Alessandro Ballestrero

Alessandro Ballestrero The Physic of LHC - Italo-Hellenic School – Lecce – May 20041

Alessandro Ballestrero

Electroweak Physics at the LHC

• PHASE Monte Carlo

• Boson Boson Scattering and Gauge Invariance

• Boson Boson Fusion and Higgs

• Conclusions

• Introduction

• W production

• Two boson production

• W mass measurement

• Boson Boson scattering and unitarity

• EVBA : extrapolation and deconvolution?

• EW and QCD


Introduction

what we expect from LHC Higgs and SUSY is the most common answer

Higgs as a scalar poses problems (quadratic divergences) if we admit a physical cutoff in the theory

SUSY removes this cutoff far away (to the Plank scale) and solves the problems of fine tuning

But if we admit that SM is valid only up to a certain scale, other possible scenarios are also possible:

no Higgs , dynamical symmetry breaking, technicolor,......

Electroweak physics is requested for accurate theoretical predictions

They will be important for

precision physics

higgs searches and measures of its properties,

establishing possible deviations from standard model,

evaluating backgrounds to all searches for any kind of new physics.

Moreover we cannot exclude new phenomena that we do not expect


EW and QCD

Strong interactions will be dominating: • αS ten times bigger than αem

• gluons more abundant than quarks in protons • also quarks prefer to interact via QCD.

But the distinction between Strong and Electroweak physics is somewhat artificial: They are complementary and are both necessary to the understanding

of SM and BEYOND

Consider top production and top mass measurement:

• It is a strong process

LHC is an hadronic collider.

(x(x11xx221010-3-3))

90%90%

10%10%

but ....


EW and QCD

• Cross section determined to NLO precision

-Total NLO(tt) = 834 ± 100 pb

(largest uncertainty from scale variation)

low lumi 10 fb-1

high lumi 100 fb-1

107 tt at low luminosity LHC is a top factory !

This will allow to reach 1 GeV (in one year?) precision in top mass measurement

Lepton side

Hadron side


EW and QCD

top mass has a strong influence on electroweak precision predictions via ew corrections.

but ....


EW and QCD

A=gV gA /(gV2 + gA

2) = asimmetry right left

Data fitted :

• The Z parameters

- lineshape and lepton asymmetry at LEP: mZ ΓZ σh Rl and AlFB

- Ae and Aτ from τ polarization at LEP

- Al from polarised left-right asymmetry by SLD

- Heavy quark (b and c) measurementes at LEP and SLD: Rb Rc AbFB Ac

FB Ab Ac

- sin2 θleff from quark forward-backward asymmetry at LEP

• W mass mW at LEP and Tevatron

• Top mass mT at Tevatron

• sin2 θW from νN scattering data by the NuTeV experiment

Input parameters for the calculations: α (mZ) mZ Gμ

αS (mZ) mt mh ( for the corrections )

Parameters of the fit:mZ mt mh αS (mZ) and Δαh

(5) (mZ) (light quark contribution to running of alfa)


EW and QCD

QCD uncertainties (both theoretical and experimental) are generally big. so if we can isolate ew contributions these will in generally give a clean prediction

The luminosity of LHC will allow anyhow precision measures.Hence we need in some cases QCD predictions to NNLO and NLO EW corrections

EW corrections to QCD observables have started to appear

Maina S. Moretti Ross ...


EW and QCD

For the precise knowledge of tt cross section one should go to NNLO

There are not EW corrections available for tt production

They are probably not useful by themselves as tt bar productions is a much more complicated process

In reality one has to deal not only with the two signal diagrams

has more than 300 diagrams

has more than 700


EW and QCD

Weak corrections are available for the similar process

b massless


EW and QCD

The same group has also analyzed Weak corrections to p p γ , Z + jet


EW logs

:For 4 or more fermions in the final state complete NLO EW are not availableand in many cases one has to rely on approximations

Leading Pole Approximation, Leading Log Approximation, Final State Radiation .....

In the following I will mainly discuss the physics ofvector bosons (W,Z) production and scattering

why ew corrections can give important enhancements at high energies ?

Sudakov logs corrections appear, which become important for s >> MW2

Many NLO EW calculations have been performed, and NLO MC's start to appear

One must however realize that

At LHC they are of the order


EW logs

SUDAKOV LOGS2 IN A NUTSHELLCiafaloni ..Denner....Beenaker........

• Correspond to soft and collinear singularities in theories with massless bosons In that case they are canceled by real radiation

• Regulated by boson mass in EW. They are finite

• Real emission of EW bosons has not necessarily to be summed It is considered that a W can always be distinguished by the emitting fermion

• In the Feynman gauge they are associated with virtual graphs where soft collinear bosons are exhanged between external legs

• Can be computed in eikonal approximation

• DL are universal: only depend on external particles


EW logs


Radiative correctionsRadiative corrections affect three level relations between SM parametersaffect three level relations between SM parameters

W mass measurement

It is possible to determine mH fom measuremnt of mt and mW (sin2 θW,, mZ) or assess the consistency of SM predictions with precision measurements


Status of inputs WC2004:Status of inputs WC2004:mmtt=174.3 ±5.1(exp) GeV/c=174.3 ±5.1(exp) GeV/c22

mmWW=80.426 ±0.034(exp) GeV/c=80.426 ±0.034(exp) GeV/c22

mmZZ=91.1875 ±0.0021(exp) GeV/c=91.1875 ±0.0021(exp) GeV/c22

ZZ=2.4952 ±0.0023(exp) GeV=2.4952 ±0.0023(exp) GeVdirect

indirect

EXCLU

DED

SM predictions SM predictions from ZFITTER from ZFITTER and TOPAZ0 and TOPAZ0 programsprograms

Direct and indirect data favour a light Higgs !Direct and indirect data favour a light Higgs !

W mass measurement


201673

Hm((mmHH/m/mH H 25%)25%)

Using Using hadhad=0.00012=0.00012

Thanks to M.Grunewald

direct

Perspective at the LHCPerspective at the LHCmmWW=15 MeV; =15 MeV; mmtt=1 GeV=1 GeV (world combined will look better (world combined will look better thanthanthese ! – Tevatron run II, LEP2)these ! – Tevatron run II, LEP2)(current central values assumed)(current central values assumed)

SM constraints on mSM constraints on mHH::

Chances of ruling out the Chances of ruling out the SM ?SM ?

EXCLU

DED

W mass measurement

After LEP and Tevatron mmWW=30 MeV=30 MeV it will probably be possible to reachit will probably be possible to reach

mmWW=15 MeV =15 MeV in the low lumi phase !in the low lumi phase !


W mass measurement

mtop and MW: equal weight in the EW fit if MW 0.007 mtop

at LHC: mtop 2 GeV gives the precision MW : 15 MeV

W-pair cross-section is too lowW-pair cross-section is too lowSingle W: no direct determination of mSingle W: no direct determination of mWW possible possible because of the missing neutrino, but huge statistics !because of the missing neutrino, but huge statistics !

e

W beam line

u

cos12 TTl

TW ppm

W mass : fit exp. shape to MC sample with different Values of MW

< 2 MeV/y as a statistical uncertaintysyst. error: MC modelling of physics and detector response

upp

T

l

T

(missing p(missing pTT))

transverse transverse massmass


W production

Main uncertainty is due to QCD corrections (5%) expecially for transwerse momentum of W due to gluon emission.

Two different types of ew. corrections:

Resummation of final state radiaton in pole approximation Complete ew corrections O(α).

Drell Yan mechanism not only important to measure W mass:

Rapidity distributions can provide information on PDF'sAlso important as a background to new phisics at high pt.

Tree level is trivial


Famous example: Ew corrections to four fermion processes at e+ e- computed in double pole approximation

W production

Pole approximation LPA

When one has resonant diagrams e.g.

one can make an expansion of the complete amplitude around the complex polesretaining only leading order (residue at the poles)

p2 – MW2 + i Г MW

Corresponds to retaining the propagator and projecting, in the rest of the computation, the two four momenta on mass shell of the decaying particle (the procedure is not univoque)

It is a gauge invariant procedure (which is not considering only resonant diagrams)

This approximation can be taken at any order in perturbation theory

Normally it is not used at tree level but as a useful approximation forNLO corrections


W production

Resummation of final state radiation in pole approximationYFS exponentiation

Pavia shift extimate with a "pseudo experiment"

HORACECarloni Calame Montagna Nicrosini

WINHAC Placzek Jadach

exponentiation


W production

Combined effect of QCD Resummation and QED radiative corrections NLO QED included in RESBOS

Cao and Yuan


W production

Complete ew corrections O(α)

Dittmaier Kramers

single Z p p Z l+ l- ZGRAD2 Baur Hollikl Wackeroth ...

single W p p W l ν

O(α) parton cross section contain mass singuraties α ln(mq)

These collinear singularities are reabsorbed in PDF

This is done with

Absorption would require inclusion of O(α) corrections in DGLAP and experimental fit to data (but the effect is well below 1%)


W production

Dittmaier Kramers


W productionDittmaier Kramers


Two boson production

Vector boson pair production: test for non abelian structure of SM.

New physics at energies much larger than those tested at LEP2 could modify these interactions.

Effects of anomalous couplings will eventually be measured at LHC

Eg. chargino neutralino gold plated signal for Susy 3 charged leptons + missing pT

Background to new physics:

Full ME's and O(αS) ) at NLO with full spin correlations available and cross checked

Dixon, Kunszt, Signer, Ellis, ....

QCD corrections quite significant: increase xsect by a factor 2 (10 for high pT )

But with a jet veto they reduce to 10%



EW corrections only in leading log. They factorize for arbitrary process.

Accomando Denner Pozzorini

Computed for and for in leading log approximation (log2 and log of S/MW) neglecting logs of other invariants ( valid for , at large angles with respect to the beam ) and non factorizable corrections.

EW corrections non negligible in the high energy region for large transverse momentum and small rapidity separation of the emitted bosons,

Region of relevance for new physics effects

Mc has full processes and at Born level (IBA)

Corrections in (single or double) Pole approximations

We are still far from complete ew corrections for four fermions but in this case they are probably not needed




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



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



differences betweendifferent scenariosalso at low MWW

with much morestatistics



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



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

For mH -> LL dominates at high MWW



LL dominates also for light higgs athigh 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


Conclusions

We have a lot of expectations from LHC

Electroweak Physics will take part in many interesting physics problems

Only a cooperation among the different areas and methodwill allow to exploit all potentialities of LHC

A lot of challenging work is ahead of you

Have fun !

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Alessandro Ballestrero