VH production at the LHC: recent theory progress

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1 VH production at the LHC: recent theory progress Giancarlo Ferrera Università di Milano & INFN Milano LHC Higgs Cross Section Working Group CERN June 12th 214

2 Motivations Associated vector boson Higgs (VH) production (with H b b and V l 1 l 2 decay) Important channel at the LHC (access to Hb b coupling) but challenging. LHC experiments are close to the SM H b b sensitivity. To improve these results, precise theoretical predictions are needed = computation of higher-order QCD corrections. 95% asymptotic CL limit on µ CMS -1 s = 7 TeV, L = 5. fb -1 s = 8 TeV, L = 18.9 fb pp VH; H bb CL S Observed CL S H125 injected CL S Expected CL S Expected ± 1 σ CL S Expected ± 2 σ 95% C.L. limit on σ/σ SM ATLAS Preliminary VH(bb) Observed (CLs) Expected (CLs) ± 1σ ± 2σ s = 8 TeV s = 7 TeV -1 Ldt = 2.3 fb -1 Ldt = 4.7 fb m H [GeV] m H [GeV] VH production at the LHC: recent theory progress 2/12

3 Associated VH production and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X where V = Z,W ± and l 1 l 2 = l + l,lν l >. h f b/h2 (x 2,µ The framework: QCD factorization formula 2 2 F ) h 1 > f a/h1 (x 1,µ 2 F ). a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) V H dγ H X b b l 1 l 2 1 dσ VH = 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O a,b ) p (with p 1): Non perturbative power-corrections (higher-twist). ( ΛQCD Q f a/h (x,µ 2 F ): Non perturbative universal parton densities (PDFs), µ F Q. ( ΛQCD ) p dˆσ ab : Hard scattering cross section. calculable with a perturbative expansion in α S (Q) dˆσ ab = dˆσ () ab +dˆσ(1) ab (µ2 R )+dˆσ(2) ab (µ2 R )+O(α3 S ). Precise predictions for σ depend on good knowledge of both ˆσ ab and f a/h (x,µ 2 F) VH production at the LHC: recent theory progress 3/12 Q

4 Associated VH production h 1 > and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X f a/h1 (x 1,µ 2 F ) where V = Z,W ± and l 1 l 2 = l + l,lν l >. The framework: QCD factorization formula h 2 f b/h2 (x 2,µ 2 F ) dσ VH = a,b 1. a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) V H dγ H X b l 1 l 2 ( ΛQCD ) p dσ = VH Vb b dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q b VH production at the LHC: recent theory progress 4/12

5 Associated VH production h 1 > and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X f a/h1 (x 1,µ 2 F ) where V = Z,W ± and l 1 l 2 = l + l,lν l >. The framework: QCD factorization formula h 2 f b/h2 (x 2,µ 2 F ) dσ VH = a,b 1. a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) V H dγ H X b l 1 l 2 ( ΛQCD ) p dσ = VH Vb b dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q b VH production at the LHC: recent theory progress 4/12

6 Associated VH production h 1 > and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X f a/h1 (x 1,µ 2 F ) where V = Z,W ± and l 1 l 2 = l + l,lν l >. The framework: QCD factorization formula h 2 f b/h2 (x 2,µ 2 F ) dσ VH = a,b 1. a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) V H dγ H X b l 1 l 2 ( ΛQCD ) p dσ LO+lo VH Vb b = dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q b VH production at the LHC: recent theory progress 4/12

7 Associated VH production h 1 > and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X f a/h1 (x 1,µ 2 F ) where V = Z,W ± and l 1 l 2 = l + l,lν l >. The framework: QCD factorization formula h 2 f b/h2 (x 2,µ 2 F ) dσ VH = a,b 1. a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) V H dγ H X b l 1 l 2 ( ΛQCD ) p dσ NLO+lo VH Vb b = dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q b VH production at the LHC: recent theory progress 4/12

8 Associated VH production h 1 > and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X f a/h1 (x 1,µ 2 F ) where V = Z,W ± and l 1 l 2 = l + l,lν l >. The framework: QCD factorization formula h 2 f b/h2 (x 2,µ 2 F ) dσ VH = a,b 1. a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) V H dγ H X b l 1 l 2 ( ΛQCD ) p dσ NLO+nlo VH Vb b = dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q b VH production at the LHC: recent theory progress 4/12

9 Associated VH production and H b b decay h 1(p 1)+h 2(p 2) V +H +X l 1l 2 +b b +X where V = Z,W ± and l 1 l 2 = l + l,lν l >. h f b/h2 (x 2,µ The framework: QCD factorization formula 2 2 F ) h 1 > f a/h1 (x 1,µ 2 F ). a(x 1 p 1 ) dˆσ ab b(x 2 p 2 ) V H dγ H X b b l 1 l 2 dσ VH = a,b 1 1 dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)dˆσ ab (x 1p 1,x 2p 2;µ 2 F)+O dγ H b b : H b b decay rate has an analogous perturbative expansion dγ H b b = dγ() H b b +dγ(1) H b b (µ2 R )+dγ(2) H b b (µ2 R )+O(α3 S ). By using the zero width approximation (Γ H m H ) ( ΛQCD ) p dσ NNLO+nlo VH Vb b = dσ (k) VH ( )( ) dγ (k) H b b = dσ () VH +dσ(1) VH +dσ(2) VH... dγ () H b b +dγ(1) H b b +... k= k= Q VH production at the LHC: recent theory progress 4/12

10 pp VH lνb b: total cross section b H b NNLO QCD corrections for WH are basically the same of DY ( 1-3% at the LHC) [VanNeerven et al.( 91)],[Brein,Harlander,Djouadi( )] vh@nnlo For ZH, gg HZ top-loop g 2 λ 2 tα 2 S (non DY-like) corr. (+5% at the LHC) [Kniehl( 9)],[Brein,Harlander,Djouadi ( )] vh@nnlo, [Englert,McCullough,Spannowsky( 14)]. N 3 LO, gg HZ top-loop corrections (in the large-m top limit) also large: correction factor K 2 [Altenkamp,Dittmaier,Harlander,Rzehak,Zirke( 13)]. NNLO top-mediated contributions g 3 λ tα 2 S to VH ( 1-2% at the LHC) recently computed: [Brein,Harlander,Wiesemann,Zirke( 11)]. NLO EW corrections ( 5-1%) [Ciccolini,Dittmaier,Krämer( 3)] [Denner,Dittmaier,Kallweit,Mück( 11)] The inclusive H b b decay rate is known up to α 4 S in QCD (.1%) [Baikov,Chetyrkin,Kuhn( 5)], and up to NLO in the EW theory ( 1-2%) [Dabelstein, Hollik; Kniehl ( 92)]. VH production at the LHC: recent theory progress 5/12 V

11 pp VH lνb b: differential distributions Fraction of events E max in 2 jet rate with y cut =.1 LO NLO NNLO E max /m H Energy spectrum of the leading jet in the H b b decay. Jet clustering: JADE alg. y cut =.1. NNLO fully-differential decay rate H b b through non-linear mapping method: [Anastasiou,Herzog,Lazopoulos( 12)]. HV + /1 jet at NLO with the POWHEG BOX interfaced to GoSam and merged within Multiscale Improved NLO (MiNLO) method [Luisoni,Oleari,Nason,Tramontano( 13)]. N 3 LO gg HZ top-loop corrections in the boosted region [Altenkamp,Dittmaier,Harlander, Rzehak,Zirke( 13)]. Resummation of jet-veto and p T logarithms performed [Y.Li,Liu( 14)][Shao,C.S.Li,H.T.Li ( 13)],[Dawson,Han,Lai,Leibovich,Lewis( 12)] Fully differential NLO EW corrections for VH [Denner,Dittmaier,Kallweit,Mück( 11)] HAWK, including leptonic V decay and photon induced processes. VH production at the LHC: recent theory progress 6/12

12 pp VH lνb b: differential distributions T [pb/gev] dσ/dp j 2 ratio T [pb/gev] dσ/dp j 2 ratio HWJ+Pythia NLO p j 2 T [GeV] HWJ+Pythia NLO p j 2 T [GeV] HWJ-MiNLO+PYTHIA and the NLO HWJ result for the p T of the 2nd hardest jet, at the LHC at 8 TeV. NNLO fully-differential decay rate H b b through non-linear mapping method: [Anastasiou,Herzog,Lazopoulos( 12)]. HV + /1 jet at NLO with the POWHEG BOX interfaced to GoSam and merged within Multiscale Improved NLO (MiNLO) method [Luisoni,Oleari,Nason,Tramontano( 13)]. N 3 LO gg HZ top-loop corrections in the boosted region [Altenkamp,Dittmaier,Harlander, Rzehak,Zirke( 13)]. Resummation of jet-veto and p T logarithms performed [Y.Li,Liu( 14)][Shao,C.S.Li,H.T.Li ( 13)],[Dawson,Han,Lai,Leibovich,Lewis( 12)] Fully differential NLO EW corrections for VH [Denner,Dittmaier,Kallweit,Mück( 11)] HAWK, including leptonic V decay and photon induced processes. VH production at the LHC: recent theory progress 6/12

13 pp VH lνb b: differential distributions NLO hadronic cross section (upper), and NLO K-factor (lower) for s = 8TeV (dashed) and s = 14TeV (solid) in the inclusive (left) and boosted (right) case. NNLO fully-differential decay rate H b b through non-linear mapping method: [Anastasiou,Herzog,Lazopoulos( 12)]. HV + /1 jet at NLO with the POWHEG BOX interfaced to GoSam and merged within Multiscale Improved NLO (MiNLO) method [Luisoni,Oleari,Nason,Tramontano( 13)]. N 3 LO gg HZ top-loop corrections in the boosted region [Altenkamp,Dittmaier,Harlander, Rzehak,Zirke( 13)]. Resummation of jet-veto and p T logarithms performed [Y.Li,Liu( 14)][Shao,C.S.Li,H.T.Li ( 13)],[Dawson,Han,Lai,Leibovich,Lewis( 12)] Fully differential NLO EW corrections for VH [Denner,Dittmaier,Kallweit,Mück( 11)] HAWK, including leptonic V decay and photon induced processes. VH production at the LHC: recent theory progress 6/12

14 pp VH lνb b: differential distributions Σ p W T p W T,min pb pp W H NNLO NNLL'p NNLO p W T,min GeV NNLO cross sections with (red solid) and without (blue dotted) the NNLL jet-veto resummation for W + H production at LHC14. The error bars reflect the scale uncertainties (anti-k T, R = 1.2, p T,veto = 25GeV). [Y.Li,Liu( 14)]. NNLO fully-differential decay rate H b b through non-linear mapping method: [Anastasiou,Herzog,Lazopoulos( 12)]. HV + /1 jet at NLO with the POWHEG BOX interfaced to GoSam and merged within Multiscale Improved NLO (MiNLO) method [Luisoni,Oleari,Nason,Tramontano( 13)]. N 3 LO gg HZ top-loop corrections in the boosted region [Altenkamp,Dittmaier,Harlander, Rzehak,Zirke( 13)]. Resummation of jet-veto and p T logarithms performed [Y.Li,Liu( 14)][Shao,C.S.Li,H.T.Li ( 13)],[Dawson,Han,Lai,Leibovich,Lewis( 12)] Fully differential NLO EW corrections for VH [Denner,Dittmaier,Kallweit,Mück( 11)] HAWK, including leptonic V decay and photon induced processes. VH production at the LHC: recent theory progress 6/12

15 pp VH lνb b: differential distributions dσ/dpt,h[fb/gev] δew[%] pt,h[gev] pt,h[gev] Hl + ν Hl ν 28 δhl rec + ν δhl bare + δhl rec ν ν δ bare Hl ν 28 p T,H spectra for WH (NNLO QCD + NLO EW) at s = 7TeV in the boosted region (from Yellow Rep. II). LHC Higgs XS WG LHC Higgs XS WG NNLO fully-differential decay rate H b b through non-linear mapping method: [Anastasiou,Herzog,Lazopoulos( 12)]. HV + /1 jet at NLO with the POWHEG BOX interfaced to GoSam and merged within Multiscale Improved NLO (MiNLO) method [Luisoni,Oleari,Nason,Tramontano( 13)]. N 3 LO gg HZ top-loop corrections in the boosted region [Altenkamp,Dittmaier,Harlander, Rzehak,Zirke( 13)]. Resummation of jet-veto and p T logarithms performed [Y.Li,Liu( 14)][Shao,C.S.Li,H.T.Li ( 13)],[Dawson,Han,Lai,Leibovich,Lewis( 12)] Fully differential NLO EW corrections for VH [Denner,Dittmaier,Kallweit,Mück( 11)] HAWK, including leptonic V decay and photon induced processes. VH production at the LHC: recent theory progress 6/12

16 VH production and decay in higher-order QCD G.F.,Grazzini,Tramontano arxiv: , arxiv: Fully differential NNLO QCD calculation for VH (both DY like and gg HZ top-loop corrections), including NLO H b b and V l 1l 2 decays with spin correlations. NNLO calculation for h 1h 2 VH +X production within q T -subtraction formalism [Catani, Grazzini( 7)] requires: Up to dσ VH+jets NLO. H VH(1) and H VH(2) [Catani,Cieri,de Florian,G.F.,Grazzini( 9, 12)]: contains the finite-part of the one- and two-loops amplitude c c VH. Up to dσnlo: CT depends by the (universal) q T -resummation coeff. A 1, B 1, A 2 and B 2. H b b decay at NLO calculated with dipole subtraction. Fully inclusive QCD effects in the H decay taken into account by normalizing the Hb b branching fraction to the precise result from the LHCHXSWG-YR. Fully exclusive calculation at NNLO for production and NLO for H b b decay, implemented in a parton-level Monte Carlo code. VH production at the LHC: recent theory progress 7/12

17 VH production and decay in higher-order QCD G.F.,Grazzini,Tramontano arxiv: , arxiv: Fully differential NNLO QCD calculation for VH (both DY like and gg HZ top-loop corrections), including NLO H b b and V l 1l 2 decays with spin correlations. NNLO calculation for h 1h 2 VH +X production within q T -subtraction formalism [Catani, Grazzini( 7)] requires: Up to dσ VH+jets NLO. H VH(1) and H VH(2) [Catani,Cieri,de Florian,G.F.,Grazzini( 9, 12)]: contains the finite-part of the one- and two-loops amplitude c c VH. Up to dσnlo: CT depends by the (universal) q T -resummation coeff. A 1, B 1, A 2 and B 2. H b b decay at NLO calculated with dipole subtraction. Fully inclusive QCD effects in the H decay taken into account by normalizing the Hb b branching fraction to the precise result from the LHCHXSWG-YR. Fully exclusive calculation at NNLO for production and NLO for H b b decay, implemented in a parton-level Monte Carlo code. VH production at the LHC: recent theory progress 7/12

18 VH production and decay in higher-order QCD G.F.,Grazzini,Tramontano arxiv: , arxiv: Fully differential NNLO QCD calculation for VH (both DY like and gg HZ top-loop corrections), including NLO H b b and V l 1l 2 decays with spin correlations. NNLO calculation for h 1h 2 VH +X production within q T -subtraction formalism [Catani, Grazzini( 7)] requires: Up to dσ VH+jets NLO. H VH(1) and H VH(2) [Catani,Cieri,de Florian,G.F.,Grazzini( 9, 12)]: contains the finite-part of the one- and two-loops amplitude c c VH. Up to dσnlo: CT depends by the (universal) q T -resummation coeff. A 1, B 1, A 2 and B 2. H b b decay at NLO calculated with dipole subtraction. Fully inclusive QCD effects in the H decay taken into account by normalizing the Hb b branching fraction to the precise result from the LHCHXSWG-YR. Fully exclusive calculation at NNLO for production and NLO for H b b decay, implemented in a parton-level Monte Carlo code. VH production at the LHC: recent theory progress 7/12

19 Associated WH production LHC8 with CUTS Left panel: p T spectrum of the b-jets pair. Right panel: Spectra normalized to the full NLO results (perturbative scale - µ R,µ F,µ Rdec uncertainty bands are shown). VH production at the LHC: recent theory progress 8/12

20 Associated WH production LHC8: Invariant mass distribution of the b-jets pair. Left panel: without jet veto. Right panel: with jet veto. VH production at the LHC: recent theory progress 9/12

21 Associated WH production LHC14 fat-jet analysis. Left panel: p T spectrum of the fat jet. Right panel: Spectra normalized to the full NLO results (Perturbative scale - µ R,µ F,µ Rdec uncertainty bands are shown). MC@NLO result (green dots) with fixed scale is also shown. VH production at the LHC: recent theory progress 1/12

22 Associated ZH production Left panel: LHC8 analysis p T spectrum of the b-jets pair. Right panel: LHC14 fat-jet analysis p T spectrum of the fat jet. Lower panels: spectra normalized to the full NLO results (perturbative scale - µ R,µ F uncertainty bands are shown). VH production at the LHC: recent theory progress 11/12

23 Conclusions Associated vector boson Higgs (VH) production important channel at the LHC (access to Hb b coupling) but challenging. LHC experiments are close to the SM sensitivity. To improve these results, precise theoretical predictions are already available (and more are needed). Calculation of NNLO QCD corrections to VH production with NLO QCD H bb decay in hadron collision using the q T -subtraction formalism, included in a fully-exclusive parton-level Monte Carlo code. Compared perturbative results with NLO parton-shower Monte Carlo predictions. Studied the NNLO(+nlo) uncertainty band: first reliable estimate of perturbative uncertainty. Perturbative corrections are important and strongly depend on the experimental selection cuts. VH production at the LHC: recent theory progress 12/12

24 Back up slides VH production at the LHC: recent theory progress 13/12

25 Associated WH production LHC8 with CUTS + VETO (on light jets) Left panel: p T spectrum of the b-jets pair. Right panel: Spectra normalized to the full NLO results (Perturbative scale - µ R,µ F,µ Rdec uncertainty bands are shown). VH production at the LHC: recent theory progress 14/12

26 Associated WH production LHC14 fat-jet analysis. Invariant mass distribution of the fat jet computed at fixed-order QCD and at without hadronization (black dots) and with default (magenta dots). VH production at the LHC: recent theory progress 15/12

27 LHC8 with NO CUTS (except the b-jet selection). Left panel: p T spectrum of the b-jets pair. Right panel: Spectra normalized to the full NLO results (Perturbative scale - µ R,µ F,µ Rdec uncertainty bands are shown). VH production at the LHC: recent theory progress 16/12

28 dσ/dp T,H [fb/gev] Hl + ν Hl ν LHC Higgs XS WG 211 dσ/dp T,H [fb/gev] Hl + l Hν ν LHC Higgs XS WG p T,H [GeV] p T,H [GeV] 28 3 Yellow Report II:arXiv: Distributions in p T,H for pp WH lνh (NNLO QCD + NLO EW) and for pp ZH ll/ννh (NLO QCD + NLO EW) at s = 7TeV. Boosted setup: η l < 2.5, p T,l > 2 GeV, p T,ν > 25 GeV, p T,H > 2 GeV, p T,W/Z > 19 GeV. We produced similar results at s = 8TeV. VH production at the LHC: recent theory progress 17/12

29 pp WH( lνb b) p T spectra of the fat jet at the LHC@14TeV for m H = 12GeV at LO (dots), NLO (dashes) and NNLO (solid). Selection strategy of [Butterworth et al.( 8)]: search a large-p T Higgs boson thorough a collimated b b pair decay. Cuts: Leptons: pt l > 3GeV, ηl < 2.5, pt miss > 3GeV, pt W > 2GeV. Jets: Cambridge/Aachen algorithm with R=1.2. Fat jet (contain the b b) pt J > 2GeV, η J < 2.5 Jet veto: No other jets with p T > 2GeV and η < 5. Large negative higher-order corrections: NLO (NNLO) effects -52%/-36% (-6%/-19%), depending on the scale choice (factor two around µ F = µ R = m W +m H ). Jet veto strongly affect the higher order corrections stability of fixed order calculation challenged. VH production at the LHC: recent theory progress 18/12