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).