Electroweak Corrections for the Study of the Higgs Potential at the LC

Transcription

1 2005 Intrnational Linar ollidr orkshop Stanford, U.S.A. Elctrowak orrctions for th Study of th Higgs Potntial at th L F. Boudja LAPTH, BP.110, Anncy-l-Viux F-74941, Franc J.Fujioto, T.Ishikawa, T.Kanko, Y.Shiizu High Enrgy Acclrator Rsarch Organization(KEK), Tsukuba, Ibaraki , Japan K.Kato Kogakuin Univrsity, Nishi-Shinjuku 1-24, Shinjuku, Tokyo , Japan Y.Yasui Tokyo Managnt ollg, Futaata, Ichikawa, hiba , Japan Th full lctrowak radiativ corrction is calculatd for th procss which is a window for th study of th Higgs potntial at th futur linar collidr. Th calculation is don by using RAE, th autoatd syst for th calculation of Fynan diagras. Th agnitud of th wak corrction in th µ sch is sall in th high nrgy rgion whr this procss doinats ovr th ZHH production. 1. INTRODUTION Th + linar collidr (L) will b a grat asst for high-nrgy physics. On of th ost iportant targts of th L is th study of th Higgs particl. In Fig.1, w show various channls that ar rquird for a study of th proprtis of th Higgs. Most of ths channls hav 3 or 4 particls in th final stat. For instanc, th procss + ZH is only iportant at low nrgis, lik at LEP2. It is quickly ovrco by th procss ννh at highr nrgis typical of th L[1]. Probing th structur of th Higgs potntial is achivd through th 3- and 4-body final stats + ZHH and which involv th Higgs slf coupling. For th analyss of xprintal data with high accuracy, w nd th radiativ corrctions(r) for ths procsss in th standard lctrowak(e) thory. Though th R for th ulti-body final stats is tchnically vry coplicatd, th iportanc of ths procsss warrants a thortical ffort. A ky solution for this task is th us of autoatd systs. Th brakthrough was th coputation of th coplt E R for ννh in Sptbr 2002[2]. Sinc thn othr channls hav bn tackld by svral Figur 1: Tr-lvl cross sctions for Higgs production at th L.

2 groups[3-10]. In this talk, th rsults for th E R for is prsntd[11]. This coplts th R for Higgs production in th ajor channls for th futur L. 2. RESULTS hav alrady studid th R for ZHH production in [7]. Howvr, th xtnsion to ννhh production is andatory, sinc th lattr cross sction is largr than th forr in th high nrgy rgion as shown in Fig.1. Th ννhh production is or coplicatd and w nd th rduction of 6-point functions. In th ZHH procss, th s-channl chanis, i.., annihilats into Z-boson, doinats whil in th ννhh procss th -fusion, which w call t-channl chanis, is doinant at th high nrgy. Th calculation is don through th xtnsiv us of RAE, th autoatd syst for th valuation of Fynan diagras[12]. Th syst gnrats th corrsponding Fynan diagras for th spcifid procss. For ν ν HH, th nubr of tr (on-loop) diagras is 81(19638) and that for µ ν µ ν HH is 27(8292). (hn w dnot, it stands for th su ovr th thr gnrations of nutrinos.) Th diagras ar producd basd on th E thory with th non-linar gaug(nl) fixing[12, 13]. Th introduction of th NL provids a systatic chck ovr th nurical calculation. Th nubr of diagras quotd abov rfrs to th full st of diagras that ar usd for th gaug invarianc chck. At th th production or valuation stag, a sallr st of diagras is usd, obtaind aftr discarding th coupling btwn th scalars and th lctron. Th nubr of diagras for th production st is 12(3416) for lctron nutrino and 6(1754) for th uon/tau nutrino. Each product of a tr diagra and a on-loop diagra is procssd by th sybolic anipulation progra REDUE or FORM to gnrat a FORTRAN cod for that aplitud. Th nurator including loop onta is procssd by a rduction thod (s,.g., [10]), so that th 5- and 6-point functions ar convrtd into th su of 4-point functions (and lowr-point functions). Ths loop intgrals ar thn fd into th FF loop intgrals library[14]. So of th box intgrals including infrard divrgnc ar calculatd by an in-hous library. Th paratr st for th calculation is as follows: M = V, M Z = V, Γ =2.4952V, M Z H =120 V, t =180V, =2 E ba =400 ~ 2000V, k cut =0.05E ba. Th width of th Z only appars at th rsonant pols. Th corrsponding valu of r = dfin th wak corrction factor δ in th convntional way by subtraction of th QED corrction fro th full E corrction (s,.g., [7]). Th corrction in th µ -sch, δ, is dfind as δ = δ 4 r. hav coputd δ for ν µ ν HH and found that th valus ar siilar to thos for + ZHH shown µ in Fig.3 of [7]. 1 In Fig.2 and Fig.3, w show th calculatd valus of δ and δ for ν ν HH and for ννhh. Th prliinary rsults for th forr was rportd in [11]. 2 Th nrgy dpndnc diffrs fro that in ZHH channl, bcaus th t-channl chanis is doinant in th high nrgy rgion. Th corrction δ around 1 TV 1 Th xact coparison is not possibl, as th ass of top-quark is 174V in [7]. 2 Th plottd valus ar updatd fro thos prsntd in th talk at LS05. ralizd that th output fils of RAE wr not proprly cobind (anually!) for th figurs of th LS05 prsntation.

3 and at highr nrgy is lss than. Th xprintal obsrvation of such a corrction will b difficult sinc th agnitud of cross sction is O(1fb) or lss δ 10 δ δ (%) δ (%) 5 δ 0 δ Figur 2: Th wak corrction for ν ν HH Figur 3: Th wak corrction for 3. HH Th procss consists of s-channl and t- channl diagras. In th high nrgy rgion, th t-channl chanis doinats, so that th study of th procss HH could provid th bas for an approxiation to. At tr-lvl, 6 diagras dscrib HH. Thy ar classifid into A-, B-, and -trs, i.., Annihilation, Boson-xchang, and ontact trs. Th ffct of th Higgs potntial, i.., th slf-coupling of th Higgs, is includd in th A-tr. It should b notd that th sign of th aplitud of B-tr is opposit to that of A-and -trs. Th thod of coputation and th input paratrs ar th sa as in. Th rsult is shown in Fig.4. In ordr to chck th consistncy btwn this rsult and that for, w hav considrd th following δ(%) Figur 4: δ δ Th wak corrction to HH. approxiation for δ for +.

4 δ(%) 2 1 δ δ Lading t tr tr Fν ( M) σ ( M) δ ( M) dm / F ( M) σ ( M) dm + 2 r ν (1) tr whr F ν (M), σ and δ ar th distribution of invariant ass of Higgs pairs in, th tr cross sction of HH, and th δ for HH. In th nrgy rgion abov 1TV, this approxiation rproducs δ for within 1%. Sotis th lading t forula is usd as an approxiation to th R to th Higgs vrtics. Th lading t corrctions for th tripl Higgs vrtx, H vrtx and HH vrtx ar as follows: H t t t πs M MH 8πs M 12s 8πs M 6s Figur 5: Th xact wak corrctions copard to thos obtaind with th lading t approxiation for HH. 2s + 3 8s + 3 Hr, th corrction factor is dfind so that th corrctd vrtx is (1+) tis th vrtx at tr-lvl. Th corrctions for A-, B-, and -trs ar H +, 2, and 4, rspctivly. Th nurical valus of th s in Eq.(2) ar , , and , rspctivly. If w tak an artificially larg valu for t, say 100 tis th physical valu, th loop corrction coputd by RAE is wll dscribd by this forula. Howvr, with th physical valu, i.., t =180V, th valu of th loop aplitud diffrs fro that givn by ths t forula. This is bcaus in th ral world th asss of Higgs and gaug bosons ar not so sall copard with t, and th nrgy is quit largr than t. In Fig.5, w show th coparison btwn th xact δ for HH and that by th factors givn abov Eq. (2). (2) 4. FINAL REMARKS hav studid th R for in th full E thory. Th nrgy dpndnc of th corrction diffrs fro that for + ZHH. Th agnitud of th wak corrction δ with M H =120V is only a fw prcnt in ost of th nrgy rgion whr this procss is iportant. Although this is a larg scal coputation, th RAE syst has prford wll and givn inforation and rsults only an xact calculation can provid. Th study of R for HH is also don hr and it is shown that this is th cntral chanis in th TV rgion. Also, th validity and th liitation of th lading t approxiation is prsntd through a coparison with th full coputation. ith th rsults in this papr, th E Rs for all procsss shown in Fig.1 hav bn calculatd. Ths rsults ar indispnsabl for Higgs studis at th futur L.

5 Acknowldgnts This work was supportd in part by th Japan Socity for Prootion of Scinc undr rant-in-aid for Scintific Rsarch B(No ). This rsarch is carrid out undr th auspics of Autoatd alculations in Particl Physics (APP) - an Intrnational Rsarch roup unit coprisd of rsarchrs fro Franc, Russia and Japan (DRI 397 of th Frnch NRS). also thank IDRIS, Institut du Dévlopnt t ds Rssourcs n Inforatiqu Scintifiqu, for th us of thir coputing rsourcs. Rfrncs [1] S, for xapl, M.. runwald, hp-x/ , with updats [2]. Bélangr, F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko, K. Kato, Y.Shiizu, Phys.Ltt. B559 (2003) 252. [3] A. Dnnr, S. Dittair, M. Roth, M. M. br, Nucl.Phys. B660 (2003) 289. [4]. Bélangr, F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko, K. Kato, Y. Shiizu, Y. Yasui, Phys.Ltt. B571 (2003) 163. [5] You Yu, Ma n-an, hn Hui, Zhang Rn-You, Sun Yan-Bin, Hou Hong-Shng, Phys.Ltt. B571 (2003) 85. [6] A. Dnnr, S. Dittair, M. Roth, M.M. br, Phys.Ltt. B575 (2003) 290. [7]. Bélangr, F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko Y. Kurihara, K. Kato, Y. Shiizu, Phys.Ltt. B576 (2003) 152. [8] Zhang Rn-You, Ma n-an, hn Hui, Sun Yan-Bin, Hou Hong-Shng, Phys.Ltt. B578 (2004) 349. [9] F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko, K. Kato, Y. Kurihara, Y. Shiizu, Y. Yasui., Phys.Ltt. B600 (2004) 65. [10] F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko, K. Kato, Y.Kurihara, Y. Shiizu, S. Yaashita, Y. Yasui, Nucl.Instru.Mth. A534 (2004) 334. [11] Prliinary rsults wr rportd by Y.Yasui in EFA 2004 at Durha, Spt [12]. Bélangr, F. Boudja, J. Fujioto, T. Ishikawa, T. Kanko, K. Kato, Y.Shiizu, hp-ph/ (2003). [13] F. Boudja, E.hopin, Z.Phys. 60 (1996) 757. [14].J.van Oldnborgh, oput.phys.oun. 58 (1991) 1.