Precise prediction for ILC experiment HAN Liang Univ

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

Introduction on motivation l Hadron colliders as discovery machinary: SPS, Tevatron I & II, LHC W boson, top quark, Higgs? SUSY? l Precise measurement at linear colliders LC LEP, TESLE/ILC/NLC QF & SM precise test, eg W boson mass, top physics etc Higgs characteristic and couplings: Hff, HZZ, HWW, HHHH New physics, eg SUSY parameter determination l Challenges for LC phenomenology: QCD & EW quantum radiative correction effects, NLO and 2 -loop calculations multiplicity (>=3) final states 2007 -02 -05 L. HAN@9 th ILC, Beijing 2

W boson mass measurement -- W boson mass at NLO -- Higgs mass determination with W 80, 398 ± 25 Me. V/c 2 combined latest CDF http: //www. fnal. gov/pub/presspass/images/Lighter. Higgs-images. html 2007 -02 -05 L. HAN@9 th ILC, Beijing 3

Measurement of e+e- W(*)W ln+ln u on-shell di-W bosons 2 2 in double-pole approximation + + Passarino-Veltman reduction N≤ 4 u Theoretical uncertainty ~ 0. 7% (@170 Ge. V) LEP 2 ~ 1% Off-shell 2 4 of threshold scan in W mass uncertainty ~ 7 Me. V + N=6 u high mass region 2 4 e+e- WW qq+lv in for anomalous couplings [#] For reference S. Dittmaier Hep-ph/0308079, and A. Denner et al Hep-ph/0505042 2007 -02 -05 L. HAN@9 th ILC, Beijing 4

Challenge on theoretical prediction The confrontation of high-precise ILC measurement with phenomenology: better understanding on QCD and EW effects ISR/FSR treatment high multiplicity nf≥ 3 in final states complication of topology N≥ 5 -point Feynman loop integrals stability in numerical calculation software : Feyn. Arts, Form. Calc, Loop. Tools etc 2007 -02 -05 L. HAN@9 th ILC, Beijing 5

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

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

One-loop radiative corrections to 2 nf N-point Feynman integrals as 1 to 4 -point integrals given in G. Passarino and M. Veltman, NLB 160(1979)151 2007 -02 -05 L. HAN@9 th ILC, Beijing 8

(N≤ 4)-point loop integrals Passarino-Veltman: 3 -point tensor integral as example --- Decompose to Lorentz-covariant tensor + coefficient --- Use Gram determinant to calculate coefficient Cij would raise singularity in N≥ 5 -point integrals 2007 -02 -05 L. HAN@9 th ILC, Beijing 9

New development on (N≥ 5)-point integrals u 5 -point integral by A. Denner and S. Dittmaier, NPB 658(2003)175 where u 5 -dimensional Cayley matrix Y used to replace Gram matrix u 6 -point loop function by A. Denner and S. Dittmaier, hep-ph/0509141 2007 -02 -05 L. HAN@9 th ILC, Beijing 10

EW corrections to e+e- tt. H [†] Y. You et al, hep-ph/0306036, Phys. Lett. B 571(2003)85 EW RC=self-energy(376) + vertex(425) + box(145) + pentagon(29), where part of N=5 diagrams as u For Ultraviolet UV divergence in N=2 and 3 -point integrals, dimensional regularization + COMS [†] S. Dawson et al, PRD 59(1999)054012: QCD k=1. 5 for Mh=100 Ge. V@√s=500 Ge. V 2007 -02 -05 L. HAN@9 th ILC, Beijing 11

u For Infrared IR divergence in N=2 to 5 -point integrals, + virtual : photon mass regularization mg + massive electron + real emission = soft photon limit + phase-space slicing (DE) + hard radiation 2007 -02 -05 L. HAN@9 th ILC, Beijing 12

u Conclusion : remarkable O(5%) EW correction to tt. H at LC u consistency check given by S. Dittmaier in hep-ph/0308079 [66] G. Belanger et al Hep-ph/0307029, Phys. Lett. B 571(2003)163 [67] A. Denner et al, Hep-ph/0307193, Phys. Lett. B 575(2003)290 2007 -02 -05 L. HAN@9 th ILC, Beijing 13

EW corrections to e+e- ZHH R. Y. Zhang et al, hep-ph/0308203, Phys. Lett. B 578(2004)349 • O(0. 1)fb @ √s<1 Te. V, • 10% precision on cross-section 18% on l. HHH 2007 -02 -05 L. HAN@9 th ILC, Beijing 14

Cancellation of IR singularity: virtual + soft-photon limit mg + phase-space-slicing DE + hard radiation --- phase-space-slicing stability 2007 -02 -05 --- independence of mg @ L. HAN@9 th ILC, Beijing 15

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

u Consistency check with Grace people, hep-ph/0309010, Phys. Lett. B 576(2003)152 2007 -02 -05 L. HAN@9 th ILC, Beijing 17

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 tt. H, 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 2007 -02 -05 L. HAN@9 th ILC, Beijing 18

• • G. Passarino and M. Veltman, NLB 160(1979)151 F. Aguila et al. , JHEP 0407(2004)017, up to 4 -point T. Binoth et al. , hep-ph/9911342, NPB 572(2000)361 A. Denner et al. , hep-ph/0212259 (5 -point) T. Binoth et al. , hep-ph/0210023 , NPB 654(2003)277 (hexagon) A. Denner et al. , hep-ph/0509141 (6 -point) L. Guo et al. , internal note (5 and 6 -point) 2007 -02 -05 L. HAN@9 th ILC, Beijing 19

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

EW corrections to e+e- ZHH Y. J. Zhou et al, hep-ph/0604127 , Phys. Re. V. D 73(2006) 073009 • O(0. 5)fb @ √s<1 Te. V for intermediate Higgs (115 -200 Ge. V) • sensitivity on l. HVV measurement 2007 -02 -05 L. HAN@9 th ILC, Beijing 21

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

Guo’s method for 6 -point integral 2021/6/13 23