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 electroweak symmetry. The non observation of the higgs particle until now makes its search and the understanding of the mechanism of the symmetry breaking one of the major goals of the physics at LHC. Together with gluon gluon fusion vector bosons fusion are the most important higgs production modes.

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.

Boson -Boson scattering and unitarity WW scattering Consider longitudinally polarised W`s The complete set of diagrams including the higgs is:

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

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 M crit

Boson-Boson scattering and gauge invariance The vector bosons which initiate the scattering process in the subset: are in reality off shell Where :

and Parametrize the off shellness of the incoming bosons

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....

PP us cdW W The vector boson scattering subprocess is no higgs ratio m_h=200 m WW >300 ratio σ (pb) σ (pb) unitary ww / all unitary ww / all All diagrams 1.86 E-2 All diagrams 8.50 E-3 WW fusion 358 WW fusion 765 6.67 6.50 diagrams diagrams Feynman gauge has still big cancellations but about a factor 30 less than unitary! no higgs ratio m_h=200 m WW >300 ratio σ (pb) σ (pb) feynman ww / all feynman ww / all All diagrams 1.86 E-2 All diagrams 8.50 E-3 WW fusion WW fusion 13 26 0.245 0.221 diagrams diagrams 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)

Distributions of different kinematical variables confirm this σ d dMWW all diagrams unitary WW fusion ratio unitary pp → us → dc W + W - NO HIGGS ratio = WW fusion / all ratio feynman feynman WW fusion

σ d θ d W + all diagrams ratio unitary unitary WW fusion pp → us → dc W + W - NO HIGGS feynman WW fusion ratio feynman

The inclusion of higgs diagrams does not make big difference σ d θ d W NO HIGGS + all diagrams ratio unitary unitary WW fusion pp → us → dc W + W - Higgs M=200 GeV with M WW > 300 GeV all diagrams unitary WW fusion ratio unitary

ratio unitary unitary WW fusion pp → us → dc W + W - t 1 all diagrams feynman WW fusion ratio feynman t 2 t 1 t 2

t 1 a cut on M WW does ratio unitary ratio feynman not change qualitatively but worsen the ratios no cut 0.71 0.63 t 2 ratio feynman ratio unitary M WW > 1000 GeV 0.2 2.76

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 Where ; -c)The emitted vector bosons from the fermion lines are taken on shell.

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

Application of the EVBA method to the process PP us cdW W and comparisons with the exact results The vector boson scattering subprocess is The expression of the mommentum and polarizations in the center of mass of the W`s

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 on shell cross section invariant mass of the vector bosons The form factors for different polarizations are:

σ d nen dMWW a Because of the photon propagator a singularity for on shell W`s scattering a cut on their CM angle scattering is applied theta > 10 degree a EVBA EXACT 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 E cm = 14 Tev (with pdfs) without higgs no higgs ratio σ (pb) Evba/ exact EVBA 1.36 E-2 EXACT 6.30 E-3 2.16

σ d dMWW EVBA Same cuts EXACT E cm = 1Tev (fixed energy) without higgs no higgs ratio σ (pb) Evba/ exact EVBA 3.90 E-2 EXACT 2.17 1.78 E-2

σ d dMWW EVBA Same cuts EXACT E cm = 1Tev (fixed energy) Mh=130 Gev Mh =130 Gev ratio σ (pb) Evba/ exact EVBA 3.94 E-2 EXACT 2.3 1.71 E-2

σ d dMWW Same cuts EVBA EXACT E cm = 1Tev (fixed energy) Mh=250 Gev Mh =250 Gev ratio σ (pb) Evba/ exact EVBA 4.61 E-2 EXACT 1.12 4.09 E-2

σ d dMWW EVBA Same cuts EXACT E cm = 1Tev (fixed energy) Mh=500 Gev Mh=500 Gev ratio σ (pb) Evba/ exact EVBA 4.42 E-2 EXACT 1.77 2.50 E-2

σ d Sensitivity to the theta cuts dMWW Mh=500 Gev Theta cut = 10 , 30 , 60 degree respectively EVBA EXACT

Comparison with Pythia P T > 30 Gev Mh=500 Gev � Only longitudinal modes � In Pythia luminosities of the W`s are computed in the LLA (leading log approximation) P T > 100 Gev + Cut on PT of W in CM frame of the W`s Mh=500 Gev

Distributions in Mww for Pt P T > 30 Gev ww diagrams and the complete set Feynman gauge � Only longitudinal modes + � Cut on P T of W in CM frame of the W`s P T > 100 Gev

� 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

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 M WW are lower.

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 one 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

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 + l ν 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 + l ν + l' ν ' and pp → 2 forward backward quark + 4 l To this end the PHASE Monte Carlo has been created

PHASE PHact Adaptive Six Fermion Event Generator (E. Accomando, A. Ballestrero, E. Maina) Features All processes with 6 fermions final states 6 → ν O α q q q q q q l ( ) up to now 1 2 3 4 5 6 • Monte Carlo for LHC dedicated studies Complete helicity matrix elements and full physics and detector simulation of Possible selection of particular set of diagrams soon New adaptive multi-channel method for efficient mapping of all possible peaks Boson Boson Fusion and scattering Higgs Production in this channel One shot : Unweighted event generation of tt production all processes (several hundreds) Triple and Quadruple Boson Couplings or any subset in a single run Three Boson Production Parton shower and hadronization via Les Houches Protocol (Pythia up to now)