Multi-boson Production in Weak Boson Fusion Michael Rauch | DIS 2014, Apr 2014 I NSTITUTE FOR T HEORETICAL P HYSICS KIT – University of the State of Baden-Wuerttemberg and www.kit.edu National Research Center of the Helmholtz Association
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 DIS First studied in context of Higgs searches [Han, Valencia, Willenbrock; Figy, Oleari, Zeppenfeld; . . . ] ∼ 10 % compared to main production mode gluon fusion NLO QCD corrections moderate ( O ( � 10 %)) NLO EW same size, opposite sign as QCD for M H ∼ 126 GeV [Ciccolini et al. , Figy et al. ] NNLO QCD known for subsets: no significant contributions [Harlander et al. , Bolzoni et al. ] advantageous scale choice: momentum transfer q 2 of intermediate vector bosons DIS 2014, Apr 2014 2/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Diboson-VBF production ager, Oleari, Zeppenfeld (VV); Campanario, Kaiser, Zeppenfeld (W ± γ )] [Bozzi, J¨ [Denner, Hosekova, Kallweit (W + W + )] e + µ - ν e α Γ V ν e Part of the NLO wish list γ ,Z e + ν µ ν µ W - W + µ - u u u u [Les Houches 2005] γ ,Z γ ,Z background to Higgs searches c c c c (a) (b) access to anomalous triple and quartic gauge couplings µ - u u W - γ ,Z ν µ e + u u αβ ν e W T VV ν µ c c ν e µ - γ ,Z W + e + c c (c) (d) µ - ν e W - W + e + ν µ u u u u W - W + µ - ν e αβ αβ T W + V T W - V e + ν µ γ ,Z γ ,Z c c c c (e) (f) DIS 2014, Apr 2014 3/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Scale dependence Dependence on factorization and renormalization scale [Bozzi, J¨ ager, Oleari, Zeppenfeld] pp → W + Zjj pp → W + W − jj sizable scale dependence at LO: ∼ ± 10% strongly reduced at NLO: ∼ ± 2% (up to 6% in distributions) K-factor around 0.98 for µ = m V , 1.04 for µ = Q (momentum transfer) DIS 2014, Apr 2014 4/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Distributions Differential distributions: p T ( j ) (W + W − ) [J¨ ager, Oleari, Zeppenfeld] p T of the leading tagging jet K factor not constant over range of distribution → shape of distributions changes → simple rescaling with K factor not sufficient p T of the second tagging jet DIS 2014, Apr 2014 5/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Distributions Differential distributions: m jj (W + W + ) [J¨ ager, Oleari, Zeppenfeld] → scale choice µ 0 = Q leads to flatter differential K factor DIS 2014, Apr 2014 6/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
QCD-Diboson production Calculations at NLO QCD: W ± W ± jj, W + W − jj, W ± Z jj, W ± γ jj, γ γ jj [Melia, Melnikov, R¨ ontsch, Zanderighi; Greiner, Heinrich, Mastrolia, Ossola, Reiter, Tramontano] [Campanario, Kerner, Ninh, Zeppenfeld; Gehrmann, Greiner, Heinrich] W + W − jj W + W − jj & W + W + jj (latter after changing quark flavors appropriately) + diagrams where quark line without attached vector bosons is replaced by gluons DIS 2014, Apr 2014 7/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
QCD-Diboson production pp → e + ν e µ + ν µ [Campanario, Kerner, Ninh, Zeppenfeld] Impact of NLO QCD corrections K factors typically between 1 and 1.5 → ν µ ν + + pp e jj+X µ 10 e corrections < 20 % for s = 14TeV invariant mass of two leading jets LO [ fb/TeV ] NLO > 200 GeV µ ’ /2 1 0 µ ’ huge correction for small m jj due 0 µ 2 ’ jj /dm 0 to new phase-space region σ d (almost collinear quark-gluon ›1 10 splitting) good scale choice (interpolates ›2 10 between different regions): 2 1.5 K 0 = 1 � � 1 µ ′ p T , i exp | y i − y 12 | 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 jets ) 2 ) 0 µ ’ µ ( σ ( σ 1 � � � p 2 T , i + m 2 + W , i 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 m [ TeV ] W jj ( y 12 = ( y 1 + y 2 ) / 2) DIS 2014, Apr 2014 8/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
QCD-EW interference pp → e + ν e µ + ν µ [Campanario, Kerner, Ninh, Zeppenfeld] Comparing contributions at LO QCD and EW contributions of 1.6 similar size → ν µ ν + + pp e jj+X µ e 1.4 (destructive interference for QCD, 14TeV, Inc, LO full 1.2 no gluon-initiated contributions) EW+QCD EW 1 VBF QCD-EW interference largest for [fb] QCD tags 0.8 Int large p T , j , small ∆ y tags y ∆ /d up to 20% reducing to 10% (3%) 0.6 σ d for loose (tight) VBF cuts 0.4 0.2 VBF contribution by far dominant in VBF region (96%) 0 100 → good approximation 80 [%] 60 40 δ 20 0 0 1 2 3 4 5 6 7 ∆ y tags EW: full O ( α 6 ) calculation VBF: VBF approximation (only t-/u-channel diagrams) DIS 2014, Apr 2014 9/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Matching with parton shower NLO calculation LO + parton shower normalization correct to NLO LO normalization only additional jet at high- p T further high- p T jets badly accurately described described theoretical uncertainty reduced Sudakov suppression at small p T low- p T jet emission badly events at hadron level possible modeled parton level description POWHEG-BOX [Alioli, Hamilton, Nason, Oleari, Re] implementation of W + W − , W ± W ± and ZZ via VBF available [J¨ ager, Zanderighi] DIS 2014, Apr 2014 10/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Matching with parton shower W + W − via VBF [J¨ ager, Zanderighi] Relative position of third jet with respect to the two tagging jets: y ⋆ = y j 3 − y j 1 + y j 2 2 0.08 0.03 POWHEG+PYTHIA POWHEG+PYTHIA 0.07 NLO 0.025 NLO p t,j3 > 10 GeV p t,j3 > 25 GeV 0.06 d σ /d y* [fb] d σ /d y* [fb] 0.02 0.05 0.04 0.015 0.03 0.01 0.02 0.005 0.01 0 0 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 y* y* Extra jet activity in central region predicted by parton-shower calculation Relevant differences to pure NLO calculation DIS 2014, Apr 2014 11/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Unitarization of WW-scattering Test of electro-weak symmetry breaking Longitudinal WW scattering contains Higgs graphs: + + + + necessary for correct high-energy behaviour (otherwise unitarity violation at ∼ 1 TeV) s M H ∼ Signal amplitude for s-, t- and u-channel exchange of H v 2 M B ∼ − s continuum electroweak background amplitude v 2 0.1 SM-H (126 GeV) H (126 GeV), κ 2 0.01 V =0.7 no H 0.001 d σ /dm WW [fb/GeV] 0.0001 exact cancellation only for SM couplings 1e-05 (Higgs part may be split 1e-06 over different bosons with 1e-07 i g 2 h i VV = g 2 � HVV , SM , e.g. 2HDM) 1e-08 1e-09 1e-10 0 500 1000 1500 2000 2500 3000 3500 4000 m WW [GeV] DIS 2014, Apr 2014 12/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
Anomalous quartic gauge couplings New physics at high scale Λ could influence gauge couplings ⇒ anomalous gauge couplings [Eboli et al. ; recent review: Wackeroth (ed.), Degrande, MR et al. ] Different approaches to parametrize effects → Effective field theory f ( d ) Λ d − 4 O ( d ) � � i L EFT = i d i Operators O with low energy degrees of freedom respect gauge symmetries Dimension-8 operators in Lagrangian ( Φ Higgs doublet, W µν / B µν : SU(2)/U(1) field strength tensors): � † D β Φ �� � � � B µν B µν D β Φ W αν W µβ W µβ W αν � � � � e.g. L M , 2 ∝ × L T , 1 ∝ × , , . . . (at least) four gauge fields in each term → modify quartic gauge couplings triple gauge couplings contribute as well in general unitarity violation at high energies DIS 2014, Apr 2014 13/16 M. Rauch – Multi-boson Production in Weak Boson Fusion → avoid region or apply unitarization method ( K -matrix, formfactor, . . . )
Anomalous quartic gauge couplings [Schlimpert, Zeppenfeld] Normalized | η | max Normalized / p t distribution distribution ℓ 8 0.9 Standard Model Standard Model 10 − 3 GeV − 1 � fM 2 / Λ 4 = 800 TeV − 4 7 fM 2 / Λ 4 = 800 TeV − 4 0.8 fT 1 / Λ 4 = 25 TeV − 4 fT 1 / Λ 4 = 25 TeV − 4 6 fWWW / Λ 2 = 10 TeV − 2 0.7 fWWW / Λ 2 = 10 TeV − 2 1 /σ d σ/ d | η | max ℓ 0.6 5 0.5 4 � p T 0.4 1 /σ d σ/ d / 3 0.3 2 0.2 1 0.1 0 0 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 | η | max p T [ GeV ] / ℓ Anomalous couplings enhance predominantly high-energy region ∆ σ ∼ O ( 1 − 4 %) for total cross section, ∆ σ ∼ O ( 20 − 100 %) in high-energy region, m T WW > 800 GeV Visible changes in distributions, different for individual couplings → distinguish between different couplings DIS 2014, Apr 2014 14/16 M. Rauch – Multi-boson Production in Weak Boson Fusion
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