Electroweak Correction for the Study of Higgs Potential

Electroweak Correction for the Study of Higgs Potential in LC LAPTH-Minamitateya Collaboration LCWS 05 2005. 3. 19, Stanford U. presented by K. Kato(Kogakuin U. )

Introduction • LC ： high-precision experiments Requires the same level theoretical prediction = Needs higher order calculation • Higgs study : Central target Interesting channels = multi-body final states • 1 -loop correction to e+e- 3, 4 -bodies : Great Progress since Sept. 2002

Higgs@LC: tree cross sections Main channels WWH vs ZZH Yukawa coupl. Higgs Potential 2 3, 4 processes important

number of diagrams (GRACE: NLG model) A. Denner, J. Kublbeck, R. Mertig, M. Bohm, Z. Phys. C 56(1992) 261; B. A. Kniehl, Z. Phys. C 55(1992) 605. 10 years required to develop 2 3 tools Automated Systems tree 1 -loop 4(1) 341(119) RADCOR / Loops & Legs Sept. 2002 12(2) 12(6) 27(6) 42(2) 1350(249) 2327(758) 5417(1597) 4470(510) with(without) e-scalar couplings

Full 1 -loop RC available GRACE, PLB 559(2003)252 Denner et al. , NPB 660(2003)289 GRACE, PLB 571(2003)163 You et al. , PLB 571(2003)85 Denner et al. , PLB 575(2003)290 GRACE, PLB 576(2003)152 Zhang et al. , PLB 578(2004)349 GRACE, PLB 600(2004)65 GRACE, NIM A 534(2004)334 GRACE, Talk by Y. Yasui at Durham(Sep. 2004) Denner etal. , hepph/0502063

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

Higgs Potential Something required to provide mass Key for the structure of standard model Window to New Physics Double (triple) Higgs production Process

e+e- ννＨＨ HHH coupling dependence SM: δΛ＝０ tree old parameter set

ννＨＨ ｖｓ ＺＨＨ Tree

Low W FULL calculation High W dominant mechanism (approximation)

e+e- ννＨＨ

W+W- HH Annihilation Boson Contact Exchange Interaction

W+W- HH • tree … 6 diagrams Annihilation, Boson exch. , Contact int. B A, C … opposite sign • 1 -loop … 827 diagrams 13 groups A : vertex corr. HHH, WWH, AWW, ZWW B : vertex corr. WWH, WχH C : Box

Check : Cuv independence Cuv=0 Cuv=10000

Linear Gauge vs Non-Linear Gauge NLG Cuv=0 Cuv=100 LG Cuv=0

leading mt formulas A: CH+CW B: 2 CW -0. 11779616 C: C 4 MW=80. 4163 MZ=91. 1876 MH=120 mt=180 α=1/137. 0359895 -0. 02535196 -0. 07033663

real world : NOT mt >> W, MH, MZ, … proof of the formulas and the performance of GRACE system OK

tree+leading mt correction full EW correction (w/o QED)

W+W- HH δW δV λ=10 -12 Gev δW(Gm) δV QED

e+e- ννＨＨ • number of diagrams νe. . . tree= 81 loop=19638 (prod. set = 12 x 3416) 50 M lines of Fortran code νmu. . . tree= 27 loop=8292 (prod. set = 6 x 1754)

e+e- ννＨＨ

“s-channel” hep-ph/030910 Phys. Lett. B 576(2003)152.

e+e- ννＨＨ Full calculation MH=120 Ge. V

e+e- ννＨＨ Tree Invariant mass of HH W=2. 5 Te. V W=2. 0 Te. V W=1. 5 Te. V W=1. 0 Te. V W=0. 5 Te. V M(HH) (Te. V)

Summary • Higgs Potential channel ee ννＨＨ cross section and its EW correction is calculated. σ＝Ｏ（１００ ａｂ）and greater than ee ZHH in high-E LC region ( ≧ 1 Te. V). δ(Gmu) is ~10% for >700 Ge. V. Large diviation from ee ZHH dominated by s-channel. • WW HH is studied to check the t-channel structure of ee ννＨＨ and has shown validity and limitation of the leading mt formulas.

e+e- ννＨＨ

hep-ph/0212261 Phys. Lett. B 559(2003) 252. s, t channels show different behavior genuine weak correction in G-scheme is -2～-4%

hep-ph/0307029 Phys. Lett. B 571(2003) 163.

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.

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

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

Non-linear gauge fixing terms

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

Non-linear gauge • Numerator structure is the same as Feynman gauge Loop integral library • Vertices modified • general values #diagrams “old” usage reduce #diagram Check gauge invariance Independence on gauge parameters