Cosmological Constraints on Unparticles

arXiv:0709.2350v2[hep-ph]16Apr2008CosmologicalConstraintsonUnparticlesJohnMcDonald1CosmologyandAstroparticlePhysicsGroup,UniversityofLancaster,LancasterLA14YB,UKApril16,2008AbstractWestudythecosmologicalconstraintsonunparticleinteractionsandthetemperatureoftheUniverseforanunparticlesectorwithdimensionaltransmu-tationscaleΛU∼1TeV.ByconsideringthermalbackgroundquarkdecaytounparticlesviaascalaroperatorofdimensiondU,weshowthattheconditionthattheUniverseisnotdominatedbyunparticlesatnucleosynthesisimposesalowerboundonthescaleoftheinteractionoftheunparticlesector,withMU∼20−2600TeVfor1.1≤dU≤2.0and2≤dBZ≤4.TheexistenceofanunparticlesectoralsoimposesanupperboundonthetemperatureoftheUniverseduringradiation-domination,[e-mail]11IntroductionRecentlytherehasbeenmuchinterestinthepossibleexistenceofaconformally-invarianthiddensectorconsistingof’unparticles’[1,2]1;see[4-11].Inthispic-ture,theconformally-invariantunparticlesectorisgeneratednon-perturbativelyfromaBanks-Zaks(BZ)sectorconsistingofvector-likenon-Abeliangaugefieldsandmass-lessfermions[14],whichareassumedtointeractveryweaklywiththeSMsectorviaoperatorssuppressedbyamassscaleMU.TheBZsectorundergoesdimensionaltrans-mutationtotheunparticlephase,correspondingtoastronglyself-coupledconformalfieldtheory(CFT),belowaninfra-redfixedpointenergyΛU.ThisunparticlephasehasnoparticledescriptionbutinteractswiththeSMviaunparticleoperatorsofmassdimensiondU,whichcreatestatesmadeoftheconformalfields.Theremarkablechar-acteristicofunparticlesisthatthephasespaceindecayprocessestounparticlestuffisthesameasthephasespacefordecaytodUmasslessparticles,wheredUcanbenon-integral.Thiscouldprovideadistinctivesignalforunparticleproductionincol-liderexperimentsinthecasewheretheunparticledescriptionisvalidatfuturecolliderenergies,correspondingtoΛU∼1TeV.ThecouplingsoftheunparticleoperatorsandthevalueofdUwilldependontheunderlyingBZoperatorsandtheinfra-reddynamicsofdimensionaltransmutation.Sincethesearemodel-dependent,moststudiesofunparticlephysicshaveintroducedseveralpossibleunparticleoperatorswithunknowncoefficientsandinvestigatedtheirconsequences.Underreasonableassumptionsregardingtheunknowns,themassscaleMUcanthenbeconstrainedbytherequirementthattheunparticlesectordoesnotconflictwithpresentphenomenological[4],astrophysical[5],long-rangeforce[6]andcosmological[8]observations.HereweconsidertheeffectofanunparticlesectoronthecosmologyoftheSMandtheresultingconstraintsonunparticleinteractionsandthetemperatureoftheUni-verse.TodothiswecalculatethedecayandannihilationratesofthermalbackgroundSMquarkstounparticles.Forclarity,wefocusonaspecificinteractionbetweenSM1Similarideaswereproposedearlierin[3].1quarksandascalarunparticleoperator,leavingamoregeneraloperatoranalysisforfuturework.Thearticleisorganisedasfollows.InSection2wereviewunparticlesandtheirinterpretationintermsofdeconstructingscalars.Wealsorelatethesescalarstoaphysicalinterpretationoftheunparticlestates.InSection3wecalculatethedecayandpairannihilationratesofthermalSMquarkstounparticlesandderiveboundsfromrequiringthattheunparticleenergydensitydoesnotdisturbnucleosynthesis.InSection4wepresentourconclusions.2TheModelTheunparticlemodel[1,2]isbasedonaninteractionbetweenBanks-Zaks(BZ)fieldsandSMfieldsmediatedbyexchangeofheavyparticlesofmassMU1MkUOSMOBZ.(1)OBZisanoperatorwithmassdimensiondBZmadeoutofBZfields.AtanenergyscaleslessthanΛUtheBZsectorundergoesdimensionaltransmutationandascale-invariantunparticlesector,correspondingtoastronglyself-coupledCFT,isformed.TheBZoperatorsmatchontounparticleoperatorsandEq.(1)becomesCUΛdBZ−dUUMkUOSMOU,(2)wheredUisthescalingdimensionoftheunparticleoperatorsOU.ThevalueofCUanddUwillbedeterminedbytheinfra-reddynamicsoftheBanks-ZaksfieldsandtheformofOBZ.Thesewillbeconsideredasfreeparametersinthefollowing.TostudyhowtheunparticlesectorinfluencesthecosmologyoftheSM,wefocusonaspecificinteractionbetweenSMquarksandascalarunparticleoperatorOU[1],iλΛdUUqγμ(1−γ5)q′∂μOU+h.c..(3)Hereλ≡CU(ΛU/MU)dBZisadimensionlesscoupling.2Ausefulconceptualframeworkforunderstandingtheunparticlesectorwaspre-sentedin[9].Itwasshownthatbybreakingscale-invarianceinacontrolledway,thecontinuousenergyspectrumoftheunparticlesectorcanbereplacedbyadiscretetowerofdeconstructingscalarparticlesφnofmassMn,withmassspacingcontrolledbyamassparameterΔsuchthatM2n=nΔ2.InthiscasetheunparticleoperatorOUisreplacedbyasumovercanonicallynormalizeddeconstructingscalarfieldsφn,∞Xn=1iλFnΛdUUqγμ(1−γ5)q′∂μφn+h.c.,(4)whereF2n=AdU2πΔ2(M2n)dU−2andAdU=16π5/2(2π)2dUΓ(dU+1/2)Γ(dU−1)Γ(2dU).AdUisaconventionallychosenphasespacefactorforunparticles[1];onlythecombi-nationCUA2dUappearsinphysicalprocesses.InthelimitΔ→0,thesumoverdecaysq′→q+φnforallkinematicallyallowedvaluesofnproducesanexpressionfordΓ/dEqinagreementwiththedirectunparticlecalculationofq′→q+UbasedonOU[9].Theindividualq+φnfinalstatesofenergyEq=(m2q′−M2n)/2mq′mergeintoacontinuumdecayrateasafunctionofEqasΔ→0,reproducingtheunparticleresult.Howshouldtheunparticlesbeinterpretedphysically?In[10]