Multijet merging at NLO

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1 Multijet merging at Institute for Particle Physics Phenomenology 09/0/0 arxiv:.0, arxiv:0.588 arxiv: , arxiv: arxiv:08.85 Multijet merging at

2 MC@ -merging Merging with massive quarks Conclusions The SHERPA event generator framework JHEP0(009)007 Two multi-purpose Matrix Element (ME) generators AMEGIC++ JHEP0(00)044 COMIX JHEP(008)039 CS subtraction EPJC53(008)50 A Parton Shower (PS) generator CSSHOWER++ JHEP03(008)038 A multiple interaction simulation à la Pythia AMISIC++ hep-ph/0600 A cluster fragmentation module AHADIC++ EPJC36(004)38 A hadron and τ decay package HADRONS++ A higher order QED generator using YFS-resummation PHOTONS++ JHEP(008)08 Sherpa s traditional strength is the perturbative part of the event MEPS (CKKW), MC@, MEPS, MEPS@ full analytic control mandatory for consistency/accuracy Multijet merging at

3 MC@ -merging Merging with massive quarks Conclusions The SHERPA event generator framework JHEP0(009)007 Two multi-purpose Matrix Element (ME) generators AMEGIC++ JHEP0(00)044 COMIX JHEP(008)039 CS subtraction EPJC53(008)50 A Parton Shower (PS) generator CSSHOWER++ JHEP03(008)038 A multiple interaction simulation à la Pythia AMISIC++ hep-ph/0600 A cluster fragmentation module AHADIC++ EPJC36(004)38 A hadron and τ decay package HADRONS++ A higher order QED generator using YFS-resummation PHOTONS++ JHEP(008)08 Sherpa s traditional strength is the perturbative part of the event MEPS (CKKW), MC@, MEPS, MEPS@ full analytic control mandatory for consistency/accuracy Multijet merging at

4 Motivation PS LO LO LO LO pp with parton showers + exponentiation of large IR logarithms poor hard/wide angle emission pattern vs. 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-type LO+(N)LL accuracy in every jet multiplicity scale setting scheme integral to preserve PS-resummation properties Multijet merging at 3

5 Motivation ME LO LO LO LO LO pp with parton showers + exponentiation of large IR logarithms poor hard/wide angle emission pattern vs. 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-type LO+(N)LL accuracy in every jet multiplicity scale setting scheme integral to preserve PS-resummation properties Multijet merging at 3

6 Motivation ME PS LO LO LO LO LO LO LO LO pp with parton showers + exponentiation of large IR logarithms poor hard/wide angle emission pattern vs. 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-type LO+(N)LL accuracy in every jet multiplicity scale setting scheme integral to preserve PS-resummation properties Multijet merging at 3

7 Motivation ME PS LO LO LO LO LO LO LO α k+n s (µ eff ) = α k s(µ) α s (t ) α s (t n ) LO pp with parton showers + exponentiation of large IR logarithms poor hard/wide angle emission pattern vs. 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-type LO+(N)LL accuracy in every jet multiplicity scale setting scheme integral to preserve PS-resummation properties Multijet merging at 3

8 Motivation PS promote LOPS to PS (POWHEG, (part I) Multijet merging at 4

9 O +PS = dφ B(A) B (Φ B ) (A) (t 0, µ Q) O(Φ B ) Frixione, Webber JHEP06(00)09 + µ Q dφ i D (A) i (Φ B, Φ ) (A) (t, µ i t 0 B(Φ B ) Q) O(Φ R ) + dφ R R(Φ R ) D (A) i (Φ R ) O(Φ R ) i Höche, Krauss, MS, Siegert arxiv:.0 weighted Born configuration B (A) = B + Ṽ + I + dφ D (A) D (S) use D (A) i as resummation kernels: choice D (A) i = D (S) i Θ(µ Q t) (A) (t, t ) = exp t dφ t D (A) /B = exp α s log (t/t ) f +... resummation phase space limited by µ Q = t max starting scale of parton shower evolution (exponent vanishes) should be of the order of the hard resummation scale first implementation to allow to study µ Q uncertainty Multijet merging at 5

10 O +PS = dφ B(A) B (Φ B ) (A) (t 0, µ Q) O(Φ B ) Frixione, Webber JHEP06(00)09 + µ Q dφ i D (A) i (Φ B, Φ ) (A) (t, µ i t 0 B(Φ B ) Q) O(Φ R ) + dφ R R(Φ R ) D (A) i (Φ R ) O(Φ R ) i Höche, Krauss, MS, Siegert arxiv:.0 weighted Born configuration B (A) = B + Ṽ + I + dφ D (A) D (S) use D (A) i as resummation kernels: choice D (A) i = D (S) i Θ(µ Q t) (A) (t, t ) = exp t dφ t D (A) /B = exp α s log (t/t ) f +... resummation phase space limited by µ Q = t max starting scale of parton shower evolution (exponent vanishes) should be of the order of the hard resummation scale first implementation to allow to study µ Q uncertainty Multijet merging at 5

11 Case study: Inclusive jet & dijet production Describe wealth of experimental data with a single sample (LHC@7TeV) MC@ di-jet production: Höche, MS arxiv:08.85 µ R/F = 4 H T, µ Q = p CT0 PDF (α s (m Z ) = 0.8) hadron level calculation fully hadronised including MPI virtual MEs from BLACKHAT Giele, Glover, Kosower Nucl.Phys.B403(993) Bern et.al. arxiv:.3940 p j > 0 GeV, pj > 0 GeV Uncertainty estimates: µ Q variation MPI variation µ F, µ R variation µ R/F, µdef R/F µ Q, µ def Q MPI activity in tr. region ± 0% Multijet merging at 6

12 -merging Merging with massive quarks Conclusions Case study: Inclusive jet & dijet production Describe wealth of experimental data with a single sample (LHC@7TeV) MC@ di-jet production: Höche, MS arxiv:08.85 µ R/F = 4 H T, µ Q = p CT0 PDF (α s (m Z ) = 0.8) hadron level calculation fully hadronised including MPI virtual MEs from BLACKHAT Giele, Glover, Kosower Nucl.Phys.B403(993) Bern et.al. arxiv:.3940 p j > 0 GeV, pj > 0 GeV Uncertainty estimates: µ R/F, µdef R/F µ Q, µ def Q MPI activity in tr. region ± 0% σ pb MC/data Inclusive jet multiplicity (anti-kt R=0.4) µr, µf variation µ Q variation MPI variation Sherpa+BlackHat ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa MC@ µr = µf = 4 HT, µ Q = p Njet Multijet merging at 6

13 -merging Merging with massive quarks Conclusions Case study: Inclusive jet & dijet production dσ/dp pb/gev Jet transverse momenta (anti-kt R=0.4) ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa MC@ µr = µf = 4 HT, µ Q = p µr, µf variation µ Q variation MPI variation st jet MC/data MC/data.4. Höche, MS arxiv: st jet nd jet th jet 0 3 Sherpa+BlackHat 3rd jet 0 nd jet 0 MC/data MC/data rd jet 4th jet p GeV p GeV Multijet merging at 7

14 -merging Merging with massive quarks Conclusions Case study: Inclusive jet & dijet production R3 MC/data jets over jets ratio (anti-kt R=0.5) µf, µr variation µ Q variation MPI variation Sherpa+BlackHat CMS data Phys. Lett. B 70 (0) 336 Sherpa MC@ µr = µf = 4 HT, µ Q = p HT TeV 3-jet-over--jet ratio Höche, MS arxiv:08.85 determined from incl. sample -jet rate at +NLL 3-jet rate at LO+LL common scale choices varied simultaneously at large H T large MPI uncertainties better MPI physics needed (soft QCD) similar description of related ATLAS observables Multijet merging at 8

15 -merging Merging with massive quarks Conclusions Case study: Inclusive jet & dijet production de/dη GeV MC/data Forward energy flow in dijet events, p jets > 0 GeV CMS data JHEP (0) 48 Sherpa MC@ µr = µf = 4 HT, µ Q = p Sherpa+BlackHat µf, µr variation µ Q variation MPI variation η Forward energy flow Höche, MS arxiv:08.85 energy flow in rapidity interval per event with a central back-to-back di-jet pair normalisation reduces µ R/F and µ Q dependence dominated by MPI modeling uncertainty Multijet merging at 9

16 -merging Merging with massive quarks Conclusions W + n jet production dσ/dp pb/gev MC/data MC/data MC/data Jet transverse momenta Sherpa+BlackHat W+,,3 jets p (third jet) ATLAS data µ F/R = µ/...µ MC@ PL µ Q = µ/... µ p (second jet) p (first jet) p GeV Höche, Krauss, MS, Siegert arxiv:0.588 pp W +,, 3 jets 3 separate samples/calculations accuracy for inclusive observables of respective jet multiplicity resummation of softest/lo jet, i.e. 4th jet in pp W + 3 jets no resummation of sample-defining jet multiplicity, i.e. first 3 jets in pp W + 3 jets scales: µ R/F = Ĥ T, µ Q = p (j n ) Data: ATLAS Phys.Rev.D85(0)0900 Multijet merging at 0

17 Motivation PS promote LOPS to PS (POWHEG, (part I) combine PS for successive multiplicities into incl. sample preserve +(N)LL accuracy in every jet multiplicity restore resummation wrt. to inclusive sample (part II) scale setting scheme integral to preserve PS-resummation properties Multijet merging at

18 Motivation ME PS LO LO LO LO promote LOPS to PS (POWHEG, (part I) promote lowest multiplicity to : merge one PS with MEPS MEPS combine PS for successive multiplicities into incl. sample (MEPS@), preserve +(N)LL accuracy in every jet multiplicity restore resummation wrt. to inclusive sample (part II) Marek Schönherr scale setting scheme integral to preserve PS-resummation properties Multijet merging at

19 Motivation ME PS promote LOPS to PS (POWHEG, (part I) combine PS for successive multiplicities into incl. sample preserve +(N)LL accuracy in every jet multiplicity restore resummation wrt. to inclusive sample (part II) scale setting scheme integral to preserve PS-resummation properties Multijet merging at

20 Motivation ME PS α k+n s (µ eff ) = α k s(µ) α s (t ) α s (t n ) promote LOPS to PS (POWHEG, MC@) (part I) combine PS for successive multiplicities into incl. sample (MEPS@), preserve +(N)LL accuracy in every jet multiplicity restore resummation wrt. to inclusive sample (part II) scale setting scheme integral to preserve PS-resummation properties Multijet merging at

21 merging LO merging: LO accuracy for n n max -jet processes preserve LL accuracy of the parton shower merging: accuracy for n n max -jet processes preserve LL accuracy of the parton shower Catani, Krauss, Kuhn, Webber JHEP(00)063 Lönnblad JHEP05(00)046 Höche, Krauss, Schumann, Siegert JHEP05(009)053 Hamilton, Richardson, Tully JHEP(009)038 Lönnblad, Prestel JHEP03(0)09 Lavesson, Lönnblad JHEP(008)070 Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: Multijet merging at

22 -merging Merging with massive quarks Conclusions Results: pp W+jets Inclusive Jet Multiplicity σ(w + Njet jets) pb p jet > 30GeV ATLAS data MePs@Nlo MePs@Nlo µ/...µ MEnloPS MEnloPS µ/...µ Mc@Nlo p jet > 0GeV ( 0) pp W +jets ; LO) µ R/F, µ CKKW scale uncertainty much reduced dependece for pp W +0,, jets LO dependence for pp W +3,4 jets Q cut = 30 GeV Njet good data description ATLAS data Phys.Rev.D85(0)0900 Multijet merging at 3

23 -merging Merging with massive quarks Conclusions Results: pp W+jets dσ/dp pb/gev MC/data MC/data 0 3 First Jet p W+ jet ( ) W+ jets ( 0.) W+ 3 jets ( 0.0) ATLAS data MePs@Nlo MePs@Nlo µ/...µ MEnloPS MEnloPS µ/...µ Mc@Nlo pp W +jets ; LO) µ R/F, µ CKKW scale uncertainty much reduced dependece for pp W +0,, jets LO dependence for pp W +3,4 jets Q cut = 30 GeV good data description ATLAS data Phys.Rev.D85(0)0900 MC/data Multijet merging at 3

24 -merging Merging with massive quarks Conclusions Results: pp W+jets ATLAS data Phys.Rev.D85(0)0900 R Distance of Leading Jets Azimuthal Distance of Leading Jets dσ/d R pb ATLAS data MePs@Nlo MePs@Nlo µ/...µ MEnloPS MEnloPS µ/...µ Mc@Nlo dσ/d φ pb ATLAS data MePs@Nlo MePs@Nlo µ/...µ MEnloPS MEnloPS µ/...µ Mc@Nlo MC/data MC/data R(First Jet, Second Jet) φ(first Jet, Second Jet) Multijet merging at 4

25 Results: pp h+jets dσ/dp (H) fb/gev Ratio p distribution of the Higgs boson PRELIMINARY HqT (+NLL) Sherpa MC@ Sherpa MEPS@ p (H) GeV pp h+jets LO) µ R/F, µ CKKW scale uncertainty much reduced dependece for pp h+0, jets LO dependence for pp h+ jets Q cut = 30 GeV HqT: µ R/F, m h Multijet merging at 5

26 Results: pp h+jets dσ/dp (j ) fb/gev Ratio p distribution of hardest jet: p (j ) PRELIMINARY Sherpa MC@ Sherpa MEPS@ p (j ) GeV pp h+jets LO) µ R/F, µ CKKW scale uncertainty much reduced dependece for pp h+0, jets LO dependence for pp h+ jets Q cut = 30 GeV HqT: µ R/F, m h Multijet merging at 5

27 Public availability merging automated in SHERPA except for virtual GOSAM (public) automated one-loop code also convenience libraries NJETS (public) one-loop code for pp jets OPEOPS (to be public) automated one-loop code BLACKHAT (to be public) one-loop library for pp (V +)jets either dedicated interfaces or BLHA interface dσ/dpt,jpb/gev Ratio W + 3 jets: leading jet transverse momentum PRELIMINARY Sherpa LO GoSam+Sherpa LHC 8 TeV parton level cteq6me pdf pt,jgev scales: µ R/F = H T Multijet merging at 6

28 γ -merging Merging with massive quarks Conclusions Merging with massive quarks MEPS (CKKW) with massive quarks e.g. m b, m c 0 no conceptual problem take massive quarks also into initial state (5 flavour PDFs) factorisation of massive initial state à la ACOT consistent ME and PS merging still only one parameter procedure (Q cut ) same as MEPS (CKKW) with massless quarks no additional heavy flavour overlap removal or similar available since SHERPA-.3.0 (pb/gev) T dσ/dp pp γ + b-jet production - DØ, L = 8.7 fb (x0.3) γ data, y <.0 γ data,.5 < y <.5 (Stavreva, Owens) k T fact. (Lipatov, Zotov) SHERPA, v.3. PYTHIA, v6.40 jet jet y <.5, p >5 GeV T γ p (GeV) T D0/ data arxiv: Multijet merging at 7

29 Conclusions SHERPA s MC@ formulation allows full evaluation of perturbative uncertainties (µ F, µ R, µ Q ) non-perturbative uncertainties can be consistently estimated MC@ can be easily combined with MEPS MEPS MC@ is a necessary input for merging MEPS@ MEPS@ gives full benefits of calculations (scale dependences, normalisations) while also retaining full (N)LL accuracy of parton shower will be included in next major release Current release: SHERPA precise theoretical calculations need to be confronted with data as differentially as possible over as large a phase space as possible Multijet merging at 8

30 Thank you for your attention! Multijet merging at 9

31 -merging Merging with massive quarks Conclusions Short-comings of fixed-order QCD poor description in phase space regions with strongly hierarchical scales poor perturbative jet-modeling (at most two constituents) no hadronisation, MPI effects very pronounced in inclusive & dijet production jet-p turn negative in forward region unless y-dependent scale is used (e.g. H (y) T ) σ pb MC/data Inclusive Jet Multiplicity (R=0.4) Sherpa+BlackHat ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa µf = µr = HT Njet taken from Bern et.al. arxiv:.3940 Multijet merging at 0

32 -merging Merging with massive quarks Conclusions Short-comings of fixed-order QCD poor description in phase space regions with strongly hierarchical scales poor perturbative jet-modeling (at most two constituents) no hadronisation, MPI effects very pronounced in inclusive & dijet production jet-p turn negative in forward region unless y-dependent scale is used (e.g. H (y) T ) dσ/dp pb/gev MC/data Transverse momentum of the leading jet (R=0.4) ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa µf = µr = HT Sherpa+BlackHat p (leading jet) GeV taken from Bern et.al. arxiv:.3940 Multijet merging at 0

33 -merging Merging with massive quarks Conclusions Short-comings of fixed-order QCD poor description in phase space regions with strongly hierarchical scales poor perturbative jet-modeling (at most two constituents) no hadronisation, MPI effects very pronounced in inclusive & dijet production jet-p turn negative in forward region unless y-dependent scale is used (e.g. H (y) T ) dσ/dp pb/gev MC/data 0 5 Transverse momentum of the nd leading jet (R=0.4) Sherpa+BlackHat ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa µf = µr = HT p (nd leading jet) GeV taken from Bern et.al. arxiv:.3940 Multijet merging at 0

34 -merging Merging with massive quarks Conclusions Short-comings of fixed-order QCD poor description in phase space regions with strongly hierarchical scales poor perturbative jet-modeling (at most two constituents) no hadronisation, MPI effects very pronounced in inclusive & dijet production jet-p turn negative in forward region unless y-dependent scale is used (e.g. H (y) T ) dσ/dp pb/gev MC/data Transverse momentum of the 3rd leading jet (R=0.4) Sherpa+BlackHat ATLAS data Eur.Phys.J. C7 (0) 763 Sherpa µf = µr = HT p (3rd leading jet) GeV taken from Bern et.al. arxiv:.3940 Multijet merging at 0

35 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

36 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

37 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

38 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

39 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

40 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

41 merging O MEPS@ = + + dφ n B(A) n (A) n (t 0, µ Q) O n µ Q + t 0 dφ n+ R n D (A) dφ n+ B(A) n+ (A) Dn dφ n B n Höche, Krauss, MS, Siegert arxiv: Gehrmann, Höche, Krauss, MS, Siegert arxiv: (A) n (t n+, µ Q) Θ(Q cut Q) O n+ Θ(Q cut Q) (PS) n (t n+, µ Q) O n+ + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) Θ(Q Q cut ) tn+ (A) (A) n+ (t Dn+ 0, t n+ ) O n+ + dφ (A) n+ t 0 B (t n+, t n+ ) O n+ n+ + dφ n+ R n+ D (A) n+ (PS) n+ (t n+, t n+ ) (PS) n (t n+, µ Q) Θ(Q Q cut ) O n+ Multijet merging at

42 merging Renormalisation scales: determined by clustering using PS probabilities and taking the respective nodal values t i α s (µ R )k = k α s (t i ) i= change of scales µ R µ R in MEs necessitates one-loop counter term ( ) α s ( µ R) k α s( µ R ) k β 0 ln t i π µ R Factorisation 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 R ) log µ n ) F dz π µ F x a z P ac(z) f c (x a /z, µ F ) +... c=q,g i= Multijet merging at

43 merging Generation of MC counterterm + B n+ B n+ µ Q t n+ dφ K n same form as exponent of Sudakov form factor (PS) n (t n+, µ Q ) truncated parton shower on n-parton configuration underlying n + -parton event no emission retain n + -parton event as is first emission at t with Q > Q cut, multiply event weight with B n+/ B (A) n+, restart evolution at t, do not apply emission kinematics 3 treat every subsequent emission as in standard truncated vetoed shower generates + B n+ B n+ µ Q t n+ dφ K n (PS) n (t n+, µ Q) identify O(α s ) counterterm with the emitted emission Multijet merging at 3

Uncertainties in NLO+PS matched calculations of inclusive jet and dijet production

Uncertainties in NLO+PS matched calculations of inclusive jet and dijet production Institute for Particle Physics Phenomenology 26/09/202 arxiv:.220, arxiv:208.285 Uncertainties in NLO+PS matched calculations