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**Electroweak Physics at the LHC**

Alessandro Ballestrero • 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 Alessandro Ballestrero

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**Alessandro Ballestrero**

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,...... Moreover we cannot exclude new phenomena that we do not expect 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. Alessandro Ballestrero

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**They are complementary and are both necessary to the understanding**

EW and QCD LHC is an hadronic collider. 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: (x1x210-3) 90% 10% • It is a strong process but .... Alessandro Ballestrero

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**Alessandro Ballestrero**

EW and QCD • Cross section determined to NLO precision Total NLO(tt) = 834 ± 100 pb (largest uncertainty from scale variation) 107 tt at low luminosity LHC is a top factory ! low lumi 10 fb-1 high lumi 100 fb-1 Lepton side Hadron side This will allow to reach 1 GeV (in one year?) precision in top mass measurement Alessandro Ballestrero

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**EW and QCD top mass has a strong influence on**

electroweak precision predictions via ew corrections. but .... Alessandro Ballestrero

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**Alessandro Ballestrero**

EW and QCD 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 AcFB 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 A=gV gA /(gV2 + gA2) = asimmetry right left 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) Alessandro Ballestrero

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**The luminosity of LHC will allow anyhow precision measures.**

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 ... Alessandro Ballestrero

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**Alessandro Ballestrero**

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 Alessandro Ballestrero

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**Alessandro Ballestrero**

EW and QCD Weak corrections are available for the similar process b massless Alessandro Ballestrero

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**Alessandro Ballestrero**

EW and QCD The same group has also analyzed Weak corrections to p p γ , Z + jet Alessandro Ballestrero

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**and in many cases one has to rely on approximations**

EW logs In the following I will mainly discuss the physics of vector bosons (W,Z) production and scattering Many NLO EW calculations have been performed, and NLO MC's start to appear One must however realize that :For 4 or more fermions in the final state complete NLO EW are not available and in many cases one has to rely on approximations Leading Pole Approximation, Leading Log Approximation, Final State Radiation ..... why ew corrections can give important enhancements at high energies ? Sudakov logs corrections appear, which become important for s >> MW2 At LHC they are of the order Alessandro Ballestrero

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**Alessandro Ballestrero**

EW logs Ciafaloni .. Denner.... Beenaker... ..... SUDAKOV LOGS2 IN A NUTSHELL • 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 Alessandro Ballestrero

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**Alessandro Ballestrero**

EW logs Alessandro Ballestrero

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**Alessandro Ballestrero**

W mass measurement Radiative corrections affect three level relations between SM parameters 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 Alessandro Ballestrero

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

W mass measurement Status of inputs WC2004: mt=174.3 ±5.1(exp) GeV/c2 mW= ±0.034(exp) GeV/c2 mZ= ±0.0021(exp) GeV/c2 Z= ±0.0023(exp) GeV direct indirect EXCLUDED SM predictions from ZFITTER and TOPAZ0 programs Direct and indirect data favour a light Higgs ! Alessandro Ballestrero

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**Alessandro Ballestrero**

W mass measurement Thanks to M.Grunewald Perspective at the LHC mW=15 MeV; mt=1 GeV (world combined will look better than these ! – Tevatron run II, LEP2) (current central values assumed) SM constraints on mH: direct EXCLUDED Using had= (mH/mH 25%) After LEP and Tevatron mW=30 MeV it will probably be possible to reach mW=15 MeV in the low lumi phase ! Chances of ruling out the SM ? Alessandro Ballestrero

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**Alessandro Ballestrero**

W mass measurement mtop and MW: equal weight in the EW fit if MW mtop at LHC: mtop 2 GeV gives the precision MW : 15 MeV W-pair cross-section is too low Single W: no direct determination of mW possible because of the missing neutrino, but huge statistics ! e n W beam line transverse mass (missing pT) W mass : fit exp. shape to MC sample with different Values of MW < 2 MeV/y as a statistical uncertainty syst. error: MC modelling of physics and detector response Alessandro Ballestrero

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**W production Drell Yan mechanism not only important to measure W mass:**

Rapidity distributions can provide information on PDF's Also important as a background to new phisics at high pt. Tree level is trivial 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). Alessandro Ballestrero

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**Pole approximation LPA**

W production Pole approximation LPA When one has resonant diagrams e.g. p2 – MW2 + i Г MW one can make an expansion of the complete amplitude around the complex poles retaining only leading order (residue at the poles) 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 Famous example: Ew corrections to four fermion processes at e+ e- computed in double pole approximation Alessandro Ballestrero

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**Alessandro Ballestrero**

W production Resummation of final state radiation in pole approximation YFS exponentiation WINHAC Placzek Jadach Pavia shift extimate with a "pseudo experiment" HORACE Carloni Calame Montagna Nicrosini exponentiation Alessandro Ballestrero

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W production Combined effect of QCD Resummation and QED radiative corrections NLO QED included in RESBOS Cao and Yuan Alessandro Ballestrero

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**Alessandro Ballestrero**

W production Complete ew corrections O(α) single Z p p Z l+ l- ZGRAD2 Baur Hollikl Wackeroth ... single W p p W l ν Dittmaier Kramers 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%) Alessandro Ballestrero

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**Alessandro Ballestrero**

W production Dittmaier Kramers Alessandro Ballestrero

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**Alessandro Ballestrero**

W production Dittmaier Kramers Alessandro Ballestrero

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**Alessandro Ballestrero**

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 Background to new physics: Eg. chargino neutralino gold plated signal for Susy charged leptons + missing pT 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% Alessandro Ballestrero

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Two boson production 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. 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 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 Alessandro Ballestrero

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**Alessandro Ballestrero**

Two boson production Alessandro Ballestrero

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**Alessandro Ballestrero**

Boson Boson scattering and unitarity WW scattering Consider longitudinally polarized W's: For ! single diagram proportional to: Alessandro Ballestrero

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**Alessandro Ballestrero**

Boson Boson scattering and unitarity gauge cancellations at work For the three diagrams without Higgs It still violates unitarity HIGGS RESTORES UNITARITY provided (qualitatively) Alessandro Ballestrero

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**Alessandro Ballestrero**

Boson Boson scattering and unitarity More precisely : Partial wawes unitarity requires Limit on mH and energy at which new physics should appear if mH too large Alessandro Ballestrero

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**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

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**from low order amplitudes**

Boson Boson scattering and unitarity Different ways of constructing amplitudes which satisfy unitarity constraints from low order amplitudes e.g. Alessandro Ballestrero

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**Alessandro Ballestrero**

EVBA : extrapolation and deconvolution ? Equivalent Vector Boson Approximation a V a A V a Alessandro Ballestrero

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**Alessandro Ballestrero**

EVBA : extrapolation and deconvolution ? a b Alessandro Ballestrero

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**Alessandro Ballestrero**

EVBA : extrapolation and deconvolution ? -1 n+1 q 2 off shell is a function of q1 and q (spacelike) The approximation consists in projecting it on boson mass shell Different approximations can also be taken in evaluating the boson luminosities L(x) The approximation is valid to ~ 10% for photons, much worse for Z and W Results depend on cuts. Alessandro Ballestrero

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**EVBA : extrapolation and deconvolution ?**

Finding information on boson boson scattering from experimental data needs 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 Alessandro Ballestrero

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**Alessandro Ballestrero**

EVBA : extrapolation and deconvolution ? Hard processes under consideration will not contain only contributions from but also from all diagrams of the type 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 Moreover final partons are fermions with all diagrams for 6 fermion final state which depend on the final state at hand Alessandro Ballestrero

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**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

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**Boson Boson Scattering and Gauge Invariance**

The interference A.B. AccomandoBelhouari Maina Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

Already known since a long time Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

Previous results are confirmed by PP-> u s -> d c W+ W- (on shell W's) no higgs unitary σ (pb) ratio ww / all All diagrams 1.86 E-2 358 WW fusion diagrams 6.67 m_h=200 mWW>300 unitary σ (pb) ratio ww / all All diagrams 8.50 E-3 765 WW fusion diagrams 6.50 Feynman gauge has still big cancellations but about a factor 30 less than unitary! no higgs feynman σ (pb) ratio ww / all All diagrams 1.86 E-2 13 WW fusion diagrams 0.245 m_h=200 mWW>300 feynman σ (pb) ratio ww / all All diagrams 8.50 E-3 26 WW fusion diagrams 0.221 Distributions show huge interference effect which are not constant: they depend very much on the value of the variable Is it possible to find regions with low interference and use it to define WW scattering signal? Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

all diagrams unitary WW fusion ratio unitary pp us dc W+W- NO HIGGS ratio = WW fusion / all ratio feynman feynman WW fusion Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

all diagrams ratio unitary unitary WW fusion pp us dc W+W- NO HIGGS feynman WW fusion ratio feynman Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

Differences do not depend on Higgs NO HIGGS all diagrams unitary WW fusion ratio unitary pp us dc W+W- Higgs M=200 GeV with MWW > 300 GeV all diagrams unitary WW fusion ratio unitary Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

ratio unitary unitary WW fusion pp us dc W+W- t1 all diagrams feynman WW fusion ratio feynman t2 t1 t2 Alessandro Ballestrero

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**Boson Boson Scattering and Gauge Invariance**

a cut on MWW does not change qualitatively but worsen the ratios ratio unitary ratio feynman no cut 0.63 0.71 t2 ratio feynman ratio unitary MWW > 1000 GeV 0.2 2.76 Alessandro Ballestrero

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**PHASE PHASE Monte Carlo - Purpose**

PHact Adaptive Six Fermion Event Generator (E. Accomando, A. Ballestrero, E. Maina) Monte Carlo for LHC dedicated studies and full physics and detector simulation of Boson Boson Fusion and scattering Higgs Production in this channel tt production Triple and Quadruple Boson Couplings Three Boson Production Alessandro Ballestrero

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**PHASE Monte Carlo - Purpose**

The processes we have considered involve in reality 6 fermion final states 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 For them so far we have: • 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 & , MADGRAPH & MADEVENT, O'MEGA & WHIZARD, PHEGAS & HELAC ] 'generic' -> 'dedicated' is not a trivial step We aim at a complete (all processes and all diagrams) and dedicated MC Full generation and simulation with high efficiency Interface to detector simulations Useful also for comparison with different approach Non irreducible backgrounds by other MC Alessandro Ballestrero

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**Alessandro Ballestrero**

PHASE Monte Carlo - Processes Consider l (e.g. ) in the final state We want to compute and generate in one shot all processes : Up to now only em6 : How many are Let us consider all outgoing and fix 2q as All processes of the type Alessandro Ballestrero

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**4 W PHASE Monte Carlo - Processes Process**

Initial state multipl. Boson Boson scattering subprocess 7 diag diag diag diag Total Number of Diagrams 2 202 x 1 Alessandro Ballestrero

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**2 W 2 Z PHASE Monte Carlo - Processes Process**

Initial state multipl. Boson Boson scattering subprocess 7 diag diag diag diag Total Number of Diagrams 2 x 422 1 Alessandro Ballestrero

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**Mixed : 4 W + 2W2Z PHASE Monte Carlo - Processes Process**

Initial state multip. Boson Boson scattering subprocess 7 diag diag diag diag Total Number of Diagrams 2 x 312 Alessandro Ballestrero

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**how may processes and diagrams?**

PHASE Monte Carlo - Processes how may processes and diagrams? Outgoing particles Type Diagram number Number of processes Initial mult. 2 Initial mult. 1 161 processes have different matrix elements 4W 202 6 2 2Z2W 422 6 2 2Z2W 422 10 1 2Z2W 422 10 1 processes which differ at least for pdf: 141 x = 302 x 4 (CC +Fam)= 1208 This only for em6 2Z2W 233 15 2Z2W 422 6 2 2Z2W 422 10 1 2Z2W 422 10 1 2Z2W 233 15 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 610 6 2 Misto 312 15 Misto 1046 6 2 141 20 Alessandro Ballestrero

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**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

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**Alessandro Ballestrero**

PHASE Monte Carlo - Amplitude 2 6 202 4W 422 2Z2W 1046 Misto 15 312 610 1 10 466 3 1266 233 I 1 Initial mult. 2 Number of Processes diagrams Type Outgoing particles Diagrams which belong to the same group of 8 outgoing particle can be computed in the same way Therefore do not consider 1208 or but 16 different types of amplitude Many groups have identical number of diagrams ... 141 20 Alessandro Ballestrero

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**Further simplification: subdiagrams**

PHASE Monte Carlo - Amplitude 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: Simple arithmetics: 202=101 x =211 without hbb = =211 x 2 466=233 x =211 x hbb =312 x =422 x 3 cxchange of identical particles Only independent diagrams Further simplification: subdiagrams But the combinatorics is complicated Alessandro Ballestrero

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**Alessandro Ballestrero**

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

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**PHASE combines in a new way the two strategies**

PHASE Monte Carlo - Integration PHASE combines in a new way the two strategies . 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 space and a careful treatment of exchange of identical particles are employed Alessandro Ballestrero

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**full experimental simulation procedure**

PHASE Monte Carlo - Generation One shot a la WPHACT One shot : Unweighted event generation of all processes (several hundreds) or any subset in a single run Interface with Les Houches Protocol to be used in a full experimental simulation procedure Alessandro Ballestrero

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**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 complete processes "dominated" by Boson Boson fusion and Higgs production in the same channel in presence of complete irreducible background Alessandro Ballestrero

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**Boson Boson Fusion and Higgs**

Higgs peak and evident difference between normal SM Higgs scenarios and unexpected ones for high MWW Alessandro Ballestrero

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**Boson Boson Fusion and Higgs**

differences between different scenarios also at low MWW with much more statistics Alessandro Ballestrero

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**Boson Boson Fusion and Higgs**

difference between light higgs and no Higgs (mH -> ) at high MWW Alessandro Ballestrero

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**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

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**Boson Boson Fusion and Higgs**

LL dominates also for light higgs at high MWW Alessandro Ballestrero

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**Boson Boson Fusion and Higgs**

1 < η(d) < > η(u) > -5.5 E(u,d,c,s,μ) > 20 GeV Pt(u,d,c,s,μ) > 10 GeV 70< M(sc, μν) < 90 mH = 120 GeV ptW cut : ptW > MW With LL and pt cut (as needed by EVBA) one looses a lot in cross section Alessandro Ballestrero

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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 method will allow to exploit all potentialities of LHC A lot of challenging work is ahead of you Have fun ! Alessandro Ballestrero

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