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

PITHA03/11

CERN-TH/2003-286

hep-ph/0311335

November25,2003

arXiv:hep-ph/0311335v1 26 Nov 2003Factorizationofheavy-to-lightformfactorsinsoft-collineare ectivetheoryM.BenekeaandTh.FeldmannbaInstitutf¨urTheoretischePhysikE,RWTHAachenD–52056Aachen,GermanybCERN,TheoryDivision,CH-1211Geneva,SwitzerlandAbstractHeavy-to-lighttransitionformfactorsatlargerecoilenergyofthelightmesonhavebeenconjecturedtoobeyafactorizationformula,wherethesetofformfactorsisreducedtoasmallernumberofuniversalformfactorsuptohard-scattering

corrections.Inthispaperweextendourpreviousinvestigationofheavy-to-lightcurrentsinsoft-collineare ectivetheoryto nalstateswithinvariantmassΛ2asisappropriatetoexclusiveBmesondecays.Thee ectivetheorycontainssoftmodesandtwocollinearmodeswithvirtualitiesofordermbΛ(‘hard-collinear’)andΛ2.Integratingoutthehard-collinearmodesresultsinthehardspectator-scatteringcontributionstoexclusiveBdecays.Wediscusstherepresentationofheavy-to-lightcurrentsinthee ectivetheoryafterintegratingoutthehard-collinearscale,andshowthatthepreviouslyconjecturedfactorizationformulaisvalidtoallordersinperturbationtheory.Thenaivefactorizationofmatrixelementsinthee ectivetheoryintocollinearandsoftmatrixelementsmaybeinvalidatedbydivergencesinconvolutionintegrals.Inthefactorizationproofwecircumventtheexplicitregularizationofendpointdivergencesbyade nitionoftheuniversalformfactorsthatincludeshard-collinear,collinearandsofte ects.