NLO+PS matching and multijet merging - Institute for Particle ...

MC@NLO NLO-merging ConclusionsNLO+PS matching and multijet mergingMarek SchönherrInstitute for Particle Physics PhenomenologyCambridge, 18/10/2012arXiv:1111.1220, arXiv:1201.5882arXiv:1207.5030, arXiv:1207.5031arXiv:1208.2815Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 1

MC@NLO NLO-merging ConclusionsIntroduction• Monte-Carlo event generators heavily used tools for fully exclusiveSM/BSM predictions on hadron level→ directly comparable to experimental data• standard LO+PS calculations have limited accuracy in regions probed bycurrent colliders→ multiple hard objects in final state• standard NLO calculations have limited accuracy in strongly hierarchicalconfigurations⇒ Tevatron and LHC allow for both at the same time• a number of solutions to combine the observable independent resummationof PS with fixed-order accuracy in hard multiparton final states exist⇒ imperative to know about implicit choices/assumptions and how toassess uncertainties for phenomenological studiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 2

MC@NLO NLO-merging ConclusionsMotivationPSLOLOLOLO pp → 2 with parton showers+ exponentiation of large IR logarithms− poor hard/wide angle emission patternvs.LO pp → n matrix elements+ dominant terms for hard/wide angle rad.− breakdown of α s-expansion in log. region• MEPS schemes: CKKW-type, MLM-typeLO+(N)LL accuracy in every jet multiplicity• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 3

MC@NLO NLO-merging ConclusionsMotivationMELO LO LO LOLO pp → 2 with parton showers+ exponentiation of large IR logarithms− poor hard/wide angle emission patternvs.LO pp → n matrix elements+ dominant terms for hard/wide angle rad.− breakdown of α s-expansion in log. region• MEPS schemes: CKKW-type, MLM-typeLO+(N)LL accuracy in every jet multiplicity• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 3

MC@NLO NLO-merging ConclusionsMotivationMEPSLOLOLOLOLOLOLOLO pp → 2 with parton showers+ exponentiation of large IR logarithms− poor hard/wide angle emission patternvs.LO pp → n matrix elements+ dominant terms for hard/wide angle rad.− breakdown of α s-expansion in log. region• MEPS schemes: CKKW-type, MLM-typeLO+(N)LL accuracy in every jet multiplicity• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 3

MC@NLO NLO-merging ConclusionsMotivationMEPSLOLOLOLOLOLOLOα k+ns (µ eff ) = α k s(µ) α s (t 1 ) · · · α s (t n )LO pp → 2 with parton showers+ exponentiation of large IR logarithms− poor hard/wide angle emission patternvs.LO pp → n matrix elements+ dominant terms for hard/wide angle rad.− breakdown of α s-expansion in log. region• MEPS schemes: CKKW-type, MLM-typeLO+(N)LL accuracy in every jet multiplicity• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 3

MC@NLO NLO-merging ConclusionsMotivationPSNLONLONLO• promote LOPS to NLOPS (POWHEG, MC@NLO)→ can assess uncertainties (part I)• combine NLOPS for successive multiplicities into incl. sample (MEPS@NLO),preserve NLO+(N)LL accuracy in every jet multiplicityrestore resummation wrt. to inclusive sample (part II)• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 4

MC@NLO NLO-merging ConclusionsMotivationMEPSNLONLONLONLONLONLONLO• promote LOPS to NLOPS (POWHEG, MC@NLO)→ can assess uncertainties (part I)• combine NLOPS for successive multiplicities into incl. sample (MEPS@NLO),preserve NLO+(N)LL accuracy in every jet multiplicityrestore resummation wrt. to inclusive sample (part II)• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 4

MC@NLO NLO-merging ConclusionsMotivationMEPSNLONLONLONLONLONLONLO• promote LOPS to NLOPS (POWHEG, MC@NLO)→ can assess uncertainties (part I)α k+ns (µ eff ) = α k s(µ) α s (t 1 ) · · · α s (t n )• combine NLOPS for successive multiplicities into incl. sample (MEPS@NLO),preserve NLO+(N)LL accuracy in every jet multiplicityrestore resummation wrt. to inclusive sample (part II)• scale setting scheme integral to preserve PS-resummation propertiesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 4

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••••MC@NLO NLO-merging ConclusionsShort-comings of fixed-order QCD• poor description in phase spaceregions with strongly hierarchicalscales• poor perturbative jet-modeling(at most two constituents)• no hadronisation, MPI effects•10 510 410 310 22.42.221.81.61.41.210.8T )• very pronounced in inclusive &dijet production• jet-p ⊥ turn negative in forwardregion unless y-dependent scaleis used (e.g. H (y)σ [pb]MC/dataInclusive Jet Multiplicity (R=0.4)10 710 6Sherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa NLOµF = µR = 1 2 HT• • • • •2 3 4 5 6NjetBern et.al. arXiv:1112.3940Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 6

••••••••MC@NLO NLO-merging ConclusionsShort-comings of fixed-order QCD• poor description in phase spaceregions with strongly hierarchicalscales•10 310 210 1110 −1 21.81.61.41.210.8T )• poor perturbative jet-modeling(at most two constituents)• no hadronisation, MPI effects• very pronounced in inclusive &dijet production• jet-p ⊥ turn negative in forwardregion unless y-dependent scaleis used (e.g. H (y)dσ/dp ⊥ [pb/GeV]MC/data10 4 Transverse momentum of the leading jet (R=0.4)Sherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa NLOµF = µR = 1 2 HT• • • • • • • • •100 200 300 400 500 600 700 800p ⊥(leading jet) [GeV]Bern et.al. arXiv:1112.3940Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 6

•••••••••MC@NLO NLO-merging ConclusionsShort-comings of fixed-order QCD• poor description in phase spaceregions with strongly hierarchicalscales•10 310 210 1110 −110 −21.210.80.60.40.2T ) 0• poor perturbative jet-modeling(at most two constituents)• no hadronisation, MPI effects• very pronounced in inclusive &dijet production• jet-p ⊥ turn negative in forwardregion unless y-dependent scaleis used (e.g. H (y)dσ/dp ⊥ [pb/GeV]MC/data10 5 Transverse momentum of the 2nd leading jet (R=0.4)10 4Sherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa NLOµF = µR = 1 2 HT• • • • • • • • • •100 200 300 400 500 600 700 800p ⊥(2nd leading jet) [GeV]Bern et.al. arXiv:1112.3940Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 6

•••••••MC@NLO NLO-merging ConclusionsShort-comings of fixed-order QCD• poor description in phase spaceregions with strongly hierarchicalscales•10 210 1110 −110 −22.521.51T ) 0.5• poor perturbative jet-modeling(at most two constituents)• no hadronisation, MPI effects• very pronounced in inclusive &dijet production• jet-p ⊥ turn negative in forwardregion unless y-dependent scaleis used (e.g. H (y)dσ/dp ⊥ [pb/GeV]MC/data10 3 Transverse momentum of the 3rd leading jet (R=0.4)Sherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa NLOµF = µR = 1 2 HT• • • • • • • •100 150 200 250 300 350 400 450 500p ⊥(3rd leading jet) [GeV]Bern et.al. arXiv:1112.3940Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 6

MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionDescribe wealth of experimental data with a single sample (LHC@7TeV)MC@NLO di-jet production:Höche, MS arXiv:1208.2815• µ R/F = 1 4 H T , µ Q = 1 2 p ⊥• CT10 PDF (α s (m Z ) = 0.118)• hadron level calculationfully hadronised including MPI• virtual MEs from BLACKHATGiele, Glover, KosowerNucl.Phys.B403(1993)633-670Bern et.al. arXiv:1112.3940• p j1⊥> 20 GeV, pj2⊥> 10 GeVUncertainty estimates:µ QvariationMPIvariationµ F , µ Rvariation• µ R/F ∈ [ 1 2, 2] µdefR/F• µ Q ∈ [ 1 √2, √ 2] µ defQ• MPI activity in tr. region ± 10%Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 7

•••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionDescribe wealth of experimental data with a single sample (LHC@7TeV)MC@NLO di-jet production:Höche, MS arXiv:1208.2815• µ R/F = 1 4 H T , µ Q = 1 2 p ⊥• CT10 PDF (α s (m Z ) = 0.118)• hadron level calculationfully hadronised including MPI• virtual MEs from BLACKHATGiele, Glover, KosowerNucl.Phys.B403(1993)633-670Bern et.al. arXiv:1112.3940• p j1⊥> 20 GeV, pj2⊥> 10 GeVUncertainty estimates:• µ R/F ∈ [ 1 2, 2] µdefR/F• µ Q ∈ [ 1 √2, √ 2] µ defQ• MPI activity in tr. region ± 10%σ [pb]MC/data10 6 Inclusive jet multiplicity (anti-kt R=0.4)10 510 410 310 21.510.5µR, µF variationµ Q variationMPI variationSherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥• • • • •2 3 4 5 6NjetMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 7

•••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productiondσ/dp ⊥ [pb/GeV]10 4 Jet transverse momenta (anti-kt R=0.4)10 310 210 110 −1 110 −210 −310 −410 −54th jet×10 −3Sherpa+BlackHat•ATLAS dataEur.Phys.J. C71 (2011) 1763Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥µR, µF variationµ Q variationMPI variation3rd jet×10 −21st jet2nd jet×10 −1100 200 300 400 500 600 700 800p ⊥ [GeV]MC/data MC/data MC/data MC/data1.41.21Höche, MS arXiv:1208.2815• • • • • • • • •0.81st jet0.61.41.21• • • • • • • • • •0.82nd jet0.61.510.51.510.5• • • • • • • •• • • •3rd jet4th jet100 200 300 400 500 600 700 800p ⊥ [GeV]Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 8

•••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionR32MC/data0.80.60.40.23 jets over 2 jets ratio (anti-kt R=0.5)1µF, µR variationµ Q variationMPI variationSherpa+BlackHat01.21.11.00.90.8• •• • • • •• •• •• ••CMS dataPhys. Lett. B 702 (2011) 336Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥• • • • • • • • • • • • • • • • • • • • • • • • • • • • • •0.2 0.5 1 2HT [TeV]3-jet-over-2-jet ratioHöche, MS arXiv:1208.2815• determined from incl. sample2-jet rate at NLO+NLL3-jet rate at LO+LL• common scale choices→ varied simultaneously• at large H T large MPIuncertainties→ better MPI physics needed(soft QCD)• similar description of relatedATLAS observablesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 9

••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productiondσ/dp ⊥ [pb/GeV]Inclusive jet transverse momenta in different rapidity ranges10 810 710 610 510 410 310 210 110 −1 110 −210 −310 −410 −510 −610 −710 −810 −910 −10Sherpa+BlackHat•ATLAS dataPhys. Rev. D86 (2012) 014022Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥Sherpa MC@NLOµR = µF = 4 1 H(y) T , µ Q = 1 2 p ⊥µR, µF variationµ Q variationMPI variation10 2 10 3p ⊥ [GeV]MC/data MC/data MC/data MC/data MC/data MC/data MC/data1.510.51.510.51.510.51.510.51.510.51.510.51.510.5Höche, MS arXiv:1208.2815• • • • • • • • • • • • • • • •|y| < 0.32 3• • • • • • • • • • • • • • • •0.3 < |y| < 0.82 3• • • • • • • • • • • • • • • •0.8 < |y| < 1.22 3• • • • • • • • • • • • • • •1.2 < |y| < 2.12 3• • • • • • • • • • • •2.1 < |y| < 2.82 3• • • • • • • • •• • • • • •2.8 < |y| < 3.62 33.6 < |y| < 4.410 2 10 3p ⊥ [GeV]Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 10

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionHöche, MS arXiv:1208.281510 19 Dijet invariant mass spectra in different rapidity ranges m12 [TeV]dσ/dm12 [pb/TeV]10 1810 1710 1610 1510 1410 1310 1210 1110 1010 910 810 710 610 510 410 310 210 1110 −1•ATLAS dataPhys. Rev. D86 (2012) 014022Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥Sherpa MC@NLOµR = µF = 4 1 H(y) T , µ Q = 2 1 p ⊥µR, µF variationµ Q variationMPI variationSherpa+BlackHat10 −1 1MC/data MC/data MC/data MC/data MC/data MC/data MC/data MC/data MC/data1.510.51.510.51.510.51.510.51.510.51.510.51.510.51.510.51.510.54.0 < y ∗ < 4.413.5 < y ∗ < 4.013.0 < y ∗ < 3.512.5 < y ∗ < 3.012.0 < y ∗ < 2.511.5 < y ∗ < 2.011.0 < y ∗ < 1.51• •• • • • • • • • •• • • • • • • • • • • •• • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • •0.5 < y ∗ < 1.01• • • • • • • • • • • • • • • • • • • •y ∗ < 0.510 −1 1m 12 [GeV]Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 11

MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionTry different scale• µ R/F = 1 4 H(y) TwithH (y)T= ∑ i∈jets p ⊥,i e 0.3|y boost−y i|with y boost = 1/n jets∑i∈jets y i• reduces to µ R/F = 1 2 p ⊥ e 0.3y∗with y ∗ = 1 2 |y 1 − y 2 | for 2 → 2and captures real emissiondynamicsEllis, Kunszt, Soper PRD40(1989)2188• better description of data atlarge rapidities, as expecteddescription of most other observablesworsenedneed proper description of forwardphysics (e.g. (B)FKL)MC/dataMC/dataMC/dataMC/dataMC/dataMC/dataMC/dataMC/dataMC/data1.510.51.510.51.510.51.510.51.510.51.510.51.510.51.510.51.510.54.0 < y ∗ < 4.413.5 < y ∗ < 4.013.0 < y ∗ < 3.512.5 < y ∗ < 3.012.0 < y ∗ < 2.511.5 < y ∗ < 2.011.0 < y ∗ < 1.51Höche, MS arXiv:1208.2815• •• • • • • • • • •• • • • • • • • • • • •• • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • •0.5 < y ∗ < 1.01• • • • • • • • • • • • • • • • • • • •y ∗ < 0.510 −1 1m 12 [GeV]Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 11

MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionMarek SchönherrTry different scale• µ R/F = 1 4 H(y) TwithH (y)T= ∑ i∈jets p ⊥,i e 0.3|y boost−y i|with y boost = 1/n jets∑i∈jets y i• reduces to µ R/F = 1 2 p ⊥ e 0.3y∗with y ∗ = 1 2 |y 1 − y 2 | for 2 → 2and captures real emissiondynamicsEllis, Kunszt, Soper PRD40(1989)2188• better description of data atlarge rapidities, as expecteddescription of most other observablesworsenedneed proper description of forwardphysics (e.g. (B)FKL)MC/dataMC/dataMC/dataMC/data1.41.210.80.61.41.210.80.61.510.51.510.5Höche, MS arXiv:1208.2815• • • • • • • • •1st jet• • • • • • • • • •2nd jet• • • • • • • •• • • •3rd jet4th jet100 200 300 400 500 600 700 800p ⊥ [GeV]IPPP DurhamNLO+PS matching and multijet merging 11

•••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionGap FractionInclusive jet transverse momenta in different rapidity ranges10Leading dijetselection•ATLAS dataJHEP 09 (2011) 053Sherpa MC@NLOMC/data1.510.5Höche, MS arXiv:1208.2815• • • • • • • • • • •240 GeV < ¯p ⊥ < 270 GeV8µR = µF = 1 4 HT, µ Q = 1 2 p ⊥µF, µR variationµ Q variationMPI variationMC/data1.510.5• • • • • • • • • • •210 GeV < ¯p ⊥ < 240 GeV642Sherpa+BlackHat240 GeV < ¯p ⊥ < 270 GeV+6• • • • •210 GeV < ¯p ⊥ < 240 GeV+5• • • •180 GeV < ¯p ⊥ < 210 GeV+4150 GeV < ¯p ⊥ < 180 GeV+3• • •• •• • •• • • •• •• •120 GeV < ¯p ⊥ < 150 GeV+290 GeV < ¯p ⊥ < 120 GeV+170 GeV < ¯p ⊥ < 90 GeV• •00 1 2 3 4 5 6∆yMC/data MC/data MC/data MC/data MC/data1.51• • • • • • • • • • • •0.5 180 GeV < ¯p ⊥ < 210 GeV1.51• • • • • • • • • • • •0.5 150 GeV < ¯p ⊥ < 180 GeV1.510.51.51• • • • • • • • • • • •120 GeV < ¯p ⊥ < 150 GeV• • • • • • • • • • • •90 GeV < ¯p ⊥ < 120 GeV0.51.51• • • • • • • • • • • •70 GeV < ¯p ⊥ < 90 GeV0.50 1 2 3 4 5 6∆yMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 12

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productionGap FractionInclusive jet transverse momenta in different rapidity ranges10Forward-backwardselection•ATLAS dataJHEP 09 (2011) 053Sherpa MC@NLOMC/data1.510.5• • • • • • • • • •240 GeV < ¯p ⊥ < 270 GeVHöche, MS arXiv:1208.28158µR = µF = 1 4 HT, µ Q = 1 2 p ⊥µF, µR variationµ Q variationMPI variationMC/data1.510.5• • • • • • • • • • •210 GeV < ¯p ⊥ < 240 GeV642Sherpa+BlackHat240 GeV < ¯p ⊥ < 270 GeV+6• • •210 GeV < ¯p ⊥ < 240 GeV+5• •• • • •• •• •• • •• • •• •180 GeV < ¯p ⊥ < 210 GeV+4150 GeV < ¯p ⊥ < 180 GeV+3120 GeV < ¯p ⊥ < 150 GeV+290 GeV < ¯p ⊥ < 120 GeV+170 GeV < ¯p ⊥ < 90 GeV• •• •00 1 2 3 4 5 6∆yMC/data MC/data MC/data MC/data MC/data1.51• • • • • • • • • • • •0.5 180 GeV < ¯p ⊥ < 210 GeV1.51• • • • • • • • • • • •0.5 150 GeV < ¯p ⊥ < 180 GeV1.510.51.51• • • • • • • • • • • •120 GeV < ¯p ⊥ < 150 GeV• • • • • • • • • • • •90 GeV < ¯p ⊥ < 120 GeV0.51.51• • • • • • • • • • • •70 GeV < ¯p ⊥ < 90 GeV0.50 1 2 3 4 5 6∆yMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 13

MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet production• small-∆y region⇒ small uncertainty onadditional jet production• large-∆y region⇒ all uncertainties sizableMC/dataMC/data1.510.51.510.5• • • • • • • • • •240 GeV < ¯p ⊥ < 270 GeVHöche, MS arXiv:1208.2815• • • • • • • • • • •210 GeV < ¯p ⊥ < 240 GeVMarek Schönherr• small-¯p ⊥ region⇒ dominated by perturbativeuncertainties• large-¯p ⊥ region⇒ non-perturbativeuncertainties as large asperturbative uncertaintiesReduction of theoretical uncertaintynecessitates better understandingof soft QCD and nonfactorisablecontributionsMC/dataMC/dataMC/dataMC/dataMC/data1.510.51.510.51.510.51.510.51.51• • • • • • • • • • • •180 GeV < ¯p ⊥ < 210 GeV• • • • • • • • • • • •150 GeV < ¯p ⊥ < 180 GeV• • • • • • • • • • • •120 GeV < ¯p ⊥ < 150 GeV• • • • • • • • • • • •90 GeV < ¯p ⊥ < 120 GeV• • • • • • • • • • • •70 GeV < ¯p ⊥ < 90 GeV0.50 1 2 3 4 5 6∆yIPPP DurhamNLO+PS matching and multijet merging 13

•••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet productiondE/dη [GeV]MC/dataForward energy flow in dijet events, p jets⊥ > 20 GeV70060050040030020010001.41.210.8•CMS dataJHEP 1111 (2011) 148Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥Sherpa+BlackHatµF, µR variationµ Q variationMPI variation• • • • •3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8ηForward energy flowHöche, MS arXiv:1208.2815• energy flow in rapidity intervalper event with a centralback-to-back di-jet pair• normalisation reduces µ R/F andµ Q dependence• dominated by MPI modelinguncertaintyMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 14

••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsResults: e + e − → hadrons1/σ dσ/dln(y23)MC/data1/σ dσ/dln(y45)MC/data10 −1 Durham jet resolution 3 → 2 (E CMS = 91.2 GeV)10 −210 −310 −410 −510 −61.41.210.80.6• • • • • • • • • • • • • • • • • • • • • • • • •• ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •1 2 3 4 5 6 7 8 9 10−ln(y23)Durham jet resolution 5 → 4 (E CMS = 91.2 GeV)• • • • • • • •10 −110 −210 −310 −410 −51.41.210.80.6Marek Schönherr• ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •4 5 6 7 8 9 10 11 12−ln(y45)• •• • •1/σ dσ/dln(y34)MC/data1/σ dσ/dln(y56)MC/dataDurham jet resolution 4 → 3 (E CMS = 91.2 GeV)• • • • • • • •10 −110 −210 −310 −410 −51.41.210.80.6• ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •2 3 4 5 6 7 8 9 10 11−ln(y34)Durham jet resolution 6 → 5 (E CMS = 91.2 GeV)• • • • • •10 −110 −210 −310 −410 −51.41.210.80.6• ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •4 5 6 7 8 9 10 11 12 13−ln(y56)• •• •• •ee → hadrons(2,3,4 @ NLO;5,6 @ LO)Jet resolutions(Durham measure)• MEPS@NLO vsMENLOPS• at y ≪ 1dominated byhadr. effects→ needsretuning• much improvedren. scaledependenceALEPH dataEPJC35(2004)457-486IPPP DurhamNLO+PS matching and multijet merging 16

••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsResults: e + e − → hadronsALEPH data EPJC35(2004)457-4861/σ dσ/dT10 1 Thrust (E CMS = 91.2 GeV)10 −1 110 −210 −3• •• •• •• •• • •• • • • • • •• ••ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo1/σ dσ/dS10 1 Sphericity (E CMS = 91.2 GeV)10 −1 110 −210 −310 −4• • • • • • • • • • • • • • • • • • • • • • ••ALEPH dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• •• •MC/data1.41.21• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •0.80.60.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95TMC/data1.41.21• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •0.80.60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9SMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 17

••••••••••••MC@NLO NLO-merging ConclusionsResults: pp → W+jetsσ(W + ≥ Njet jets) [pb]10 4 Inclusive Jet Multiplicity10 310 210 1p jet⊥ > 30GeVATLAS dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlop jet⊥ > 20GeV(×10)0 1 2 3 4 5Njetpp → W +jets (0,1,2 @ NLO; 3,4 @ LO)• µ R/F ∈ [ 1 2 , 2] µ defscale uncertainty much reduced• NLO dependence forpp → W +0,1,2 jetsLO dependence forpp → W +3,4 jets• Q cut = 30 GeV• good data descriptionATLAS data Phys.Rev.D85(2012)092002Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 18

••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsResults: pp → W+jetsdσ/dp ⊥ [pb/GeV]MC/dataMC/data10 3 First Jet p ⊥10 210 110 −1 110 −210 −310 −41.510.51.510.5W+ ≥ 1 jet (×1)W+ ≥ 2 jets (×0.1)• •W+ ≥ 3 jets (×0.01)• ••ATLAS dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo• •• • • • • • • • • •• • • • • • • • • •pp → W +jets (0,1,2 @ NLO; 3,4 @ LO)• µ R/F ∈ [ 1 2 , 2] µ defscale uncertainty much reduced• NLO dependence forpp → W +0,1,2 jetsLO dependence forpp → W +3,4 jets• Q cut = 30 GeV• good data descriptionATLAS data Phys.Rev.D85(2012)092002MC/data1.510.5• • • • • • • • • •50 100 150 200 250 300Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 18

•••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsResults: pp → W+jetsATLAS data Phys.Rev.D85(2012)092002∆R Distance of Leading JetsAzimuthal Distance of Leading Jetsdσ/d∆R [pb]1008060•ATLAS dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlodσ/d∆φ [pb]14012010080•ATLAS dataMePs@NloMePs@Nlo µ/2...2µMEnloPSMEnloPS µ/2...2µMc@Nlo4060202• •• • • • •40202• •• •• • • •MC/data1.510.5• • • • • • • • • • • • • • • • • • • • • • • • • • • •MC/data1.510.5• • • • • • • • • • • • • • • •01 2 3 4 5 6 7 8∆R(First Jet, Second Jet)00 0.5 1 1.5 2 2.5 3∆φ(First Jet, Second Jet)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 19

MC@NLO NLO-merging ConclusionsResults: pp → h+jetsdσ/dp (H)⊥ [fb/GeV]Ratio10 −1 110 −21.41.210.80.6p ⊥ distribution of the Higgs bosonPRELIMINARYHqT (NLO+NNLL)Sherpa MC@NLOSherpa MEPS@NLO0 20 40 60 80 100p (H)⊥ [GeV]pp → h+jets (0,1 @ NLO; 2 @ LO)• µ R/F ∈ [ 1 2 , 2] µ CKKWscale uncertainty much reduced• NLO dependence forpp → h+0,1 jetsLO dependence for pp → h+2jets• Q cut = 30 GeV• HqT: µ R/F ∈ [ 1 2 , 2] · 12 m hµ expR∝ ph ⊥Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 20

MC@NLO NLO-merging ConclusionsResults: pp → h+jetsdσ/dp (j 1)⊥ [fb/GeV]Ratiop ⊥ distribution of hardest jet: p (j 1)⊥10 −110 −210 −310 −41.41.210.80.6PRELIMINARYSherpa MC@NLOSherpa MEPS@NLO100 200 300 400 500p (j 1)⊥ [GeV]pp → h+jets (0,1 @ NLO; 2 @ LO)• µ R/F ∈ [ 1 2 , 2] µ CKKWscale uncertainty much reduced• NLO dependence forpp → h+0,1 jetsLO dependence for pp → h+2jets• Q cut = 30 GeV• HqT: µ R/F ∈ [ 1 2 , 2] · 12 m hµ expR∝ ph ⊥Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 20

MC@NLO NLO-merging ConclusionsConclusions• SHERPA’s MC@NLO formulation allows full evaluation of perturbativeuncertainties (µ F , µ R , µ Q )• MC@NLO can be easily combined with MEPS → MENLOPS• MC@NLO is a necessary input for NLO merging → MEPS@NLO• MEPS@NLO gives full benefits of NLO calculations (scale dependences,normalisations) while also retaining full (N)LL accuracy of parton shower⇒ will be included in SHERPA-2.0.α (upcoming)Current release: SHERPA-1.4.2http://sherpa.hepforge.org• better description of perturbative QCD is only part of the story to achievehigher precission for (hard) collider observablesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 21

MC@NLO NLO-merging ConclusionsThank you for your attention!Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 22

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet production1/σ dσ/d∆φ [pb]Dijet azimuthal decorrelation in various p lead•CMS data10 5 Phys. Rev. Lett. 106 (2011) 122003Sherpa MC@NLOµR = µF = 4 1 HT, µ Q = 2 1 p ⊥10 4µR, µF variationµ Q variationMPI variation10 3×10 4×10 3MC/data MC/data1.510.51.510.5Höche, MS arXiv:1208.2815• • • • • • • • • •300 GeV < p lead⊥• • • • • • • • • • • • • • •200 GeV < p lead⊥ < 300 GeV10 210 1110 −110 −2⊥ bins ∆φ×10 2×10 1×10 0Sherpa+BlackHatMC/data MC/data MC/data1.510.51.510.51.510.5• • • • • • • • • • • • • • • • • • • •140 GeV < p lead⊥ < 200 GeV• • • • • • • • • • • • • • • • • • • •110 GeV < p lead⊥ < 140 GeV• • • • • • • • • • • • • • • • • • • •80 GeV < p lead⊥ < 110 GeV1.6 1.8 2 2.2 2.4 2.6 2.8 31.6 1.8 2 2.2 2.4 2.6 2.8 3∆φMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 23

••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet production1/N dN/dln(τ ⊥,C) [pb]Central transverse thrust in different leading jet p ⊥ ranges1.41.21•CMS dataPhys. Rev. Lett. 106 (2011) 122003Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥µR, µF variationµ Q variationMPI variationMC/data1.41.210.80.6Höche, MS arXiv:1208.2815• • • • • • • • • • • •200 GeV < p jet 1⊥• •1.40.8• •1.20.6200 GeV < p jet 1⊥+0.7MC/data10.8• • • • • • • • • • • • • •• •0.6125 GeV < p jet 1⊥ < 200 GeV0.4125 GeV < p jet 1⊥ < 200 GeV+0.41.41.20.2090 GeV < p jet 1⊥ < 125 GeV+0.1• • •Sherpa+BlackHat-12 -10 -8 -6 -4 -2ln(τ ⊥,C)MC/data10.80.6• • • • • • • • • • • • •90 GeV < p jet 1⊥ < 125 GeV-12 -10 -8 -6 -4 -2ln(τ ⊥,C)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 24

•••••••••••••••••••••••••••••••••••••MC@NLO NLO-merging ConclusionsCase study: Inclusive jet & dijet production1/N dN/dln(T m,C) [pb]Central transverse thrust minor in different leading jet p ⊥ ranges1.41.21•CMS dataPhys. Rev. Lett. 106 (2011) 122003Sherpa MC@NLOµR = µF = 1 4 HT, µ Q = 1 2 p ⊥µR, µF variationµ Q variationMPI variationMC/data1.41.210.80.61.4Höche, MS arXiv:1208.2815• • • • • • • • • • • •200 GeV < p jet 1⊥0.81.20.6200 GeV < p jet 1⊥+0.7MC/data10.8• • • • • • • • • • • • • •0.4125 GeV < p jet 1⊥ < 200 GeV+0.4• •0.61.41.2125 GeV < p jet 1⊥ < 200 GeV0.2090 GeV < p jet 1⊥ < 125 GeV+0.1Sherpa+BlackHat-6 -5 -4 -3 -2 -1ln(T m,C)MC/data10.80.6• • • • • • • • • • • • •90 GeV < p jet 1⊥ < 125 GeV-6 -5 -4 -3 -2 -1ln(T m,C)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 25

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫]〈O〉 NLO = dΦ B[B(Φ B ) + V(Φ B ) + I(Φ B ) O(Φ B )∫ [+ dΦ R − ∑ i∫]+ dΦ R[R(Φ R )O(Φ R )]D (S)i (Φ R ) O(Φ Bi )• introduce second set of subtraction functions D (A)i• D (A)iand D (S)ineed to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limitMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫]〈O〉 NLO = dΦ B[B(Φ B ) + V(Φ B ) + I(Φ B ) O(Φ B )∫+∫+dΦ R[ ∑dΦ R[R(Φ R ) − ∑ iiD (A)i (Φ R ) O(Φ Bi ) − ∑ i]D (A)i (Φ R ) O(Φ R ) + 〈O〉 (A)corr• introduce second set of subtraction functions D (A)i• D (A)iand D (S)i]D (S)i (Φ R ) O(Φ Bi )need to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limit〈O〉 (A)corr = ∫ ∑ [dΦ R i D(A) i O(ΦR ) − O(Φ Bi ) ]Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫]〈O〉 NLO = dΦ B[B(Φ B ) + V(Φ B ) + I(Φ B ) O(Φ B )+ ∑ ∫ [dΦ R D (A)i (Φ R ) − D (S)i (Φ R )i∫+dΦ R[R(Φ R ) − ∑ i]D (A)i (Φ R ) O(Φ R ) + 〈O〉 (A)corr]O(Φ Bi )• introduce second set of subtraction functions D (A)i• D (A)iand D (S)ineed to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limitMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫]〈O〉 NLO = dΦ B[B(Φ B ) + V(Φ B ) + I(Φ B ) O(Φ B )+ ∑ ∫ [dΦ Bi dΦ i 1 D (A)ii∫ [+ dΦ R R(Φ R ) − ∑ i](Φ Bi , Φ i 1) − D (S)i (Φ Bi , Φ i 1) O(Φ Bi )]D (A)i (Φ R ) O(Φ R ) + 〈O〉 (A)corr• introduce second set of subtraction functions D (A)i• D (A)iand D (S)ineed to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limitMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫]〈O〉 NLO = dΦ B[B(Φ B ) + V(Φ B ) + I(Φ B ) O(Φ B )∫∑∫ [+ dΦ B∫+idΦ i 1dΦ R[R(Φ R ) − ∑ iD (A)i](Φ B , Φ i 1) − D (S)i (Φ B , Φ i 1) O(Φ B )]D (A)i (Φ R ) O(Φ R ) + 〈O〉 (A)corr• introduce second set of subtraction functions D (A)i• D (A)iand D (S)ineed to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limitMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsGeneral NLO calculations• NLO calculation with subtraction methods∫〈O〉 NLO = dΦ ¯B(A) B (Φ B ) O(Φ B )∫+dΦ R[R(Φ R ) − ∑ i]D (A)i (Φ R ) O(Φ R ) + 〈O〉 (A)corr• introduce second set of subtraction functions D (A)i• D (A)iand D (S)ineed to have same momentum maps and IR limit- full spin-correlations in collinear limit- full colour-correlations in soft limitMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 26

MC@NLO NLO-merging ConclusionsParton showers and resummation• parton shower/resummation kernel K i (Φ 1 ), Φ 1 = {t, z, φ}→ K i incorporates divergent propagator and DGLAP splitting kernels〈O〉 PS =∫dΦ B B(Φ B ) O(Φ B )=∫dΦ B B(Φ B ) O(Φ B ) +• Sudakov form factor ∆ (K) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 K(Φ 1 )resummation features• 〈O〉 (K)corr generated by one parton shower stepcontainsMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 27

MC@NLO NLO-merging ConclusionsParton showers and resummation• parton shower/resummation kernel K i (Φ 1 ), Φ 1 = {t, z, φ}→ K i incorporates divergent propagator and DGLAP splitting kernels〈O〉 PS ==∫∫[∫dΦ B B(Φ B ) ∆ (K) (t 0 , µ 2 F ) O(Φ B ) +dΦ B B(Φ B ) O(Φ B ) +µ 2 Ft 0dΦ 1 K(Φ 1 ) ∆ (K) (t, µ 2 F ) O(Φ R )]• Sudakov form factor ∆ (K) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 K(Φ 1 )resummation features• 〈O〉 (K)corr generated by one parton shower stepcontainsMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 27

MC@NLO NLO-merging ConclusionsParton showers and resummation• parton shower/resummation kernel K i (Φ 1 ), Φ 1 = {t, z, φ}→ K i incorporates divergent propagator and DGLAP splitting kernels〈O〉 PS ==∫∫[∫dΦ B B(Φ B ) ∆ (K) (t 0 , µ 2 F ) O(Φ B ) +dΦ B B(Φ B ) O(Φ B ) +∫µ 2 Fµ 2 Ft 0dΦ R B · K(Φ 1 )t 0dΦ 1 K(Φ 1 ) ∆ (K) (t, µ 2 F ) O(Φ R )[]O(Φ R ) − O(Φ B ) + O(αs)2]• Sudakov form factor ∆ (K) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 K(Φ 1 )resummation features• 〈O〉 (K)corr generated by one parton shower stepcontainsMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 27

MC@NLO NLO-merging ConclusionsParton showers and resummation• parton shower/resummation kernel K i (Φ 1 ), Φ 1 = {t, z, φ}→ K i incorporates divergent propagator and DGLAP splitting kernels〈O〉 PS ==∫∫[∫dΦ B B(Φ B ) ∆ (K) (t 0 , µ 2 F ) O(Φ B ) +dΦ B B(Φ B ) O(Φ B ) + 〈O〉 (K)corr + O(α 2 s)µ 2 Ft 0dΦ 1 K(Φ 1 ) ∆ (K) (t, µ 2 F ) O(Φ R )]• Sudakov form factor ∆ (K) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 K(Φ 1 )resummation features• 〈O〉 (K)corr generated by one parton shower stepcontainsMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 27

MC@NLO NLO-merging ConclusionsGeneral NLO+PS matching∫[〈O〉 NLO+PS = dΦ ¯B(A) B (Φ B ) ∆ (A) (t 0 , µ 2 Q) O(Φ B )∫+dΦ R[R(Φ R ) − ∑ i∫ µ2QD (A) (Φ B , Φ 1 )+ dΦ 1t 0B(Φ B )]D (A)i (Φ R )O(Φ R ) + 〈O〉 (A)corr∆ (A) (t, µ 2 Q) O(Φ R )]• use D (A)i as resummation kernels• resummation phase space limited by µ 2 Q = t max→ starting scale of parton shower evolution→ should be of the order of the scale of the hard interaction• POWHEG and MC@NLO now differ in choice of D (A)i and µ 2 QMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 28

MC@NLO NLO-merging ConclusionsGeneral NLO+PS matching∫[〈O〉 NLO+PS = dΦ ¯B(A) B (Φ B ) ∆ (A) (t 0 , µ 2 Q) O(Φ B )∫+dΦ R[R(Φ R ) − ∑ i∫ µ2QD (A) (Φ B , Φ 1 )+ dΦ 1t 0B(Φ B )]D (A)i (Φ R )O(Φ R )∆ (A) (t, µ 2 Q) O(Φ R )]• use D (A)ias resummation kernels• resummation phase space limited by µ 2 Q = t max→ starting scale of parton shower evolution→ should be of the order of the scale of the hard interaction• POWHEG and MC@NLO now differ in choice of D (A)iMarek Schönherr∆ (A) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 D (A) /B= exp [ −α s log 2 t t+ . . . ]′and µ 2 QIPPP DurhamNLO+PS matching and multijet merging 28

MC@NLO NLO-merging ConclusionsGeneral NLO+PS matching∫[〈O〉 NLO+PS = dΦ ¯B(A) B (Φ B ) ∆ (A) (t 0 , µ 2 Q) O(Φ B )∫+dΦ R[R(Φ R ) − ∑ i∫ µ2QD (A) (Φ B , Φ 1 )+ dΦ 1t 0B(Φ B )]D (A)i (Φ R )O(Φ R )∆ (A) (t, µ 2 Q) O(Φ R )]• use D (A)ias resummation kernels• resummation phase space limited by µ 2 Q = t max→ starting scale of parton shower evolution→ should be of the order of the scale of the hard interaction• POWHEG and MC@NLO now differ in choice of D (A)iMarek Schönherr∆ (A) (t, t ′ ) = exp[− ∫ ]t ′dΦt 1 D (A) /B= exp [ −α s log 2 t t+ . . . ]′and µ 2 QIPPP DurhamNLO+PS matching and multijet merging 28

MC@NLO NLO-merging ConclusionsPOWHEGSpecial choices:Nason JHEP11(2004)040, Frixione et.al. JHEP11(2007)070• exponentiation kernel D (A)i = ρ i · R with ρ i = D (S)i / ∑ i D(S) i→ each ρ i · R contains only one divergence structure as defined by D (S)iConsequences:• no H-events, resummation scale µ 2 Q at kinematic limit 1 2 s had• in CS-subtraction instabilities in ρ i due to different cuts on R and D (S)i• exponentiation of R through matrix element corrected parton showerNLO accuracy depends crucially on presence of exact same terms insubtraction and parton showerModifications:• introduce suppression function f(p ⊥ ) = h 2 /(p 2 ⊥ + h2 ) Alioli et.al. JHEP04(2009)002→ D (A)i = ρ i · R · f(p ⊥ )→ continuous dampening of resummation kernel at large p ⊥Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 29

MC@NLO NLO-merging ConclusionsPOWHEGSpecial choices:Nason JHEP11(2004)040, Frixione et.al. JHEP11(2007)070• exponentiation kernel D (A)i = ρ i · R with ρ i = D (S)i / ∑ i D(S) i→ each ρ i · R contains only one divergence structure as defined by D (S)iConsequences:• no H-events, resummation scale µ 2 Q at kinematic limit 1 2 s had• in CS-subtraction instabilities in ρ i due to different cuts on R and D (S)i• exponentiation of R through matrix element corrected parton showerNLO accuracy depends crucially on presence of exact same terms insubtraction and parton showerModifications:• introduce suppression function f(p ⊥ ) = h 2 /(p 2 ⊥ + h2 ) Alioli et.al. JHEP04(2009)002→ D (A)i = ρ i · R · f(p ⊥ )→ continuous dampening of resummation kernel at large p ⊥Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 29

MC@NLO NLO-merging ConclusionsPOWHEGSpecial choices:Nason JHEP11(2004)040, Frixione et.al. JHEP11(2007)070• exponentiation kernel D (A)i = ρ i · R with ρ i = D (S)i / ∑ i D(S) i→ each ρ i · R contains only one divergence structure as defined by D (S)iConsequences:• no H-events, resummation scale µ 2 Q at kinematic limit 1 2 s had• in CS-subtraction instabilities in ρ i due to different cuts on R and D (S)i• exponentiation of R through matrix element corrected parton showerNLO accuracy depends crucially on presence of exact same terms insubtraction and parton showerModifications:• introduce suppression function f(p ⊥ ) = h 2 /(p 2 ⊥ + h2 ) Alioli et.al. JHEP04(2009)002→ D (A)i = ρ i · R · f(p ⊥ )→ continuous dampening of resummation kernel at large p ⊥Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 29

MC@NLO NLO-merging ConclusionsMC@NLO – traditional schemeSpecial choices:• exponentiation kernelConsequences:Frixione, Webber JHEP06(2002)029D (A)i = B · K i with K i parton shower kernels• resummation scale µ 2 Q = t max parton shower starting scale• in general, D (A)i only leading colour approximation and spin-avaragedNLO accuracy depends crucially on correctness of IR-limitModifications:• introduce soft modification function f(p ⊥ ) such thatFrixione, Nason, Webber JHEP08(2003)007∑B · Ki · f(p ⊥ )• f(p ⊥ ) process dependent in generalp ⊥ → 0−→∑ D (S)iMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 30

MC@NLO NLO-merging ConclusionsMC@NLO – traditional schemeSpecial choices:• exponentiation kernelConsequences:Frixione, Webber JHEP06(2002)029D (A)i = B · K i with K i parton shower kernels• resummation scale µ 2 Q = t max parton shower starting scale• in general, D (A)i only leading colour approximation and spin-avaragedNLO accuracy depends crucially on correctness of IR-limitModifications:• introduce soft modification function f(p ⊥ ) such thatFrixione, Nason, Webber JHEP08(2003)007∑B · Ki · f(p ⊥ )• f(p ⊥ ) process dependent in generalp ⊥ → 0−→∑ D (S)iMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 30

MC@NLO NLO-merging ConclusionsMC@NLO – traditional schemeSpecial choices:• exponentiation kernelConsequences:Frixione, Webber JHEP06(2002)029D (A)i = B · K i with K i parton shower kernels• resummation scale µ 2 Q = t max parton shower starting scale• in general, D (A)i only leading colour approximation and spin-avaragedNLO accuracy depends crucially on correctness of IR-limitModifications:• introduce soft modification function f(p ⊥ ) such thatFrixione, Nason, Webber JHEP08(2003)007∑B · Ki · f(p ⊥ )• f(p ⊥ ) process dependent in generalp ⊥ → 0−→∑ D (S)iMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 30

MC@NLO NLO-merging ConclusionsMC@NLO – D (A)i= D (S)ischemeSpecial choices:• exponentiation kernelConsequences:D (A)i• simplification of ¯B (A) -integral= D (S)i Θ(µ 2 Q − t)SH, FK, MS, FS arXiv:1111.1220• resummation scale µ 2 Q = t max set by phase space limitation of subtractionterms→ subtraction constrained in parton shower t needed for physicalresummation• trivially NLO correct independent of the process without arbitraryparameter choicesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 31

MC@NLO NLO-merging ConclusionsMC@NLO – D (A)i= D (S)ischemeSpecial choices:• exponentiation kernelConsequences:D (A)i• simplification of ¯B (A) -integral= D (S)i Θ(µ 2 Q − t)SH, FK, MS, FS arXiv:1111.1220• resummation scale µ 2 Q = t max set by phase space limitation of subtractionterms→ subtraction constrained in parton shower t needed for physicalresummation• trivially NLO correct independent of the process without arbitraryparameter choicesMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 31

MC@NLO NLO-merging ConclusionsMC@NLO – D (A)i= D (S)ischemeImplemented in SHERPA – full-colour first parton shower emissionTricky point: D (A)i < 0 e.g. for subleading colour dipolesUse modified Sudakov veto algorithmSH, FK, MS, FS arXiv:1111.1220• Assume f(t) as function to be generated, and overestimate g(t)Standard probability for one acceptance with n rejections{ ∫f(t)t1} n[g(t) g(t) exp ∏ ∫ tn+1(− d¯t g(¯t)dt i 1 − f(t ) { ∫ ti+1} ]i)g(t i ) exp − d¯t g(¯t)g(t i )ti=1ti−1ti• Can split weight into MC and analytic part using auxiliary function h(t){f(t)g(t) h(t) exp −∫ t1w(t, t 1 , . . . , t n ) = g(t)h(t)t} n[∏ ∫ tn+1d¯t h(¯t)n∏i=1i=1ti−1g(t i ) h(t i ) − f(t i )h(t i ) g(t i ) − f(t i )(dt i 1 − f(t ) {i)h(t i ) exp −g(t i )∫ ti+1ti} ]d¯t h(¯t)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 32

MC@NLO NLO-merging ConclusionsMC@NLO – D (A)i= D (S)ischemeImplemented in SHERPA – full-colour first parton shower emissionTricky point: D (A)i < 0 e.g. for subleading colour dipolesUse modified Sudakov veto algorithmSH, FK, MS, FS arXiv:1111.1220• Assume f(t) as function to be generated, and overestimate g(t)Standard probability for one acceptance with n rejections{ ∫f(t)t1} n[g(t) g(t) exp ∏ ∫ tn+1(− d¯t g(¯t)dt i 1 − f(t ) { ∫ ti+1} ]i)g(t i ) exp − d¯t g(¯t)g(t i )ti=1ti−1ti• Can split weight into MC and analytic part using auxiliary function h(t){f(t)g(t) h(t) exp −∫ t1w(t, t 1 , . . . , t n ) = g(t)h(t)t} n[∏ ∫ tn+1d¯t h(¯t)n∏i=1i=1ti−1g(t i ) h(t i ) − f(t i )h(t i ) g(t i ) − f(t i )(dt i 1 − f(t ) {i)h(t i ) exp −g(t i )∫ ti+1ti} ]d¯t h(¯t)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 32

MC@NLO NLO-merging ConclusionsMC@NLO – D (A)i= D (S)ischemeImplemented in SHERPA – full-colour first parton shower emissionTricky point: D (A)i < 0 e.g. for subleading colour dipolesUse modified Sudakov veto algorithmSH, FK, MS, FS arXiv:1111.1220• Can split weight into MC and analytic part using auxiliary function h(t){f(t)g(t) h(t) exp −∫ t1w(t, t 1 , . . . , t n ) = g(t)h(t)Identify f(t), g(t), h(t):t} n[∏ ∫ tn+1d¯t h(¯t)n∏i=1i=1ti−1g(t i ) h(t i ) − f(t i )h(t i ) g(t i ) − f(t i )• f(t) determined by MC@NLO ⇒ D (A)i• h(t) determined by parton shower ⇒ D (PS)i• g(t) can be chosen freely ⇒ const. · fconstraints: sign(f) = sign(g), |f| ≤ |g|(dt i 1 − f(t ) {i)h(t i ) exp −g(t i )∫ ti+1ti} ]d¯t h(¯t)Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 32

MC@NLO NLO-merging ConclusionsNLO mergingLO merging:• LO accuracy for n ≤ n max -jet processes• preserve LL accuracy of the parton showerNLO merging:• NLO accuracy for n ≤ n max -jet processes• preserve LL accuracy of the parton showerCatani, Krauss, Kuhn, Webber JHEP11(2001)063Lönnblad JHEP05(2002)046Höche, Krauss, Schumann, Siegert JHEP05(2009)053Hamilton, Richardson, Tully JHEP11(2009)038Lönnblad, Prestel JHEP03(2012)019Lavesson, Lönnblad JHEP12(2008)070Höche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 33

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging〈O〉 MEPS@NLO∫=∫+∫+dΦ n ¯B(A) n[∆ (A)n (t 0 , µ 2 Q) O n∫ µ2Q+t 0[dΦ n+1 R n − D (A)dΦ n+1 ¯B(A) n+1×[[dΦ D (A)n1nB nHöche, Krauss, MS, Siegert arXiv:1207.5030Gehrmann, Höche, Krauss, MS, Siegert arXiv:1207.5031∆ (A)n (t n+1 , µ 2 Q) Θ(Q cut − Q) O n+1]]Θ(Q cut − Q) ∆ (PS)n (t n+1 , µ 2 Q) O n+1∫ ]µ2QdΦ 1 K n¯B n+1 t n+11 + B n+1∆ (A)n+1 (t 0, t n+1 ) O n+1 +∫ tn+1t 0∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut )dΦ 1D (A)n+1B n+1∆ (A)n+1 (t n+2, t n+1 ) O n+2]∫ []+ dΦ n+2 R n+1 − D (A)n+1 ∆ (PS)n+1 (t n+2, t n+1 ) ∆ (PS)n (t n+1 , µ 2 Q) Θ(Q − Q cut ) O n+2Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 34

MC@NLO NLO-merging ConclusionsNLO merging – Generation of MC counterterm[1 + B ∫ ]µ2Qn+1dΦ 1 K n¯B n+1 t n+1• same form as exponent of Sudakov form factor ∆ (PS)n (t n+1 , µ 2 Q )• truncated parton shower on n-parton configuration underlying n + 1-partonevent1 no emission → retain n + 1-parton event as is2 first emission at t ′ with Q > Q cut, multiply event weight with B n+1/¯B (A)n+1 ,restart evolution at t ′ , do not apply emission kinematics3 treat every subsequent emission as in standard truncated vetoed shower• generates [1 + B ∫ ]µ2Qn+1dΦ 1 K n ∆¯B (PS)n (t n+1 , µ 2 Q)n+1 t n+1⇒ identify O(α s ) counterterm with the emitted emissionMarek SchönherrIPPP DurhamNLO+PS matching and multijet merging 35

MC@NLO NLO-merging ConclusionsNLO mergingRenormalisation scales:• determined by clustering using PS probabilities and taking the respectivenodal values t iα s (µ 2 ∏R )k = k α s (t i )i=1• change of scales µ R → ˜µ R in MEs necessitates one-loop counter term()α s (˜µ 2 R) k 1 − α s(˜µ 2 R ) k∑β 0 ln t i2π˜µ 2 RFactorisation scale:• µ F determined from core n-jet process• change of scales µ F → ˜µ F in MEs necessitates one-loop counter term(B n (Φ n ) α s(˜µ 2 R ) log µ2 ∑ n ∫ )1Fdz2π ˜µ 2 Fx az P ac(z) f c (x a /z, ˜µ 2 F ) + . . .c=q,gi=1Marek SchönherrIPPP DurhamNLO+PS matching and multijet merging 36