mass limit (Pak Steinhauser 10 Yellow Report 1 of the Higgs Cross Section Working Group, arxiv: Higgs at large transverse momentum (in association with 1 jet NLO-QCD with exact quark/squark mass dependence (Brein Hollik 03 07, Field Dawson Smith, 04 Langenegger Spira Starodumov Trueb 06 Higgs differential distributions NLO with exact quark mass dependence, squarks and gluinos in heavy mass limit (zero mixing and equal squark and gluino masses (Harlander Hoffman Mantler 10 Missing: NLO MSSM result matched with a QCD shower

70 MSSM: perturbative content dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T B( Φ 1 = B gg ( Φ 1 + V gg ( Φ 1 + LO and NLO virtual corrections + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad { ˆR gg ( Φ1, Φ rad + q dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad } + c. r. LO: quarks and squarks virtual corrections: full MSSM in the effective potential approach (Degrassi Slavich gluon corrections to quark/squark diagrams gluino/quark/squark corrections (IR finite subset only top and bottom are treated exactly for m H < 2 m Q exact results are well approximated by the Taylor expansion NLO-EW virtual corrections: only light quark diagrams, complete factorization scheme (Aglietti Bonciani Degrassi AV 04

71 MSSM: virtual corrections, Feynman diagrams

72 MSSM: perturbative content dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T B( Φ 1 = B gg ( Φ 1 +V gg ( Φ 1 + LO and NLO virtual corrections + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad { ˆR gg ( Φ1, Φ rad + q dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad } + c. r. LO: quarks and squarks virtual corrections: full MSSM in the effective potential approach (Degrassi Slavich gluon corrections to quark/squark diagrams gluino/quark/squark corrections (IR finite subset only top and bottom are treated exactly for m H < 2 m Q exact results are well approximated by the Taylor expansion NLO-EW virtual corrections: only light quark diagrams, complete factorization scheme NLO real corrections only quark/squark, but no gluino in the internal loop (Aglietti Bonciani Degrassi AV 04 (Bonciani Degrassi AV 07

73 MSSM: perturbative content dσ = B( Φ 1 d Φ 1 { ( Φ1,p min T B( Φ 1 = B gg ( Φ 1 +V gg ( Φ 1 + LO and NLO virtual corrections + ( Φ1,p T R ( Φ1, Φ rad B ( Φ1 dφ rad { ˆR gg ( Φ1, Φ rad + q dφ rad } + q R q q ( Φ1, Φ rad d Φ1 dφ rad ˆR gq ( Φ1, Φ rad + ˆRqg ( Φ1, Φ rad } + c. r. LO: quarks and squarks virtual corrections: full MSSM in the effective potential approach (Degrassi Slavich gluon corrections to quark/squark diagrams gluino/quark/squark corrections (IR finite subset only top and bottom are treated exactly for m H < 2 m Q exact results are well approximated by the Taylor expansion NLO-EW virtual corrections: only light quark diagrams, complete factorization scheme NLO real corrections (Aglietti Bonciani Degrassi AV 04 only quark/squark, but no gluino in the internal loop (Bonciani Degrassi AV 07 at the moment the processes bg bh and b bbar Hg are NOT included relevant in the low MA, high tanβ region

74 MSSM: Numerical results the input file is like in the old POWHEG implementation, with a flag that specifies the model (MSSM if the model chosen is MSSM, the program expects to find a SLHA format input file with all the MSSM parameters at present, all the parameters are computed using SOFT-SUSY in the DRbar scheme the interface with FeynHiggs (OS scheme has been extensively tested and will be part of the public code using the MSSM parameters, we compute the coupling of the Higgs to each quark / squark (once couplings and masses are available, the amplitude can be evaluated scenario mhmax parameter scan with 90 MA 0 GeV, 10 tanβ 50 parameters evaluated at M_Q = M_U = M_D = 500 GeV Xt = 1250 GeV M3 =2 M2 = 4 M1 = 0 GeV for each point in the (MA,tanβ plane we compute the values of mh and MH squark masses and mixing angles we considered both μ=±0 GeV the comparison with the SM results is done for the same value of mh (or of MH using DRbar quark masses also in the SM the results shown are obtained with on-shell Higgs the decay in different channels is implemented in PYTHIA/HERWIG (we are cross-checking the consistency with the POWHEG side

75 MSSM: total cross section, light higgs, both MSSM and SM results computed in the DRbar scheme the SM value is computed for the same mh obtained in the MSSM ratio MSSM vs SM µ = 0 GeV µ = 0 GeV μ>0 tanβ-dependent corrections suppress Higgs to (sbottom couplings μ<0 tanβ-dependent corrections enhance Higgs to (sbottom couplings

76 MSSM: total cross section, light higgs, ratio full MSSM vs MSSM only quarks the squarks induce always a negative correction: moderate when σ(mssm σ(sm more sizeable when σ(mssm < σ(sm µ = 0 GeV µ = 0 GeV In the Yellow Report arxiv: the cross section for neutral Higgs production have been computed including only the quark contributions. The squarks, although heavy, interfere with the bottom loop and yield a negative correction

77 MSSM: light higgs transverse momentum distribution the exact treatment of the squark masses in the real emission amplitudes is relevant for Higgs transverse momenta larger than 250 GeV exact vs heavy squarks 2.5 LHC 7 TeV m H = 1 GeV - tan(! = - m A0 = 180 GeV R MSSM full squarks mass dependence MSSM heavy squarks mass limit p t H (GeV

78 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? Higgs transverse momentum distribution POWHEG+PYTHIA 2.5 LHC 7 TeV m H = 106 GeV - tan(! = 16 - m A0 = 110 GeV The blue point indicates the (MA, tanβ pair considered R = ratio MSSM vs SM (DRbar R SM DRBAR MSSM MA GeV H p t (GeV LHC 7 TeV m H = 106 GeV - tan(! = 16 - m A0 = 110 GeV tan Β R = ratio MSSM full vs MSSM-ONLY QUARKS mh=106 GeV R MSSM ONLY QUARKS MSSM

79 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? The bottom loop is not dominant, squark loops harden at small pth the distribution LHC 7 TeV m H = 114 GeV - tan(! = - m A0 = 114 GeV 1.5 R = ratio MSSM vs SM (DRbar R SM DRBAR MSSM MA GeV H p t (GeV LHC 7 TeV m H = 114 GeV - tan(! = - m A0 = 114 GeV tan Β R = ratio MSSM full vs MSSM-ONLY QUARKS mh=114 GeV R 1 MSSM ONLY QUARKS MSSM

80 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? 2.5 LHC 7 TeV m H = 118 GeV - tan(! = 24 - m A0 = 125 GeV R = ratio MSSM vs SM (DRbar R SM DRBAR MSSM MA GeV H p t (GeV LHC 7 TeV m H = 118 GeV - tan(! = 24 - m A0 = 125 GeV tan Β R = ratio MSSM full vs MSSM-ONLY QUARKS mh=118 GeV R MSSM ONLY QUARKS MSSM

81 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? 2.5 LHC 7 TeV m H = 1 GeV - tan(! = 30 - m A0 = 1 GeV SM DRBAR MSSM R = ratio MSSM vs SM (DRbar R MA GeV H p t (GeV LHC 7 TeV m H = 1 GeV - tan(! = 30 - m A0 = 1 GeV tan Β MSSM ONLY QUARKS MSSM R = ratio MSSM full vs MSSM-ONLY QUARKS mh=1 GeV R

82 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? 2.5 LHC 7 TeV m H = 121 GeV - tan(! = 38 - m A0 = 135 GeV SM DRBAR MSSM R = ratio MSSM vs SM (DRbar R MA GeV H p t (GeV LHC 7 TeV m H = 121 GeV - tan(! = 38 - m A0 = 135 GeV tan Β MSSM ONLY QUARKS MSSM R = ratio MSSM full vs MSSM-ONLY QUARKS mh=121 GeV R

83 If a scalar is found and σ(sm= σ(mssm, does the Higgs pt help to disentangle? The tanβ enhancement yields a stronger Sudakov suppression (w.r.t. SM probably due to the bottom quark diagrams LHC 7 TeV m H = 122 GeV - tan(! = 44 - m A0 = 1 GeV SM DRBAR MSSM R = ratio MSSM vs SM (DRbar R MA GeV H p t (GeV LHC 7 TeV m H = 122 GeV - tan(! = 44 - m A0 = 1 GeV tan Β MSSM ONLY QUARKS MSSM R = ratio MSSM full vs MSSM-ONLY QUARKS mh=122 GeV R

84 Comments the Higgs transverse momentum distribution can provide, in some regions of the parameter space (even in the most ambiguous, a way to discriminate between SM and MSSM the effects stem from the interference between the bottom loop and the heavy particles loops are possibly enhanced by tanβ are evident (measurable in the region where the cross section is large (pth < 50 GeV the exact dependence on the bottom mass is crucial to appreciate these effects

85 Conclusions Higgs production via gluon fusion in the POWHEG approach with NLO-(QCD+EW accuracy: in the SM with exact dependence on the quark masses in the full MSSM with exact dependence on the quark masses, squarks and gluinos in the heavy mass limit in the virtual corrections exact dependence on the squark masses in the real amplitudes a first study has been performed for on-shell Higgs the SM branch of the code is publicly available, with all the decay channels active the MSSM branch of the code is close to be released SM: for light Higgs, the bottom quark yields O(10% corrections at NLO-QCD stronger Sudakov suppression (w.r.t. infinite top mass for vanishing Higgs pt positive correction for intermediate pt MSSM: realistic estimate of total cross section (with acceptance cuts including all SUSY particles MSSM: important role of the bottom quark, emphasized by the Sudakov form factors realistic differential distributions offer the possibility to discriminate between SM and MSSM

86 Back-up slides

87 Gluon fusion: NLO-EW corrections, light fermions NLO results Aglietti, Bonciani Degrassi, AV, Phys.Lett.B595 (04 ^

88 Gluon fusion: NLO-EW corrections, heavy fermions Degrassi, Maltoni Nucl.Phys.B724: ,05. NLO results

89 Gluon fusion: NLO-EW corrections, numerical results Aglietti, Bonciani Degrassi, AV real mass complex mass δ only light quarks m H (GeV Large corrections below the WW threshold due to the light fermions Absence of yukawa suppression and of heavy mass suppression in the loop The spikes at the WW and ZZ thresholds suggest the need of a complex mass to describe unstable particles Results available in a very compact analytical form, in terms of GHPL, both in fortran and C++

90 Gluon fusion:the need of complex masses H γγ W are unstable need to Dyson resum the self-energy insertions i.e. to introduce the W decay width Square root singularity same problem in gluon fusion appears at 3-loop complex masses

91 Gluon fusion: NLO-EW corrections, numerical results Actis, Passarino, Sturm, Uccirati, Nucl.Phys.B811 (09 182, Phys.Lett.B669 (08 62 Fully numerical evaluation of NLO-EW corrections The EW corrections involving the (t,b doublet play a role at the t-tbar threshold

92 Hadronic cross-section and mixed EW-QCD corrections Actis, Passarino, Sturm, Uccirati, Phys.Lett.B670 (08 12 σ (0 G ij σ (0 (1 [ + δ EW G ij σ (0 G ij σ (0 G ij + αsδ 2 EW G (0 ] ij Complete Factorization Partial Factorization The universality of the QCD collinear logs is not implemented (PF In this approach the EW corrections modifies only the 2 1 kinematics the increase of the total cross-section is only of 1-2%, depending on MH

93 SM: open questions about the Higgs transverse momentum distribution uncertainties of HqT + Herwig POWHEG+Pythia under scale variation about the central value MH shapes of are compatible with those of HqT uncertainties at large pth are smaller in HqT

94 MSSM: perturbative content

95 MSSM: perturbative content