Azimuthal angle correlation
in VBF processes at LHC
arXiv:0809.XXXX
Mawatari, Kentarou
馬渡 健太郎
마와타리 켄타로
Heidelberg U.
with K.Hagiwara (KEK) and Q.Li (Karlsruhe)
Sep. 10, 2008
Kentarou Mawatari (KIAS) @ Taiwan
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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
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Introduction
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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
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Dell’Aquila,Nelson(1986)
S.Y.Choi et al.(2003)
Buszello et al.(2004)
T.Plehn et al.(2002)
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Higgs production at LHC
A.Djouadi
hep-ph/0503172
WBF
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Azimuthal angle correlations in WBF

The anomalous HWW
couplings
T.Plehn, D.Rainwater, D.Zeppenfeld
PRL88(2002)051801
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) ?

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WBF vs. GF

V. Del Duca et al.
NPB616(2001)367
H+2 jet events are produced also via gluon fusion (GF);
(a) qq>qqH, (b) qg>qgH, (c) gg>ggH.
w/ minimal cuts
• minimal cuts:
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The distinctive kinematics of WBF
D.Rainwater
hep-ph/0702124


Far forward and
backward jets.
The Higgs boson is
produced centrally.
the t-channel weakboson propagator
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WBF vs. GF with VBF cuts


V. Del Duca et al.
NPB616(2001)367
Minimal cuts:
VBF cuts:
w/ minimal cuts
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w/ minimal and VBF cuts
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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.
w/ minimal and VBF cuts
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V. Del Duca et al.
NPB616(2001)367
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Parton-shower effect
Sep. 10, 2008
V. Del Duca et al.
JHEP0610(2006)016

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.
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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.
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Formalism and Kinematics


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Helicity amplitude formalism
Kinematics
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Helicity formalism

For the VBF process

the completeness relation for space-like vector-boson

the conserved current
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X decay to a vector-boson pair
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Kinematics
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Helicity amplitudes
for the VBF process



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Fermion current amplitudes
Gluon current amplitudes
Off-shell VBF amplitudes
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Off-shell vector-boson Current amplitudes

For the production

Fermion currents:

Gluon currents:
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Fermion current amplitudes
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Gluon current amplitudes
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XVV vertex

Off-shell VBF amplitudes

The XVV vertex

The polarization tensor and the GXX vertices
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VBF amplitudes for Higgs bosons

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.
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VBF amplitudes for gravitons

For
, the λX=±2 states are dominantly
produced through the collisions of the vector-bosons which
have the opposite-sign transverse polarization.
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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.
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Azimuthal angle correlations


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Higgs bosons
Massive gravitons
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Quantum interference
between the different helicity states

The VBF helicity amplitude for Higgs bosons (λX=0)


Using the relative phases
Azimuthal correlations
 H(WBF):
 H(GF):
 A:
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• minimal cuts:
• VBF cuts:
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.
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Azimuthal correlation of massive-gravitons

The full helicity amplitude for massive-gravitons
 The λX=±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:0805.2554]
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Azimuthal correlation of massive-gravitons
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Summary



We have studied heavy-particle (Higgs boson and massivegraviton) 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.
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Supplements
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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
the collinear limit
For the decay

z’: the energy fraction of the time-like vectorboson that is carried off by the final parton
the collinear limit
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(unregularized) splitting functions
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Gluon current amplitudes
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Kinematical cuts

Minimal cuts:
VBF cuts:

Additional pT cut:

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Azimuthal correlation of massive-gravitons
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