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NLO BFKL tests using the proton structure function $F_2$ measured at HERA

We propose a phenomenological study of the next-to-leading Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach applied to the data on the proton structure function $F_2$ measured at HERA in the small-$x_{Bj}$ region.

NLOBFKLtestsusingtheprotonstructurefunctionF2measuredatHERA

C.Royon

Servicedephysiquedesparticules,CEA/Saclay,91191Gif-sur-Yvettecedex,France

Fermilab,Batavia,USA

Abstract.Weproposeaphenomenologicalstudyofthenext-to-leadingBalitsky-Fadin-Kuraev-Lipatov(BFKL)approachappliedtothedataontheprotonstructurefunctionF2measuredatHERAinthesmall-xBjregion.

arXiv:hep-ph/0507101v1 8 Jul 2005INTRODUCTIONPrecisephenomenologicaltestsofQCDevolutionequationsareoneofthemaingoalsofdeepinelasticscatteringphenomenology.FortheDokshitzer-Gribov-Lipatov-Altarelli-Parisi(DGLAP)evolutioninQ2ithasbeenpossibletotestitinvariouswayswithNLO(next-to-leadinglogQ2)andnowNNLOaccuracyanditworksquitewellinalargerangeofQ2andxBj.TestingpreciselytheBalitsky-Fadin-Kuraev-Lipatov(BFKL)evolutioninenergy(orxBj)beyondleadingorderappearsmoredif cult.The rstexperimentalresultsfromHERAcon rmedtheexistenceofastrongriseoftheprotonstructurefunctionF2withenergywhich,intheBFKLframework,canbewelldescribedbyasimple(3parameters)LO-BFKL tThemainissueofwasthatnotonlytherisewithenergybutalsothescalingviolationsobservedatsmallxBjareencodedintheBFKLframeworkthroughtheQ2variationoftheeffectiveanomalousdimension.Howeveronewasledtointroduceaneffectivebutunphysicalvalueofthestrongcouplingconstantα~.07 .09insteadofα~.2intheQ2-rangeconsideredfor

HERAsmall-xBjphysics,revealingtheneedforNLOcorrections.Indeed,therunningofthestrongcouplingconstantisnottakenintoaccount.

Infact,thetheoreticaltaskofcomputingthesecorrectionsappearstobequitehard.Itisnowingoodprogressbutstillundercompletion.FortheBFKLkernel,theyhavebeencalculatedaftermuchefforts[5].Itwasrealized[4]thatthemainproblemcomesfromtheexistenceofspurioussingularitiesbroughttogetherwiththeNLOcorrections,whichoughttobecancelledbyanappropriateresummationatallordersoftheperturbativeexpansionresummationrequiredbyconsistencywiththeQCDrenormalizationgroup.

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