Putting non Point-like Behavior of Fundamental Particles to Test
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arXiv:hep-ph/0111302v3 24 Mar 2003PuttingnonPoint-likeBehaviorofFundamentalParticlestoTest
IrinaDymnikova∗,AlexanderSakharov†,J¨urgenUlbricht†andJiaweiZhao‡
∗InstituteofMathematicsandInformatics,UWMinOlsztyn,PL–10-561Olsztyn,Poland
†Laborf¨urH¨ochenergiephysik,ETH-H¨onggerberg,HPK–Geb¨aude,CH–8093Z¨urich,Switzerland
‡ChineseUniversityofScienceandTechnology,USTC,Anhui230029Hefei,P.R.China
Abstract.Wereviewtheexperimentallimitsonthosehypotheticalinteractionswherethefundamentalparticlescouldexhibitnonpoint-likebehavior.InparticularwehavefocusedontheQEDreactionmeasuringthedifferentialcrosssectionsfortheprocesse+e−→γγ(γ)atenergiesaround91GeVand209GeVwithdatacollectedfromtheL3detectorfrom1991to2001.WithaglobalfitL3setlowerlimitsat95%CLonacontactinteractionenergyscaleparameterΛ>1.6TeV,whichrestrictsthecharacteristicQEDsizeoftheinteractionregiontoRe<1.2×10−17cm.AlltheinteractionregionsarefoundtobesmallerthantheComptonwavelengthofthefundamentalparticles.Thisconstraintweusetoestimatealowerlimitontheinternaldensityofparticle-likestructurewiththedeSittervacuumcore.Someapplicationsofobtainedlimitstothestringandquantumgravityscalesarealsodiscussed.
INTRODUCTIONWhenonestartstothinkaboutunificationofallknowninteractionsthequestionwhetherthequarksandleptonsarestructureless,orwewillfindthattheyhaveanextendedstructure,becomesveryimportant.Thepointisthattherenormaliza-tionprocedurewhichallowstoextractfinitepredictionsforprocessesinvolvingthestrong,weakandelectro–magneticinteractionsfailswhengravitationalinteractionistakenintoaccount.Thusweareforcedtouseframeworkslikethestringtheory[1]toincorporategravitywithotherinteractions.Asanessentialpartofstringtheoryisthattheparticlesofstandardmodelmusthaveanextendedstructure.Thestringshavenewdegreesoffreedomthatoftentaketheclassicalgeometrydescriptionofpropagationinextradimensions.Thismeansthat,therewillbeadditionalmodificationsofstandardmodelamplitudes.Inparticular,someofthestringexcitationscouldbevisibleinlowenergeticlimitasacontactinteraction[2,3].Someotherphenomenologicalapproaches,dealingwiththeexplanationofmassspectrumoffermionsfamilies(seeforexample[4]andreferencestherein)orDeSitter-Schwarzschildbehaviorofparticle–likeobjects[6],towhichwepaypar-ticularattentioninthispaper,alsocouldrequirenonpoint–likenessoffundamentalparticles1.Thusitturnstobeveryimportanttostudypossibleexperimentalsig-naturesofoperatorscausingthenonpoint–likebehaviorofelectron.Totestthesizeoffundamentalparticles(FP)twoexperimentalapproacheshavebeendeveloped.InoneapproachasearchisperformedforexcitedstatesofFPandcorrespondingmassisestimated[7].ThistestwouldindicateanewsubstructureoftheFP.InthesecondapproachacharacteristicscaleparameterΛ[8]orformfactorF[9]isdetermined,constrainingthecharacteristicsizeoftheinteractionregionforthereaction[10].AllthesetestssearchforphysicsbeyondtheStandardModel(SM).Inthefirstpartofthispaperwesummarizethestringentexperimentalrestric-tionssetonthemassofexcidetstatesofFP[11,13–15].Theobtainedlimitsontheparametersofexitedstatesandcontactinteractionsetboundsonpossibleex-tensionsofinteractionsareasandhenceonthesizesofFPs.ItturnsoutthatalltheselimitsaremuchsmallerthantheComptonwavelengthsλ−cofFPs.Furtherweapplytheexperimentallimits,obtainedforexitedstatesofFP,tostudyTeVscalequantumgravityinsuperstringtheoryframework,likeithasbeenproposedin[2,3].Therestofthepaperisdedicatedtothemodelingofanextendedparticle-likeobjectsbydeSitter-Schwarzschildself-gravitatingcore[16].
EXPERIMENTALLIMITSONTHESIZESOFFUNDAMENTALPARTICLES
Totestthefinitesizeoffundamentalparticles,experimentsareperformedtosearchforcompositeness,toinvestigateanon-pointlikebehaviororformfactorsinstrong,electromagneticandelectroweakinteractions.Eachinteractionisassumedtohaveitscharacteristicenergyscalerelatedtothecharacteristicsizeofinteractionregion.Inthefollowingsub-sectionswereviewtheexperimentallimitsonexcitedparticlemasses,energyscalesΛandformfactorsRforallthreeinteractions.
STRONGINTERACTION-Totestthecolorchargeofthequarks,theentrancechannelandtheexitchannelsofthereactioninthescatteringexper-imentshouldbedominatedbythestronginteraction.Thisconditionisful-filledbytheCDFp¯pdata[14]whichexcludeexcitedquarksq∗withamassbetween80and570GeVat95%CL.TheUA2data[15]excludeu∗andd∗quarkmassessmallerthan288GeVat90%CL.Inthiscasecharacteristicen-ergyscaleisgivenbythemassoftheexcitedquark.Associatedcharacteristicsizeisrq∼¯h/(m∗qc)<3.5×10−17cm.