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Theoretical calculations for precise measurement of multi-final-state processes

Theoretical calculations for precise measurement of multi-final-state processes. Renyou ZHANG, Liang HAN USTC phenomenology group. Hadron colliders as discovery machinary. Tevatron, LHC.  W boson, top quark, Higgs? SUSY?. Precise measurement at linear colliders LC. ILC.

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Theoretical calculations for precise measurement of multi-final-state processes

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  1. Theoretical calculations for precise measurement of multi-final-state processes Renyou ZHANG, Liang HAN USTC phenomenology group

  2. Hadron colliders as discovery machinary Tevatron, LHC  W boson, top quark, Higgs? SUSY? • Precise measurement at linear colliders LC ILC • SM precise test, eg W boson mass, top physics etc • Higgs characteristic and couplings: Hff, HZZ, HWW, HHH, HHHH • New physics, eg SUSY parameter determination • Challenges for hep phenomenology  QCD & EW quantum effects, NLO, 2-loop calculations and NLL resummation  multi-particle (>=3) final states, resonance effects Introduction on motivation

  3. Outline Higgs potential, self-coupling ( HHZ production, 5-point loop integral ) 2. Charged Higgs production, Higgs gauge coupling (Φ0H+W-(Φ0 =h0,H0,A0) production, Higgs resonance) 3. Higgs Yukawa coupling ( ttH / bbH / tbH production, ttbb production, 6-point loop integral, phase space integral )

  4. Higgs potential, self-coupling, e+e-ZHH SM: MSSM: trilinear coupling : quartic coupling : multi-Higgs boson production! : 500~1000 GeV : >1 TeV Therefore, in the first stage of a LC, HHZ production is the most promising channel to measure the trilinear Higgs self-coupling.

  5. 0.1~0.2fb @ √s<1TeV, • 8% on lHHH  10% precision on cross-section

  6. N-point loop integral: (N≤4)-point loop integrals 1 to 4-point integrals given in G.Passarino and M.Veltman, NPB160(1979)151 Passarino-Veltman reduction:3-point integral as example --- Decompose to Lorentz-covariant tensor + coefficient (Gram Matrix method)

  7. New development on (N=5)-point integrals

  8. 5-point integral by A.Denner and S.Dittmaier, NPB658(2003)175 where • 5-dimensional Cayley matrix Y used to replace Gram matrix

  9. --- independence of cutoff --- independence of mg @ Cancellation of IR singularity: virtual+soft-photon radiation +hard photon radiation (mg,DE)

  10. Conclusion : --- O(10%) EW correction to intermediate(115-200GeV) HHZ production at LC --- maximum cross-section in √s = 600~800GeV for intermediate Higgs

  11. --- tendency of the QED and weak corrections:

  12. consistency check given by G.Belanger et al (Grace group) PLB578(2004)349

  13. Charged Higgs production, Higgs gauge coupling light charged Higgs production

  14. heavy charged Higgs production, Higgs gauge coupling

  15. complex charged Higgs mass 1. charged Higgs resonance 2. double counting problem and gauge invariance

  16. SPS1a’ Supersymmetry Parameter Analysis (SPA)

  17. Conclusion : ---EW relative correction decreases from 20% to -15% as the increment of MA PRD75 053007(2007)

  18. Higgs Yukawa coupling Higgs production associated with top pair 1. an important discovery mode for a Higgs boson around 120-130GeV at the LHC 2. Yukawa coupling of the top quark to the Higgs boson 5.5% (Yukawa coupling) model: SM, MSSM NLO calculation! K factor=? Major source of background: (QCD) (EW)

  19. tree-level cross section SM Higgs MSSM heavy CP-even Higgs resonance at 2 Mt

  20. QCD correction (SM) SM: --- K factor > 1.4 @ √s=500 GeV

  21. QCD correction (MSSM) MSSM: intermediate Higgs mass region, 2.5<tanbeta<50, 500GeV : ~ 0.75 fb CP even Higgs H,h < 0.01 fb CP odd Higgs A

  22. renormalization of e : xf=mZ , mf <mZ EW correction (MSSM)

  23. --- EW correction: -15% ~ -30% PRD72 033010(2005)

  24. SM: suppressed due to the smallness of the bbh Yukawa coupling MSSM: Yukawa coupling is enhanced by large tanbeta a large resonant contribution from contribution from Z boson exchange 500 GeV, tanbeta = 40 MSSM, LO

  25. 500 GeV, MS=500 GeV bbH production (QCD corrected) Precise measurement of the product of the Higgs couplings:

  26. MSSM: --- QCD K factor: ~ -0.8(Tevatron) , 1.2(LHC) , insensitive to SUSY input parameters hep-ph/0505086

  27. SPS1b, mass = 250 GeV (LHC), 175 GeV (Tevatron) --- QCD relative correction: ~ -50%(Tevatron) , -40%(LHC) PRD73 015012(2006)

  28. ttbb production: background of tth production ! 6-point integral 1. Cayley matrix method:

  29. 2. Gram matrix method: define:

  30. 4-body phase space integral general method:

  31. improved method:

  32. QCD corrections

  33. hard real gluon emission ! PLB654(2007)13

  34. Summary • Precise measurements of interested multi-final-states processes at LHC/ILC eg HHZ, Htt, ttbb etc require good control of theoretical predictions, which would involve loop integrals with multi-legs, multi-body phase integral and resonance effects, and have to be treated case-by-case for stability of numerical calculations • QCD and EW NLO corrections to Higgs property studies could be as significant as ~O(10%), which are at the same level to or larger than the expected experiment accuracy and have to be taken into account.

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