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Midterm presentation Aissa Belhouari Under the supervision of Pro - - PowerPoint PPT Presentation
Midterm presentation Aissa Belhouari Under the supervision of Pro - - PowerPoint PPT Presentation
Midterm presentation Aissa Belhouari Under the supervision of Pro . A. Ballestrero INTRODUCTION Among the most important confirmations of the standard model predictions is gauge boson (W,Z) detection. Evidence of the breaking of the
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The physics of the bosonic sector depend on
- The higgs existence
- On its mass value.
Vector boson scattering VV VV could provide a good way to probe the interactions of this sector.
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Boson -Boson scattering and unitarity
WW scattering
Consider longitudinally polarised W`s The complete set of diagrams including the higgs is:
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The amplitude of the these diagrams alone has bad high energy behaviour In fact : violate unitarity Adding higgs diagrams Unitarity is restored but not for every higgs mass value
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Performing partial wave expansion: The unitarity constraint The S wave amplitude expression in the limit allow to derive a critical higgs mass value Unitarity constraint implies that Mcrit
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Boson-Boson scattering and gauge invariance
The vector bosons which initiate the scattering process in the subset: are in reality off shell Where :
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and Parametrize the off shellness of the incoming bosons
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To avoid this bad behaviour one has to take into account the complete set of feynman diagrams (a) + (b)
permutations
+....
Complete set of diagrams for
Diagrams (a) contain the essential part of the bosonic sector physics but....
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PP us cdW W The vector boson scattering subprocess is
6.67 WW fusion diagrams 358 1.86 E-2 All diagrams ratio ww / all
σ (pb)
no higgs unitary 6.50 WW fusion diagrams 765 8.50 E-3 All diagrams ratio ww / all
σ (pb)
m_h=200 mWW>300 unitary
Feynman gauge has still big cancellations but about a factor 30 less than unitary!
0.245 WW fusion diagrams 13 1.86 E-2 All diagrams ratio ww / all
σ (pb)
no higgs feynman 0.221 WW fusion diagrams 26 8.50 E-3 All diagrams ratio ww / all
σ (pb)
m_h=200 mWW>300 feynman
The ratio values are indication of the relevance of the diagrams of bremstrastrahlung-type set (b) and the interferences between them and WW fusion diagrams set (a)
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Distributions of different kinematical variables confirm this
pp→ us → dc W+W-
all diagrams unitary WW fusion ratio unitary feynman WW fusion ratio feynman NO HIGGS
d dMWW σ
ratio = WW fusion / all
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all diagrams unitary WW fusion
d d W σ θ
+
ratio unitary
pp→ us → dc W+W-
feynman WW fusion ratio feynman NO HIGGS
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all diagrams unitary WW fusion
d d W σ θ
+
ratio unitary
The inclusion of higgs diagrams does not make big difference
NO HIGGS
pp→ us → dc W+W-
all diagrams unitary WW fusion ratio unitary
Higgs M=200 GeV with MWW > 300 GeV
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unitary WW fusion feynman WW fusion all diagrams
t1 t2
ratio unitary
pp→ us → dc W+W-
ratio feynman
t1 t2
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ratio feynman
0.71
a cut on MWW does not change qualitatively but worsen the ratios t1 t2
ratio unitary ratio unitary
0.63 2.76
no cut ratio feynman
0.2
MWW > 1000 GeV
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The effective vector boson approximation EVBA
In analogy to the effective photon approximation (Weizsäcker-Williams-approximation )of QED, EVBA is applied to the scattering of massive vector bosons . This approximation consist in:
- a) Considering only diagrams involving
vector bosons fusion
- b) The cross section is written as product of probability
distributions and cross sections of vector boson fusions sub process
- c)The emitted vector bosons from the
fermion lines are taken on shell. Where ;
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In the literature some assumptions and approximations were made to compute the probability distributions of the vector bosons:
- Neglecting the vector bosons mass and their transverse momentum.
- Considering only longitudinal polarizations .
- Neglecting interference terms between longitudinal and transverse
polarizations Comparisons with exact calculations have shown that the method leads to reasonable results at least for higgs boson production Generally the EVBA agrees with the complete perturbative calculation to about 10% ~20% but in some cases can overestimate the exact results by a factor 3 or more and the agreement depends on the cuts
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Application of the EVBA method to the process and comparisons with the exact results
PP us cdW W The vector boson scattering subprocess is
The expression of the mommentum and polarizations in the center of mass of the W`s
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In our implementation we did not take any approximation to but we just extrapolated on shell the "incoming" W's
The extrapolation can be discribed by simple proportionality factors invariant mass of the vector bosons The form factors for different polarizations are:
- n shell cross section
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nen a a a
Because of the photon propagator singularity for on shell W`s scattering a cut on their CM angle scattering is applied theta > 10 degree and another cut on their invariant masse . Mww > 200 Gev Also cuts on the c and d quarks azimuthal angles to avoid form factor singularities. cut =10 degree
d dMWW σ
EVBA EXACT
Ecm = 14 Tev (with pdfs) without higgs
6.30 E-3 EXACT 2.16 1.36 E-2 EVBA ratio Evba/ exact
σ (pb)
no higgs
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d dMWW σ
EVBA EXACT
Same cuts Ecm = 1Tev (fixed energy) without higgs
1.78 E-2 EXACT 2.17 3.90 E-2 EVBA ratio Evba/ exact
σ (pb)
no higgs
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d dMWW σ
EVBA EXACT
Same cuts Ecm = 1Tev (fixed energy) Mh=130 Gev
1.71 E-2 EXACT 2.3 3.94 E-2 EVBA ratio Evba/ exact
σ (pb)
Mh =130 Gev
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d dMWW σ
EVBA EXACT
Same cuts Ecm = 1Tev (fixed energy) Mh=250 Gev
4.09 E-2 EXACT 1.12 4.61 E-2 EVBA ratio Evba/ exact
σ (pb)
Mh =250 Gev
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d dMWW σ
EVBA EXACT
Same cuts Ecm = 1Tev (fixed energy) Mh=500 Gev
2.50 E-2 EXACT 1.77 4.42 E-2 EVBA ratio Evba/ exact
σ (pb)
Mh=500 Gev
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d dMWW σ
Sensitivity to the theta cuts Mh=500 Gev Theta cut = 10 , 30 , 60 degree respectively
EVBA EXACT
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PT > 30 Gev
Mh=500 Gev
Comparison with Pythia
Only longitudinal modes In Pythia luminosities of the W`s are computed in the LLA (leading log approximation)
PT > 100 Gev
Mh=500 Gev + Cut on PT of W in CM frame
- f the W`s
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Pt PT > 30 Gev Distributions in Mww for ww diagrams and the complete set Feynman gauge
Only longitudinal modes Cut on PT of W in CM frame
- f the W`s
+
PT > 100 Gev
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Interferences are huge even for longitudinal polarized W`s especially away from the higgs peak, the fact that at the peak the cancellations are less important could explain the reasonable result given by EVBA in this region. But the general conclusion -from all the previous results - is that the consideration of the non ww fusion diagrams (breamstrahlung –type) is unavoidable ,so one has to take into account the complete set of diagrams and not only ww fusion diagrams in order to get reliable results But also for the complete set different EWSB patterns can be found
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Comparison of and for realistic cuts
Difference in total cross sections is ~ 20-30 % It becomes much higher at high invariant masses. The difference between a realistic higgs and no higgs is greater for the full calculation but the cross sections at high MWW are lower.
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The effects of the physics of the symmetry breaking sector can be seen also in the total partonic cross section
?
So instead of focusing on studying distributions only
- ne
can also think to study the total partonic cross section P P Our preliminary results show growth of with s in no higgs case but this has to be checked because of present numerical instabilities
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For a realistic study of this kind of physics and a realistic simulation at LHC, all processes contributing to six fermions final states will be needed.
In particular pp → 2 forward backward quark + 2 central quarks + lν is needed for studying processes containing WW → WW sub diagrams pp → 2 forward backward quark + 2 central quarks +l l is needed for studying processes containing ZW → ZW and WW → ZZ sub diagrams But also pp → 2 forward backward quark + lν + l'ν' and pp → 2 forward backward quark + 4 l
To this end the PHASE Monte Carlo has been created
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PHASE
PHact Adaptive Six Fermion Event Generator
(E. Accomando, A. Ballestrero, E. Maina)
Features All processes with 6 fermions final states
up to now
) (
6
→ α ν O l q q q q q q
6 5 4 3 2 1
- Monte Carlo for LHC dedicated studies
and full physics and detector simulation of
Complete helicity matrix elements
Possible selection of particular set
- f diagrams soon
New adaptive multi-channel method
for efficient mapping of all possible peaks
Boson Boson Fusion and scattering Higgs Production in this channel tt production Triple and Quadruple Boson Couplings Three Boson Production One shot : Unweighted event generation of
all processes (several hundreds)
- r any subset in a single run
Parton shower and hadronization
via Les Houches Protocol (Pythia up to now)
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2 6 202 4W 2 6 422 2Z2W 2 6 1046 Misto 15 312 Misto 2 6 610 2Z2W 1 10 466 2Z2W 2 3 1266 2Z2W 1 10 466 2Z2W 2 3 1266 2Z2W 15 233 2Z2W 1 10 422 2Z2W 1 10 422 2Z2W 2 6 422 2Z2W 15 233 2Z2W 1 10 422 2Z2W 1 10 422 2Z2W Initial mult. 1 Initial mult. 2 Number of processes Diagram number Type Outgoing particles
ν µ s c d d u u ν µ s c s c u d ν µ s c b b b b ν µ s c c c u u ν µ s c s s u u ν µ s c b b u u ν µ s c d d d d ν µ s c c c d d ν µ s c s s d d ν µ s c b b d d ν µ s c c c c c ν µ s c b b c c ν µ s c b b s s ν µ s c s s c c ν µ s c s s s s ν µ s c u u u u 141 20
how may processes and diagrams?
161 processes have different matrix elements processes which differ at least for pdf: 141 x 2 + 20= 302 x 4 (CC +Fam)= 1208 This only for αem
6
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