NLO Electroweak Corrections in Di-Boson Production. Ansgar Denner, Würzburg

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1 NLO Electroweak Corrections in Di-Boson Production Ansgar Denner, Würzburg in collaboration with B. Biedermann, M. Billoni, S. Dittmaier, L. Hofer, B. Jäger, L. Salfelder Multi-Boson Interactions, Madison, August 24 26, Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion

2 Outline 1 Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 1/25

3 Electroweak di-boson production at the LHC V V V V V,V = γ,z,w± Physics issues: precision test of electroweak sector of Standard Model search for anomalous triple-gauge-boson couplings sensitivity grows with energy of gauge bosons EW corrections significant αlog 2 (E/M W ) important class of background processes to Higgs production: H WW /ZZ 4f invariant masses below VV thresholds, proper description of off-shell VV production needed! to new-physics searches at high invariant masses EW corrections significant Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 1/25

4 Approximations for di-boson production Treatment of hard process pp VV 4leptons (massive VV ): On-shell VV production + ok for total cross section no treatment of physical final state Narrow-width approximation (Γ ) production and decay of on-shell vector bosons + includes decays of vector bosons and possibly spin correlations neglects terms of order Γ/M and irreducible background + different final states treated on same footing (Double-)pole approximation (D)PA + includes off shell effects of resonant bosons and phase space matrix elements include only resonant parts no interferences, no irreducible background + PA only for virtual NLO corrections! + different final states treated on same footing Full calculation + includes off-shell effects, irreducible background, interferences complicated calculation, depends on final state Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 2/25

5 Known corrections to VV production State-of-the-art predictions: Wγ/Zγ (full calculation with leptonic decays) NNLO QCD Grazzini, Kallweit, Rathlev 14, 15 NLO EW Denner, Dittmaier, Hecht, Pasold 14, 15 WW,WZ,ZZ NNLO QCD NLO EW including leptonic decays ZZ (distributions) Cascioli et al. 14 Grazzini, Kallweit, Rathlev 15 WW (distributions) Gehrmann et al. 14 Grazzini, et al. 16 WZ (inclusive rates) Grazzini, et al. 16 gg VV 4 leptons Binoth et al. 5, 6 + NLO corrections for on-shell V s Caola et al. 15 inclusion of decays non-trivial stable W/Z bosons Bierweiler, Kasprzik, Kühn, Uccirati 12, 13 Baglio, Le, Weber 13 approximative inclusion in HERWIG++ Gieseke, Kasprzik, Kühn 14 (via correction factor) pp WW 4 leptons in DPA Billoni, Dittmaier, Jäger, Speckner 13 full off-shell calculation Biedermann et al. 16 Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 3/25

6 EW corrections to massive di-boson production stable/on-shell W/Z bosons Bierweiler, Kasprzik, Kühn 13 t EW corrections small for integrated cross section ( 1%... 5%) several 1% corrections in distributions from Sudakov logarithms αln 2 (E/M W ) Photonic corrections radiative tails below thresholds and resonances enhanced by QED logarithms αln(e/m l ) on-shell calculation not applicable below VV threshold! Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 4/25

7 Photonic contributions to WW production stable/on-shell W bosons dσ/dpt [pb/gev] dσ/dy(pb).1 LHC at 14 TeV, MWW > 1 GeV σ q q,w LO σ q q,w+ σ gg LO LO 1 σ γγ LO 1 1 y 1 q q (NLO EW) q q (LO) gg (LO) 2 q q (NLO QCD) δ(%) γγ (LO) γγ (NLO) q q (EW NLO) 2 q q (EW virtual) 1 5 γ induced pp W + W 3 γ radiated 1 6 γγ (LO) s = 14 TeV, µ = γγ (NLO) 2MW p W+ T [GeV] 7 d σ/dσ Born [%] δew W δγγ δgg δqcd/1 y pp W + W s = 14 TeV, µ = 2MW p W+ T [GeV] 1 Bierweiler, Kasprzik, Kühn 12 Note: large contribution by γγ channel for high invariant WW masses! large uncertainty of photon PDFs 2 Baglio, Le, Weber Note: large impact of qγ collisions (qγ qw) overwhelmed by QCD corrections eliminated by jet veto Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 5/25

8 Outline 1 Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 6/25

9 Leading-order contributions WW production q q µ + ν µ e ν e q q W Z,γ W µ + νµ νe e q q W W µ + νµ νe e 2 W resonances 1 W resonance σ γγ µ + ν µ e ν e γ γ W W µ + νµ νe e 2 W resonances 1.% TeV pure EW processes ZZ production q q µ + µ e + e q q Z,γ Z,γ µ + µ e + e q q Z,γ Z,γ µ + µ e + e 2 Z resonances 1 Z resonance σ γγ µ + µ e + e γ γ Z,γ µ e + e µ + 1 Z resonance.2% TeV return Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 6/25

10 Double-pole approximation vs. full calculation double-pole approximation full off-shell calculation q V V q on-shell production f 1 V f 2 f 3 V f 4 on-shell decays q q f 1 W f 3 f 2 γ,z f 4 f 3 d d W u W f 2 f 3 f 1 f 2 γ,z f 3 f 4 expansion about resonance poles for virtual corrections only factorizable & non-fact. corrs. 1 2 diagrams (2 2 production) + numerically fast valid only for ŝ > 2M V +O(Γ V ) error estimate for ŝ <.5 1TeV: α Γ V log(...).5 2% π M V off-shell calculation for qq 4f with complex-mass scheme 1 3 off-shell diagrams/channel CPU intensive + NLO accuracy everywhere global error estimate: δ NNLOEW δ 2 NLOEW approaches compared for e + e WW 4f Denner, Dittmaier, Roth, Wieders 5 and pp WW 4f Biedermann et al. 16 Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 7/25

11 Details of the full 4f NLO calculation Virtual corrections matrix elements numerically with RECOLA Actis et al. 13, 16 (Recursive computation of one-loop amplitudes) generator for arbitrary LO and NLO matrix elements in SM loop integrals evaluated with COLLIER Denner, Dittmaier, Hofer 16 (Complex one-loop library in extended regularizations) numerically stable and fast calculation of tensor one-loop integrals W/Z resonances in complex-mass scheme Denner et al. 99, 5 applicable and gauge-invariant everywhere in phase space G µ scheme for electromagnetic coupling absorbs running of α from to M W and universal corrections related to ρ parameter photonic corrections with α() Assumptions massless light fermions u, d c, s, b; e, µ, τ flavour mixing neglected Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 8/25

12 Details of the full 4f NLO calculation Real corrections and Monte Carlo integration IR singularities treated with dipole subtraction Catani, Seymour 96; Dittmaier 99; Dittmaier et al. 8 collinear-unsafe ( bare ) and -safe ( dressed ) leptons supported multi-channel Monte Carlo integration γ-induced contributions using NNPDF2.3QED Ball et al. 13 Checks γγ processes included at LO (small contributions) qγ contributions taken into account (NLO) independent diagrammatic calculation as for e + e WW 4f Denner et al. 5 additional checks with FEYNARTS/FORMCALC in the framework of POLE Accomando et al. 5 two independent calculations of all important ingredients Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 9/25

13 Collinear final-state radiation off leptons p Universal logarithmically enhanced corrections α n ln n (m 2 l/q 2 ) q from final-state radiation q possible treatments: p bare leptons (typical for muons, non-collinear-safe (NCS) case) photons are experimentally separated from leptons collinear singularities regularised by lepton (muon) mass logarithmically enhanced corrections large radiative tails dressed leptons (typical for electrons, collinear safe (CS)) recombination of leptons with (collinear) photons mass-singular logarithms cancel, collinear-safe observables predictions depend on photon-recombination scheme smaller radiative tails dedicated photonic parton showers, e.g. PHOTOS Placzek, Jadach 3; Carloni Calame et al. 4; Golonka, Was 7 full FSR not universal, in general not separable from EW corrections combination of PHOTOS with full EW corrections difficult in practice γ l γ Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 1/25

14 Outline 1 Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 11/25

15 Setups for WW production Lepton photon recombination for R γl <.1 Jet definition: p T,j > 25GeV, y j < 5 Inclusive scenario p T,l > 2GeV, y l < 2.5 R lj >.4 for p T,j > 25GeV p T,j < 1GeV (jet veto to avoid large QCD corrections) ATLAS scenario (following and ) p T,l1 > 25GeV, p T,l2 > 2GeV, y l < 2.5 R e µ + >.1, M e µ + > 1GeV, p T,miss > 25GeV, p T,j < 25GeV no jets Higgs-search scenario (following ) ATLAS scenario with p T,miss > 2GeV plus 1GeV < M e µ + < 55GeV, φ e µ + < 1.8 Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 11/25

16 NLO EW cross section for W-pair production 13TeV LHC σ LO qq [fb] δnlo qq [%] δqγ q b [%] δ γγ [%] δ EW [%] δ bγ [%] Inclusive ATLAS Higgs bkgd photon-induced contributions below one percent photon-bottom-induced contributions involve tw production 13TeV LHC σ LO qq [fb] δnlo,dpa qq,cus [%] δ NLO qq,cus [%] δnlo qq,cs [%] Inclusive ATLAS Higgs bkgd accuray of DPA (only for virtual NLO) below one per mille difference between collinear-safe and unsafe scenario:.5% relative corrections for 8TeV similar Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 12/25

17 W-pair production: EW corrections δ[%] Transverse-momentum distribution (ATLAS setup) LO EW qγ qq γγ p T,e [GeV] dσ [ ] fb dp T,e GeV pp νµµ + e νe +X spp = 13TeV ATLAS WW setup µ treated coll. unsafe EW corrections qq: 45% at p T,e = 1TeV γγ: +12% at p T,e = 1TeV large uncertainty from PDFs qγ: negligible owing to jet veto Biedermann et al. 16 Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 13/25

18 W-pair production: DPA versus full off-shell EWC Rapidity and invariant-mass distributions Biedermann et al pp νµµ + e νe +X spp = 13TeV ATLAS cuts µ treated coll. unsafe dσ dy(e ) [fb] dσ [ ] fb dm e µ + GeV pp νµµ + e νe +X spp = 13TeV ATLAS cuts µ treated coll. unsafe LO qq LO DPA 1 3 LO qq LO DPA δ[%] δ qq δ qq DPA δ[%] δ qq δ qq DPA y(e ) M e µ + [GeV] electron rapidity: agreement as for integrated cross section M e µ + distribution: deviation 1 3% for M e + µ > 5GeV importance of singly-resonant diagrams grows with invariant mass Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 14/25

19 Error estimate of DPA Error estimate of full NLO calculation (missing 2-loop EW corrections) (δ EW ) 2 Error estimate of DPA { (δ ) DPA 2, α Γ W DPA max EW ln(...), δew DPA σ LO σlo DPA } π M } W σ {{} LO DPA <.5% missing 2-loop EW corrections missing off-shell contributions in regions where DPA applies change of NLO corrections due to failure of DPA Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 15/25

20 W-pair production: DPA versus full off-shell EWC δ[%] Transverse-momentum distribution of a single lepton Biedermann et al. 16 ν µ µ LO qq LO DPA pt(e )[GeV] [ ] dσ fb dpt(e ) GeV pp νµµ + e νe +X spp = 13TeV ATLAS cuts µ treated coll. unsafe δ qq δ qq DPA difference of 5% (1%) at 5GeV (1TeV) full off-shell calculation necessary q q γ,z e W ν e e p T(µ + ν µ ν e) p T(e ) impact of singly-resonant diagrams where e takes recoil from (µ + ν µ ν e) doubly-resonant diagrams do not favour high-p T leptons decay products of resonances prefer lower p T Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 16/25

21 W-pair production: DPA versus full off-shell EWC δ[%] 1 Transverse-momentum distribution of the charged lepton pair Biedermann et al LO qq LO DPA δ qq δ qq DPA pt(e µ + )[GeV] [ ] dσ fb dpt(e µ + ) GeV pp νµµ + e νe +X spp = 13TeV ATLAS cuts µ treated coll. unsafe 8 1 q q γ,z µ W e ν e µ + ν µ p T(e µ + ) p T( ν e) p T(ν µ) doubly-resonant diagrams extremely suppressed! singly-resonant diagrams dominate where (e µ + ) recoil against (ν µ ν e) DPA fails for p T > 2GeV, since off-shell production dominates! Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 17/25

22 Outline 1 Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 18/25

23 Setups for ZZ production Lepton photon recombination for R γl <.2 Inclusive scenario (following ATLAS ) p T,l > 15GeV, y l < 2.5, R ll >.2 Higgs-search scenario (motivated by ATLAS/CMS and ) p T,l > 6GeV, y l < 2.5, R ll >.2 4GeV < M l + < 12GeV, 12GeV < M 1 l 1 l + 2 l 2 M 4l > 1GeV Processes: pp µ + µ e + e,µ + µ µ + µ Lepton pairing for identical leptons < 12GeV leading lepton pair l + 1 l 1 : pair ij with M l il j closest to M Z sub-leading lepton pair l + 2 l 2 : pair of remaining two leptons Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 18/25

24 Gauge-invariant splitting of corrections for ZZ Gauge-invariant splitting into weak and photonic corrections for processes without charged currents at LO photonic corrections: diagrams with a photon in a loop coupling to external fermion lines q Z,γ µ + q Z,γ µ + q Z,γ µ + γ µ e + Z µ e + γ µ e + q Z e q γ e q γ e weak corrections: remaining diagrams including all (gauge-invariant) fermion-loop diagrams q q Z,γ Z Z µ + µ e + e q q γ NC interaction in SM equivalent to U(1) γ U(1) Z gauge theory renormalizable theory, gauge-invariant EW corrections photonic corrections separately gauge invariant since U(1) charges can be freely chosen f f Z,γ γ µ + µ e + e Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 19/25

25 Cross section and interference for ZZ production Processes: pp µ + µ e + e : [2µ2e] pp µ + µ µ + µ : [4µ] effective symmetry factor 1/2 13TeV LHC σ LO qq [fb] δweak qq (%) δ phot qq,cs (%) δphot qq,cus (%) δγγ(%) δqγ(%) incl. [2µ2e] incl. [4µ] Higgs [2µ2e] Higgs [4µ] weak corrections moderate photonic corrections negligible Higgs-search scenario few percent for collinear-unsafe case (.7% per muon) photon-induced contributions negligible (γγ singly resonant, qγ not enhanced by t-channel W exchange) deviation from on-shell calculation O(1%) Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 2/25

26 Cross section and interference for ZZ production 13TeV LHC σ LO qq [fb] δweak qq (%) δ phot qq,cs (%) δphot qq,cus (%) δγγ(%) δqγ(%) incl. [2µ2e] incl. [4µ] Higgs [2µ2e] Higgs [4µ] Interference effects for equal-flavour final states q q Z,γ Z,γ µ + (1) µ (2) µ + (3) µ (4) q q Z,γ Z,γ µ + (1) µ (4) µ + (3) µ (2) interference suppressed by Γ Z /M Z per resonance LO effect σ LO[2µ2e] 2σ LO[4µ] interference suppression inclusive: 1.3.3% (Γ Z /M Z ) 2 Higgs-specific: % Γ Z /M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 2/25

27 Z-pair production: EW corrections and interference Invariant 4-lepton-mass distribution (inclusive scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l δ[%] δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] M4l[GeV] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV M Z M Z + 2p T,min 2M Z 2 regions: 2M Z < M 4l doubly-resonant contributions M Z +2p T,min < M 4l < 2M Z singly-resonant contributions M 4l < M Z +2p T,min non-resonant contributions M 4l M Z: Z-boson resonance diagrams radiative tails below thresholds and peaks weak corrections below 5% positive below ZZ threshold negative above ZZ threshold 2% for M 4l = 1TeV plot photonic contribution < 1% Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 21/25

28 Z-pair production: EW corrections and interference Invariant 4-lepton-mass distribution (inclusive scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l [2µ2e]/(2 [4µ]) LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV LO: [2µ2e]/(2 [4µ]) NLO: [2µ2e]/(2 [4µ]) M4l[GeV] 2 distribution does not depend on lepton pairing [2µ2e]/(2 [4µ]) gives interference interference mainly LO effect interference effect: permille level in doubly-resonant region suppression (Γ Z/M Z) 2 2% in singly-resonant region suppression (Γ Z/M Z) 7% in non-resonant region no suppression 4µ matrix elements needed M Z M Z + 2p T,min 2M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 21/25

29 Z-pair production: EW corrections and interference Distribution in angle between decay planes (sensitive to Higgs coupling structure) (inclusive scenario) 2 Biedermann et al. preliminary dσ dφ [fb] [2µ2e]/(2 [4µ]) LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV LO: [2µ2e]/(2 [4µ]) NLO: [2µ2e]/(2 [4µ]) φ[rad] f 2 f 2 Z H φ Z f 1 f 1 distribution does not depend on interchange of lepton pairs [2µ2e]/(2 [4µ]) gives interference few percent interference effect: small angle: destructive interference (like-sign muons parallel) large angle: constructive interference similar for Higgs-bkgd scen. Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 22/25

30 Z-pair production: EW corrections and interference Distribution in angle between decay planes (sensitive to Higgs coupling structure) (inclusive scenario) 2 Biedermann et al. preliminary dσ dφ [fb] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] distribution dominated by resonant ZZ production s = 13 TeV EW/weak corrections weak corrections distort distribution by 3% (2% for Higgs-background scenario) δ[%] δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] photonic corrections 1% (φ insensitive to collinear photon emission off leptons) φ[rad] Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 22/25

31 Z-pair production: EW corrections/muon pair selection Transverse-momentum distribution of the (leading) muon (inclusive scenario) Biedermann et al. preliminary ] [ fb GeV dσ dp Tµ + [2µ2e]/(2 [4µ]) s = 13 TeV leading µ + LO: [2µ2e]/(2 [4µ]) NLO: [2µ2e]/(2 [4µ]) LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] sensitive to event selection leading muon from muon pair with M µµ closer to M Z differences between 4µ and 2e2µ 2e2µ: distribution at high p T dominated by muons not resulting from a resonance (compare WW production) 4µ: distribution of leading muon dominated by doubly-resonant contributions suppressed for high p T (sub-leading muon enhanced) p Tµ + [GeV] Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 23/25

32 Z-pair production: EW corrections/muon pair selection Transverse-momentum distribution of the (leading) muon (inclusive scenario) Biedermann et al. preliminary 1 1 ] [ fb GeV dσ dp Tµ + δ[%] s = 13 TeV leading µ + LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] EW/weak corrections larger for leading muon (4µ) (smaller for sub-leading muon) Sudakov logarithms larger for doubly-resonant contributions photonic corrections yield constant offset of 2% for 2µ2e < 1% for 4µ p Tµ + [GeV] Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 23/25

33 ] [ fb GeV dσ d φ µ + µ [2µ2e]/(2 [4µ]) Z-pair production: EW corrections/muon pair selection Azimuthal-angle difference between (leading) muons (inclusive scenario) s = 13 TeV leading µ + µ pair φ µ + µ [GeV] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] LO: [2µ2e]/(2 [4µ]) NLO: [2µ2e]/(2 [4µ]) Biedermann et al. preliminary distribution dominated by doubly-resonant contributions with M 4l > 2M Z leading muons dominantly back to back large φ µ + µ region of small φ µ + µ : muon pair in 2e2µ (as sub-leading muon pair) enhanced by photon pole truncated by cut on lepton-separation R ll leading muon pair suppressed (dominantly from on-shell Z boson) Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 24/25

34 Z-pair production: EW corrections/muon pair selection Azimuthal-angle difference between (leading) muons Biedermann et al. preliminary (inclusive scenario) 1 1 EW/weak corrections large φ µ + µ : as for σint ] [ fb GeV dσ d φ µ + µ δ[%] s = 13 TeV leading µ + µ pair φ µ + µ [GeV] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] small φ µ + µ : increased negative corrections owing to larger contributions from high-energetic muons leading muon pair: large negative correction 2µ2e, sub-leading µ pair: contribution of Zγ smaller correction photonic corrections 1 2% larger where doubly-resonant diagrams dominate Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 24/25

35 Outline 1 Introduction 2 Calculational details of full NLO EW calculation 3 Numerical results for WW production 4 Numerical results for ZZ production 5 Conclusion Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 25/25

36 Conclusion Di-boson production at the LHC sensitive to non-abelian gauge-boson self-interactions important background to new-physics searches to precision Higgs analyses in pp H WW/ZZ 4f precise predictions with QCD and EW corrections required NLO EW corrections to pp WW/ZZ 4 leptons (fully off shell) exist EW corrections of several 1% in tails of distributions Excursion radiative tails near resonances and thresholds, enhanced for bare muons DPA fails for transverse momentum distributions where singly-resonant contributions become sizeable corrections negative above VV threshold but positive below per-cent level interference effects for pp µ + µ µ + µ below VV threshold photon-induced contributions small for WW and negligible for ZZ EW corrections for pp WZ 4 leptons in preparation Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 25/25

37 Outline 6 Backup Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 26/25

38 Triple vector-boson production 2 6 process: pp VV V 6l Existing calculations: NLO QCD corrections for on-shell vector bosons: pp ZZZ Lazopoulos, Melnikov, Petriello 7 pp VV V (massive) Binoth, Ossola, Papadopoulos, Pittau 8 NLO QCD corrections including leptonic decays: pp WWZ Hankele, Zeppenfeld 7 (VBFNLO) pp VV V Campanario et al (VBFNLO) NLO EW corrections for on-shell vector bosons: pp VV V (massive) Nhung, Ninh, Weber 13 NLO EW corrections to production with leptonic decays in NWA: pp WZZ,WWW Shen Yong-Bai et al. 15, 16 Automated tools: RECOLA, OPENLOOPS, MADGRAPH5_AMC@NLO calculation of EW corrections (in PA) within reach Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 26/25

39 Vector-boson scattering 2 6 process: pp VV +2j 4l+2j enormously complex! EW production: O(α 6 ) QCD-induced production: O(α 2 sα 4 ) Existing building blocks: full LO predictions: Ballestrero, Franzosi, Maina 1 NLO QCD corrections to EW diagrams: Jäger, Oleari, Zeppenfeld (+ Bozzi) 6, 7, 9 (VBFNLO); Denner, Hosekova, Kallweit 12 NLO QCD corrections to QCD diagrams: Melia, Melnikov, Röntsch, Zanderighi 1, 11; Greiner et al. 12; Campanario, Kerner, Ninh, Zeppenfeld 13, 14 (VBFNLO) NLO EW corrections for on-shell vector-boson scattering VV VV Automated tools: RECOLA, OPENLOOPS, MADGRAPH5_AMC@NLO calculation of EW corrections (in DPA) within reach return Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 27/25

40 Z-pair production: EWC for large transverse momentum Invariant 4-lepton-mass distribution (inclusive scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l δ[%] M4l[GeV] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] regions: 2M Z < M 4l doubly-resonant contributions M Z +2p T,min < M 4l < 2M Z singly-resonant contributions M 4l < M Z +2p T,min non-resonant contributions M 4l M Z: Z-boson resonance radiative tails below thresholds and peaks weak corrections 2% for M 4l = 1TeV positive below ZZ threshold negative above ZZ threshold return Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 28/25

41 Z-pair production: photonic contributions Invariant 4-lepton-mass distribution (inclusive scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l δ[%] M4l[GeV] LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV δ γγ[4µ] δ qγ[4µ] δ γγ[2µ2e] δ qγ[2µ2e] M Z M Z + 2p T,min 2M Z 2 regions: 2M Z < M 4l doubly-resonant contributions M Z +2p T,min < M 4l < 2M Z singly-resonant contributions M 4l < M Z +2p T,min non-resonant contributions M 4l M Z: Z-boson resonance photon-induced contributions: per-mille level in doubly-resonant region < 1% in singly-resonant region 1% in non-resonant region vanishing for M 4l = M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 29/25

42 Z-pair production: collinear safe vs. collinear unsafe Invariant 4-lepton-mass distribution (inclusive scenario) Biedermann et al. preliminary 1 1 s = 13 TeV regions: ] [ fb GeV dσ dm4l δ[%] δ EW qq [4µ] unsafe δ EW δ EW qq [2µ2e] unsafe qq [4µ] safe δ EW qq [2µ2e] safe 1 LO [4µ] NLO EW unsafe [4µ] LO [2µ2e] NLO EW unsafe [2µ2e] M4l[GeV] M Z < M 4l doubly-resonant contributions M Z +2p T,min < M 4l < 2M Z singly-resonant contributions M 4l < M Z +2p T,min non-resonant contributions M 4l M Z: Z-boson resonance radiative tails below thresholds and peaks enhanced for each collinear-unsafe muon M Z M Z + 2p T,min 2M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 3/25

43 Z-pair production: EW corrections and interference Invariant 4-lepton-mass distribution (Higgs scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l 1 1 LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV regions: 2M Z < M 4l doubly-resonant contributions M Z +2p T,min < M 4l < 2M Z singly-resonant contributions M 4l < M Z +2p T,min non-resonant contributions δ[%] δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] radiative tails below thresholds and peaks weak corrections below 5% positive below ZZ threshold negative above ZZ threshold 2% for M 4l = 1TeV M4l[GeV] 18 2 photonic contributions < 1% M Z + 2p T,min 2M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 31/25

44 Z-pair production: EW corrections and interference Invariant 4-lepton-mass distribution (Higgs scenario) Biedermann et al. preliminary ] [ fb GeV dσ dm4l [2µ2e]/(2 [4µ]) LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] s = 13 TeV LO: [2µ2e]/(2 [4µ]) NLO: [2µ2e]/(2 [4µ]) distribution does not depend on lepton pairing [2µ2e]/(2 [4µ]) gives interference invariant-mass cuts depend on lepton pairing interference mainly LO effect interference effect: 1% in doubly-resonant region 1% in singly-resonant region 4µ matrix elements needed M4l[GeV] 18 2 M Z + 2p T,min 2M Z Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 31/25

45 Z-pair production: EW corrections ] [ fb GeV dσ dm µ + µ δ[%] Invariant subleading di-lepton-mass distribution (inclusive scenario) δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] 2 LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] M µ + µ [GeV] Distribution Biedermann et al. preliminary for [2µ2e] dominated by on-shell e + e pair for subleading lepton pair: similar outside resonance suppressed near resonance EW corrections radiative tails below resonance weak corrections change sign near resonance (interference between photon and Z changes sign) corrections for subleading pair similar to µ + µ pair in [2µ2e] Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 32/25

46 Z-pair production: EW corrections ] [ fb GeV dσ dm µ + µ δ[%] Invariant leading di-lepton-mass distribution (inclusive scenario) δ EW δ weak qq [4µ] δ EW qq [4µ] δ weak qq [2µ2e] qq [2µ2e] 2 LO [4µ] NLO EW [4µ] LO [2µ2e] NLO EW [2µ2e] M µ + µ [GeV] Biedermann et al. preliminary Distribution depends on lepton pairing for [2µ2e] dominated by on-shell e + e pair for leading muon pair suppressed outside resonance peak near 45GeV due to Z resonance in M 4l EW corrections radiative tails below resonance weak corrections change sign near resonance (interference between photon and Z changes sign) corrections for leading pair differ from µ + µ pair in [2µ2e] Multi-Boson Interactions, Madison, August 24 26, 216 Ansgar Denner, Würzburg EWC in di-boson production 33/25