ww scattering saurabh d. rindaniindiacms/lhcworkshop/talks/040906/... · 2006-09-05 · ww...

Introduction WLWL scattering and symmetry breaking WLWL scattering beyond Higgs mechanism WLWL scattering at LHC Summary

WW scattering

Saurabh D. Rindani

Physical Research LaboratoryAhmedabad

Workshop on LHC Physics 2006, TIFR, Mumbai


Outline

1 Introduction

2 WLWL scattering and symmetry breakingEquivalence Theorem

3 WLWL scattering beyond Higgs mechanism

4 WLWL scattering at LHCEquivalent vector-boson approximationBackgroundsDistinguishing the signal

5 Summary


Higgs and WW scattering

Amplitudes with massive spin-1 particles have worsehigh-energy behaviour

εµ

L (k)≈ k µ

mV

Can make theory non-renormalizable

In theories with spontaneous symmetry breaking,high-energy behaviour is better

Higgs exchange can cancel bad high-energy behaviour

If Higgs mass is too high (s << m2H ), amplitude can be

large:Strong gauge sector

Can be studied with WW scattering


WW scattering and symmetry breaking

The equivalence theorem relates WLWL scatteringamplitude to the amplitude for scattering of thecorresponding “would-be" Goldstone scalars at highenergy (s >> m2

W )

Goldstone boson interactions are governed by low-energytheorems for energy below the symmetry breaking scale(s << m2

SB)

Thus, when there is no light Higgs (with mH < 1 TeV or so),there is a range of s values where the low-energytheorems combined with equivalence theorem can predictWLWL scattering amplitudes

This range is m2W << s << m2

SB

In other words, WLWL scattering gives information aboutthe symmetry breaking sector in this range


The Equivalence Theorem

SM relation

m2H =−2µ

2 = 2λv2 = λ√

2/GF

Since v and GF are fixed from experiment, large mH

means large λ .

For mH>∼ (GF /

√2)−1, perturbation theory is not valid.

This corresponds to mH ≈ 300 GeV

A limit may be obtained from unitarity, if the tree amplitudesare to be valid at high energies.

Vector boson scattering amplitudes at high energies maybe calculated using the equivalence theorem (Dicus &Mathur; Lee, Quigg & Thacker)


Derivation of the equivalence theorem

The scalar Lagrangian is

L = (Dµφ)†(Dµφ)−µ

2φ

†φ −λ (φ†

φ)2.

We write

φ =

(φ0

φ−

)=

1√2

(φ1 + iφ2

φ3 + iφ4

).

Then φ†φ = 12

(φ2

1 +φ22 +φ2

3 +φ24

). The Lagrangian thus has a

global O(4) symmetry, under which φi (i = 1,2,3,4) transformsas a four-dimensional representation. Explicitly,

L =12

4

∑i=1

(∂µφi∂

µφi −µ

2φiφi

)− λ

4

(4

∑i=1

φiφi

)2

,

where we have not included the gauge fields, which do nothave the full SO(4)≡ SU(2)×SU(2) symmetry.


We define~π ≡ (φ2,φ3,φ4), σ = φ1.

The Lagrangian is then

L =12

∂µ~π ·∂ µ~π +12

∂µσ∂µ

σ− 12

µ2~π ·~π− 1

2µ

2σ

2− λ

4

(~π ·~π +σ

2)2

.

The O(4) is equivalent to SU(2)V ×SU(2)A. We now allow forspontaeous symmetry breaking,

σ = φ1 = 〈φ1〉+H = 〈σ〉+H,

with〈σ〉2 = v2 =−µ

2/λ .

Rewrite the Lagrangian in terms of the shifted fields:

L =12

∂µ~π ·∂ µ~π +12

∂µH∂µH− 1

2m2

HH2−m2

H

2v(H2+~π2)−

m2H

8v2 (H2+~π2).

H is the only physical field. The ~π fields correspond to thelongitudinal degrees of freedom of the massive gauge bosons


Equivalence theorem (continued)

π3 = z (≡ ZL)

π± = w± (≡W±

L ).

For example, one can check that the H →WLWL width comesout right:

M ≈−m2

H

v,

Γ =1

8π

GF√2

m3H .


Unitarity limit

The Higgs cannot be very heavy, or else the unitarity limit wouldbe crossed too soon. To see this, write the old-fashionedscattering amplitude fcm, so that |fcm|2 = dσ

dΩ . Then we have

fcm =1

8π√

sM .

The scattering amplitude has the partial wave expansion

f (θ) =1k ∑

l

(2l +1)Pl(cosθ)al

where al = eiδl sinδl is the partial wave amplitude written interms of the phase shift δl . Unitarity is expressed by the opticaltheorem relation

σ =4π

kℑf (0).


Unitarity

For elastic scattering, the phase shift δl is real, but has apositive imaginary part if there is inelasticity. A convenient wayto express elastic unitarity is

ℑ1al

=−1.

From this it follows that

|al | ≤ 1; |ℜal | ≤12.

The l = 0 partial-wave unitarity for large s for WW scatteringthen gives

GF m2H

4√

2π< 1,

or

m2H <

4√

2π

GF.

This gives a limit of mH < 1.2 TeV.


Models with no light Higgs

Light Higgs tames high energy behaviour of WLWL

scatteringIn the absence of light Higgs, WLWL interactions becomestrongViolation of unitarity is prevented in different ways,depending on the modelModels can have extra fermions and extra gaugeinteractions, which give additional contributions to WLWL

scattering, e.g., resonancesAn example is techni-rho resonance in techni-color model,or new MVB’s in Higgsless modelsA no-resonance scenario is described in a chiralLagrangian (EWCL) model, where one can write effectivebosonic operatorsUnitarization can be built in by the use of Padéapproximants or N/D method and these can generateresonances


WW contribution vs. others

+

u

s

W

d

c

d

c

W

W

u

s

+.....Permutations

W

W

WW

s

u

(a)

d

c

(b)

Z, γ

W

W

Z, γ

Figure: Main diagram topologies for the process us → cdW+W−


Equivalent vector-boson approximation

Equivalent photon approximation (Weizsäcker-Williamsapproximation) relates cross section for a charged particlebeam (virtual photon exchange) to cross section for realphoton beam:

σ =∫

dxσγ(x)fq/γ(x)

Photon distribution with momentum fraction x in acharged-particle beam of energy E :

fe/γ(x) =q2α

2πxln(

Eme

)[x +(1−x)2]

This is generalized to a process with weak bosons(Dawson; Kane et al.; Lindfors; Godbole & Rindani):

fe/V±(x) =α

2πxln(

EmV

)[(vf ∓af )

2 +(1−x)2(vf ±af )2]

fe/VL(x) =

α

πx(1−x)

[v2

f +a2f

]


Effective vector boson approximation

Use of effective vector boson approximation entails:Restricting to vector boson scattering diagramsNeglecting diagrams of bremsstrahlung typePutting on-shell momenta of the vector bosons which takepart in the scatteringNote that the on-shell point q2

1,2 = M2V1,2

is outside the

physical region q21,2 ≤ 0.

Approximating the total cross section of the processf1f2 → f3f4V3V4 by the convolution of the vector bosonluminosities L V1V2

Pol1Pol2(x) with the on-shell cross section:

σ(f1f2 → f3f4V3V4) =∫

dx∑V1,V2 ∑pol1pol2 L V1V2pol1pol2

(x)

×σonpol(V1V2 → V3V4,xsqq)

Here x = M(V1V2)2/sqq, while M(V1V2) is the vector boson

pair invariant mass and sqq is the partonic c.m. energy.


Improved Equivalent vector-boson approximation

Even if only dominant (?) longitudinal polarization is kept,EVBA overestimates the true cross section

Transverse polarization contribution is found to becomparable to longitudinal one (Godbole & Rindani)

Improved EVBA (Frederick, Olness& Tung), going beyondthe leading approximation still overestimates the crosssection (Godbole & Olness)

Further improvements have been attempted (Kuss &Spiesberger)


Backgrounds

Backgrounds are of two types:1. Bremsstrahlung processes – which do not contribute toVV scattering2. Processes which fake VV final state

It is important to understand the first inherent background,and device cuts which may enhance the signal.

However, it may be possible to live with it – provided VVscattering signal is anyway enhanced because it is strong.In that case, one simply makes predictions for thecombined process of PP → VV +X

The second background is crucial to take care of,otherwise we do not know if we are seeing a VV pair in thefinal state or not.


Experimental backgrounds

Signature of signal is WLWL pair in final state

For no light Higgs TeV region may contain a resonance, orno resonance

For model with a TeV scalar (spin-0, isospin-0) resonance,most useful detection modes are W +W− and ZZ , whichcontain large isospin-0 channel contributions

For a model with TeV vector (spin-1, isospin-1) resonance,the most useful mode is W±Z mode

If no resonances are present, then all WW modes areimportant, including W±W±

Cleanest final state is through pure leptonic mode of eachgauge boson (BR 2/9 for W and 0.06 for Z ).


Experimental backgrounds

The intrinsic SM background in the TeV region can begenerated by calculating the SM production rate offf → ffWW with a light SM Higgs boson.

For example, the WLWL signal rate in the TeV region froma 1 TeV Higgs boson is equal to the difference between theevent rates calculated using a 1 TeV Higgs boson and a100 GeV Higgs boson

Other backgrounds:W + 2 jets (“fake W " mimicked by two QCD jets)t t pair (which subsequently decays into a WW pair)


Backgrounds in ZZ leptonic decay modes

Signal is an event with four isolated leptons with high pT

(for both Z decaying into `+`−) ortwo isolated leptons associated with large missing pT (forone Z decaying into `+`− and the other to νν)Dominant background processes are qq → ZZX ,gg → ZZX where the X can be additional QCD jet(s)Final state Z pairs produced in these processes tend to betransversely polarizedAlso, Z pairs produced from intrinsic electroweakbackground process are mostly transversely polarized.This is because coupling of a transverse W to a lightfermion is stronger than that of a longitudinal W athigh-energyKinematic cuts needed to enhance events withlongitudinally polarized W emitted from incoming fermions,and hence enhance WLWL →WLWL signal event


Background in leptonic decay of W +W−

For W +(→ `+ν)W−(→ `−ν) mode

Background processes qq →W +W−X , gg →W +W−X

tt + jet, with top decays giving W +W− pair


Background in semi-leptonic decay of W +W−

For W +(→ `+ν)W−(→ q1q2) mode

The signature is isolated lepton with high pT , large missingpT , and two jets with invariant mass about mW

Electroweak-QCD process W + + jets can mimic the signalwhen the invariant mass of the two jets is around mW

Potential background from QCD processesqq,gg → t tX ,Wtb and t t +jets), in which a W can comefrom the decay of t or t .


Distinguishing signal from background

We concentrate on W +(→ `+ν)W−(→ q1q2) modeW boson pairs produced from the intrinsic electroweakprocess qq → qqW +W− tend to be transversely polarizedCoupling to W + of incoming quark is purely left-handedHence helicity conservation implies that outgoing quarkfollows the direction of incoming quark for longitudinal W ,and it goes opposite to direction of incoming quark fortransverse (left-handed) WHence outgoing quark jet is less forward in backgroundthan in signal event, and tagging of the forward jet can helpCharged particle multiplicity of the signal event (purelyelectroweak) is smaller than that typical electroweak-QCDprocess like qq → gW +W−

One can reject events with more than two hard jets incentral rapidity region, which would also removebackground from t t production


Other ways of reducing background

1 Isolated lepton in W + → `+ν

Background event has more hadronic activity in the centralrapidity regionHence the lepton produced from W decay in backgroundevent is less isolated than that in signalRequiring isolated lepton with high pT is thus useful forsuppressing background

2 W → q1q2 decay modeAfter imposing veto of central jet and tagging of forward jet,t t background is smallCan be further suppressed by vetoing event with b jetcoming from top decay


Axial gauge vs. unitary gauge vs. EVBA vs. exactresults

The feasibility of extracting WW scattering from experimentand comparison of EVBA with exact results was recentlystudied by Accomando et al., hep-ph/0608019It is known that when W ’s are allowed to be off mass shell,amplitude grows faster with energy, as compared to whenthey are on shell (Kleiss & Stirling, 1986)Problem of bad high-energy behavious of WW scatteringdiagrams can be avoided by the use of axial gauge (Kunsztand Soper 1988)In axial gauge, Goldstone and gauge fields mix, with thegauge propagator given by(

−gµν +qµnν +nµqν

q ·n− n2

(q ·n)2 qµqν

)(q2−m2

W )−1


Axial gauge vs. unitary gauge vs. EVBA vs. exactresults

Accomando et al. examine

Role of choice of gauge in WW fusion

Reliability of EVBA

Determination of regions of phase space, in suitablegauge, which are dominated by the signal (WW scatteringdiagrams)

Results show that

WW scattering digrams do not constitute the dominantcontribution in any gauge or phase space region

There is no substitute to the complete amplitude forstudying WW fusion process at LHC


WW contribution vs. others

No Higgs

σ(pb)

Gauge All diagrams WW diagrams ratio WW/all

Unitary 1.86 10−2 6.67 358Feynman 1.86 10−2 0.245 13Axial 1.86 10−2 3.71 10−2 2

Table: No Higgs contribution, using the CTEQ5 Pdf set with scale MW

MH = 200 GeV

σ(pb)

Gauge All diagrams WW diagrams ratio WW/all

Unitary 8.50 10−3 6.5 765Feynman 8.50 10−3 0.221 26Axial 8.50 10−3 2.0 10−2 2.3

Table: Mh =200 GeV Higgs and M(WW ) > 300 GeV .


WW invariant mass distribution

(GeV)WWM

200 400 600 800 1000 1200 1400

(p

b/G

eV)

WW

/dM

σd

0

0.05

0.1

0.15

0.2

0.25

0.3

-310× WW invariant mass distribution

WW Feynman gauge

1/20×WW Unitary gauge WW Axial gauge

Total diagrams

(GeV)WWM

200 400 600 800 1000 1200 1400

Rat

io

1

10

210

310

410 Unitary gauge

Feynman gaugeAxial gauge

WW invariant mass ratio

Figure: Distribution of dσ/dMWW for the processPP → us → cdW +W− for All diagrams, WW diagrams and their ratioin Unitary, Feynman and Axial gauge in the infinite Higgs mass limit.The Unitary gauge data in the left hand plot have been divided by 20for better presentation.


Comparison with EVBA results: WW invariant mass

(Gev)WWM

200 300 400 500 600 700 800 900 1000

(p

b/G

ev)

WW

/dM

σd

-610

-510

-410

Invariant mass distribution of the W pair

EVBAEXACT

(GeV)WWM

200 300 400 500 600 700 800 900 1000

(

pb/G

eV)

WW

/dM

σd

-610

-510

-410

Invariant mass distribution of the W pair

EVBAEXACT

Figure: WW invariant mass distribution M(WW ) for the processus → dcW +W− with EVBA (black solid curve) and with exactcomplete computation (red dashed curve) for no Higgs (left) andMh=250 GeV (right)


Comparison with EVBA: Total cross section

Mh EVBA (pb) EXACT (pb) Ratio∞ 3.90 10−2 1.78 10−2 2.17

130 GeV 3.94 10−2 1.71 10−2 2.3250 GeV 4.61 10−2 4.09 10−2 1.12500 GeV 4.42 10−2 2.5 10−2 1.77

Table: Total cross sections computed with EVBA and exact computation andtheir ratio for the process us → cdW+W− at fixed CM energy

√s = 1 TeV.

θcut EVBA (pb) EXACT (pb) Ratio10 4.42 10−2 2.5 10−2 1.7730 1.33 10−2 2.06 10−2 0.6460 6.06 10−3 1.28 10−2 0.47

Table: Total cross section in EVBA and exact computation and their ratio fordifferent angular cuts. The CM energy is

√s = 1 TeV and the Higgs mass

Mh=500 GeV.


Large invariant mass region

(GeV)WWM

1000 1500 2000 2500 3000

(p

b/G

eV)

WW

/dM

σd

-1110

-1010

-910

-810

-710

-610NohHiggs

W+W- Invariant mass distribution The WW invariant

mass distribution in

PP → us → cdW+W−

for no Higgs mass (solid

curves) and for Mh=200 GeV

(dashed curve). The two

intermediate (red) curves are

obtained imposing cuts shown

below.The two lowest (blue) curves refer to the process PP → us → cdµ−νµ e+νe

with further acceptance cuts: El > 20 GeV, pTl> 10 GeV , |ηl |< 3.

E(quarks)> 20 GeVPT (quarks,W)> 10 GeV

2 < |η(quark)|< 6.5|η(W)|< 3

Table: Selection cuts applied


Some references

WW scattering in the context of heavy Higgs boson:ATLAS Collaboration, CERN/LHCC/94-13,CERN/LHCC/99-15; CMS Collaboration,CERN/LHCC/94-38Electroweak chiral Lagrangian (EWChL): T. Appelquist andC. Bernard, PRD 22, 200 (1980); A. Longhitano, PRD 22,11 (1980); NPB 188, 118 (1981)“WW scattering at CERN LHC", J.M. Butterworth, B.E.Cox, J.R. Forshaw, PRD 65, 096014 (2002)“Collider phenomenology of the Higgless models", A.Birkedal, K. Matchev, M. Perelstein, PRL 94, 191803(2005)“Off-shell scattering amplitudes for WW scattering and therole of the photon pole", J. Bartels and F. Schwennsen,PRD 72, 034035 (2005)


Summary

In the absence of a light Higgs, WW interactions becomestrong at TeV scales

Study of WW scattering can give information of theelectroweak symmetry breaking sector and discriminatebetween models

In general there are large cancellations between thescattering and bremsstrahlung diagrams

Hence extraction of WW scattering contribution from theprocess PP →W +W−X needs considerable effort

EVBA overestimates the magnitude in most kinematicdistributions

Cuts to reduce background were discussed

ww scattering saurabh d. rindaniindiacms/lhcworkshop/talks/040906/... · 2006-09-05 · ww...

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