Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects

Transcription

1 Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects Michael Rauch 25 Jul 2016 INSTITUTE FOR THEORETICAL PHYSICS KIT University of the State of Baden-uerttemberg and National Research Center of the Helmholtz Association

2 VBF event topology VBF (vector-boson fusion) topology shows distinct signature two tagging jets in forward region reduced jet activity in central region leptonic decay products typically between tagging jets two-sided deep-inelastic scattering First studied in context of Higgs searches [Han, Valencia, illenbrock; Figy, Oleari, Zeppenfeld;... ] 10% compared to main production mode gluon fusion NLO QCD corrections moderate (O( 10%)) NLO E same size [Ciccolini et al., Figy et al. ] NNLO QCD known for subsets: no significant contributions for integrated c.s. [Harlander et al., Bolzoni et al. ] corrections up to 10% in distributions incl. NNNLO QCD: tiny effects [Cacciari et al. ] [Dreyer, Karlberg] advantageous scale choice: momentum transfer q 2 of intermediate vector bosons M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

3 Diboson-VBF production Important process for LHC run-ii Part of the NLO wish list [Bozzi, Jäger, Oleari, Zeppenfeld (VV); Campanario, Kaiser, Zeppenfeld ( ± γ)] [Les Houches 2005] background to Higgs searches access to anomalous triple and quartic gauge couplings NLO QCD implementation of all boson combinations leptonic and semi-leptonic decays including off-shell and non-resonant contributions VBF approximation VBFNLO [MR, Zeppenfeld et al.] u c u c u c + αβ T + V ν e e γ,z (a) - ν e e + (c) - (e) ν e e + γ,z µ - [Denner, Hosekova, Kallweit ( + + )] µ - ν µ u c ν µ u µ - c ν µ u c u c u c u c γ,z αβ T VV + Γ V α (b) γ,z γ,z (d) αβ T - V (f) γ,z ν e e + e + ν e ν µ µ - - γ,z e + ν e ν µ µ - u µ - ν µ c u c u c M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

4 Introduction VBFNLO Vector-Boson-Fusion at Next-to-Leading Order M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

5 Introduction VBFNLO Physics Vector-Boson- Fusion at Next-to-Leading Order M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

6 Introduction VBFNLO F Physics Vector-Boson- Fusion at Next-to-Leading Order Fully flexible parton-level Monte Carlo for processes with electroweak bosons accurate predictions needed for LHC (both signal and background) MC efficient solution for high number of final-state particles (decays of electroweak bosons included) general cuts and distributions of final-state particles various choices for renormalization and factorization scales any pdf set available from LHAPDF (or hard-wired CTEQ6L1, CT10, MRST2004qed, MST2008) event files in Les Houches Accord (LHA) or HepMC format BLHA interface to Monte-Carlo event generators NLO event output (LO only) M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

7 Process overview List of implemented processes (New in VBFNLO 2.7.1/3.0.0β1) vector-boson fusion production at NLO QCD of } Higgs (+NLO E, NLO SUSY) Higgs plus third hard jet (including Higgs decays) Higgs plus photon Higgs pair vector boson (, Z, γ) two vector bosons ( +, ± ±, Z, ZZ, γ, Zγ) diboson production diboson (, Z, ZZ, γ, Zγ, γγ) (NLO QCD) diboson via gluon fusion (, ZZ, Zγ, γγ) (part of NNLO QCD contribution to diboson) diboson (, Z, ZZ, γ) plus hard jet (NLO QCD) diboson ( ± ±, Z, γ, ZZ, Zγ) plus two hard jets (NLO QCD) triboson production (NLO QCD) triboson (all combinations of, Z, γ) triboson (γγ) plus hard jet Higgs plus vector boson (NLO QCD) (including Higgs decays) Higgs plus vector boson (H) Higgs plus vector boson plus hard jet (H) Higgs plus two jets via gluon fusion (one-loop LO) (including Higgs decays) new physics models anomalous Higgs, triple and quartic gauge couplings K-matrix unitarization for selected couplings Higgsless and spin-2 models Two-Higgs model BLHA interface for VBF processes M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

8 NLO plus Parton Shower Combine advantages of NLO calculations and parton shower NLO calculation normalization correct to NLO additional jet at high-p T accurately described theoretical uncertainty reduced Parton shower Sudakov suppression at small p T events at hadron level possible State of the Art Implementations for specific VBF processses POHEG-BOX currently available VBF implementations: Z [Jäger, Schneider, Zanderighi] ±, Z [Schissler, Zeppenfeld] ± ±, ± [Jäger, Zanderighi] ZZ [Jäger, Karlberg, Zanderighi] VBF-H with POHEG method HJets++ [Alioli, Hamilton, Nason, Oleari, Re] [D Errico, Richardson] [Campanario, Figy, Plätzer, Sjödahl] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

9 Herwig 7 fully automated matching of NLO to parton showers through Matchbox module [work led by S. Plätzer with substantial contributions by J. Bellm, A. ilcock, MR, C. Reuschle] subtractive (MC@NLO-type, ) and multiplicative (POHEG-type, ) matching angular-ordered (QTilde, PS) and dipole (Dipoles) shower matrix elements through binary interface, no event files MG5_aMC HJets++ Recola ColorFull CVolver GoSam NJet Amplitude-based Colour structure OpenLoops VBFNLO 3 BLHA2 Herwig 7 Subtractive Matching (MC@NLO-type) Angular-ordered shower Eikonal MPI Matchbox Multiplicative Matching (POHEG-type) Dipole shower Cluster Hadronization Built-in ME BSM & UFO Decays M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

10 VBFNLO 3 & Herwig 7 this talk matrix elements from VBFNLO via BLHA2 interface extensions to make accessible phase-space sampling (electroweak) random helicity summation anomalous couplings [Binoth et al., Alioli et al.] MG5_aMC HJets++ Recola ColorFull CVolver GoSam NJet Amplitude-based Colour structure OpenLoops VBFNLO 3 BLHA2 Herwig 7 Subtractive Matching (MC@NLO-type) Angular-ordered shower Eikonal MPI Matchbox Multiplicative Matching (POHEG-type) Dipole shower Cluster Hadronization Built-in ME BSM & UFO Decays M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

11 Validation Compare LO results between VBFNLO stand-alone run and interfaced to Herwig 7 via Matchbox (inclusive cuts, with leptonic gauge boson decays into single different-flavour combination, Higgs non-decaying) LO stand-alone Matchbox 10 3 σ [fb] σ/σ stand-alone Herwig 7 VBFNLO 3 H jj + jj - jj Z l jj Z ν jj γ jj Hγ jj good agreement at or below permill level HH jj + - jj + Z l jj - Z l jj Z l Z l jj Z l Z ν jj + + jj - - jj + γ jj - γ jj Z l γ jj Z ν γ jj 0.20 % 0.15 % 0.10 % 0.05 % 0.00 % % % % % M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

12 Validation Compare NLO results between VBFNLO stand-alone run and interfaced to Herwig 7 via Matchbox (inclusive cuts, with leptonic gauge boson decays into single different-flavour combination, Higgs non-decaying) NLO stand-alone Matchbox 10 3 σ [fb] σ/σ stand-alone Herwig 7 VBFNLO 3 H jj + jj - jj Z l jj Z ν jj γ jj Hγ jj???? HH jj + - jj + Z l jj - Z l jj Z l Z l jj Z l Z ν jj + + jj - - jj + γ jj - γ jj Z l γ jj Z ν γ jj good agreement V γ processes: ±0.7% deviation beyond errors under investigation 0.5 % 0.4 % 0.3 % 0.2 % 0.1 % 0.0 % -0.1 % -0.2 % M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

13 Setup Process: [Plätzer, MR] pp ( (Hjj ) + jj ) e + ν eµ ν µjj via VBF Cuts: p T,j > 30 GeV, y j < 4.5, anti-k T jets with R = 0.4, b-quark veto p T,l > 20 GeV, y l < 2.5, m e +,µ > 15 GeV, m j1,j2 > 600 GeV, y j1 y j2 > 3.6 (inspired from ATLAS VBF category in H, CMS similar) PDF: MMHT2014 central scale choice: transverse momentum of the leading jet µ 0 = p T,j1 M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

14 Distributions Process as example: pp ( (Hjj ) + jj ) e + ν eµ ν µjj via VBF Four-lepton invariant mass dσ/d M( e + ν e µ - ν - µ ) [fb/gev] σ i /σ NLO Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS M( e + ν e µ - ν - µ ) [GeV] Higgs peak at 125 GeV continuum production above 180 GeV significant cancellation between diagrams at high invariant masses ideal test for anomalous couplings M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

15 Distributions Process as example: pp ( (Hjj ) + jj ) e + ν eµ ν µjj via VBF Four-lepton invariant mass dσ/d M( e + ν e µ - ν - µ ) [fb/gev] σ i /σ NLO Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS M( e + ν e µ - ν - µ ) [GeV] all parton-shower results smaller than NLO cross section additional K -factor effect for LO Dipoles result (K = 77) no relevant shape changes (as expected: insensitive to QCD effects) M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

16 Migration Effects Vary transverse momentum cut of jets (default: p T,j > 30 GeV) dσ/d M( e + ν e µ - ν - µ ) [fb/gev] σ i /σ NLO Herwig 7 VBFNLO 3 NLO NLO p T,j >20 GeV NLO p T,j >40 GeV NLO Dipoles M( e + ν e µ - ν - µ ) [GeV] same effect when slightly raising p T,j cut additional parton splittings: if hard & wide-angle emission separate jet reduces energy and transverse momentum of emitting parton p T,j cut, VBF cut m jj > 600 GeV M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

17 Migration Effects Vary transverse momentum cut of jets (default: p T,j > 30 GeV) dσ/d p T,j1 [fb/gev] NLO NLO p T,j >20 GeV NLO p T,j >40 GeV NLO Dipoles σ i /σ NLO 10-7 Herwig 7 VBFNLO p T,j1 [GeV] less pronounced for small p T,j1 VBF cut main source migration of events across cut boundary generation-level vs. analysis-level cuts no tuning of acceptance criteria required generation-level cuts nevertheless chosen weaker M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

18 Four-lepton Invariant Mass dσ/d M( e + ν e µ - ν - µ ) [fb/gev] σ i /σ NLO µ F µ R µ Q µ tot Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS M( e + ν e µ - ν - µ ) [GeV] central scale µ 0 = p T,j1 transverse momentum of leading jet band: scale variation {µ F, µ R, µ Q } /µ 0 [ 1 2 ; 2] µ i /µ j [ 1 2 ; 2] factorization scale µ F /µ 0 [ 1 2 ; 2] renormalization scale µ R /µ 0 [ 1 2 ; 2] shower scale µ Q /µ 0 [ 1 2 ; 2] all three scales M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

19 Four-lepton Invariant Mass dσ/d M( e + ν e µ - ν - µ ) [fb/gev] σ i /σ NLO µ F µ R µ Q µ tot Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS M( e + ν e µ - ν - µ ) [GeV] consistent variation of scales between hard process and parton shower large factorization scale dependence for LO result larger dependence for down variation of renormalization scale in angular-ordered shower: larger α s more splittings bigger migration effects small variations from shower-scale changes modest remaining overall uncertainty M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

20 Transverse Momentum Third Jet dσ/d p T,j3 [fb/gev] σ i /σ NLO µ F µ R µ Q µ tot Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS p T,j3 [GeV] large scale variation bands for shower scale in LO Dipoles pure parton-shower effect fact./ren. scale in NLO LO accuracy of observable reduced for both NLO + parton-shower curves still significant remaining uncertainty O(10 20%) call for multi-jet merging M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

21 Rapidity of third jet dσ/d y * 3 [fb] Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS Rapidity of third jet relative to two tagging jets y 3 = y 3 y 1+y σ i /σ NLO µ F µ R µ Q µ tot y* 3 VBF colour structure suppresses additional central jet radiation colour connection between tagging jet and remnant distinction from QCD-induced production M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

22 Rapidity of third jet dσ/d y * 3 [fb] σ i /σ NLO µ F µ R µ Q µ tot Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS y* 3 Rapidity of third jet relative to two tagging jets y 3 = y 3 y 1+y 2 2 impact of parton showers (+LO) long unclear Herwig predicts very low radiation in central region large shower-scale unc. stabilised when combining with NLO still reduction present scale variation bands not overlapping only small effects in forward region (mostly global normalization) M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

23 Rapidity of third jet POHEG dσ/d y * 3 [fb] σ i /σ NLO Herwig 7 VBFNLO 3 NLO NLO Dipoles NLO Dipoles y* 3 1 POHEG-like ( ) using resummation scheme [Plätzer]: 1 for q < (1 2ρ)Q 1 (1 2ρ q Q )2 for (1 2ρ)Q < q < (1 ρ)q 2ρ κ(q, q; ρ) = 2 (1 q Q )2 for (1 ρ)q < q < Q 2ρ 2 0 for q > Q κ natural hfact (POHEG-BOX) resummation ρ= q/q M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

24 Rapidity of third jet POHEG dσ/d y * 3 [fb] σ i /σ NLO Herwig 7 VBFNLO 3 NLO NLO Dipoles NLO Dipoles y* 3 band: joint variation µ F = µ R = µ Q [ 1 2, 2] µ 0 similar predictions from MC@NLO-like ( ) and POHEG-like ( ) matching also holds for other distributions M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

25 Effective Field Theory Assumption: new physics is heavy Classic example: µ decay Fermi theory (t-channel integrated out) µ ν µ e ν e Effective Lagrangian µ ν µ e ν e G F = L = L SM + L EFT = L SM + f (d) i O(d) Λd 4 i d>4 i operators O contain SM fields only respect SM gauge symmetries suppressed by 1/Λ d 4 (Λ: scale of new physics) keep only leading order(s) (lowest dimension d = 6) building blocks: Higgs field Φ (covariant) derivative µ, D µ field strength tensors G µν, µν, B µν fermion fields ψ 2 8 g 2 m 2 M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

26 Unitarity Violation Important gauge cancellations between different diagram types longitudinal scattering through quartic gauge boson vertex high energy limit: centre-of-mass energy s M quartic vertex s 2 cross section diverges σ s 4 /s = s 3 add triple gauge boson vertices + Z, γ + Z, γ M quartic+triple vertices s still divergent additional Higgs diagrams + Z, γ + Z, γ + H + H remove divergence exactly σ 1/s 0 Anomalous gauge couplings spoil cancellation stringent tests M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

27 Unitarization Anomalous gauge couplings spoil cancellation effects can become large unitarity violation Several solutions: consider only unitarity-conserving phase-space regions throws away information reduced sensitivity (dipole) form factor multiplying amplitudes F(s) = 1 ( 1 + s ) n Λ 2 FF, n: free parameters Λ 2 FF K -matrix unitarization [Alboteanu, Kilian, Reuter, Sekulla] based on partial-wave analysis [Jacob, ick] project amplitude back onto Argand circle Im(a) ) Re(a^ 0 00) Im(a^ 0 00) a^ 0 00-i/2 Re(a 0 00) i aj kj Re(a) SM (EV) SM anom. coupl. K-matrix form factor FF p= s [GeV] s [GeV] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

28 Cross Section Results Example Process: pp ( + + jj) e + ν eµ + ν µjj at NLO QCD accuracy dσ/dm 4l [fb/gev] SM anom. coupl. form factor K-matrix M 4l [GeV] dσ/dm 4l [fb/gev] kink FF FF, p=2 FF, p=3 FF, p= M 4l [GeV] kink form factor (simplified projection for comparison): 1 for E Λ FF,kink, F kink (E) = ( ) ΛFF,kink 4 for E > Λ E FF,kink, huge effects for un-unitarized result unphysical K -matrix method maximising contribution while staying in physical region study parton-shower and hadronization impact M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

29 Combination with Parton Shower Can also combine K-matrix in setup with parton shower [VBFNLO 3 & Herwig 7] Example: VBF- + + (pp e + ν e µ + ν µ jj) anom. coupl.: f S,1 = 100 TeV 4 fixed-order NLO NLO+PS (MC@NLO + dipole shower) cs/gev [fb/gev] cs/gev [fb/gev] SM anom. coupl. K-matrix PS+SM PS+anom. coupl. PS+K-matrix m 4l [GeV] No significant shape changes in m 4l when switching on PS (integrated c.s. PS/NLO: -3.0% (SM) / -3.8% (K-matrix) ) m 4l [GeV] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

30 Combination with Parton Shower Can also combine K-matrix in setup with parton shower [VBFNLO 3 & Herwig 7] Example: VBF- + + (pp e + ν e µ + ν µ jj) anom. coupl.: f S,1 = 100 TeV 4 m 4l Comparison p T j,3 Comparison cs/gev [fb/gev] SM PS+SM K-matrix PS+K-matrix m 4l [GeV] cs/gev [fb/gev] SM PS+SM K-matrix PS+K-matrix No significant shape changes in m 4l when switching on PS (integrated c.s. PS/NLO: -3.0% (SM) / -3.8% (K-matrix) ) pj,3 T mostly sensitive to parton-shower effects pt j3 [GeV] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

31 Conclusions Parton-shower and scale variation effects in + jj production via vector-boson-fusion important process for the LHC Higgs properties unitarity in scattering testing anomalous (triple and) quartic gauge couplings study performed with Herwig 7 & VBFNLO 3 compatible behavior of both parton showers and matching schemes small parton-shower effects for distributions of variables already present at LO mostly reduction of inclusive cross section due to additional jet radiation presence of central rapidity gap stabilised multi-jet merging to further reduce uncertainties study hadronization impact M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

32 Conclusions Parton-shower and scale variation effects in + jj production via vector-boson-fusion important process for the LHC Higgs properties unitarity in scattering testing anomalous (triple and) quartic gauge couplings study performed with Herwig 7 & VBFNLO 3 compatible behavior of both parton showers and matching schemes small parton-shower effects for distributions of variables already present at LO mostly reduction of inclusive cross section due to additional jet radiation presence of central rapidity gap stabilised multi-jet merging to further reduce uncertainties study hadronization impact M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

33 Conclusions Parton-shower and scale variation effects in + jj production via vector-boson-fusion important process for the LHC Higgs properties unitarity in scattering testing anomalous (triple and) quartic gauge couplings study performed with Herwig 7 & VBFNLO 3 compatible behavior of both parton showers and matching schemes small parton-shower effects for distributions of variables already present at LO mostly reduction of inclusive cross section due to additional jet radiation presence of central rapidity gap stabilised multi-jet merging to further reduce uncertainties study hadronization impact M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

34 BLHA Interface Defined standardized interface between Monte Carlo tools and one-loop programs Binoth Les Houches Accord (BLHA) tree-level evaluation of matrix elements well under control modular structure of NLO calculations [arxiv:100307, arxiv: ] algorithms for treatment of infrared singularities (Catani-Seymour, FKS,... ) incorporate one-loop matrix element information into MC tools Distribution of tasks: MC tool: cuts, histograms, parameters Monte Carlo integration phasespace ( VBFNLO) IR subtraction Born, colour- and spin-correlated Born (only BLHA1) One-loop provider (OLP): one-loop matrix elements 2R(M LO M virt) (coefficients of ɛ 2, ɛ 1, ɛ 0 ; M LO 2 ) Born, colour- and spin-correlated Born (only BLHA2) Setup stage via contract file (needed for tools which generate code on the fly) Run-time stage via binary interface (function calls) fast M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

35 Validation Compare LO+j results between VBFNLO stand-alone run and interfaced to Herwig 7 via Matchbox (inclusive cuts, with leptonic gauge boson decays into single different-flavour combination, Higgs non-decaying) LO+j stand-alone Matchbox σ [fb] σ/σ stand-alone Herwig 7 VBFNLO 3 H jjj + jjj - jjj Z l jjj Z ν jjj γ jjj Hγ jjj HH jjj + - jjj + Z l jjj good agreement - Z l jjj Z l Z l jjj Z l Z ν jjj + + jjj - - jjj + γ jjj - γ jjj Z l γ jjj Z ν γ jjj M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul / % 0.2 % 0.0 % -0.2 % -0.4 %

36 Setup Generation-level cuts: p T,j > 20 GeV, y j < 5.0, anti-k T jets with R = 0.4, b-quark veto p T,l > 15 GeV, y l < 3.0, m e +,µ > 15 GeV, m j1,j2 > 400 GeV, y j1 y j2 > 3.0 Analysis-level cuts: p T,j > 30 GeV, y j < 4.5, anti-k T jets with R = 0.4, b-quark veto p T,l > 20 GeV, y l < 2.5, m e +,µ > 15 GeV, m j1,j2 > 600 GeV, y j1 y j2 > 3.6 M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

37 Missing Transverse Momentum dσ/d p T,miss [fb/gev] NLO LO Dipoles NLO Dipoles NLO PS σ i /σ NLO µ F µ R 10-7 Herwig 7 VBFNLO µ Q µ tot p T,miss [GeV] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

38 Transverse Momentum of Leading Lepton dσ/d p T,l1 [fb/gev] µ R µ F σ i /σ NLO Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS 0.7 µ Q µ tot p T,l1 [GeV] M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

39 R Separation of Leading Jet and Leading Lepton dσ/d ΔR j1,l1 [fb] Herwig 7 VBFNLO 3 NLO LO Dipoles NLO Dipoles NLO PS R = y 2 + φ 2 Jacobian peak at R j1l1 = π µ tot µ Q µ R µ F σ i /σ NLO ΔR j1,l1 0.7 M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24

40 NNLO QCD Correction to VBF-H [Cacciari, Dreyer, Karlberg, Salam, Zanderighi] NNLO effects well approximated by NLO plus parton-shower results M. Rauch Vector-Boson-Fusion: Parton-shower and Anomalous-coupling Effects 25 Jul /24