NLO QCD corrections to pp W ± Z γ with leptonic decays

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1 NLO QCD corrections to pp W ± Z γ in collaboration with F. Campanario, H. Rzehak and D. Zeppenfeld Michael Rauch March 2010 I NSTITUTE FOR T HEORETICAL P HYSICS KIT University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

2 Motivation Physics motivation: Trilepton final state with missing transverse energy Background to searches beyond the Standard Model (e.g. SUSY) Possibility to obtain information about quartic gauge-boson couplings (W W Z γ and W W γ γ) q W + W + ν e e + γ q Z/γ µ µ + M. Rauch NLO QCD corrections to pp W ± Zγ March /16

3 Current Status Triple vector-boson production part of NLO wishlist NLO QCD corrections to Z Z Z production NLO QCD corrections to W W Z production NLO QCD corrections to Z Z Z, W W Z, Z Z W, W W W production NLO QCD corrections to Z Z W, W W W production NLO QCD corrections to W W γ, Z Z γ production NLO QCD corrections to W γ γ production This Talk: NLO QCD corrections to W Z γ production [Lazopoulos, Melnikov,Petriello 07] [Hankele, Zeppenfeld 08] [Binoth, Ossola, Papadopoulos, Pittau 08] [Campanario, Hankele, Oleari, Prestel, Zeppenfeld 08] [Bozzi, Campanario, Hankele, Zeppenfeld 09] [Baur, Wackeroth, Weber in progress] M. Rauch NLO QCD corrections to pp W ± Zγ March /16

4 Current Status Triple vector-boson production part of NLO wishlist NLO QCD corrections to Z Z Z production NLO QCD corrections to W W Z production NLO QCD corrections to Z Z Z, W W Z, Z Z W, W W W production NLO QCD corrections to Z Z W, W W W production NLO QCD corrections to W W γ, Z Z γ production NLO QCD corrections to W γ γ production This Talk: NLO QCD corrections to W Z γ production [Lazopoulos, Melnikov,Petriello 07] [Hankele, Zeppenfeld 08] [Binoth, Ossola, Papadopoulos, Pittau 08] [Campanario, Hankele, Oleari, Prestel, Zeppenfeld 08] [Bozzi, Campanario, Hankele, Zeppenfeld 09] [Baur, Wackeroth, Weber in progress] M. Rauch NLO QCD corrections to pp W ± Zγ March /16

5 Current Status Triple vector-boson production part of NLO wishlist NLO QCD corrections to Z Z Z production NLO QCD corrections to W W Z production NLO QCD corrections to Z Z Z, W W Z, Z Z W, W W W production NLO QCD corrections to Z Z W, W W W production NLO QCD corrections to W W γ, Z Z γ production NLO QCD corrections to W γ γ production This Talk: NLO QCD corrections to W Z γ production [Lazopoulos, Melnikov,Petriello 07] [Hankele, Zeppenfeld 08] [Binoth, Ossola, Papadopoulos, Pittau 08] [Campanario, Hankele, Oleari, Prestel, Zeppenfeld 08] [Bozzi, Campanario, Hankele, Zeppenfeld 09] [Baur, Wackeroth, Weber in progress] M. Rauch NLO QCD corrections to pp W ± Zγ March /16

6 W Z γ production q W + νe q W + γ q Z/γ µ Z/γ e + γ µ Z/γ W + νe e + µ W + µ + γ... q µ + q µ + q W + νe All resonant and non-resonant matrix elements as well as spin correlations of final state leptons included γ taken as real (otherwise part of W Z Z ) e + Interference terms due to identical particles in the final state neglected All fermion mass effects neglected In total 71 Feynman graphs for LO and 194 for LO plus jet ( real emission part) helicity amplitude method [Hagiwara, Zeppenfeld] Same building blocks for different Feynman graphs Compute only once per phase-space point and reuse ( leptonic tensors ) Hand-written code up to factor 10 faster than SHERPA M. Rauch NLO QCD corrections to pp W ± Zγ March /16

7 Checks LO and LO+j Comparison Comparison with MadGraph pointwise in phase-space (W + Zγ): Three qqv vertices VBFNLO i MadGraph i ratio of absolute values Two qqv vertices VBFNLO i MadGraph i ratio of absolute values One qqv vertex (s-channel) VBFNLO i MadGraph i ratio of absolute values Similar accuracy for all other process types (W Zγ, W + Zγj, W Zγj) Comparison with Sherpa and MadGraph/MadEvent integrated over phase-space (cross sections in ab) process VBFNLO Sherpa MadEvent W + Zγ ± ± ±1.13 W Zγ ± ± ±0.70 W + Zγj ± ±0.72 W Zγj ± ±0.55 M. Rauch NLO QCD corrections to pp W ± Zγ March /16

8 Catani-Seymour Dipole Subtraction Z σ NLO = Z dσ NLO = dσ R m+1 {z } real emission Z + dσ V m {z } virtual contributions R m+1 dσr and R m dσv are separately infrared divergent in 4 dimensions Divergences cancel in sum [Kinoshita, Lee, Nauenberg] Introduce local counterterm dσ A with the same singular behaviour as dσ R Z Z Z Z σ NLO = [dσ R ǫ=0 dσ A ǫ=0 ] + [dσ V + dσ A ] ǫ=0 + dσ C m+1 m 1 m {z } finite collinear term Numerical integration in 4 dimensions Poles cancel analytically [Catani, Seymour 96] M. Rauch NLO QCD corrections to pp W ± Zγ March /16

9 Checks Cancellation of infrared divergencies Catani-Seymour subtraction formalism: σ NLO = R 5+1 [dσr ǫ=0 dσ A ǫ=0 ] +... About 1 million phase-space points Soft Divergencies Collinear Divergencies Exact cancellation as we approach the relevant limits M. Rauch NLO QCD corrections to pp W ± Zγ March /16

10 Photon Isolation Simple (e.g. R) separation cut between photon and jet not infrared safe: Complete divergence in virtual part (integration over loop momentum) Part of divergence in real part removed by separation cuts Cancellation of infrared divergencies between virtual and real part broken Use Frixione cut (infrared safe): [Frixione 98] X δ 0 = 0.7 is fixed separation cut i E Ti Θ(δ R iγ ) p Tγ 1 cos δ 1 cos δ 0 (for all δ δ 0 ) Sufficiently soft parton (E Ti small) arbitrarily close to photon axis possible Collinear parton (R iγ = 0) only accepted for vanishing energy M. Rauch NLO QCD corrections to pp W ± Zγ March /16

11 Numerical Results Gauge dependence No distinction between e and µ in the final state multiplicity factor 4 Scale choice µ 0 = invariant mass of WZγ system Combined factorization and renormalization scale dependence µ = µ F = µ R = ξµ 0 W + Zγ W Zγ Virtual-born Total NLO Total NLO σ [fb] Virtual-box Virtual-pentagons Real LO σ [fb] Virtual-born Real Virtual-box Virtual-pentagons LO ξ K-factor(ξ = 1) = ξ K-factor(ξ = 1) = 1.94 M. Rauch NLO QCD corrections to pp W ± Zγ March /16

12 Numerical Results Distributions Transverse momentum of lepton 1 and 2 (p T -ordered) (solid red: LO; dashed blue: NLO) dσ/dp Tl1 [fb] K-factor p Tl1 p Tl1 dσ/dp Tγ [fb] K-factor p Tl2 p Tl2 K-factor varies strongly over lepton momentum Simple rescaling of LO cross section not a good approximation Need NLO differential distributions M. Rauch NLO QCD corrections to pp W ± Zγ March /16

13 Conclusions NLO QCD corrections to W ± Z γ evaluated All off-shell effects included Important background for supersymmetry Test of W W Z γ and W W γ γ gauge couplings in SM Sizable K-factors, strong variation within distributions simple multiplication of LO result with K-factor not a good approximation M. Rauch NLO QCD corrections to pp W ± Zγ March /16

14 Checks & Tricks Shifting Polarization Vectors Effective polarization vector of the vector boson can be split: ǫ µ V = x V q µ V + ǫµ V Use identity k 1 q 1 µ 1 k 1 q 1 + q 2 µ 1 k 1 q 1 µ1 µ 2 2 q 2 = q µ 2 q k 3 2 µ 3 k 2 q 3 µ 3 q 2 + q 3 k 2 µ 3 to shift contributions from pentagons to boxes Box integration quicker Can use less MC points for pentagons for same final accuracy Best choice (by trying): ǫ µ V (qw µ + qz µ ) = 0 Cross-check (Process W + Zγ, c.s. in ab): c.s. in ab with shift no shift single int. born-virtual boxes pentagons sum error M. Rauch NLO QCD corrections to pp W ± Zγ March /16

15 Experimental cuts Experimental values: pj T > 20 GeV η j < 4.5 pl T > 20 GeV η l < 2.5 pγ T > 10 GeV ηγ < 2.5 m ll > 15 GeV R ll > 0.3 R lγ > 0.4 R jγ > 0.4 R pγ,frixione = 0.7 Eff. Frixione = 1.0 m W = GeV m Z = GeV PDFs : LO : CTEQ6l1 LHC : S = 14 TeV NLO : CTEQ6m M. Rauch NLO QCD corrections to pp W ± Zγ March /16

16 Numerical Results Distributions Transverse momentum distribution of the photon (solid red: LO; dashed blue: NLO) dσ/dp Tγ [fb] 0.1 K-factor p Tγ p Tγ K-factor varies strongly over photon momentum Simple rescaling of LO cross section not a good approximation Need NLO differential distributions M. Rauch NLO QCD corrections to pp W ± Zγ March /16

17 Numerical Results Distributions Missing transverse momentum (solid red: LO; dashed blue: NLO) dσ/dp Tmiss [fb] K-factor p Tmiss p Tmiss M. Rauch NLO QCD corrections to pp W ± Zγ March /16

18 Numerical Results Distributions Transverse momentum of lepton 1 and 2 (p T -ordered) (solid red: LO; dashed blue: NLO) dσ/dp Tl1 [fb] K-factor p Tl1 p Tl1 dσ/dp Tγ [fb] K-factor p Tl2 p Tl2 M. Rauch NLO QCD corrections to pp W ± Zγ March /16