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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?
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 2
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 3
Boson Boson scattering and unitarity
Consider longitudinally polarized W's:
single diagram proportional to:
WW scattering
For
!
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 4
gauge cancellations at work
For the three diagrams without Higgs
It still violates unitarity
provided (qualitatively)
HIGGS RESTORES UNITARITY
Boson Boson scattering and unitarity
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 5
More precisely :
Partial wawes unitarity requires
Boson Boson scattering and unitarity
Limit on mH and energy at which new physics should appear if mH too large
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 6
Boson Boson scattering and unitarity
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 7
Different ways of constructing amplitudes which satisfy unitarity constraints from low order amplitudes
e.g.
Boson Boson scattering and unitarity
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 8
EVBA : extrapolation and deconvolution ?
Equivalent Vector Boson Approximation
a
A
a
V
V
a
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 9
EVBA : extrapolation and deconvolution ?
a
b
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 10
is a function of q1 and q2. (spacelike)
EVBA : extrapolation and deconvolution ?
-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.
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 11
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.
EVBA : extrapolation and deconvolution ?
The energy of the WW scattering is determined by the invariant WW mass
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 12
EVBA : extrapolation and deconvolution ?
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 13
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.
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 14
The interference
Boson Boson Scattering and Gauge Invariance
A.B. AccomandoBelhouari Maina
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 15
Already known since a long time
Boson Boson Scattering and Gauge Invariance
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 16
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
All diagrams 8.50 E-3
765WW fusion
diagrams6.50
no higgs
feynmanσ (pb)
ratio
ww / all
All diagrams 1.86 E-2
13WW fusion
diagrams0.245
m_h=200 mWW>300
feynmanσ (pb)
ratio
ww / all
All diagrams 8.50 E-3
26WW fusion
diagrams0.221
Boson Boson Scattering and Gauge Invariance
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?
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 17
Boson Boson Scattering and Gauge Invariance
pp us dc W+W-
all diagrams
unitary WW fusion ratio unitary
feynman WW fusion ratio feynman
NO HIGGS
ddMWW
ratio = WW fusion / all
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 18
Boson Boson Scattering and Gauge Invariance
pp us dc W+W-
all diagrams
unitary WW fusion
feynman WW fusion ratio feynman
NO HIGGS
ddW
ratio unitary
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 19
Boson Boson Scattering and Gauge Invariance
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 20
Boson Boson Scattering and Gauge Invariance
unitary WW fusion
feynman WW fusion
ratio unitary
ratio feynman
pp us dc W+W-
all diagrams
t1
t2
t2
t1
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 21
Boson Boson Scattering and Gauge Invariance
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 22
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)
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 23
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 24
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 25
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
PHASE Monte Carlo - Processes
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 26
ProcessInitial state multipl.
Boson Boson scattering subprocess
7 diag 7 diag 4 diag 4 diag
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
PHASE Monte Carlo - Processes
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 27
ProcessInitial state multip.
Boson Boson scattering subprocess
7 diag 7 diag 4 diag 4 diag
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
PHASE Monte Carlo - Processes
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 28
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 - Processes
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 29
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?
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 30
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
PHASE Monte Carlo - Amplitude
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 ...
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 31
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
PHASE Monte Carlo - Amplitude
cxchange of identical particles
But the combinatorics is complicated
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 32
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 33
.
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 34
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 35
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 36
Boson Boson Fusion and Higgs
Higgs peak andevident differencebetween normal SM Higgs scenariosand unexpected onesfor high MWW
PROCESS
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 37
Boson Boson Fusion and Higgs
differences betweendifferent scenariosalso at low MWW
with much morestatistics
PROCESS
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 38
Boson Boson Fusion and Higgs
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
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 39
Boson Boson Fusion and Higgs
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.
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 40
Boson Boson Fusion and Higgs
One can distinguish the contributions coming from different polarizations also for off shell W's, using
For mH -> LL dominates at high MWW.
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 41
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
Boson Boson Fusion and Higgs
ptW cut :ptW > MW
With LL and pt cut (as needed by EVBA)one looses a lotin cross section
Alessandro Ballestrero QFTHEP04 - St. Petersburg – 17-23 June 2004 42
• 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
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