Alessandro Ballestrero

1. • Introduction • EW and QCD • W mass measurement • W production • Two boson production • Boson Boson scattering and unitarity • EVBA : extrapolation and deconvolution? • Boson Boson Scattering and Gauge Invariance • PHASE Monte Carlo • Boson Boson Fusion and Higgs •Conclusions Electroweak Physics at the LHC Alessandro Ballestrero Alessandro Ballestrero

2. Introduction what we expect from LHC Higgs and SUSYis 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

3. EW and QCD 90% (x1x210-3) 10% 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: • It is a strong process but .... Alessandro Ballestrero

4. EW and QCD Lepton side Hadron side • • 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 100fb-1 This will allow to reach 1 GeV (in one year?) precision in top mass measurement Alessandro Ballestrero

5. EW and QCD top mass has a strong influence on electroweak precision predictions via ew corrections. but .... Alessandro Ballestrero

6. EW and QCD Data fitted : • The Z parameters - lineshape and lepton asymmetry at LEP: mZΓZ σh Rl and AlFB - Aeand Aτfrom 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 AbAc - sin2 θlefffrom quark forward-backward asymmetry at LEP • W mass mW at LEP and Tevatron • Top mass mT at Tevatron • sin2 θWfrom 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

7. 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

8. EW and QCD has more than 300 diagrams has more than 700 For the precise knowledge of tt cross section one should go to NNLO There are not EW corrections available for ttproduction 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 Alessandro Ballestrero

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

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

11. 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

12. 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

13. EW logs Alessandro Ballestrero

14. W mass measurement Radiative correctionsaffect 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

15. W mass measurement EXCLUDED direct indirect Status of inputs WC2004: mt=174.3 ±5.1(exp) GeV/c2 mW=80.426 ±0.034(exp) GeV/c2 mZ=91.1875 ±0.0021(exp) GeV/c2 Z=2.4952 ±0.0023(exp) GeV SM predictions from ZFITTER and TOPAZ0 programs Direct and indirect data favour a light Higgs ! Alessandro Ballestrero

16. 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=0.00012 (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

17. W mass measurement n e W beam line mtop and MW: equal weight in the EW fitifMW 0.007 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 ! 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

18. 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

19. W production Pole approximationLPA When one has resonant diagrams e.g. p2 – MW2 + iГ 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

20. 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

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

22. W production O(α) parton cross section contain mass singuratiesα ln(mq) These collinear singularities are reabsorbed in PDF Complete ew corrections O(α) single Zp p  Z  l+ l- ZGRAD2 Baur Hollikl Wackeroth ... single Wp p  W  lν Dittmaier Kramers 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

23. W production Dittmaier Kramers Alessandro Ballestrero

24. W production Dittmaier Kramers Alessandro Ballestrero

25. Two boson production Eg. chargino neutralino gold plated signal for Susy 3 charged leptons + missing pT Full ME's and O(αS) at NLO with full spin correlations available and cross checked Dixon, Kunszt, Signer, Ellis, .... 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: 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

26. Two boson production 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. Corrections in (single or double) Pole approximations Mc has full processes and at Born level (IBA) EW corrections only in leading log. They factorize for arbitrary process. Accomando Denner Pozzorini 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

27. Two boson production Alessandro Ballestrero

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

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

30. 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

31. Boson Boson scattering and unitarity 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 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 ? Alessandro Ballestrero

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

33. EVBA : extrapolation and deconvolution ?    Equivalent Vector Boson Approximation a V a a V A Alessandro Ballestrero

34. EVBA : extrapolation and deconvolution ?    a b Alessandro Ballestrero

35. EVBA : extrapolation and deconvolution ?    -1 n+1 q 2 off shell is a function of q1 and q2. (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

36. 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

37. 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

38. 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

39. Boson Boson Scattering and Gauge Invariance The interference A.B. AccomandoBelhouari Maina Alessandro Ballestrero

40. Boson Boson Scattering and Gauge Invariance Already known since a long time Alessandro Ballestrero

41. Boson Boson Scattering and Gauge Invariance 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! 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

42. 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

43. 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

44. Boson Boson Scattering and Gauge Invariance Differences do not depend on Higgs NO HIGGS all diagrams ratio unitary unitary WW fusion pp us  dc W+W- Higgs M=200 GeV with MWW > 300 GeV all diagrams unitary WW fusion ratio unitary Alessandro Ballestrero

45. 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

46. Boson Boson Scattering and Gauge Invariance t1 a cut on MWW does not change qualitatively but worsen the ratios ratio unitary ratio feynman no cut 0.71 0.63 t2 ratio feynman ratio unitary MWW > 1000 GeV 0.2 2.76 Alessandro Ballestrero

47. PHASEMonte Carlo - Purpose PHASE 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

48. PHASEMonte 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/orEVBA (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 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

49. 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 usconsider all outgoing and fix 2q as All processes of the type Alessandro Ballestrero

50. PHASE Monte Carlo - Processes 4 W Alessandro Ballestrero