NNLOPS predictions for Higgs boson production

Transcription

1 NNLOPS predictions for Higgs boson production Emanuele Re Rudolf Peierls Centre for Theoretical Physics, University of Oxford GGI Florence, 12 September 2014

2 Outline brief motivation method used results conclusion, discussion,...lunch! 1 / 17

3 NNLO Higgs production NLO not always enough: NNLO needed when 1. large NLO/LO K-factor [as in Higgs Physics] 2. very high precision needed [e.g. Drell-Yan] last couple of years: huge progress in NNLO [Anastasiou et al., 04-05] 2 / 17

4 NNLO Higgs production NLO not always enough: NNLO needed when 1. large NLO/LO K-factor [as in Higgs Physics] 2. very high precision needed [e.g. Drell-Yan] last couple of years: huge progress in NNLO Q: can we merge NNLO and PS? [Anastasiou et al., 04-05] Realistic event generation with state-of-the-art perturbative accuracy! could be important for precision studies in Higgs physics method presented here was used so far for - Higgs production [Hamilton,Nason,ER,Zanderighi, ] - neutral & charged Drell-Yan [Karlberg,ER,Zanderighi, ] 2 / 17

5 Summary of the talk Higgs at NNLO: # loops: # loops: 0 1 # loops: 0 3 / 17

6 Summary of the talk Higgs at NNLO: # loops: # loops: 0 1 # loops: 0 q T m h (a) 1 and 2 jets: POWHEG H+1j 3 / 17

7 Summary of the talk Higgs at NNLO: # loops: # loops: 0 1 # loops: 0 (q T, m h) q T (q T, q T) (q T, m h) m h (q T, q T ) (b) - integrate down to q T = 0 with MiNLO - Improved MiNLO allows to build a NLOPS generator (a) 1 and 2 jets: POWHEG H+1j 3 / 17

8 Summary of the talk Higgs at NNLO: # loops: # loops: 0 1 # loops: 0 (q T, m h) q T (q T, q T) (q T, m h) m h (q T, q T ) (c) 2 loops missing: from exact fixed-order NNLO W (y) = dσ(y)nnlo dσ(y) MiNLO (b) - integrate down to q T = 0 with MiNLO - Improved MiNLO allows to build a NLOPS generator (a) 1 and 2 jets: POWHEG H+1j 3 / 17

9 NNLO+PS what do we need and what do we already have? H (inclusive) H+j (inclusive) H+2j (inclusive) NLOPS NLO LO shower NLOPS / NLO LO NLOPS NLO NLO LO NNLOPS NNLO NLO LO 4 / 17

10 NNLO+PS what do we need and what do we already have? H (inclusive) H+j (inclusive) H+2j (inclusive) NLOPS NLO LO shower NLOPS / NLO LO NLOPS NLO NLO LO NNLOPS NNLO NLO LO a merged H-HJ generator is almost OK 4 / 17

11 NNLO+PS what do we need and what do we already have? H (inclusive) H+j (inclusive) H+2j (inclusive) NLOPS NLO LO shower NLOPS / NLO LO NLOPS NLO NLO LO NNLOPS NNLO NLO LO a merged H-HJ generator is almost OK many of the multijet NLO+PS merging approaches work by combining 2 (or more) NLO+PS generators, introducing a merging scale POWHEG + MiNLO: no need of merging scale: it extends the validity of an NLO computation with jets in the final state in regions where jets become unresolved 4 / 17

12 MiNLO Multiscale Improved NLO [Hamilton,Nason,Zanderighi, ] original goal: method to a-priori choose scales in multijet NLO computation non-trivial task: hierarchy among scales can spoil accuracy (large logs can appear, without being resummed) how: correct weights of different NLO terms with CKKW-inspired approach (without spoiling formal NLO accuracy) 5 / 17

13 MiNLO Multiscale Improved NLO [Hamilton,Nason,Zanderighi, ] original goal: method to a-priori choose scales in multijet NLO computation non-trivial task: hierarchy among scales can spoil accuracy (large logs can appear, without being resummed) how: correct weights of different NLO terms with CKKW-inspired approach (without spoiling formal NLO accuracy) - for each point sampled, build the more-likely shower history that would have produced that kinematics (can be done by clustering kinematics with k T -algo, then, by undoing the clustering, build skeleton ) - correct original NLO: α S evaluated at nodal scales and Sudakov FFs - has been used in V/H + up to 2 jets and in V H + up to 1 jet 5 / 17

14 MiNLO Multiscale Improved NLO [Hamilton,Nason,Zanderighi, ] original goal: method to a-priori choose scales in multijet NLO computation non-trivial task: hierarchy among scales can spoil accuracy (large logs can appear, without being resummed) how: correct weights of different NLO terms with CKKW-inspired approach (without spoiling formal NLO accuracy) [ ] B NLO = α 3 S(µ R ) B + α (NLO) S V (µ R ) + α (NLO) S dφ rr q T m h 5 / 17

15 MiNLO Multiscale Improved NLO [Hamilton,Nason,Zanderighi, ] original goal: method to a-priori choose scales in multijet NLO computation non-trivial task: hierarchy among scales can spoil accuracy (large logs can appear, without being resummed) how: correct weights of different NLO terms with CKKW-inspired approach (without spoiling formal NLO accuracy) [ ] B NLO = α 3 S(µ R ) B + α (NLO) S V (µ R ) + α (NLO) S dφ rr [ ( ) B MiNLO = α 2 S(m h )α S(q T ) 2 g(q T, m h ) B 1 2 (1) g (q T, m h ) +α (NLO) S V ( µ R )+α (NLO) S ] dφ rr (q T, m h ) m h (q T, m h ) q T (q T, q T ) (q T, q T ). µ R = (m 2 h q T ) 1/3 m 2 h dq 2 2 α S (q ) [. log f (q T, m h ) = q T 2 q 2 A f log m2 ] h 2π q 2 + B f. (1) f. µ F = q T (q T, m h ) = α(nlo) [ S 1 2π 2 A 1,f log 2 m2 h q T 2 + B 1,f log m2 ] h q T 2 5 / 17

16 MiNLO Multiscale Improved NLO [Hamilton,Nason,Zanderighi, ] original goal: method to a-priori choose scales in multijet NLO computation non-trivial task: hierarchy among scales can spoil accuracy (large logs can appear, without being resummed) how: correct weights of different NLO terms with CKKW-inspired approach (without spoiling formal NLO accuracy) [ ] B NLO = α 3 S(µ R ) B + α (NLO) S V (µ R ) + α (NLO) S dφ rr [ ( ) B MiNLO = α 2 S(m h )α S(q T ) 2 g(q T, m h ) B 1 2 (1) g (q T, m h ) +α (NLO) S V ( µ R )+α (NLO) S ] dφ rr (q T, m h ) m h (q T, m h ) q T (q T, q T ) (q T, q T ) Sudakov FF included on H+j Born kinematics with MiNLO, finite results from HJ also when 1st jet is unresolved (q T 0) BMiNLO ideal to extend validity of HJ-POWHEG [called HJ-MiNLO hereafter] 5 / 17

17 Improved MiNLO & NLOPS merging formal accuracy of HJ-MiNLO for inclusive observables carefully investigated [Hamilton et al., ] HJ-MiNLO describes inclusive observables at order α 2 S + α3 S to reach genuine NLO when fully inclusive (NLO (0) ), spurious terms must be of relative order α 2 S, i.e. OHJ MiNLO = OH@NLO + O(α 4 S) if O is inclusive Original MiNLO contains ambiguous O(α S ) terms 6 / 17

18 Improved MiNLO & NLOPS merging formal accuracy of HJ-MiNLO for inclusive observables carefully investigated [Hamilton et al., ] HJ-MiNLO describes inclusive observables at order α 2 S + α3 S to reach genuine NLO when fully inclusive (NLO (0) ), spurious terms must be of relative order α 2 S, i.e. OHJ MiNLO = OH@NLO + O(α 4 S) if O is inclusive Original MiNLO contains ambiguous O(α S ) terms 6 / 17

19 Improved MiNLO & NLOPS merging formal accuracy of HJ-MiNLO for inclusive observables carefully investigated [Hamilton et al., ] HJ-MiNLO describes inclusive observables at order α 2 S + α3 S to reach genuine NLO when fully inclusive (NLO (0) ), spurious terms must be of relative order α 2 S, i.e. OHJ MiNLO = OH@NLO + O(α 4 S) if O is inclusive Original MiNLO contains ambiguous O(α S ) terms Possible to improve HJ-MiNLO such that inclusive NLO is recovered (NLO (0) ), without spoiling NLO accuracy of H+j (NLO (1) ). 6 / 17

20 Improved MiNLO & NLOPS merging formal accuracy of HJ-MiNLO for inclusive observables carefully investigated [Hamilton et al., ] HJ-MiNLO describes inclusive observables at order α 2 S + α3 S to reach genuine NLO when fully inclusive (NLO (0) ), spurious terms must be of relative order α 2 S, i.e. OHJ MiNLO = OH@NLO + O(α 4 S) if O is inclusive Original MiNLO contains ambiguous O(α S ) terms - proof based on careful comparisons of MiNLO with general resummation formula 1 σ 0 q T 2 [α S, α 2 S, α3 S, α4 S, α SL, α 2 S L, α3 S L, α4 S L] exp S(q T, Q) + R f L = log(q 2 /q 2 T ) - need to include B 2 coefficient in MiNLO-Sudakovs:. highlighted terms are needed to reach NLO (0) : Q 2 dq 2 T q 2 T L m ( n α S (qt ) exp S α S (Q 2 ) n (m+1)/2 ). if I don t include B 2 in MiNLO g, I miss a term (1/q 2 T ) α2 S B 2 exp S. upon integration, violate NLO (0) by a term of relative O(α 3/2 S ) - need to evaluate α S (NLO) in HJ-MiNLO at scale qt, and µ F = q T (scaling in low-p T region is α S L 2 1!) 6 / 17

21 Improved MiNLO & NLOPS merging formal accuracy of HJ-MiNLO for inclusive observables carefully investigated [Hamilton et al., ] HJ-MiNLO describes inclusive observables at order α 2 S + α3 S to reach genuine NLO when fully inclusive (NLO (0) ), spurious terms must be of relative order α 2 S, i.e. OHJ MiNLO = OH@NLO + O(α 4 S) if O is inclusive Original MiNLO contains ambiguous O(α S ) terms Possible to improve HJ-MiNLO such that inclusive NLO is recovered (NLO (0) ), without spoiling NLO accuracy of H+j (NLO (1) ). Effectively as if we merged NLO (0) and NLO (1) samples, without merging different samples (no merging scale used: there is just one sample). 6 / 17

22 NLOPS dσ/dy H [pb] ratio H+Pythia HJ+Pythia y H dσ/dy H [pb] ratio HJ+Pythia H+Pythia y H H+Pythia : standalone POWHEG (gg H) + PYTHIA (PS level) [7pts band, µ = m H ] HJ+Pythia : HJ-MiNLO + PYTHIA (PS level) [7pts band, µ from MiNLO]! very good agreement (both value and band) Notice: band is 20 30% 7 / 17

23 Higgs at NNLO+PS I HJ-MiNLO+POWHEG generator gives NLOPS H (inclusive) H+j (inclusive) H+2j (inclusive)! NLOPS NLO NLO LO NNLOPS NNLO NLO LO 8 / 17

24 Higgs at NNLO+PS I HJ-MiNLO+POWHEG generator gives NLOPS H (inclusive) H+j (inclusive) H+2j (inclusive)! NLOPS NLO NLO LO NNLOPS NNLO NLO LO reweighting (differential on y H) of MiNLO-generated events: W (y H) = ( ( dσ dy H )NNLO dσ dy H )HJ MiNLO by construction NNLO accuracy on fully inclusive observables (σ tot, y H ) [!] to reach NNLOPS accuracy, need to be sure that the reweighting doesn t spoil the NLO accuracy of HJ-MiNLO in 1-jet region [ ] 8 / 17

25 Higgs at NNLO+PS I HJ-MiNLO+POWHEG generator gives NLOPS H (inclusive) H+j (inclusive) H+2j (inclusive)! NLOPS NLO NLO NNLOPS NNLO NLO LO reweighting (differential on y H) of MiNLO-generated events: W (y H) = ( ( dσ dy H )NNLO dσ dy H )HJ MiNLO = α2 Sc 0 + c 1α 3 S + c 2α 4 S c2 d2 1 + α 2 αsc c 1α 3 S + d 2α 4 S + O(αS) 3 S c 0 by construction NNLO accuracy on fully inclusive observables (σ tot, y H ) [!] to reach NNLOPS accuracy, need to be sure that the reweighting doesn t spoil the NLO accuracy of HJ-MiNLO in 1-jet region [!] 8 / 17

26 Higgs at NNLO+PS I HJ-MiNLO+POWHEG generator gives NLOPS H (inclusive) H+j (inclusive) H+2j (inclusive)! NLOPS NLO NLO NNLOPS NNLO NLO LO reweighting (differential on y H) of MiNLO-generated events: W (y H) = ( ( dσ dy H )NNLO dσ dy H )HJ MiNLO = α2 Sc 0 + c 1α 3 S + c 2α 4 S c2 d2 1 + α 2 αsc c 1α 3 S + d 2α 4 S + O(αS) 3 S c 0 by construction NNLO accuracy on fully inclusive observables (σ tot, y H ) [!] to reach NNLOPS accuracy, need to be sure that the reweighting doesn t spoil the NLO accuracy of HJ-MiNLO in 1-jet region [!] notice: formally works because no spurious O(α S ) terms in NLOPS 8 / 17

27 Higgs at NNLO+PS II Variants for reweighting (W (y H )) are also possible: dσ NNLO A δ(y y(φ)) W (y, p T ) = h(p T ) dσ MiNLO A δ(y y(φ)) + (1 h(p T )) (βm H ) 2 dσ A = dσ h(p T ), dσ B = dσ (1 h(p T )), h = (βm H ) 2 + p 2 T. h(p T ) controls where the NNLO/NLO K-factor is distributed (in the high-p T region, there is no improvement in including it). β cannot be too small, otherwise resummation spoiled: for Higgs, chosen β = 1/2 for Higgs (and for Drell-Yan) we used dσ NNLO δ(y y(φ)) dσb MiNLO δ(y y(φ)) W (y, p T ) = h(p T ) + (1 h(p dσ MiNLO T )) A δ(y y(φ)). one gets exactly (dσ/dy) NNLOPS = (dσ/dy) NNLO (no α 5 S terms). we used h(p j 1 T ) 9 / 17

28 Settings inputs for following plots: - results are for 8 TeV LHC - scale choices: NNLO input with µ = m H/2, HJ-MiNLO core scale m H (other powers are at q T ) - PDF: everywhere MSTW2008 NNLO - NNLO always from HNNLO - 6M events reweighted at the LH level - plots after k T-ordered PYTHIA 6 at the PS level (hadronization and MPI switched off) 10 / 17

29 NNLO+PS (fully incl.) NNLO with µ = m H /2, HJ-MiNLO core scale m H [NNLO from HNNLO, Catani,Grazzini] (7 Mi 3 NN ) pts scale var. in NNLOPS, 7pts in NNLO dσ/dy [pb] NNLOPS dσ/dy [pb] HNNLO Ratio HNNLO y Ratio NNLOPS y Notice: band is 10% (at NLO would be 20-30%) [Until and including O(α 4 S ), PS effects don t affect y H (first 2 emissions controlled properly at O(α 4 S ) by MiNLO+POWHEG)] 11 / 17

30 NNLO+PS: multi-dim reweighting for Higgs: 1-dim NNLOPS reweighting (W (y; p T )), so y H will be obviously OK does it work if Φ B is multi-dim (as in Drell-Yan)? dσ/dp T,l [pb/gev] DYNNLO Wj-MiNLO NNLOPS LHC 7 TeV p T,l [GeV] p T,l is not the observable we are using to do the NNLO reweighting! we see exactly what we expect: p T,l has NNLO uncertainty if p T,l < M W /2, and NLO if p T,l > M W /2 [ just above peak, DYNNLO uses M W, WJ-MiNLO uses p T,W and here 0 p T,W M W ] 12 / 17

31 NNLO+PS (p H T ) dσ/dp H [pb/gev] T Ratio β = (W indep. of p T ) β = 1/ [GeV] p H T HQT NNLOPS dσ/dp H [pb/gev] T Ratio [GeV] p H T HQT NNLOPS HqT: NNLL+NNLO, µ R = µ F = m H /2 [7pts], Q res m H /2 [HqT, Bozzi et al.]! β = 1/2 & : uncertainty bands of HqT contain NNLOPS at low-/moderate p T β = 1/2: HqT tail harder than NNLOPS tail (µ HqT < µ MiNLO ) NNLO will allow to say more for large p T,H β = 1/2: very good agreement with HqT resummation [ expected, since Q res m H /2] 13 / 17

32 NNLO+PS (p H T ) dσ/dp H [pb/gev] T Ratio β = (W indep. of p T ) β = 1/ [GeV] p H T NNLOPS HQT dσ/dp H [pb/gev] T Ratio [GeV] p H T NNLOPS HQT HqT: NNLL+NNLO, µ R = µ F = m H /2 [7pts], Q res m H /2 β = 1/2: NNLOPS tail NLOPS tail [ W (y, p T m H ) 1 ] larger band (affected just marginally by NNLO, so it s genuine NLO band) 14 / 17

33 NNLO+PS (p j 1 T ) ε(p T,veto ) NNLOPS JETVHETO ε(p T,veto ) JETVHETO NNLOPS 0.4 Anti kt R = Anti kt R = 1.0 #/ε central p T,veto [GeV] #/ε central ε (p T,veto) = Σ(pT,veto) σ tot = 1 σ tot p T,veto [GeV] ) dσ θ (p T,veto p j 1T JetVHeto: NNLL resum, µ R = µ F = m H /2 [7pts], Q res m H /2, (a)-scheme only [JetVHeto, Banfi et al.] nice agreement, differences never more than 5-6 % Separation of H W W from t t bkg: x-sec binned in N jet 0-jet bin jet-veto accurate predictions needed! 15 / 17

34 other NNLOPS results this year UNNLOPS [Hoeche,Li,Prestel 14] [pb] - e dσ/dη s = 7 TeV 60 GeV<m <120 GeV ll UN 2 LOPS MC@NLO NNLO m ll /2< µ <2m R/F ll m ll /2< µ <2m Q ll Sherpa+BlackHat Ratio to NNLO η - e formalism worked out also within the Geneva framework: [Alioli,Bauer, et al, 13] - work in progress, preliminary results for DY shown at PSR / 17

35 conclusions MiNLO-improved POWHEG generator allows to reach NNLOPS accuracy for simple processes shown results for Higgs at NNLOPS predictions and theoretical uncertainties match NNLO where they have to typically, quite good agreement with analytic resummation (but for Drell-Yan slightly worse...) - good news, but not yet really studied/understood formally other approaches appeared: will be interesting to compare mass effects in NNLOPS... phenomenology / 17

36 conclusions MiNLO-improved POWHEG generator allows to reach NNLOPS accuracy for simple processes shown results for Higgs at NNLOPS predictions and theoretical uncertainties match NNLO where they have to typically, quite good agreement with analytic resummation (but for Drell-Yan slightly worse...) - good news, but not yet really studied/understood formally other approaches appeared: will be interesting to compare mass effects in NNLOPS... phenomenology... Thank you for your attention! 17 / 17