1. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 1 E. Accomando A. Ballestrero A. Belhouari E. Maina INFN and Dip. Fisica Teorica Torino Boson boson scattering at LHC PHASE Monte Carlo Boson Boson Scattering and Gauge Invariance Boson Boson Fusion and Higgs Conclusions Introduction Boson Boson scattering and unitarity EVBA : extrapolation and deconvolution?

2. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 2 Introduction One of the main purposes of LHC is Higgs discovery and/or EWSB study WW scattering holds the key to EWSB (violation of unitarity for W L W L  W L W L 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 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

3. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 3 Boson Boson scattering and unitarity Consider longitudinally polarized W's: single diagram proportional to: WW scattering For !

4. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 4 gauge cancellations at work For the three diagrams without Higgs It still violates unitarity provided (qualitatively) HIGGS RESTORES UNITARITY Boson Boson scattering and unitarity

5. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 5 More precisely : Partial wawes unitarity requires Boson Boson scattering and unitarity Limit on m H and energy at which new physics should appear if m H too large

6. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 6 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

7. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 7 Different ways of constructing amplitudes which satisfy unitarity constraints from low order amplitudes e.g. Boson Boson scattering and unitarity

8. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 8 EVBA : extrapolation and deconvolution ?      Equivalent Vector Boson Approximation a A a V V a

9. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 9 EVBA : extrapolation and deconvolution ?      a b

10. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 10 is a function of q 1 and q 2. (spacelike) EVBA : extrapolation and deconvolution ?      -1 n+1 q 2 off shell 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.

11. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 11 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. EVBA : extrapolation and deconvolution ? The energy of the WW scattering is determined by the invariant WW mass

12. QFTHEP04 - St. Petersburg – 17-23 June 2004 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 Moreover final partons are fermions with all diagrams for 6 fermion final state which depend on the final state at hand 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

13. QFTHEP04 - St. Petersburg – 17-23 June 2004 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.

14. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 14 The interference Boson Boson Scattering and Gauge Invariance A.B. AccomandoBelhouari Maina

15. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 15 Already known since a long time Boson Boson Scattering and Gauge Invariance

16. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 16 no higgs unitary σ (pb) ratio ww / all All diagrams1.86 E-2 358 WW fusion diagrams 6.67 m_h=200 m WW >300 unitary σ (pb) ratio ww / all All diagrams8.50 E-3 765 WW fusion diagrams 6.50 no higgs feynman σ (pb) ratio ww / all All diagrams1.86 E-2 13 WW fusion diagrams 0.245 m_h=200 m WW >300 feynman σ (pb) ratio ww / all All diagrams8.50 E-3 26 WW fusion diagrams 0.221 Boson Boson Scattering and Gauge Invariance Distributions show huge interference effect which are not constant: they depend very much on the value of the variable 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! Is it possible to find regions with low interference and use it to define WW scattering signal?

17. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 17 Boson Boson Scattering and Gauge Invariance pp  us  dc W + W - all diagrams unitary WW fusion ratio unitary feynman WW fusion ratio feynman NO HIGGS ratio = WW fusion / all

18. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 18 Boson Boson Scattering and Gauge Invariance pp  us  dc W + W - all diagrams unitary WW fusion feynman WW fusionratio feynman NO HIGGS ratio unitary

19. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 19 Boson Boson Scattering and Gauge Invariance Differences do not depend on Higgs pp  us  dc W + W - all diagrams unitary WW fusion ratio unitary NO HIGGS Higgs M=200 GeV with M WW > 300 GeV ratio unitary

20. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 20 Boson Boson Scattering and Gauge Invariance unitary WW fusion feynman WW fusion ratio unitary ratio feynman pp  us  dc W + W - all diagrams t1t1 t2t2 t2t2 t1t1

21. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 21 Boson Boson Scattering and Gauge Invariance no cut M WW > 1000 GeV a cut on M WW does not change qualitatively but worsen the ratios t1t1 t2t2 ratio unitary ratio feynman 0.63 2.76 0.71 0.2

22. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 22 PHASE Monte Carlo - Purpose 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 PHASE PHact Adaptive Six Fermion Event Generator (E. Accomando, A. Ballestrero, E. Maina)

23. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 23 Useful also for comparison with different approach The processes we have considered involve in reality 6 fermion final states PHASE Monte Carlo - Purpose For them so far we have: We aim at a complete (all processes and all diagrams) and dedicated MC Full generation and simulation with high efficiency Interface to detector simulations 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 & GR@PPA, MADGRAPH & MADEVENT, O'MEGA & WHIZARD, PHEGAS & HELAC ] 'generic' -> 'dedicated' is not a trivial step Non irreducible backgrounds by other MC 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

24. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 24 Consider l (e.g.  ) in the final state We want to compute and generate in one shot all processes : Up to now only  em 6 : How many are Let us consider all outgoing and fix 2q as All processes of the type PHASE Monte Carlo - Processes

25. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 25 Process Initial state multipl. Boson Boson scattering subprocess 7 diag 7 diag 4 diag 4 diag Total Number of Diagrams 2202 2x 2x 2x 2x 2x 1x 1x 4 W PHASE Monte Carlo - Processes

26. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 26 Process Initial state multipl. Boson Boson scattering subprocess 7 diag 7 diag 4 diag 4 diag Total Number of Diagrams 2x422 2x 2x 2x 2x 2 1x 1x 2 W 2 Z PHASE Monte Carlo - Processes

27. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 27 Process Initial state multip. Boson Boson scattering subprocess 7 diag 7 diag 4 diag 4 diag Total Number of Diagrams 2x312 2xx 2 x 2xx 2xx 2x 2xx 2xx 2xx 2x 2xx 2xx 2xx 2xx 2 Mixed : 4 W + 2W2Z PHASE Monte Carlo - Processes

28. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 28 26 2024W 26 4222Z2W 261046Misto 015312Misto 266102Z2W 1104662Z2W 2312662Z2W 1104662Z2W 2312662Z2W 0152332Z2W 1104222Z2W 1104222Z2W 264222Z2W 0152332Z2W 1104222Z2W 1104222Z2W Initial mult. 1Initial mult. 2 Number of processes Diagram number Type Outgoing particles how may processes and diagrams? 161 processes have different matrix elements 141 20 processes which differ at least for pdf: 141 x 2 + 20= 302 x 4 (CC +Fam)= 1208 This only for  em 6 PHASE Monte Carlo - Processes

29. QFTHEP04 - St. Petersburg – 17-23 June 2004 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?

30. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 30 141 20 PHASE Monte Carlo - Amplitude 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...

31. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 31 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 Only 101 211 22 94 independent diagrams Further simplification: subdiagrams PHASE Monte Carlo - Amplitude cxchange of identical particles But the combinatorics is complicated

32. QFTHEP04 - St. Petersburg – 17-23 June 2004 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

33. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 33. 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 PHASE Monte Carlo - Integration PHASE combines in a new way the two strategies

34. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 34 PHASE Monte Carlo - Generation Interface with Les Houches Protocol to be used in a full experimental simulation procedure One shot a la WPHACT One shot : Unweighted event generation of all processes (several hundreds) or any subset in a single run

35. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 35 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 Let us consider the process It contains and many other contributions

36. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 36 Boson Boson Fusion and Higgs Higgs peak and evident difference between normal SM Higgs scenarios and unexpected ones for high M WW PROCESS

37. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 37 Boson Boson Fusion and Higgs differences between different scenarios also at low M WW with much more statistics PROCESS

38. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 38 Boson Boson Fusion and Higgs difference between light higgs and no Higgs (m H ->  ) at high M WW As W L W L grows with mh while other components remain constant, can one "define" the signal as the difference of heavy and light higgs at high M WW? ? PROCESS

39. QFTHEP04 - St. Petersburg – 17-23 June 2004 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 M WW are lower.

40. QFTHEP04 - St. Petersburg – 17-23 June 2004 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 m H ->  LL dominates at high M WW.

41. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 41 1 η(u) > -5.5 E(u,d,c,s,μ) > 20 GeV P t (u,d,c,s,μ) > 10 GeV 70< M(sc, μν) < 90 m H = 120 GeV Boson Boson Fusion and Higgs ptW cut : pt W > M W With LL and pt cut (as needed by EVBA) one looses a lot in cross section

42. QFTHEP04 - St. Petersburg – 17-23 June 2004 Alessandro Ballestrero 42 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. 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(  em 4  s 2 ) will be added - And then l + l - + 4quarks final states Much work ahead