The last talk in session-3

Full one-loop electroweak radiative corrections to single photon production in e + e - ACAT03, Tsukuba, 4 Dec LAPTH and Minamitateya Collaboration presented by K.Kato

Ｍｏｔｉｖａｔｉｏｎ Higgs and SUSY study at future colliders Detailed, high-accuracy prediction required for discovery/(major) background channels EW radiative corrections for multi-body channels … huge computation Automation of perturbative computation … essential tool for HEP

2  3 in ee GRACE, hep-ph/ Denner etal., hep-ph/ GRACE, hep-ph/ You et al., hep-ph/ Denner etal., hep-ph/ GRACE, hep-ph/ Zhang etal., hep-ph/ New results

hep-ph/ Phys.Lett.B 559(2003) 252.

hep-ph/ Phys.Lett.B 571(2003) 163.

hep-ph/ Phys.Lett.B 576(2003)152.

system components Diagram generation for input process Amplitude/Matrix element generation Kinematics and Integration (efficiency) Event generation (efficiency & weight) Peripheral tools: rule generator, diagram selection, QED radiation, PDF, loop integral library, multi-process, color flow and interface for hadronization, etc.

User input Theory model file Diagram generator amplitude generator Library CHANEL, loop Kinematics library kinematics code generated code diagram description convergence information Make file etc. symbolic code REDUCE, Form etc. PS file Drawer BASES(MC integral) SPRING (EG manager) parameter file Diagrams (figure) Events Cross sections distributions TREE LOOP FORTRAN code.fin.mdl.rin

Diagnostics How you can believe the numbers an automated system has produced? UV finiteness IR finiteness gauge invariance

Check by gauge invariance in 1-loop Independence on several gauge parameters Numerator structure is the same as Feynman gauge Vertices modified New vertices (ghost sector) appear Non-linear gauge

Non-linear gauge fixing terms

Samples of NLG Feynman rules ghost-ghost- vector-vector / ghost-ghost-scalar-scalar modified

5-point functions rank M BOX rank M-1 scalar 5-pnt BOX drop

δ(QED), δ(EW) phase space subtraction = radiator non-QED virtural corrections

ee  eeH diagrams full set (for NLG check) tree 42, 1-loop 4470 (inc. C.T.) production set (for integration) tree 2, 1-loop 510 (inc. C.T.) M W = GeV, M Z = GeV Γ Z = GeV ( appear at resonant poles only ) M H = 120GeV, m t = 174GeV E CM = 200 ～ 3000 GeV, kcut=E*0.05

| a^4 | a^3 | a^2 | a^1 | a^ | E-05 | E-05 | E-05 | E-04 | E-04 | E | E-05 | E-05 | E-06 | E-06 | E-06 | E-05 | E-05 | E-05 | E-04 | E-04 | E | E-05 | E-05 | E-06 | E-06 | E-06 : : : : 4457 | E-16 | E | E-18 | E | E-28 | E | E-18 | E sum E E E E E-04 max.62693E E E E E-04 cnt check by NLG (ee  eeH) compute for several ξ, at a point in PS

ee  eeH M H =120GeV

diagrams full set (for NLG check) tree 10, 1-loop 1099 (inc. C.T.) production set (for integration) tree 5, 1-loop 331 (inc. C.T.) M W = GeV, M Z = GeV Γ Z = GeV M H = 120GeV, m t = 174GeV E CM = 200 ～ 3000 GeV OPAL cut: (γ)p T >0.05E B, 15°<θ<165°

IR diagrams tree diagrams

check by NLG (ee  nunuA) | a^4 | a^3 | a^2 | a^1 | a^ V | E-03 | E-03 2V | E-14 | E-14 6V | E-14 | E-14 ： 18V | E-11 | E-10 | E-10 19V | E-10 | E-09 | E-09 20V | E-10 | E-10 | E-10 22V | E-10 | E-10 23V | E-42 | E-42 24V | E-09 | E-09 | E-09 26V | E-10 | E-10 27V | E-42 | E-42 28V | E-09 | E-09 | E-09 29V-| E-37 | E-36 | E-36 | E-36 | E-07 30V-| E-39 | E-39 | E-38 | E-38 | E-08 31V-| E-37 | E-37 | E-36 | E-36 | E-07 ： 854P | E-14 | E B | E-04 | E-03 | E sum E E E E max.12998E E E E cnt

M H =120GeV

conclusion Technology is established to handle full-EW RC for 2  3 processes. Gauge parameter independence in NLG is powerful to confirm the results. New results for full EW correction is obtained for