Monte Carlo for Vector Boson Scattering: Standard Modell and anomalous gauge couplings

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1 : SM Monte Carlo for Vector Boson Scattering: Stard Modell anomalous gauge couplings VBS jamboree at BNL for -VBS on behalf of: Philipp Anger, Carsten Bittrich, Christian Gumpert, Simone Pagan Griso, Nikolina Ilic, Michael Kobel, Marc-Andre Pleier, Felix Socher, Anja Vest Institut für Kern- und Teilchenphysik, TU Dresden 29 Nov 22 /26

2 : SM for -VBS Vector Boson Scattering 2 3 for -VBS /26

3 : SM for -VBS Without a low-mass SM Higgs, VBS would violate unitarity Is the excess at 25 GeV a low-mass Higgs with SM couplings? What are the couplings between three four gauge bosons? Are there additional resonances in this channel, signs of new physics models? 3/26

4 : SM EW contributions to pp : O(EW ) = 6 (α s = ) for -VBS VV scattering diagrams (including triple quartic gauge vertices, Higgs channels i/a) +... non-vbs EW diagrams (not gauge invariantly separable) +... VVV diagrams (same O(EW ), but can be gauge invariantly separated suppressed by VBS topology cuts) 4/26

5 : SM for -VBS diagrams: O(EW ) = 4 O(QCD) = : additional, gauge invariantly separable contribution to final state can be suppressed with VBS cuts to separate from EW contribution 5/26

6 : SM for -VBS Kinematic differences of EW (VBS) (non-vbs) High p T central leptons VBS events High invariant mass of forward tagging jets, 2 central leptons from W decay 3, 4 forward/backward tagging jets 5 jets2invariantmass (EW) (EWQCD) EW contribution shows higher m jj than total EWQCD process To extract the EW contribution, cut on m jj lepton centrality ζ := min{min{η l, η l2 } - min{η j, η j2 }, max{η j, η j2 } - max{η l, η l2 }} /26

7 : SM between EW QCD between INT = EWQCD - EW - QCD parametrize interference in m jj or δη jj, reweight events for -VBS fiducial cross section uncertainty due to interference: Before reweighting: 5 % After reweighting: % 7/26

8 : SM Phase space for -VBS Fiducial volume... to suppress V jj diagrams which are not contained in the NLO calculation η(j) < 5, η(l) < 5 p T (j) > 2 GeV, p T (l) > GeV R(j, j) > M(jj) > 5 GeV 8/26

9 : SM used for for -VBS LO SHERPA extensive sample production for (WW,WZ,ZZ) at LO WHIZARD of Sherpa; anomalous QGC NLO EW contribution for W ± W ± W ± Z POWHEGBOX for W ± W ± 9/26

10 : SM for -VBS Monte Carlo Samples LO cross in fiducial phase space at 7 TeV SHERPA validated against WHIZARD Final state Process l ± νl ± ν jj W ± W ± 7.32 fb 8.94 fb l ± νl νjj W ± W + ZZ 9.68 fb fb l ± νl ν jj W ± W 8.63 fb fb l ± l l ± ν jj W ± Z 4.3 fb 39.3 fb lllljj ZZ 2.88 fb 8.4 fb samples: SHERPA events with ME+PS merging Most promising channels in terms of VBS: W ± W ± : no gg initial state small QCD contribution W ± Z: three leptons final state very clean channel WW opposite sign: suffering from huge ttbar background ZZ 4l: suffering from low cross- /26 Focus on like-sign WW WZ final states at the moment

11 : SM for -VBS of ME+PS merged events Modelling of third jet is extremely important in VBS: e.g. for CJV, event shape discriminators use ME+PS merged samples which should provide good modelling of third jet kinematics of sample with PowhegBox NLO events cross section for pp jje + ν eµ + ν µ: σ = 2.73 fb (8 TeV) 3 4 (sherpameps noqedcorr (powhegboxallrescaled) 2 3 (sherpameps noqedcorr (powhegboxallrescaled) Invariant mass of first two jets η of third jet both samples normalized to same cross section PowhegBox events without PS, Sherpa events with PS /26

12 : SM Theoretical uncertainties for -VBS Scale uncertainties at 8 TeV.5 µ R µ R 2 µ R.5 µ F 6±.7 679±.7 753±.6 µ F 627±.9 642±.6 656±.6 2 µ F 669±.7 69±.6 588±.5 PDF uncertainty Scale uncertainty: -.7% ; +.6% evaluated for different pdfsets (CT/CTEQ6L) for variation of Eigenvectors total uncertainty = +3.9% ; -2.8% Higgs mass/width dependence s-channel Higgs only present in VVV diagrams no dependence on the Higgs mass/width ovserved Higgs mass [GeV] [fb] WZjj-EW [fb] /26

13 : SM Anomalous Quartic Gauge Couplings for -VBS VBS measurement can set limits on anomalous couplings of gauge bosons: triple gauge couplings (TGC), quartic gauge couplings (QGC) VBS contains TRIPLE QUARTIC gauge vertices QGC only occur in few channels besides VBS, no strict limits have been set so far anomalous QGC limit setting is one of the goals of the VBS effort in 3/26

14 : SM for -VBS - anomalous couplings Extension of the effective SM-Lagrangian with terms containing additional operators: L = L SM + c i i O Λ 2 i +... Dimension-8 operators for c VV i = c VV i,sm + g 2 c VV i (no effect on TGC) VBF@NLO model contains light SM-Higgs (for EWSB) operators: L = f Λ 4 [(D µφ) d νφ]x[(d µ Φ) D ν Φ] L = f Λ 4 [(D µφ) d µφ]x[(d ν Φ) D ν Φ] parametrization: c WW, = g2 v 2 f, 8Λ 4 (Λ: scale of new physics, e.g. 2 TeV) normalize: f i = f i TeV 4 Λ 4 WHIZARD model EWSB via Σ field light SM Higgs implemented as well operators: L 4 = α 4 (tr[v µv ν]) 2 L 5 = α 5 (tr[v µv µ ]) 2 parametrization: c WW 4,5 = g 2 α 4,5 4/26

15 : SM for -VBS model Unitarization via energy-dependent form factors: α(ŝ) = α (+ŝ/λ 2 FF )2 implemented in VBFNLO; cf. arxiv: unitarization Commonalities between the models WHIZARD model unitarization using K-MATRIX METHOD: projecting the amplitude on the Arg circle gives maximal possible, still unitarized amplitude implemented in WHIZARD; cf. arxiv: effective SM-Lagrangian extended for anomalous couplings in different parametrizations apart from unitarization, parametrizations have the following relationship: α 4 = v2 f α 8Λ 4 5 = v2 f 8Λ 4 5/26

16 : SM unitarized samples, WWss channel for -VBS cross section sigma in fb cross section sigma in fb alpha VBFNLO Fit 5 Whizard Fit 5 VBFNLO cross- 4.5 Whizard cross f / Lambda 4 * (TeV) 4 unitarized samples, WWss channel alpha VBFNLO Fit 2.6 Whizard Fit 2.6 VBFNLO cross- 2.4 Whizard cross Comparison of VBF@NLO (red) Whizard (green) for different values of α 4 /f (top) α 5 /f (bottom) according to the relationship between α 4,5 f, α i+4 = v2 f i 8Λ 4 apparently, unitarization spoils this higher sensitivity to WHIZARD model in relevant ranges WHIZARD VBF@NLO agree for SM case (α i = f i = ) f / Lambda 4 (TeV) 4 6/26

17 : SM Kinematic comparisons at generator level for -VBS Produced at 8 TeV Cuts corresponding to the fiducial volume η(j) < 5, η(l) < 5 p T (j) > 2 GeV, p T (l) > GeV R(j, j) > M(jj) > 5 GeV Final states: jje + ν ee + ν e jje + e e + ν e 7/26

18 : SM for -VBS 8/26 Kinematic distributions from for different values of f in WWss Non-unitarized events Unitarized with form-factors dσ/dm jj [fb/gev] dσ/d φ [fb] Invariantmassm jjofjets.25 fs = fs =27,7.2 fs =435,3 fs =87, m jj [GeV] φ of leptons 2 fs = fs =27,7 fs =435,3 fs =87, φ m jj φ(ll) dσ/dm jj [fb/gev] dσ/d φ [fb]. 5e Invariantmassm jjofjets fs = fs =435,3 fs =87,7 fs = m jj [GeV] φ of leptons fs = fs =435,3 fs =87,7 fs = φ

19 : SM for -VBS 9/26 Whizard unitarized vs. non-unitarized in WWss channel Non-unitarized events Unitarized with k-matrix dσ/dm jj [fb/gev] dσ/d φ [fb] Invariantmassm jjofjets.4 a 4=.35 a 4=, a 4=,2.3 a 4=, m jj [GeV] φ of leptons 8 a 4= 6 a 4=, a 4=,2 4 a 4=, φ m jj φ(ll) dσ/dm jj [fb/gev] dσ/d φ [fb] Invariantmassm jjofjets.2 a 4=. a 4=, a 4=,2.8 a 4=, m jj [GeV] φ of leptons.4 a 4= a 4=,.2 a 4=,2 a 4=, φ

20 : SM Whizard WWss (unitarized) for -VBS α 4 dσ/dm jj [fb/gev] Invariantmassm jjofjets.2 a 4=. a 4=, a 4=,2.8 a 4=, m jj [GeV] m jj α 5 dσ/dm jj [fb/gev] Invariantmassm jjofjets.8.7 a 5= a 5=,.6 a 5=,2 a 5=, m jj [GeV] dσ/d φ [fb] φ of leptons.4 a 4= a 4=,.2 a 4=,2 a 4=, φ(ll) dσ/d φ [fb] φ of leptons a 5= a 5=, a 5=,2 a 5=, φ φ 2/26

21 : SM Sensitivity of our measurement to With last background estimation numbers: for -VBS signal 5.5 background 24.5 S + B 6.32 S+B S Sensitivity: we are sensitive to exclude a cross section which gives S signal events S = S + 2 S + B = = 28.5 σ 2σ SM In Whizard s model for the jje + ν ee + ν e jje + e e + ν e, the following values of the anomalous couplings give σ = 2σ SM (for the EW contribution) as -dimensional limits: e + ν ee + ν e α 4.5 [α 5 = ] α 5.2 [α 4 = ] e + e e + ν e α 4.25 [α 5 = ] α 5.25 [α 4 = ] 2/26

22 : SM for -VBS In Monte Carlo simulations, the EW contribution to the final state (containing VBS) can be separated from QCD by fixing O(α s) = NLO calculations of VBS are currently implemented in VBF@NLO POWHEGBOX SHERPA produces ME-PS merged (LO ) events with good third-jet properties (these are being used in current studies) Limits on anomalous quartic gauge couplings can be set with 8 TeV data; different models are under investigation using WHIZARD VBF@NLO 22/26

23 : SM for -VBS BACKUP SLIDES 23/26

24 : SM Lepton centrality for -VBS Lepton centrality ζ ζ := min{min{η l, η l2 } - min{η j, η j2 }, max{η j, η j2 } - max{η l, η l2 }} leptons2 centrality EW QCD both leptons in η between tagging jets: ζ > (VBS topology) one or both leptons at larger η than closest jet: ζ < EW tends to have more positive ζ than EWQCD 24/26

25 : SM for -VBS dσ/de [fb/gev] Energy E per particle, all particles Consistency check: VBF@NLO Whizard with SM settings VBFNLO, without VBFNLO, with Whizard, without Whizard, with E [GeV] dσ/d φ [fb] φ of leptons VBFNLO, without VBFNLO, with Whizard, without Whizard, with φ VBF@NLO Whizard agree within statistical uncertainties 25/26

26 : SM for -VBS -check of Whizard s k-matrix model with SM-Higgs Comparing the SM with SM-Higgs (m = 26 GeV) to SM km with SM-Higgs SM km with σ resonance dσ/dm ll [fb/gev] Invariantmassm llofleptons dσ/dm jj [fb/gev] (WWsspartSM 4MeV).2 (WWsspartkmSM 4Me (WWsspartkm 4MeV) Invariantmassm jjofjets (WWsspartSM 4MeV) (WWsspartkmSM 4Me (WWsspartkm 4MeV) m ll [GeV] m jj [GeV] SM SM km with SM settings (incl. SM-Higgs) give consistent results 26/26