Sep. 10, 2008Kentarou Mawatari Taiwan1/30 Azimuthal angle correlation in VBF processes at LHC arXiv:0809.XXXX Mawatari, Kentarou 馬渡 健太郎 마와타리 켄타로 with K.Hagiwara (KEK) and Q.Li (Karlsruhe) Heidelberg U.

Sep. 10, 2008Kentarou Mawatari Taiwan2/30 Contents  Introduction Azimuthal correlations in H+2jet events  Formalism and Kinematics  Helicity amplitudes for the VBF process  Azimuthal angle correlations Higgs bosons Massive gravitons  Summary

Sep. 10, 2008Kentarou Mawatari Taiwan3/30 Introduction

Sep. 10, 2008Kentarou Mawatari Taiwan4/30 Motivation I: the Higgs properties  After observation of a Higgs boson at LHC, determination of its properties, i.e., all the couplings and quantum numbers, is the next goal to unravel the underlying theory. the gauge, Yukawa, and self-couplings the charge, color, spin, CP quantum numbers  Spin & CP properties at LHC Higgs decay, e.g. H->ZZ->(ll)(ll) Higgs+2jet production, pp->Hjj Dell’Aquila,Nelson(1986) S.Y.Choi et al.(2003) Buszello et al.(2004) T.Plehn et al.(2002)

Sep. 10, 2008Kentarou Mawatari Taiwan5/30 Higgs production at LHC A.Djouadi hep-ph/ WBF

Sep. 10, 2008Kentarou Mawatari Taiwan6/30 Azimuthal angle correlations in WBF  The anomalous HWW couplings  The azimuthal correlations reflects the tensor structure of the Higgs couplings.  Why is SM flat ? Why is CP-even (odd) suppressed at phi=90 (0 and 180) ? T.Plehn, D.Rainwater, D.Zeppenfeld PRL88(2002)051801

Sep. 10, 2008Kentarou Mawatari Taiwan7/30  H+2 jet events are produced also via gluon fusion (GF); (a) qq>qqH, (b) qg>qgH, (c) gg>ggH. WBF vs. GF V. Del Duca et al. NPB616(2001)367 w/ minimal cuts minimal cuts:

Sep. 10, 2008Kentarou Mawatari Taiwan8/30 The distinctive kinematics of WBF Far forward and backward jets. The Higgs boson is produced centrally. the t-channel weak- boson propagator D.Rainwater hep-ph/

Sep. 10, 2008Kentarou Mawatari Taiwan9/30 Minimal cuts: VBF cuts: WBF vs. GF with VBF cuts V. Del Duca et al. NPB616(2001)367 w/ minimal and VBF cutsw/ minimal cuts

Sep. 10, 2008Kentarou Mawatari Taiwan10/30 WBF vs. GF in the az dis.  Why is GF suppressed at phi=90 ? This reflects the effective Hgg coupling. The VBF cuts may select the t-channel VBF diagrams.  The t-channel vector-boson propagators lead to the distinctive far forward jets.  The kinematical feature is not particular only to WBF but also the QCD production via the t-channel GF processes. V. Del Duca et al. NPB616(2001)367 w/ minimal and VBF cuts

Sep. 10, 2008Kentarou Mawatari Taiwan11/30 Parton-shower effect  The present consensus seems to be that the azimuthal angle correlations predicted in the leading-order may survive even after higher-order corrections are applied.  The following analyses are done at the parton level with tree level matrix elements. V. Del Duca et al. JHEP0610(2006)016

Sep. 10, 2008Kentarou Mawatari Taiwan12/30 Motivation II: massive gravitons  As another interest to study the azimuthal correlations at LHC, we attempt to apply it to other heavy particle productions, here massive-graviton productions.  We consider the simplest Randall-Sundrum (RS) model, where only gravitons can propagate in extra dimension.  So far, several phenomenological studies have been made on the s-channel graviton resonances and their decays for the discovery and the determination of the spin-2 nature. Davoudiasl et al. (2000,2001) Allanach et al. (2000,2002), Traczyk, Wrochna (2002) Abazov et al. [D0 collaboration] (2005)  We study the massive-graviton production via the VBF process, which may have a potential to determine its properties as in the Higgs case.

Sep. 10, 2008Kentarou Mawatari Taiwan13/30 Formalism and Kinematics  Helicity amplitude formalism  Kinematics

Sep. 10, 2008Kentarou Mawatari Taiwan14/32 Helicity formalism  For the VBF process the completeness relation for space-like vector-boson the conserved current

Sep. 10, 2008Kentarou Mawatari Taiwan15/30 X decay to a vector-boson pair

Sep. 10, 2008Kentarou Mawatari Taiwan16/30 Kinematics

Sep. 10, 2008Kentarou Mawatari Taiwan17/30 Helicity amplitudes for the VBF process  Fermion current amplitudes  Gluon current amplitudes  Off-shell VBF amplitudes

Sep. 10, 2008Kentarou Mawatari Taiwan18/30 Off-shell vector-boson Current amplitudes  For the production Fermion currents: Gluon currents:

Sep. 10, 2008Kentarou Mawatari Taiwan19/30 Fermion current amplitudes

Sep. 10, 2008Kentarou Mawatari Taiwan20/30 Gluon current amplitudes

Sep. 10, 2008Kentarou Mawatari Taiwan21/30 XVV vertex  Off-shell VBF amplitudes The XVV vertex The polarization tensor and the GXX vertices

 For, where the VBF contributions dominant, WBF Higgs bosons --- produced by the longitudinally polarized weak-bosons. Loop-induced Higgs bosons --- produced by the transversely polarized vector-bosons. Sep. 10, 2008Kentarou Mawatari Taiwan22/30 VBF amplitudes for Higgs bosons

 For, the λ X =±2 states are dominantly produced through the collisions of the vector-bosons which have the opposite-sign transverse polarization. Sep. 10, 2008Kentarou Mawatari Taiwan23/30 VBF amplitudes for gravitons

Sep. 10, 2008Kentarou Mawatari Taiwan24/30 Dijet large rapidity separation  Minimal cuts:  VBF cuts:  As the large rapidity separation cuts are imposed, the VBF contributions tend to dominate the exact matrix elements.

Sep. 10, 2008Kentarou Mawatari Taiwan25/30 Azimuthal angle correlations  Higgs bosons  Massive gravitons

Sep. 10, 2008Kentarou Mawatari Taiwan26/30 Quantum interference between the different helicity states  The VBF helicity amplitude for Higgs bosons (λ X =0) Using the relative phases  Azimuthal correlations H(WBF): H(GF): A:

Sep. 10, 2008Kentarou Mawatari Taiwan27/30 Azimuthal correlation of Higgs bosons  The VBF contributions can reproduce the distributions with the exact matrix elements very well not only for WBF but also GF. minimal cuts: VBF cuts:

Sep. 10, 2008Kentarou Mawatari Taiwan28/30 Azimuthal correlation of massive-gravitons  The full helicity amplitude for massive-gravitons The λ X =±2 caes is dominant. There is no interference term.  No azimuthal dependence.  "Graviton production with 2 jets at the LHC in large extra dimensions" K.Hagiwara, P.Konar, Q.Li, K.M., D.Zeppenfeld [JHEP0804,019]  "HELAS and MadGraph/MadEvent with spin-2 particles" K.Hagiwara, J.Kanzaki, Q.Li, K.M. [appear in EPJ, arXiv: ]

Sep. 10, 2008Kentarou Mawatari Taiwan29/30 Azimuthal correlation of massive-gravitons

Sep. 10, 2008Kentarou Mawatari Taiwan30/30 Summary  We have studied heavy-particle (Higgs boson and massive- graviton) productions in association with two jets via VBF (=WBF+GF) and their decays at LHC.  We showed the helicity amp explicitly for the VBF subprocesses. the VBF amp reproduces the exact matrix elements by taking into account the dijet large rapidity separation. quantum interference between different helicity states of the intermediate vector-bosons leads to a non-trivial azimuthal angle correlation of the jets in the production and in the decay.  These correlations reflect the spin and CP nature of the heavy particles produced via VBF processes.

Sep. 10, 2008Kentarou Mawatari Taiwan31/30 Supplements

Sep. 10, 2008Kentarou Mawatari Taiwan32/30 Relation to the splitting amplitudes  For the production z: the energy fraction of the initial parton that is carried off by the space-like vector-boson  For the decay z’: the energy fraction of the time-like vector- boson that is carried off by the final parton the collinear limit

Sep. 10, 2008Kentarou Mawatari Taiwan33/32 (unregularized) splitting functions

Sep. 10, 2008Kentarou Mawatari Taiwan34/30 Gluon current amplitudes

Sep. 10, 2008Kentarou Mawatari Taiwan35/30 Kinematical cuts  Minimal cuts:  VBF cuts:  Additional p T cut:

Sep. 10, 2008Kentarou Mawatari Taiwan36/30 Azimuthal correlation of massive-gravitons