E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino

Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 1

E. Accomando A. Ballestrero A. Belhouari E. MainaINFN and Dip. Fisica Teorica

Torino

Boson boson scattering at LHC

• PHASE Monte Carlo

• Boson Boson Scattering and Gauge Invariance

• Boson Boson Fusion and Higgs

• Conclusions

• Introduction

• Boson Boson scattering and unitarity

• EVBA : extrapolation and deconvolution?


Introduction

One of the main purposes of LHC is Higgs discovery and/or EWSB study

WW scattering holds the key to EWSB

(violation of unitarity for WL WL WL WL in absence of Higgs, possible new resonances..)

WW scattering effects are buried in WW fusion processes

their study is a natural extension of Higgs searches in WW fusion channel if m_h near or above WW treshold

These are only a subset of the complete calculation for qq six fermion final states

All pp six fermion final states has to be under control to analize EWSB and possible signals of new physics connected to it


Boson Boson scattering and unitarity

Consider longitudinally polarized W's:

single diagram proportional to:

WW scattering

For

!


gauge cancellations at work

For the three diagrams without Higgs

It still violates unitarity

provided (qualitatively)

HIGGS RESTORES UNITARITY



More precisely :

Partial wawes unitarity requires


Limit on mH and energy at which new physics should appear if mH too large



If Higgs does not exist or its mass too large, new physics must appear at TeV scale (LHC)

A signal for this is an unexpected growth with energy of WW (Boson Boson) scattering

Various theories (Technicolor, dynamical symmetry breaking) and phenomenological models have been studied

All predict unexpected phenomena (e.g. formation of resonances) in Boson Boson scattering.

These are connected to new mechanisms to restore unitarity

Can Boson Boson scattering be measured at LHC ?

There is a chance for it in hard processes like u s -> c d W+ W+ or ud -> ud W+ W-which contain contributions of the type


Different ways of constructing amplitudes which satisfy unitarity constraints from low order amplitudes

e.g.



EVBA : extrapolation and deconvolution ?

Equivalent Vector Boson Approximation

a

A

a

V

V

a



a

b


is a function of q1 and q2. (spacelike)


-1 n+1q 2 off shell

The approximation consists in projecting it on boson mass shell

Different approximations can also be taken in evaluating the boson luminosities (x)The approximation is valid to ~ 10% for photons, much worse for Z and W

Results depend on cuts.


Finding information on boson boson scattering from experimental dataneeds extrapolation from q to on shell (as in EVBA) and deconvolution

of the data from the integration over PDF.


The energy of the WW scattering is determined by the invariant WW mass



Hard processes under consideration will not contain only contributions from

but also from all diagrams of the type

Moreover final partons are fermions with all diagrams for 6 fermion final statewhich depend on the final state at hand

Can all this be separated from what we would like to be "the signal" ?If not, do we have anyway see consequences of EWSB pattern in these processes?

Of course they will be anyhow fundamental for Higgs searches and measurements for a Higgs heavier than 140 GeV


Boson Boson Scattering and Gauge Invariance

We have to use complete calculations in order to

• account for all irreducible backgrounds

• deal with severe gauge problems and gauge cancellations

A prototype of these is the extremely large interference that affects

WW fusion diagrams and other diagrams with two outgoing W's.

The two sets are not separately gauge invariant

Their sum is gauge invariant, but only for on shell W's

This huge interference casts doubts on EVBA at LHC

It poses severe problems on the definition of the signal for Boson Boson Scattering studies.


The interference


A.B. AccomandoBelhouari Maina


Already known since a long time



no higgs

unitaryσ (pb)

ratio

ww / all

All diagrams 1.86 E-2

358WW fusion

diagrams6.67

m_h=200 mWW>300

unitaryσ (pb)

ratio

ww / all


765WW fusion

diagrams6.50

no higgs

feynmanσ (pb)

ratio

ww / all


13WW fusion

diagrams0.245

m_h=200 mWW>300

feynmanσ (pb)

ratio

ww / all


26WW fusion

diagrams0.221


Distributions show huge interference effect which are not constant:

they depend very much on the value of the variable

Previous results are confirmed by

PP-> u s -> d c W+ W- (on shell W's)

Feynman gauge has still big cancellations but about a factor 30 less than unitary!

Is it possible to find regions with low interference and use it to define WW scattering signal?



pp us dc W+W-

all diagrams

unitary WW fusion ratio unitary

feynman WW fusion ratio feynman

NO HIGGS

ddMWW

ratio = WW fusion / all



pp us dc W+W-

all diagrams

unitary WW fusion

feynman WW fusion ratio feynman

NO HIGGS

ddW

ratio unitary



Differences do not depend on Higgs

pp us dc W+W-

all diagrams

all diagrams

unitary WW fusion

unitary WW fusion ratio unitary

NO HIGGS

Higgs M=200 GeV with MWW > 300 GeV

ddW

ratio unitary



unitary WW fusion

feynman WW fusion

ratio unitary

ratio feynman

pp us dc W+W-

all diagrams

t1

t2

t2

t1



no cut

MWW > 1000 GeV

a cut on MWW doesnot change qualitativelybut worsen the ratios

t1

t2

ratio unitary

ratio unitary

ratio feynman

ratio feynman

0.63

2.76

0.71

0.2


PHASE Monte Carlo - Purpose

Monte Carlo for LHC dedicated studies and full physics and detector simulation of

Boson Boson Fusion and scatteringHiggs Production in this channel tt productionTriple and Quadruple Boson CouplingsThree Boson Production

PHASE

PHact Adaptive Six Fermion Event Generator(E. Accomando, A. Ballestrero, E. Maina)


Useful also for comparison with different approach

The processes we have considered involve in reality 6 fermion final states

PHASE Monte Carlo - Purpose

For them so far we have:

We aim at a complete (all processes and all diagrams) and dedicated MC

Full generation and simulation with high efficiency

Interface to detector simulations

• incomplete 6 fermion studies- PRODUCTION x DECAY approach (ALPGEN, COMPHEP,...)

most part of the analyses uses NWA and/or EVBA (PYTHIA, HERWIG)

- many final states have not been considered yet

• Multi-purpose Event Generators[ AMEGIC & SHERPA , COMPHEP, GRACE & GR@PPA ,

MADGRAPH & MADEVENT, O'MEGA & WHIZARD, PHEGAS & HELAC ]

'generic' -> 'dedicated' is not a trivial step

Non irreducible backgrounds by other MC

They will receive contributions by hundreds of different diagrams,which constitute an irreducible background to the signal we want to examine,with all the problems connected to interferences and gauge invariance


Consider l (e.g. ) in the final stateWe want to compute and generate in one shot all processes :

q4pp

Up to now only em6 :

q4Xqqpp )('

How many areq4qq '

Let us consider all outgoing

0Qi

8

1i

and fix 2q as sc

All processes of the type

scqqqq4321

PHASE Monte Carlo - Processes


ProcessInitial

state multipl.

Boson Boson scattering subprocess

7 diag 7 diag 4 diag 4 diag

Total

Number of

Diagrams

2 202

2 x 202

2 x 202

2 x 202

2 x 202

2 x 202

1 x 202

1 x 202

WWWW WWZZ WZWZ WWWW

μscscud

νμscsucd

μsccusd

μscsdcu

νμsdccus μscudsc

μssudcc

μccudss

4 W )( μscscud



ProcessInitial state multipl.



Total

Number of

Diagrams

2 x 422

2 x 422

2 x 422

2 x 422

2 x 422

2 422

1 x 422

1 x 422

WWWW WWZZ WZWZ WWWW

μscuuuu

νμsuuucu

μcuuusu

μsuuucu

μcuuuus

μuuuusc

μscuuuu

μsuucuu

2 W 2 Z )( μscuuuu



ProcessInitial state multip.



Total Number of

Diagrams

2 x 312

2 x x 312

2 x 312

2 x x 312

2 x x 312

2 x 312

2 x x 312

2 x x 312

2 x x 312

2 x 312

2 x x 312

2 x x 312

2 x x 312

2 x x 312

2 312

WWWW WWZZ WZWZ WWWW

μscdduu

Mixed : 4 W + 2W2Z )( μscdduu

μscdudu

μsdcudu

μsdducu

cμddusu

μscdudu

μsudcud

μsdudcu

cμdudus

μscuudd

μsduucd

cμduusd

μsduucd

dcμuuds

μdduusc



262024W

264222Z2W

261046Misto

015312Misto

266102Z2W

1104662Z2W

2312662Z2W

1104662Z2W

2312662Z2W

0152332Z2W

1104222Z2W

1104222Z2W

264222Z2W

0152332Z2W

1104222Z2W

1104222Z2W

Initial mult. 1Initial mult. 2

Number of

processesDiagram

numberType

Outgoing

particles

μscdduu

how may processes and diagrams?

νμscscud

μscbbbb

νμscccuu

μscssuu

μscbbuu

μscdddd

μscccdd

μscssdd

μscbbdd

μsccccc

μscbbcc

μscbbss

νμscsscc

μscssss

μscuuuu

161 processeshave differentmatrix elements

141 20

processes which differ at least forpdf:

141 x 2 + 20=302 x 4 (CC +Fam)=1208

This only for

em6



PHASE Monte Carlo - Amplitude

Helicity Amplitudes written with PHACT

program for producing fortran code in helicity method fast

and suited for modular computing (subdiagrams)

Which diagrams are effectively independent and need to be computed?


262024W

264222Z2W

261046Misto

015312Misto

266102Z2W

1104662Z2W

2312662Z2W

1104662Z2W

2312662Z2W

0152332Z2W

1104222Z2W

1104222Z2W

264222Z2W

0152332Z2W

1104222Z2W

1104222Z2W

I 1Initial mult. 2

Number of

ProcessesNumber of

diagramsType

Outgoing particles

μscdduu

νμscscud

μscbbbb

νμscccuu

μscssuu

μscbbuu

μscdddd

μscccdd

μscssdd

μscbbdd

μsccccc

μscbbcc

μscbbss

νμscsscc

μscssss

μscuuuu

141 20


Diagrams which belong to the same groupof 8 outgoing particlecan be computed in the same way

Therefore do not consider1208 or 161 but

16 different types of amplitude

Many groups haveidentical numberof diagrams ...


Are the groups with the same number of diagrams (e.g. 422) identical? Not really but can be programmed at the same time

We are left with:202 233 312 422 466 610 1046 1266

νμscscud μscbbdd μscdduu μscssdd μscbbcc μscbbbb νμscsscc μscssss

Simple arithmetics: 202=101 x 2 233=211 without hbb +22 312=101+211 422=211 x 2 466=233 x 2 610=211 x 2 +188 hbb 1046=312 x 2 + 422 1266 =422 x 3

Only 101 211 22 94 independent diagrams

Further simplification: subdiagrams


cxchange of identical particles

But the combinatorics is complicated


PHASE Monte Carlo - Integration

Several studies and tests

Two main strategies are normally used:Adaptive

- Not sufficient when one has completely orthogonal peaking structures (e.g. annihilation vs fusion vs tt)

Multichannel

- hundreds of channels (even one per diagram !)

- peaking structure of propagators What if not all propagators can be resonant at the same time? Cuts might give inefficiency Resonances can reproduce badly long non resonant parts

- Adaptive and/or weight of the various channels from the importance of single diagrams Problems with gauge cancellations of orders of magnitude among different feynman diagrams


.

With adaptive calculations only few phase spaces (channels) for completely different structures are needed

For every process the possible channels to be used are established, weights determined in thermalization

and independent runs for every channel are performed

Different mappings (up to 5) on the same variable of every phase spaceand a careful treatment of exchange of identical particles are employed

PHASE Monte Carlo - Integration

PHASE combines in a new way the two strategies


PHASE Monte Carlo - Generation

Interface with Les Houches Protocol to be used in a full experimental simulation procedure

One shot a la WPHACT

One shot : Unweighted event generation of all processes (several hundreds) or any subset in a single run


Boson Boson Fusion and Higgs

Even if difficult define Boson Boson scattering,

PHASE can be used to compute and simulate

possible consequences of EWSB in completeprocesses "dominated" by Boson Boson fusion

and

Higgs production in the same channel in presence of

complete irreducible background

Let us consider the process

It contains and many other contributions



Higgs peak andevident differencebetween normal SM Higgs scenariosand unexpected onesfor high MWW

PROCESS



differences betweendifferent scenariosalso at low MWW

with much morestatistics

PROCESS



difference between light higgsand no Higgs (mH -> ) at high MWW

As WLWL grows with mh while other componentsremain constant, can one "define" the signal as the difference of heavy and light higgs at high MWW? ?

PROCESS



Comparison of

and

for realistic cuts

Difference in totalcross sections is~ 20-30 % It becomes muchhigher at high invariantmasses. The differencebetween a realistic higgsand no higgs is greaterfor the full calculationbut the cross sections athigh MWW are lower.



One can distinguish the contributions coming from different polarizations also for off shell W's, using

For mH -> LL dominates at high MWW.


1 < η(d) < 5.5 -1 > η(u) > -5.5E(u,d,c,s,μ) > 20 GeV Pt(u,d,c,s,μ) > 10

GeV70< M(sc, μν) < 90

mH = 120 GeV


ptW cut :ptW > MW

With LL and pt cut (as needed by EVBA)one looses a lotin cross section


• EWSB studies are one of the most important challenges for LHC.

• Studies on extraction of "boson boson scattering" at LHC show difficulties due to gauge invariance. They will be continued.

• The complete calculation of these processes seem to show in any case promising clear effects of different EWSB patterns.

• A realistic study with all processes and full detector simulation seems worthwhile.

Conclusions

PHASE is a dedicated LHC six fermion event generator

- It can at present study and simulate processes with 4 quarks + an isolated lepton (+ neutrino) with complete calculations

- For a realistic approach O(em4 s

2) will be added

- And then l+ l- + 4quarks final states

Much work ahead

E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino

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