Electroweak Correction for the Study of Higgs Potential in LC

Transcription

1 Elctrowak Corrction for th Study of Higgs Potntial in LC LAPTH-Minamitatya Collaboration LCS , Stanford U. prsntd by K.Kato(Kogakuin U.)

2 Introduction LC: high-prcision xprimnts Rquirs th sam lvl thortical prdiction = Nds highr ordr calculation Higgs study : Cntral targt Intrsting channls = multi-body final stats 1-loop corrction to - 3, 4-bodis : Grat Progrss sinc Spt. 00

3 cross sctions Main channls H vs ZZH Yukawa coupl. Higgs Potntial 3,4 procsss important

4 numbr of diagrams (GRACE:NLG modl) A.Dnnr, J.Kublbck, R.Mrtig, M.Bohm, Z.Phys.C56(199) 61; B.A.Knihl, Z.Phys.C55(199) yars rquird to dvlop 3 tools Automatd Systms ZH tr 1-loop 4(1) 341(119) RADCOR / Loops & Lgs Spt. 00 ννh H tth ZHH 1() 1350(49) 1(6) 37(758) 7(6) 5417(1597) 4() 4470(510) with(without) -scalar couplings

5 tth ZHH Full 1-loop RC availabl GRACE, PLB559(003)5 ννh Dnnr t al., NPB660(003)89 H GRACE, PLB571(003)163 You t al., PLB571(003)85 Dnnr t al., PLB575(003)90 GRACE, PLB576(003)15 Zhang t al., PLB578(004)349 GRACE, PLB600(004)65 ννγ ννhh ν = ν μ, ν ν τ μ ν τ μ, GRACE, NIM A534(004)334 GRACE, Talk by Y.Yasui at Durham(Sp.004) udsc Dnnr tal., hpph/050063

6 Kinmatics library Usr input REDUCE, Form tc. Diagram gnrator diagram dscription amplitud gnrator LOOP symbolic cod TREE.fin.mdl.rin modl fil Mak fil tc. Thory Drawr Diagrams (figur) PS fil FORTRAN cod kinmatics cod gnratd cod Library CHANEL, loop convrgnc information BASES(MC intgral) paramtr fil Cross sctions distributions SPRING (EG managr) Evnts

7 Higgs Potntial Somthing rquird to provid mass Ky for th structur of standard modl H H H H indow to Nw Physics H H H Doubl (tripl) Higgs production Procss

8 - ννhh [ab/gv] 1 >hhνν (without Z) m h =10 GV RS = 1000 GV (ΛδΛ)/Λ HHH coupling dpndnc SM: δλ= Invariant mass of hh [GV] tr old paramtr st

9 ννhhvszhh M H =10 GV ZHH/nunuHH Tr σ(ab) ZHH ννhh

10 ZHH Low FULL calculation ννhh High dominant mchanism (approximation) H H

11 - ννhh

12 - HH Annihilation Boson Exchang Contact Intraction H H H, χ

13 - HH tr 6 diagrams Annihilation, Boson xch., Contact int. B A, C opposit sign 1-loop 87 diagrams 13 groups A : vrtx corr.hhh, H, A, Z B : vrtx corr. H, χh C : Box

14 Chck : Cuv indpndnc Cuv=0 Cuv=100 Cuv=10000

15 Linar Gaug vs Non-Linar Gaug NLG Cuv=0 Cuv=100 LG Cuv=0

16 lading m t formulas A: C H C B: C C: C 4 M = M Z = M H =10 m t =180 α=1/ C C C H 4 = = α m 4 t N C 3πs w M MH = α m s t N C 8πs w M 1sw α m 8s t N C 8πs w M 6sw

17 m t = ( n1) GV ( n = 1,,3,4,5) ral world : NOT m t >>, M H, M Z, proof of th formulas and th prformanc of GRACE systm OK

18 HH(tr) 6 5 σ(pb) 4 3 trlading mt corrction full E corrction (w/o QED) δ(e) & δ(mt) δ(%) 0% 15% 10% 5% 0% -5%

19 - HH δ δ(%) 40% 0% 0% -0% -40% -60% -80% HH 1-loop corrctions δ (Gm) -100% δ V λ=10-1 Gv δ V QED

20 - ννhh numbr of diagrams ν... tr= 81 loop=19638 (prod. st = 1 x 3416) 50M lins of Fortran cod ν mu... tr= 7 loop=89 (prod. st = 6 x 1754)

21 - ννhh

22 s-channl ZHH hp-ph/ Phys.Ltt.B 576(003)15.

23 nunuhh(tr) ννhh 400 σ(ab) nunuhh δ (E) Full calculation M H =10GV δ(%) δ ( G μ )

24 - ννhh 1 Tr Invariant mass of HH M H =10 GV =.5TV =.0TV =1.5TV =1.0TV M(HH) (TV) =0.5TV

25 Summary Higgs Potntial channl ννhh cross sction and its E corrction is calculatd. σ=o(100 ab)and gratr than ZHH in high-e LC rgion ( s 1TV). δ(gmu) is ~10% for s>700gv. Larg diviation from ZHH dominatd by s-channl. HH is studid to chck th t-channl structur of ννhh and has shown validity and limitation of th lading m t formulas.

26 - ννhh

27 ννh hp-ph/0161 Phys.Ltt.B 559(003) 5. s,t channls show diffrnt bhavior gnuin wak corrction in G-schm is -~-4% δ ( s ) δ ( t ) δ H 5αM t = 16πs M = 1.5% δ O(α)total δ G

28 hp-ph/ tth Phys.Ltt.B 571(003) 163.

29 systm componnts Diagram gnration for input procss Amplitud/Matrix lmnt gnration Kinmatics and Intgration (fficincy) Evnt gnration (fficincy & wight) Priphral tools: rul gnrator, diagram slction, QED radiation, PDF, loop intgral library, multi-procss, color flow and intrfac for hadronization, tc.

30 5-point functions = D D D D D d G I σ ν μ σ μν Ll l l l L j j j X r D X D = = l l l 0 0 F D E N = = 4 ) ( α α α l rank M BOX rank M = D X l = = 4 0 )] ( [ 1 α α α α D r b a j j l scalar 5-pnt BOX ν μ μν j ij i j i ij r A r g r r A 1 = = ] [ ) ( j j ij i j ij i X X D D A r r A r = = μ ν μ μ l l N

31 δ(qed), δ(e) σ = σ (1 δ QED δ 0 ) δ non-qed virtural corrctions QED V QED soft QED δ = δ δ δ phas spac subtraction δ QED = hard QED f LL =radiator ~ ~ σ ( v dσ ) ( ) 0δQED dσ 0 fll dσ1 γ d 0 fll hard

32 Non-linar gaug fixing trms ( ) ( ) A Z Z GF F F F F L ξ ξ ξ = ± = ± ± ± ± ± χ κχ χ δ χ ξ β α μ μ μ μ 3 ~ ~ ~ ~ s i H s M Z s c i A i F m m = 3 3 ~ χ ε χ ξ μ μ H c s M Z F Z Z μ F A μ A =

33 Sampls of NLG Fynman ruls )] )( ~ / (1 ) )( ~ / (1 ) ( [ μρ ν νρ μ νρ μ μρ ν ρ μν ξ α ξ α g p g p g p g p p p g A μν α χ g im A ) ~ 1 ( m μν αg A c c A ~ ± m A s i H c c δξ χ ~ 1 m m ± ghost-ghost- vctor-vctor / ghost-ghost-scalar-scalar modifid

34 Non-linar gaug Numrator structur is th sam as Fynman gaug Loop intgral library Vrtics modifid gnral valus #diagrams μν g ( for ξ = 1) old usag rduc #diagram ~ α = 1 no Aχ ~, ~, ~ α, β δ ~ ε, ~ κ Chck gaug invarianc Indpndnc on gaug paramtrs