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E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino

Boson boson scattering at LHC. E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino. • Introduction. • Boson Boson scattering and unitarity. • EVBA : extrapolation and deconvolution?. • Boson Boson Scattering and Gauge Invariance.

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E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino

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  1. Boson boson scattering at LHC E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino • Introduction • Boson Boson scattering and unitarity • EVBA : extrapolation and deconvolution? • Boson Boson Scattering and Gauge Invariance • PHASE Monte Carlo • Boson Boson Fusion and Higgs •Conclusions Alessandro Ballestrero

  2. Introduction 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 One of the main purposes of LHC is Higgs discovery and/or EWSB study 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

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

  4. 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

  5. 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

  6. 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

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

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

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

  10. 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

  11. 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

  12. 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

  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

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

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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. PHASE Monte Carlo - Processes 4 W Alessandro Ballestrero

  26. PHASE Monte Carlo - Processes 2 W 2 Z Alessandro Ballestrero

  27. PHASE Monte Carlo - Processes Mixed : 4 W + 2W2Z Alessandro Ballestrero

  28. PHASE Monte Carlo - Processes how may processes and diagrams? Number of processes Outgoing particles Type Diagram number 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 2 + 20= 302 x 4 (CC +Fam)= 1208 This only for em6 2Z2W 233 15 0 2Z2W 422 6 2 2Z2W 422 10 1 2Z2W 422 10 1 2Z2W 233 15 0 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 610 6 2 Misto 312 15 0 Misto 1046 6 2 141 20 Alessandro Ballestrero

  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

  30. PHASE Monte Carlo - Amplitude Outgoing particles Type Number of diagrams Number of Processes Initial mult. 2 I 1 4W 202 6 2 2Z2W 422 6 2 2Z2W 422 10 1 2Z2W 422 10 1 2Z2W 233 15 0 2Z2W 422 6 2 2Z2W 422 10 1 2Z2W 422 10 1 2Z2W 233 15 0 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 1266 3 2 2Z2W 466 10 1 2Z2W 610 6 2 Misto 312 15 0 Misto 1046 6 2 Diagrams which belong to the same group of 8 outgoing particle can be computed in the same way Therefore do not consider 1208 or 161 but 16 different types of amplitude Many groups have identical number of diagrams ... 141 20 Alessandro Ballestrero

  31. 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: 202 233 312 422 466 610 1046 1266 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 cxchange of identical particles Only 101 211 22 94 independent diagrams Further simplification: subdiagrams But the combinatorics is complicated Alessandro Ballestrero

  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

  33. PHASE Monte Carlo - Integration PHASE combines in a new way the two strategies . With adaptive calculations onlyfew 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 variableof every phase space and a carefultreatment of exchange of identical particlesare employed Alessandro Ballestrero

  34. 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

  35. Boson Boson Fusion and Higgs Let us consider the process It contains and many other contributions 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

  36. Boson Boson Fusion and Higgs PROCESS Higgs peak and evident difference between normal SM Higgs scenarios and unexpected ones for high MWW Alessandro Ballestrero

  37. Boson Boson Fusion and Higgs PROCESS differences between different scenarios also at low MWW with much more statistics Alessandro Ballestrero

  38. Boson Boson Fusion and Higgs PROCESS difference between light higgs and no Higgs (mH -> ) at high MWW As WLWL grows with mh while other components remain constant, can one "define" the signal as the difference of heavy and light higgs at high MWW? ? Alessandro Ballestrero

  39. Boson Boson Fusion and Higgs 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. Alessandro Ballestrero

  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

  41. Boson Boson Fusion and Higgs 1 < η(d) < 5.5 -1 > 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

  42. 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 s2) will be added - And then l+ l- + 4quarks final states • 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. Much work ahead Alessandro Ballestrero

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