Weak boson scattering at the LHC

Transcription

1 Weak boson scattering at the LHC RADCOR 2009 Barbara Jäger University of Würzburg

2 outline weak boson fusion at the LHC: Higgs production at high precision V V jj NLO QCD strongly interacting gauge boson systems heavy Higgs scenario Warped Higgsless model summary & conclusions p. 2

3 LHC discovery potential most promising production / decay modes for Higgs search at the LHC depend on M H : Signal significance 10 2 L dt = 30 fb -1 (no K-factors) ATLAS H γ γ tth (H bb) H ZZ (*) 4 l H WW (*) lνlν qqh qq WW (*) qqh qq ττ Total significance VBF qq qqh with 10 H W ± W e ± µ /p T important for M H 110 GeV m H (GeV/c 2 ) p. 3

4 a promising search channel: VBF p jet Z, W H Z, W p jet suppressed color exchange between quark lines gives rise to little jet activity in central rapidity region scattered quarks two forward tagging jets (energetic; large rapidity) Higgs decay products typically between tagging jets p. 4

5 Higgs production in NLO QCD NLO QCD: inclusive cross section: Han, Valencia, Willenbrock (1992) distributions: Figy, Oleari, Zeppenfeld (2003) Berger, Campbell (2004) NLO QCD corrections moderate and well under control (order 10% or less) p. 5

6 higher orders of QCD in VBF Harlander, Vollinga, Weber (2007): gauge invariant, finite sub-class of virtual two-loop QCD corrections to pp Hjj via VBF important due to large gluon luminosity at LHC? gg q qh, q q ggh, qg qgh, qg qgh minimal set of cuts: σ 2 loop gluon 2 % of σvbf LO VBF cuts: relative suppression by additional order of magnitude p. 6

7 Higgs production in NLO EW Ciccolini, Denner, Dittmaier (2007): NLO EW corrections to inclusive cross sections and distributions NLO EW corrections non-negligible, modify K factors and distort distributions by up to 10% dσ dσ LO 1[%] pp Hjj + X EW+QCD EW QCD dσ dσ LO 1[%] pp Hjj + X M H = 200GeV p j1,t [GeV] M H = 200GeV 45 EW+QCD EW QCD 90 φ jj p. 7

8 pp Hjj via gluon fusion VBF Higgs signal can be faked by double real corrections to gg H ( gluon fusion ) complete LO calculation (including pentagons): Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld (2001) NLO QCD calculation in m t limit: Campbell, Ellis, Zanderighi (2006) need to understand phenomenology of both processes to distinguish between them p. 8

9 pp Hjj: VBF versus GF apply cuts to separate VBF signal from gluon fusion (GF) background jj 1/σ dσ/d η gluon fusion VBF tt+jets QCD-WW [1/GeV] 1/σ dσ/dm jj gluon fusion VBF tt+jets QCD-WW η jj m jj [GeV] Klämke, Zeppenfeld (2007) p. 9

10 pp Hjj via VBF GF can VBF GF interference pollute the clean VBF signature? Z Z Georg (2005) & Andersen, Smillie (2006): neutral current graphs (no charged current interference) identical quark contributions with t u crossing Andersen et al. (2007) Bredenstein, Hagiwara, B. J. (2008): strong cancelation effects between contributions of different flavor interference effects are completely negligible p. 10

11 Higgs signal in VBF pp Hjj via VBF under excellent control QCD & EW NLO corrections at 10% level dominant NNLO QCD corrections small SUSY QCD corrections small Michael Rauch s talk interference with GF Hjj production negligible small PDF uncertainties 4% but: establishing a signal for the Higgs boson in VBF requires also calculation of background contributions p. 11

12 EW V V jj production jet jet pp V V + jj via VBF irreducible background to Higgs signal process in H V V decay mode accurate predictions essential p. 12

13 EW V V jj production experiment: don t observe V V jj final state, but hadronic or leptonic decay products 4jets + jj 4leptons + jj high statistics large backgrounds low statistics clean signature p. 13

14 EW V V jj production experiment: don t observe V V jj final state, but hadronic or leptonic decay products focus on pp 4leptons + jj via VBF (short: pp V V jj ) 4leptons + jj low statistics clean signature p. 14

15 EW V V jj production need stable, fast & flexible Monte Carlo program allowing for computation of various jet observables for W + W jj, ZZjj, W ± Zjj, and W ± W ± jj production via VBF at NLO-QCD accuracy (leptonic decay correlations are fully taken into account) straightforward implementation of cuts C. Oleari, D. Zeppenfeld, B. J. (2006) G. Bozzi, C. Oleari, D. Zeppenfeld, B. J. (2007) C. Oleari, D. Zeppenfeld, B. J. (2009) [ c.f. also Dieter Zeppenfeld s talk ] p. 15

16 pp l l l l jj : the leading order need to compute numerical value for M B 2 = at each generated phase space point in 4 dim (finite)... depending on leptonic final state: up to 580 diagrams essential: organize calculation economically employ amplitude techniques to evaluate M first (numerically) for specific helicities of external particles, then square avoid multiple evaluation of recurring building blocks p. 16

17 practical implementation develop modular structure with leptonic tensors... J µ up T µν = + + J ν low... and evaluate each building block only once per phase space point (related sub-diagrams, various flavor combinations, crossed processes... ) such recycling is used to a very small extent by automatized programs like MadGraph/MadEvent p. 17

18 not included: interference effects from identical fermions (t- and u-channel interference) identical flavor annihilation processes (s-channel contributions)... strongly suppressed in phase-space region where VBF can be observed experimentally Oleari, Zeppenfeld (2003), Georg (2005) Andersen, Smillie (2006) Ciccolini, Denner, Dittmaier (2007) p. 18

19 ... more precision... the next-to-leading order: real emission subtraction terms virtual corrections p. 19

20 real emission contributions needed: numerical value for almost 3000 diagrams M R 2 = complication: real emission contribution diverges as unobserved parton becomes soft or collinear analytic calculation: divergencies canceled directly by respective singularities in virtual contributions numerical approach: apply subtraction formalism (phase space slicing, dipole subtraction,... ) divergencies are absorbed by auxiliary counterterms p. 20

21 dipole subtraction: qq qq (g)v V via VBF continuous interpolation between soft and collinear gluon radiation: x 2 + z 2 (1 x)(1 z) M B( p) 2 analytical integration over one-particle phase space: M B (p) 2 [ 2 ε ε + const. ] p a p b Q p 2 p 1 p 3 Catani, Seymour (1996) σ NLO = m+1 [ dσ R ε=0 ] dσa ε=0 + m [ dσ V + 1 dσ A ] ε=0 p. 21

22 virtual contributions M V = = M B F(Q) [ 2 ε 2 3 ε ] + M finite V determined numerically [c. f. Denner, Dittmaier (2002,2005)] combination of real emission, virtuals, and subtraction terms: poles canceled analytically finite results phase-space integration can be performed numerically (Vegas) p. 22

23 precision tools Monte Carlo program for cross sections and distributions which allows for the implementation of realistic experimental selection cuts embedded in more general framework for various VBF-type processes vbfnlo publicly available from vbfnloweb/ p. 23

24 pp V V LHC: settings use design energy of 14 TeV, apply k T jet algorithm, CTEQ6 parton distributions, and typical VBF cuts: p Tj 20 GeV, y j 4.5, tagging jets y jj = y j1 y j2 > 4, M jj > 600 GeV jets located in opposite hemispheres p Tl 20 GeV, η l 2.5, R jl 0.4, charged leptons y j,min < η l < y j,max p. 24

25 scale uncertainty: pp W + W + jj choose default scale µ 0 = m W or µ 0 = Q set µ R = ξ R µ 0 and µ F = ξ F µ 0, with variable ξ Oleari, Zeppenfeld, B. J. (2009) LO, ξ F = ξ NLO, ξ F = ξ, ξ R = 1 NLO, ξ F = 1, ξ R = ξ NLO, ξ F = ξ, ξ R = ξ LO: no control on scale NLO QCD: scale dependence strongly reduced p. 25

26 W + W + jj distributions: invariant mass of tagging jets Oleari, Zeppenfeld, B. J. (2009) µ = ξ µ 0 p. 26

27 pp W + W + jj: energy dependence p. 27

28 M V V distribution: pp l + l l + l jj M H = 120 GeV M ZZ > 130 GeV Oleari, Zeppenfeld, B.J. (2006) M H = 500 GeV background p. 28 background + signal

29 new interactions in the gauge boson sector VBF processes are extremely sensitive to new interactions in the gauge boson sector can we spot signatures of non-standard scenarios for electroweak symmetry breaking? p. 29

30 V V scattering & unitarity W + L W L W + L W L with ε µ L s M W M = + + s M 2 W growth violates unitarity need: + Higgs with M H 1 TeV or new physics at TeV scale p. 30

31 new interactions in the gauge boson sector can we distinguish signatures of SM-type Higgs mechanism from other scenarios of EW symmetry breaking? comprehensive analysis of signal and backgrounds needed cf. Bagger et al. (1993, 1995) Englert, Worek, Zeppenfeld, B. J. (2008) minimize backgrounds with respect to signal maximize number of surviving signal events p. 31

32 framework: signal consider two prototype scenarios for the VBF signal: SM with heavy Higgs boson (M H = 1 TeV, Γ H = 0.5 TeV) naive estimate of strongly coupled sector with scalar, iso-scalar resonance at the TeV scale Warped Higgsless model with extra vector resonances ( m W2 = 700 GeV, Γ = 13.7 GeV, m Z2 = 695 GeV, Γ = 18.7 GeV, m Z3 = 718 GeV, Γ = 6.4 GeV ) p. 32

33 the Warped Higgsless model consider gauge boson sector of Randall-Sundrum scenario with one compactified extra dimension and AdS 5 metric ds 2 = R2 y 2 { g µν dx µ dx ν dy 2 } R y R Planck brane TeV brane boundary conditions along extra dimension [Csáki, Grojean, Murayama, Pilo, Terning] Kaluza-Klein decomposition of the gauge fields p. 33

34 the Warped Higgsless model W µ (x, y) = k ψ (W) k W (k) µ (x) Englert, Worek, Zeppenfeld, B. J. (2008) Z µ (x, y) = k ψ (Z) k Z (k) µ (x) k = 0 : photon k = 1 : SM Z, W ± k > 1 : KK Z k, W ± k model fully determined by R p. 34

35 framework: backgrounds backgrounds to the strongly interacting gauge boson signal in the heavy Higgs (HH) and Kaluza-Klein (KK) scenarios: EW V V jj production QCD V V jj production t t + jets production (with t Wb) p. 35

36 selection cuts for SEWSB analysis inclusive cuts VBF cuts p tag Tj > 30 GeV, η j < 4.5, R jj > 0.7, R lj > 0.4, p Tl > 20 GeV, η l < 2.5, m ll > 15 GeV η tag j,min < η l < η tag j,max, η tag j 1 η tag j 2 < 0, η jj > 4, m jj > m min jj leptonic cuts (process-specific) central jet veto b-tagging veto p. 36

37 leptonic cuts in contrast to backgrounds, signal processes feature energetic leptons of high p T and large invariant mass details of leptonic cuts depend on decay channel pp W + W jj: Englert, Worek, Zeppenfeld, B. J. (2008) p Tl > 100 GeV p T (ll) > 250 GeV m ll > 200 GeV min (m lj ) > 180 GeV inclusive cuts, VBF cuts, CJV & b-veto p T l > 100 GeV, min(m lj ) > 180 GeV p. 37

38 leptonic cuts in contrast to backgrounds, signal processes feature energetic leptons of high p T and large invariant mass details of leptonic cuts depend on decay channel pp W + W jj: Englert, Worek, Zeppenfeld, B. J. (2008) p Tl > 100 GeV p T (ll) > 250 GeV m ll > 200 GeV min (m lj ) > 180 GeV... final level of cuts p. 38

39 results: scalar resonance Process σ S σ B S/B S/ B N signal N bkgd. ZZjj 4l jj ZZjj 2l2ν jj W + W jj W ± Zjj final level of cuts & integrated luminosity fb 1 p. 39

40 results: vector resonance Process σ S σ B S/B S/ B N signal N bkgd. W ± Zjj W + W jj ZZjj 4l jj ZZjj 2l2ν jj final level of cuts & integrated luminosity fb 1 p. 40

41 LO results: scalar / vector resonances Englert, Worek, Zeppenfeld, B.J. (2008) ZZjj 4ljj W + Zjj p. 41

42 NLO-QCD corrections compute real emission diagrams compute virtual corrections 2 Re[M V M B ] α s(µ r ) 2π M B 2 [ 2ε 3ε ] + const Re[ M V M B ] handle IR divergencies by dipole subtraction approach (Catani, Seymour) p. 42

43 impact of NLO-QCD corrections Englert, Zeppenfeld, B. J. (2008) µ R = µ F = Q K = Obs(NLO) Obs(LO) NLO-QCD corrections always in the few-percent range p. 43

44 summary explicit calculations revealed that VBF reactions are perturbatively well-behaved (moderate NLO QCD and EW corrections, negligible higher order and interference effects) backgrounds are well under control signatures of new physics in the gauge boson sector should be observable at the LHC VBF crucial for understanding mechanism of electroweak symmetry breaking p. 44

45 p. 45