Electroweak corrections to W/Z+jet production at the LHC Alexander Mück in collaboration with A. Denner (PSI), S. Dittmaier (Freiburg), T. Kasprzik (Karlsruhe) HP 2 . 3rd Florence, 14th September 2010 EW corrections for W/Z+jet production – Alexander M¨ uck – p.1/ 18 EW corrections for W/Z+jet production – p. 0/ 18
Outline W/Z production at the LHC W/Z+jet production: pp → W/Z + jet → lν l /ll + jet motivation and theoretical status Electroweak and QCD corrections Numerical results for the LHC Conclusions EW corrections for W/Z+jet production – Alexander M¨ uck – p.2/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC u ν l ② ② u ν l Charged-current Drell-Yan: pp → W ± → l ± ν l ② W + W + ② ¯ ② d l ¯ l + clean signal: lepton + missing p T d huge cross section: σ W + → µ + ν µ = 3 nb (Atlas cuts at 7 TeV) ⇒ 2 events per minute at LHC right now EW corrections for W/Z+jet production – Alexander M¨ uck – p.3/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC u ν l ② ② u ν l Charged-current Drell-Yan: pp → W ± → l ± ν l ② W + W + ② ¯ ② d l ¯ l + clean signal: lepton + missing p T d huge cross section: σ W + → µ + ν µ = 3 nb (Atlas cuts at 7 TeV) very useful: M W , Γ W , luminosity, PDFs, calibration EW corrections for W/Z+jet production – Alexander M¨ uck – p.3/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC u ν l ② ② u ν l Charged-current Drell-Yan: pp → W ± → l ± ν l ② W + W + ② ¯ ② d l ¯ l + clean signal: lepton + missing p T d huge cross section: σ W + → µ + ν µ = 3 nb (Atlas cuts at 7 TeV) very useful: M W , Γ W , luminosity, PDFs, calibration Neutral-current Drell-Yan: q l − ② ② u ν l pp → Z/γ → l + l − ② Z/γ W + ② ② l + q ¯ ¯ l + clean signal: charged lepton pair d huge cross section: σ Z → µ + µ − = 0 . 5 nb (Atlas cuts at 7 TeV) very useful: calibration, luminosity, PDFs EW corrections for W/Z+jet production – Alexander M¨ uck – p.3/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC Theory status: QCD: NNLO, resummation, parton shower matching EW: NLO, leading higher order contributions EW corrections for W/Z+jet production – Alexander M¨ uck – p.4/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC Theory status: QCD: NNLO, resummation, parton shower matching EW: NLO, leading higher order contributions combined EW and QCD corrections? EW corrections for W/Z+jet production – Alexander M¨ uck – p.4/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z Production at the LHC Theory status: QCD: NNLO, resummation, parton shower matching EW: NLO, leading higher order contributions combined EW and QCD corrections? d σ = d σ MC@NLO + (d σ HORACE − d σ Born ) HERWIG − PS etc. EW Balossini et al. [arXiv:0907.0276] hard QCD radiation + EW corrections? ⇒ look at EW corrections for W/Z+jet production EW corrections for W/Z+jet production – Alexander M¨ uck – p.4/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z+jet production pp → lν l /l + l − + jet : e u ν e W d large cross section g ( ∼ 10 % of inclusive sample) d dominant SM channel for high p T leptons precision tests for jet dynamics W+jet(s) important background for many searches (high p T lepton, missing energy, jet(s)) EW corrections for W/Z+jet production – Alexander M¨ uck – p.5/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z+jet production pp → lν l /l + l − + jet : e u ν e W d large cross section g ( ∼ 10 % of inclusive sample) d dominant SM channel for high p T leptons precision tests for jet dynamics W+jet(s) important background for many searches Theoretical status: NLO QCD corrections known and available DYRAD: Giele et al. [hep-ph/9302225] MCFM: Campbell, Ellis [hep-ph/0202176] and as part of NNLO single W: Melnikov, Petriello [hep-ph/0609070] Catani et al. [arXiv:0903.2120] EW corrections for W/Z+jet production – Alexander M¨ uck – p.5/ 18 EW corrections for W/Z+jet production – p. 0/ 18
W/Z+jet production pp → lν l /l + l − + jet : e u ν e W d large cross section g ( ∼ 10 % of inclusive sample) d dominant SM channel for high p T leptons precision tests for jet dynamics W+jet(s) important background for many searches Theoretical status: NLO QCD corrections known and available EW corrections for stable (on-shell) W/Z bosons Z+jet: Kühn, Kulesza, Pozzorini, Schulze [hep-ph/0408308], [hep-ph/0507178] W+jet: Kühn, Kulesza, Pozzorini, Schulze [hep-ph/0703283], [arXiv:0708.0476] Hollik, Kasprzik, Kniehl [arXiv:0707.2553] EW corrections for W/Z+jet production – Alexander M¨ uck – p.5/ 18 EW corrections for W/Z+jet production – p. 0/ 18
EW corrections Complete EW corrections calculated W+jet: Denner, Dittmaier, Kasprzik, AM [arXiv:0906.1656] Z+jet: internal comparison just finished ν e u Z ν e e + u O (100) diagrams for W, W u g O (200) diagrams for Z d per partonic channel T15 C2 N50 physical final state all off-shell effects included part of the O ( αα s ) corrections for incl. W production EW corrections for W/Z+jet production – Alexander M¨ uck – p.6/ 18 EW corrections for W/Z+jet production – p. 0/ 18
EW corrections Complete EW corrections calculated W+jet: Denner, Dittmaier, Kasprzik, AM [arXiv:0906.1656] Z+jet: internal comparison just finished e b W ν e e + t tops in the loop for Z W g t in bottom initiated b processes W/Z+jet very similar in general more partonic channels, diagrams, helicities for Z+jet EW corrections for W/Z+jet production – Alexander M¨ uck – p.6/ 18 EW corrections for W/Z+jet production – p. 0/ 18
EW corrections Complete EW corrections calculated stable reduction scheme for tensor integrals Denner, Dittmaier [hep-ph/0509141] avoid inverse Gram determinants for pentagon reduction expand around vanishing determinants in critical phase-space regions EW corrections for W/Z+jet production – Alexander M¨ uck – p.6/ 18 EW corrections for W/Z+jet production – p. 0/ 18
EW corrections Complete EW corrections calculated stable reduction scheme for tensor integrals Denner, Dittmaier [hep-ph/0509141] complex mass scheme for resonances Denner, Dittmaier, Roth, Wieders [hep-ph/0505042] use complex W and Z masses everywhere by means of complex renormalization: M 2 V , 0 = µ 2 V + δµ 2 with: M 2 V , 0 = bare mass ( V = W , Z ) V µ 2 V = ren. complex mass δµ 2 V = complex counterterm ⇒ complex s 2 W = 1 − µ 2 W /µ 2 Z loop-integrals for complex masses needed EW corrections for W/Z+jet production – Alexander M¨ uck – p.6/ 18 EW corrections for W/Z+jet production – p. 0/ 18
EW corrections Complete EW corrections calculated stable reduction scheme for tensor integrals Denner, Dittmaier [hep-ph/0509141] complex mass scheme for resonances Denner, Dittmaier, Roth, Wieders [hep-ph/0505042] dipole subtraction for infrared divergencies Catani, Seymour [hep-ph/9605323] Dittmaier [hep-ph/9904440] subtraction formalism also for non-collinear safe observables e.g. for bare muons (without lepton–photon recombination) ⇒ muon-mass logarithms extracted analytically Dittmaier, Kabelschacht, Kasprzik [arXiv:0802.1405] phase-space slicing used as a check EW corrections for W/Z+jet production – Alexander M¨ uck – p.6/ 18 EW corrections for W/Z+jet production – p. 0/ 18
non collinear-safe subtract. usual subtraction procedure: � � � � dΦ n +1 |M| 2 = |M| 2 − |M Sub | 2 � � d k γ |M Sub | 2 dΦ n +1 + dΦ n clever choice of |M Sub | 2 � |M| 2 − |M Sub | 2 � ⇒ is integrable d k γ |M Sub | 2 can be done analytically ⇒ � EW corrections for W/Z+jet production – Alexander M¨ uck – p.7/ 18 EW corrections for W/Z+jet production – p. 0/ 18
non collinear-safe subtract. usual subtraction procedure: � � � � dΦ n +1 |M| 2 = |M| 2 − |M Sub | 2 � � d k γ |M Sub | 2 dΦ n +1 + dΦ n f M Sub ( p jet , z f ) where z f → p 0 f / ( p 0 f + p 0 γ ) , p jet → p 0 f + p 0 M Sub = � γ for collinear events only cuts on p jet , no cuts on p f ⇒ cuts independent of z f ⇒ z f integration can be done analytically EW corrections for W/Z+jet production – Alexander M¨ uck – p.7/ 18 EW corrections for W/Z+jet production – p. 0/ 18
non collinear-safe subtract. usual subtraction procedure: � � � � dΦ n +1 |M| 2 = |M| 2 − |M Sub | 2 � � d k γ |M Sub | 2 dΦ n +1 + dΦ n f M Sub ( p jet , z f ) where z f → p 0 f / ( p 0 f + p 0 γ ) , p jet → p 0 f + p 0 M Sub = � γ for collinear events only cuts on p jet , no cuts on p f ⇒ cuts independent of z f ⇒ z f integration can be done analytically non-collinear safe implementation: no recombination: cuts on p f allowed cut on z f in M Sub to ensure cancellation of singularities integrate over z f in d k γ numerically (soft divergence treated via Plus-distribution in analogy to treatment of initial-state emitters/spectators) EW corrections for W/Z+jet production – Alexander M¨ uck – p.7/ 18 EW corrections for W/Z+jet production – p. 0/ 18
photon–jet recombination Treat photon like another parton? EW corrections for W/Z+jet production – Alexander M¨ uck – p.8/ 18 EW corrections for W/Z+jet production – p. 0/ 18
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