Testing Mass Varying Neutrino With Short Gamma Ray Burst(3)

In this paper we study the possibility of probing for the absolute neutrino mass and its variation with short Gamma Ray Burst (GRB). We have calculated the flight time difference between a massive neutrino and a photon in two different approaches to mass v

wherem0andQ0aretheneutrinomassandthevalueofQuintessenceatpresenttime,andMplisthePlankscale.Nowtheformulaforthetime-delayisgivenby

t1d=p)21M2pl)

t0

(1+β

Q

tQ

˙23

(ρB+

3

inradiation-dominatedandωB=0in

thematter-dominatedUniverse.

Foranumericalstudy,weconsideramodelofQuintessencewithainversepower-lawpotential[25],

V=V0Q α.

(13)

Thistypeofmodelisshown[25,26]tohavethepropertyoftrackingbehavior.Inthecalculationwetakeα=0.5whichgivesrisetoωQ0< 0.78constrainedbytheWMAP.InFig.3weplotthenumericalvalueoftd.FromFig.3onecanseethetimedelaytdisenhanced

t

z=3

z=0.17

m/p

FIG.3:Plotoftd(unitinsecond)asafunctionof

m0

p

)2～10 7,andβ= 3,tdcan

reach1624secondsatz=3.Forcomparisonaconstantneutrinomassβ=0reducestdto1075seconds.

Forthecaseofhierarchicalneutrinomasspatter,theheavyneutrinomasssetbytheatmosphareneutrinoos-cillationism～0.05eV.Withthisvalueonecanseefrom

3

Fig.3thattdisonly0.5secondsfortheconstant-mass

neutrinoswithenergyp=12Mevandredshiftz=3.ThisvalueismuchsmallerthantheshortGRBdurationandwillbedi culttobeobservable.Iftheneutrinomassvaries,asshowninFig.3tdwillbeenhancedsubstan-tially.NumericallyFig.3showsthattdcanbeincreasedto3seconds.

CertainlytheresultsshowninFig.3dependsontheQuintessencemodel.Foranillustration,weconsideranotherQuintessencemodel

V=V0exp(

λ

p

.The

threecurvescorrespondtoparametersβ=0(solid),-2(dash),10(dot)respectivelyforagivenredshift.

Insummarywehaveinthispaperdiscussedthepossi-bilityofusingtheShortGRBtoprobefortheabsoluteneutrinomassesanditsvariation.Byadetailedcalcu-lationwehaveshownthatwiththecurrentcosmologicallimitsonthedegeneratedneutrinomassesthetimedelaytdwillbeingenerallongerthanthetimeoftheduration,furthermorethechangestothetdcausedbythevariationoftheneutrinomassesarealsoexpectedtobelargerthanthetimeoftheduration.Ourresultsindicatethepossi-bilityoftestingthescenarioofmassvaryingneutrinointhefutureneutrinotelescope.

Acknowledgments:WeareindebtedtoDrs.MinzheLi,BoFengandXiaojunBiforenlighteningdiscussionsandProfs.RobertoPeccei,SandipPakvasaandDr.HeinrichPaesforreadingthemanuscript.WethankDr.NanLiangforhelpfuldiscussionsonGRBs.ThisworkwassupportedinpartbyNationalNaturalScienceFoundationofChina(grantNos.90303004,19925523,10233010and10221001)andbyMinistryofScienceandTechnologyofChina(underGrantNo.NKBRSFG19990754).