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

2. 2007-02-05L.HAN@9th 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

3. 2007-02-05L.HAN@9th 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 http://www.fnal.gov/pub/presspass/images/LighterHiggs-images.html

4. 2007-02-05L.HAN@9th 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 % (@170GeV) LEP2 ~ 1 %  Off-shell 2  4 of threshold scan in + W mass uncertainty ~ 7 MeV [#] For reference S.Dittmaier Hep-ph/0308079, and A.Denner et al Hep-ph/0505042  high mass region 2  4 e + e -  WW  qq+lv in for anomalous couplings N=6

5. 2007-02-05L.HAN@9th 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

6. 2007-02-05L.HAN@9th ILC,Beijing6 The status of precise calculation

7. 2007-02-05L.HAN@9th ILC,Beijing7 Theoretical requirement for LC physics

8. 2007-02-05L.HAN@9th 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

9. 2007-02-05L.HAN@9th 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

10. 2007-02-05L.HAN@9th ILC,Beijing10  6-point loop function by A.Denner and S.Dittmaier, hep-ph/0509141  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

11. 2007-02-05L.HAN@9th ILC,Beijing11 EW corrections to e + e -  ttH [†] Y.You et al, hep-ph/0306036, 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 =100GeV@√s=500GeV

12. 2007-02-05L.HAN@9th 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

13. 2007-02-05L.HAN@9th ILC,Beijing13  Conclusion : remarkable O(5%) EW correction to ttH at LC  consistency check given by S.Dittmaier in hep-ph/0308079 [66] G.Belanger et al Hep-ph/0307029, Phys.Lett. B571(2003)163 [67] A.Denner et al, Hep-ph/0307193, Phys.Lett. B575(2003)290

14. 2007-02-05L.HAN@9th ILC,Beijing14 EW corrections to e + e -  ZHH R.Y.Zhang et al, hep-ph/0308203, Phys. Lett. B578(2004)349 O(0.1)fb @ √s<1TeV, 10% precision on cross-section  18% on HHH

15. 2007-02-05L.HAN@9th ILC,Beijing15 Cancellation of IR singularity: virtual + soft-photon limit m  + phase-space-slicing  E + hard radiation --- phase-space-slicing stability --- independence of m  @

16. 2007-02-05L.HAN@9th ILC,Beijing16  Conclusion : --- O(10%) EW correction to intermediate(115-200GeV) HHZ production at LC --- maximum cross-section in √s ~800GeV for intermediate Higgs

17. 2007-02-05L.HAN@9th ILC,Beijing17  Consistency check with Grace people, hep-ph/0309010, Phys.Lett. B576(2003)152

18. 2007-02-05L.HAN@9th 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

19. 2007-02-05L.HAN@9th 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/9911342, NPB572(2000)361 A.Denner et al., hep-ph/0212259 (5-point) T.Binoth et al., hep-ph/0210023,NPB654(2003)277 (hexagon) A.Denner et al., hep-ph/0509141 (6-point) L.Guo et al., internal note (5 and 6-point)

20. 2007-02-05L.HAN@9th ILC,Beijing20 Backup

21. 2007-02-05L.HAN@9th ILC,Beijing21 EW corrections to e + e -  ZHH Y.J.Zhou et al, hep-ph/0604127, Phys. ReV. D73(2006) 073009 O(0.5)fb @ √s<1TeV for intermediate Higgs (115-200GeV) sensitivity on HVV measurement

22. 2007-02-05L.HAN@9th ILC,Beijing22  Conclusion : --- O(10%) EW correction to intermediate(115-200GeV) ZZH production at LC

23. 2016-7-623 Guo’s method for 6-point integral

24. 2016-7-624