Factorization of heavy-to-light form factors in soft-colline(5)

时间:2025-04-03

Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of universal form factors up to hard-scattering corrections

InSection3weturnourattentiontotherepresentationoftheheavy-to-lightcurrentinthee ectivetheorywiththehard-collinearscaleremoved.Weintegrateoutthehard-collinearmodesintreegraphsbysolvingtheclassical eldequationsforthehard-collinearquarkandgluon elds.Despitethecomplexbranchingsoftherelevanttrees,thesolu-tioncanbefoundbychoosingaspecialgaugeforthecalculationandreconstructingthe¯ completeresultthroughgaugeinvariance.The rsttermwithanon-vanishing π|...|B

3/2matrixelementintheexpansionofthecurrentisλ3suppressed,whichexplainsthe1/mbsuppressionofheavy-to-lightformfactorsatlargerecoil.Thecalculationalsoshowsthat

thee ectiveoperatorishighlynon-local,implyingconvolutionsintwolight-likedirections.Theconvolutionsaredivergent,asexpected,butwealso ndthatquark-antiquark-gluonamplitudesintheBmesonandinthelightmesoncontributeatleadingpower,whichisanewfeatureofheavy-to-lighttransitions.Attheendofthissectionwebrie ydis-cusshard-collinearquantumcorrectionstodeterminethegeneralformofoperatorsandshort-distancekernelsinthee ectivetheoryofsoftandcollinearmodes.

Theexistenceofdivergentconvolutionssignalsthatheavy-to-lightformfactorsdonotfactorizestraightforwardly.InSection4wereturntothefactorizationformula(1),andshowthatitisindeedvalidtoallordersinthestrongcouplingandtoleadingpowerin1/mb.Weshallde netheuniversalformfactorξπasamatrixelementinSCETbeforeintegratingouthard-collineare ects.Wethenshowthatthetermsnotcontainedinthisde nitionfactorizeintoconvolutionsoflight-conedistributionamplitudeswithconvergentintegralsafterintegratingouthard-collinearmodes.Theproofofconvergencereliesonpowercounting,boostinvariance,andthecorrespondenceofcollinearandsoftendpointdivergencesthroughsoft-collinearfactorization.WeconcludeinSection5.

2Thescalar“photon”vertex

Thepurposeofthissectionistodemonstratebytheexampleofaspeci cFeynmaninte-gralthatthedistinctionofhard-collinearandcollinearmodeshasatechnicalmeaning.Weshallalsoseehowthefactorizationofcollinearandsoftmodesintroduces“endpointsingu-larities”inthelongitudinalintegrations,andhowthesingularitiesarerelatedtocancelinthesumofallterms.Finally,wesketchhowthediagrammaticresultwouldbeinterpretedinthecontextofe ective eldtheory.

Weconsiderthescalarintegral

I= [dk]1

i µ2eγE(2π)d=µe2 γEddk

…… 此处隐藏:482字,全部文档内容请下载后查看。喜欢就下载吧 ……
Factorization of heavy-to-light form factors in soft-colline(5).doc 将本文的Word文档下载到电脑

精彩图片

热门精选

大家正在看

× 游客快捷下载通道(下载后可以自由复制和排版)

限时特价:7 元/份 原价:20元

支付方式:

开通VIP包月会员 特价:29元/月

注:下载文档有可能“只有目录或者内容不全”等情况,请下载之前注意辨别,如果您已付费且无法下载或内容有问题,请联系我们协助你处理。
微信:fanwen365 QQ:370150219