Precise prediction for ILC experiment HAN, Liang Univ. of Science &Technology of China ( on behalf of U.S.T.C Hep Phenomenology Group )

ILC,Beijing2  QF & 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 Precise measurement at linear colliders LC LEP, TESLE/ILC/NLC Hadron colliders as discovery machinary: SPS, Tevatron I & II, LHC  W boson, top quark, Higgs? SUSY? Challenges for LC phenomenology:  QCD & EW quantum radiative correction effects, NLO and 2-loop calculations  multiplicity (>=3) final states Introduction on motivation

ILC,Beijing3 W boson mass measurement -- W boson mass at NLO -- Higgs mass determination with W 80,398 ± 25 MeV/c 2 combined latest CDF

ILC,Beijing4 Measurement of e + e -  W (*) W  l +l double-pole approximation + + Passarino-Veltman reduction N≤4  on-shell di-W bosons 2  2 in Theoretical uncertainty ~ 0.7 % LEP2 ~ 1 %  Off-shell 2  4 of threshold scan in + W mass uncertainty ~ 7 MeV [#] For reference S.Dittmaier Hep-ph/ , and A.Denner et al Hep-ph/  high mass region 2  4 e + e -  WW  qq+lv in for anomalous couplings N=6

ILC,Beijing5 The confrontation of high-precise ILC measurement with phenomenology:  better understanding on QCD and EW effects  ISR/FSR treatment  high multiplicity n f ≥3 in final states  complication of topology  N≥5-point Feynman loop integrals  stability in numerical calculation  software : FeynArts, FormCalc, LoopTools etc Challenge on theoretical prediction

ILC,Beijing6 The status of precise calculation

ILC,Beijing7 Theoretical requirement for LC physics

ILC,Beijing8 One-loop radiative corrections to 2  n f 1 to 4-point integrals given in G.Passarino and M.Veltman, NLB160(1979)151 N-point Feynman integrals as

ILC,Beijing9 Passarino-Veltman: 3-point tensor integral as example --- Use Gram determinant to calculate coefficient C ij would raise singularity in N≥5-point integrals (N≤4)-point loop integrals --- Decompose to Lorentz-covariant tensor + coefficient

ILC,Beijing10  6-point loop function by A.Denner and S.Dittmaier, hep-ph/  5-point integral by A.Denner and S.Dittmaier, NPB658(2003)175 where New development on (N≥5)-point integrals  5-dimensional Cayley matrix Y used to replace Gram matrix

ILC,Beijing11 EW corrections to e + e -  ttH [†] Y.You et al, hep-ph/ , Phys. Lett. B571(2003)85  For Ultraviolet UV divergence in N=2 and 3-point integrals, dimensional regularization + COMS EW RC=self-energy(376) + vertex(425) + box(145) + pentagon(29), where part of N=5 diagrams as [†] S.Dawson et al, PRD59(1999)054012: QCD k=1.5 for M h

ILC,Beijing12  For Infrared IR divergence in N=2 to 5-point integrals, + virtual : photon mass regularization  m  + massive electron +  real emission = soft photon limit + phase-space slicing (  E) + hard radiation

ILC,Beijing13  Conclusion : remarkable O(5%) EW correction to ttH at LC  consistency check given by S.Dittmaier in hep-ph/ [66] G.Belanger et al Hep-ph/ , Phys.Lett. B571(2003)163 [67] A.Denner et al, Hep-ph/ , Phys.Lett. B575(2003)290

ILC,Beijing14 EW corrections to e + e -  ZHH R.Y.Zhang et al, hep-ph/ , Phys. Lett. B578(2004)349 √s<1TeV, 10% precision on cross-section  18% on HHH

ILC,Beijing15 Cancellation of IR singularity: virtual + soft-photon limit m  + phase-space-slicing  E + hard radiation --- phase-space-slicing stability --- independence of m

ILC,Beijing16  Conclusion : --- O(10%) EW correction to intermediate( GeV) HHZ production at LC --- maximum cross-section in √s ~800GeV for intermediate Higgs

ILC,Beijing17  Consistency check with Grace people, hep-ph/ , Phys.Lett. B576(2003)152

ILC,Beijing18 Summary Precise prediction for high multiplicity final state processes is being a frontier of ILC phenomenology -- NLO EW quantum correction could be as large as 5% to ttH, HZZ and HHZ production, which have to be taken into account for Yukawa, HHH self-coupling and HVV coupling measurement -- method development on high rank N≥5 one-loop integrals and the stability of numerical calculation is essential

ILC,Beijing19 G.Passarino and M.Veltman, NLB160(1979)151 F.Aguila et al., JHEP 0407(2004)017, up to 4-point T.Binoth et al., hep-ph/ , NPB572(2000)361 A.Denner et al., hep-ph/ (5-point) T.Binoth et al., hep-ph/ ,NPB654(2003)277 (hexagon) A.Denner et al., hep-ph/ (6-point) L.Guo et al., internal note (5 and 6-point)

ILC,Beijing20 Backup

ILC,Beijing21 EW corrections to e + e -  ZHH Y.J.Zhou et al, hep-ph/ , Phys. ReV. D73(2006) √s<1TeV for intermediate Higgs ( GeV) sensitivity on HVV measurement

ILC,Beijing22  Conclusion : --- O(10%) EW correction to intermediate( GeV) ZZH production at LC

Guo’s method for 6-point integral