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NNLO Matching and Parton Shower Developments

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NNLO Matching and Parton Shower Developments NNLO matching and parton shower developments Stefan Prestel Radcor/Loopfest 2015 UCLA, June 19, 2015 (in collaboration with Stefan Höche and Ye Li) 1 / 38 Outline • Motivation / introduction: • A pessimist’s view on NLO matching, LO merging, NLO merging and NNLO matching (e.g. everything that I usually turn to) • New parton showers for PYTHIA and SHERPA • Summary 2 / 38 Event generators should describe multijet observables 106 W(→ lν) + jets 1.4 BLACKHAT+SHERPA ) [pb] ATLAS Data, 1.2 jets anti-kt jets, R=0.4, -1 j j s = 7 TeV, 4.6 fb 1 5 p > 30 GeV, |y | < 4.4 10 T BLACKHAT+SHERPA (W+N 0.8 Pred. / Data σ HEJ ATLAS 0.6 ALPGEN ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 104 SHERPA 1.4 HEJ Njets MEPS@NLO 1.2 103 1 0.8 Pred. / Data 0.6 2 10 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 1.4 ALPGEN Njets 1.2 . 10 1 0.8 Pred. / Data 1 0.6 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 1.4 SHERPA Njets 10-1 1.2 1 0.8 Pred. / Data -2 MEPS@NLO 10 0.6 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 Njets Njets (Figures taken from EPJC 75 (2015) 2 82 and CMS summary of https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsCombined) 3 / 38 Event generators should describe multijet observables 106 W(→ lν) + jets 1.4 BLACKHAT+SHERPA ) [pb] ATLAS Data, 1.2 jets anti-kt jets, R=0.4, -1 j j s =Mar 7 TeV, 2015 4.6 fb 1 5 p > 30 GeV, |y | < 4.4 CMS Preliminary 10 T BLACKHAT+SHERPA (W+N 0.8 Pred. / Data -1 σ HEJ ATLAS ≤ 0.6 7 TeV CMS measurement (L 5.0 fb ) -1 ALPGEN ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 ≤ [pb] 5 8 TeV CMS measurement (L 19.6 fb ) 104 10 σ SHERPA 1.4 HEJ 7 TeV Theory prediction Njets MEPS@NLO 1.2 8 TeV Theory prediction 3 4 1 10 10 CMS 95%CL limit 0.8 Pred. / Data 0.6 2 10 3 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 10 1.4 ALPGEN Njets 1.2 . 10 102 1 0.8 Pred. / Data 1 0.6 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 10 1.4 SHERPA Njets 10-1 1.2 1 1 Production Cross Section, 0.8 Pred. / Data -2 MEPS@NLO 10 0.6 -1 ≥0 ≥1 ≥2 ≥3 10≥4 ≥5 ≥6 ≥7 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 Njets Njets γγ→ W ≥1j ≥2j ≥3j ≥4j Z ≥1j ≥2j ≥3j ≥4j Wγ Zγ WW WZ ZZ EW WVγ tt 1j 2j 3j t tW t ttγ ttZ ggH VBF VH ttH WW qqll t-ch s-ch qqH ∆σ ∆σ All results at: http://cern.ch/go/pNj7 Th. H in exp. (Figures taken from EPJC 75 (2015) 2 82 and CMS summary of https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsCombined) 3 / 38 Event generators should describe multijet observables 106 W(→ lν) + jets 1.4 BLACKHAT+SHERPA ) [pb] ATLAS Data, 1.2 jets anti-kt jets, R=0.4, -1 j j s =Mar 7 TeV, 2015 4.6 fb 1 5 p > 30 GeV, |y | < 4.4 CMS Preliminary 10 T BLACKHAT+SHERPA (W+N 0.8 Pred. / Data -1 σ HEJ ATLAS ≤ 0.6 7 TeV CMS measurement (L 5.0 fb ) -1 ALPGEN ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 ≤ [pb] 5 8 TeV CMS measurement (L 19.6 fb ) 104 10 σ SHERPA 1.4 HEJ 7 TeV Theory prediction Njets MEPS@NLO 1.2 8 TeV Theory prediction 3 4 1 10 10 CMS 95%CL limit 0.8 Pred. / Data 0.6 2 Combine10 multiple3 accurate fixed-order≥0 ≥1 calculations≥2 ≥3 ≥4 ≥5 with≥6 ≥7 each 10 1.4 ALPGEN Njets 1.2 . other,10 and with shower resummation, into a single flexible 102 1 0.8 prediction. =⇒ Matching /Pred. / Data merging 1 0.6 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 10 1.4 SHERPA Njets 10-1 1.2 1 1 Production Cross Section, 0.8 Pred. / Data -2 MEPS@NLO 10 0.6 -1 ≥0 ≥1 ≥2 ≥3 10≥4 ≥5 ≥6 ≥7 ≥0 ≥1 ≥2 ≥3 ≥4 ≥5 ≥6 ≥7 Njets Njets γγ→ W ≥1j ≥2j ≥3j ≥4j Z ≥1j ≥2j ≥3j ≥4j Wγ Zγ WW WZ ZZ EW WVγ tt 1j 2j 3j t tW t ttγ ttZ ggH VBF VH ttH WW qqll t-ch s-ch qqH ∆σ ∆σ All results at: http://cern.ch/go/pNj7 Th. H in exp. (Figures taken from EPJC 75 (2015) 2 82 and CMS summary of https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsCombined) 3 / 38 . ⋄ in the real-emission dominated region, since (smearing of NLO ”seed” cross section into) real emission treated differently; ⇒ Merging with further accurate multi-jet calculations helps. ⋄ in the resummation region, since exponentiation different. ⇒ Compare to inclusive resummation, improve shower accuracy. NLO+PS matched predictions NLO+PS methods mostly behave well, but may sometimes show large differences 4 / 38 . ⋄ in the resummation region, since exponentiation different. ⇒ Compare to inclusive resummation, improve shower accuracy. NLO+PS matched predictions . NLO+PS methods mostly behave well, but may sometimes show large differences ⋄ in the real-emission dominated region, since (smearing of NLO ”seed” cross section into) real emission treated differently; ⇒ Merging with further accurate multi-jet calculations helps. 4 / 38 NLO+PS matched predictions . NLO+PS methods mostly behave well, but may sometimes show large differences ⋄ in the real-emission dominated region, since (smearing of NLO ”seed” cross section into) real emission treated differently; ⇒ Merging with further accurate multi-jet calculations helps. ⋄ in the resummation region, since exponentiation different. ⇒ Compare to inclusive resummation, improve shower accuracy. 4 / 38 Leading-order merging Start with seed cross sections and no-emission probabilities ∫t0 BnFn(Φn) , ∆(t0, t) = exp − dΦradαs(ΦR)P(ΦR) t ∫tn u − ∆ (tn, tMS) = 1 Bn+1Fn+1(Φn+1)∆(tn, t) (”unitarised Sudakov”) tMS . − ∼ where Fm(Φm) = Θ(t(Φm) tMS), t0 Q. Two multiplicities merged by u O Bn∆ (t0, tMS)∆(tMS, tcut) 0(S+0) ∫t0 [ ] − u O + dΦR Bnαs(ΦR)P(ΦR)(1 Fn+1)∆ (t0, tMS)∆(tMS, tcut) + Bn+1Fn+1∆(t0, t1)∆(t1, t2) 1(S+1) ∫t0 + dΦRR Bn+1Fn+1∆(t0, t1)∆(t1, t2)αs(ΦR)P(ΦR)O2(S+2) + further emissions in (t2, tcut] 5 / 38 Leading-order merging Start with seed cross sections and no-emission probabilities ∫t0 BnFn(Φn) , ∆(t0, t) = exp − dΦradαs(ΦR)P(ΦR) t ∫tn u − ∆ (tn, tMS) = 1 Bn+1Fn+1(Φn+1)∆(tn, t) (”unitarised Sudakov”) tMS − ∼ . where Fm(Φm) = Θ(t(Φm) tMS), t0 Q. Three multiplicities merged by u O Bn∆ (t0, tMS)∆(tMS, tcut) 0(S+0) ∫t0 [ ] − u O + dΦR Bnαs(ΦR)P(ΦR)(1 Fn+1)∆ (t0, tMS)∆(tMS, tcut) + Bn+1Fn+1∆(t0, t1)∆(t1, t2) 1(S+1) ∫t0 [ − u + dΦRR Bn+1Fn+1∆(t0, t1)(1 Fn+2)∆ (t1, tMS)∆(tMS, tcut)αs(ΦR)P(ΦR) ] + Bn+2Fn+2∆(t0, t1)∆(t1, t2)∆(t2, t3) O2(S+2) + further emissions in (t3, tcut] 6 / 38 Leading-order merging Start with seed cross sections and no-emission probabilities ∫t0 BnFn(Φn) , ∆(t0, t) = exp − dΦradαs(ΦR)P(ΦR) t ∫tn ∆u( , ) = − B (Φ )∆( , ) Merging methods validtn fortMS any multiplicity.1 n+1Fn+1 n+1 tn t Merging methods use shower SudakovtMS factors ⇒ Improve when − ∼ . whereshowersFm(Φ improve.m) = Θ(t(Φm) tMS), t0 Q. Three multiplicities merged by u → NB: Usual CKKW approximation ∆ (tn, tMS) ∆(tn, tMS) calls for B ∆u( , )∆( , )O ( ) ≫n t0 tMS tMS tcut→0 S+0 O tMS tcut or BnP(Φ) Bn+1. We use tMS = (1GeV) later. ∫t0 [ ] − u O + dΦR Bnαs(ΦR)P(ΦR)(1 Fn+1)∆ (t0, tMS)∆(tMS, tcut) + Bn+1Fn+1∆(t0, t1)∆(t1, t2) 1(S+1) ∫t0 [ − u + dΦRR Bn+1Fn+1∆(t0, t1)(1 Fn+2)∆ (t1, tMS)∆(tMS, tcut)αs(ΦR)P(ΦR) ] + Bn+2Fn+2∆(t0, t1)∆(t1, t2)∆(t2, t3) O2(S+2) + further emissions in (t3, tcut] 6 / 38 NLO merging Any NLO matching method contains only approximate multi-jet kinematics (given by PS). Any LO merging method X only ever contains approximate virtual corrections. Use the full NLO results for any multi-jet state! NLO multi-jet merging from LO scheme X: ⋄ Subtract approximate X O(αs)-terms, add multiple NLO calculations. ⋄ Make sure fixed-order calculations do not overlap careful by cutting, vetoing events and/or vetoing emissions (e.g. remove real contribution to n-jet in favour of n + 1-jet NLO). ⋄ Adjust higher orders to suit other needs (e.g. to preserve the inclusive cross section). ⇒ X@NLO 7 / 38 . Still O(50%) differences in resummation region – important uncertainty for analyses that use jet binning! NLO-merged predictions for Higgs + jets Figure: p⊥,H and ∆ϕ12 for gg→H after merging (H+0)@NLO, (H+1)@NLO, (H+2)@NLO, (H+3)@LO, compared to other generators. ⇒ LH study: The generators come closer together if NLO merging is employed. 8 / 38 NLO-merged predictions for Higgs + jets . Still O(50%) differences in resummation region – important Figure: p⊥,H and ∆ϕ12 for gg→H after merging (H+0)@NLO, (H+1)@NLO, (H+2)@NLO,uncertainty (H+3)@LO, for analyses compared that touse other jet generators. binning! ⇒ LH study: The generators come closer together if NLO merging is employed.
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