Cosmic rays and antishadowing

We note that antishadowing could help in the explanation of cosmic rays phenomena such as knee in the energetic spectrum and existence of penetrating and long-flying particles.

5

2

y

a

M

7

2

3

v

81

1

5

/

h

p

-

p

e

:hv

i

X

r

aCosmicraysandantishadowingS.M.Troshin ,N.E.TyurinInstituteforHighEnergyPhysics,Protvino,MoscowRegion,142281,RussiaAbstractWenotethatantishadowingcouldhelpintheexplanationofcosmicraysregularitiessuchaskneeintheenergeticspectrumandexistenceofpene-tratingandlong- yingparticles.PACS:13.85.Tp

We note that antishadowing could help in the explanation of cosmic rays phenomena such as knee in the energetic spectrum and existence of penetrating and long-flying particles.

Cosmicraysarethechargednucleiarrivingfromtheoutsideofthesolarsys-tem.Thecosmicraysinvestigationsareanimportantsourceofastrophysicalin-formation(cf.e.g.

[1])and

simultaneously

they

provideawindowtothefutureofacceleratorstudies1.

10-410-6

10-8

- 2- 1

dF/dlnE, cm s ster-110101010101010210410610810101012

E, GeV/particle

Figure1:Energyspectrumofthecosmicrays, gurefromthe rstreferenceof

[3].

Investigationsofcosmicraysgiveusacluethatthehadroninteractionand√mechanismofparticlegenerationischangingintheregionof

Itshouldbenotedhoweverthattheresultsforthetotalcross–sectionextractedfromcosmicraysmeasurementssigni cantlyrelyonparticularmodel,becausecosmicraysdonotprovideinformationonelasticscatteringcross–section[2]1

2

We note that antishadowing could help in the explanation of cosmic rays phenomena such as knee in the energetic spectrum and existence of penetrating and long-flying particles.

However,thereisanotherpossibilitytotreatthosecosmicraysphenomenaastheavatarsoftheantishadowscatteringmodeatsuchenergies[5].UnitarityofthescatteringmatrixSS+=1implies,inprinciple,anexistenceathighenergiess>s0,wheres0isathreshold2ofthenewscatteringmode–antishadowone.Ithasbeenrevealedin[5]anddescribedinsomedetail(cf.[6]andreferencestherein)andthemostimportantfeatureofthismodeistheself-dampingofthecontributionfromtheinelasticchannels.

Antishadowingleadstoasymptoticallydominatingroleofelasticscattering.Thecross–sectionofinelasticprocessesriseswithenergyaslns,whileelasticandtotalcross–sectionsbehaveasymptoticallyasln2s.Theantishadowscatter-ingmodecouldbede nitelyrevealedattheLHCenergiesandthephenomenaobservedinthecosmicraysstudiescon rmit.Startingatsomethresholdenergys0(whereamplitudereachestheblackdisklimitatb=0),antishadowingcanoc-curathigherenergisinthelimitedregionofimpactparametersb<R(s)(whileatlargeimpactparametersonlyshadowscatteringmodecanberealized).Notethatashadowscatteringmodecanexistwithoutantishadowing,buttheoppositeisnottrue.

η(s,b)

1/41/4η(s,b)

shadow

scatteringantishadow

scatteringshadowscattering

b=R(s)bb=R(s)b

Figure2:Impactparameterdependenceoftheinelasticoverlapfunctioninthestandardunitarizationscheme(leftpanel)andintheunitarizationschemewithantishadowing(rightpanel).

Theinelasticoverlapfunctionη(s,b)becomesperipheralwhenenergyisbeyonds=s0.Atsuchenergiestheinelasticoverlapfunctionreachesitsmaximumvalueatb=R(s)whereR(s)istheinteractionradius.So,beyondthetransitionenergy

s0 2TeV[7]

3

We note that antishadowing could help in the explanation of cosmic rays phenomena such as knee in the energetic spectrum and existence of penetrating and long-flying particles.

rangetherearetworegionsinimpactparameterspace:thecentralregionofanti-shadowscatteringatb<R(s)andtheperipheralregionofshadowscatteringatb>R(s).Theimpactparameterdependenceoftheinelasticchannelcontributionη(s,b)ats>s0arerepresentedinFig.2forthecaseofstandardunitarizationschemeandfortheunitarizationschemewithanishadowing.

Attheenergiess>s0smallimpactparameterscatteringismostlyelasticone.Thushead–oncollidingparticleswillprovideappearanceofpenetratinglong- yingcomponentintheEASandsuchparticleswillspendonlysmallpartoftheirenergyfortheproductionofsecondaries.Thehead-oncollisionswillleadtosmallernumberofsecondaryparticleanditwillprovidefasterdecreaseoftheenergyspectrumofcosmicrays,i.e.itwillresultintheappearanceoftheknee.Thisqualitativepicturewillbeexplainedinmoredetailinwhatfollows.

Antishadowingleadstosuppressionofparticleproductionatsmallimpactpa-rameters,andthemaincontributiontotheintegralmultiplicityn¯(s) ∞n¯(s,b)η(s,b)bdbn¯(s)=0

We note that antishadowing could help in the explanation of cosmic rays phenomena such as knee in the energetic spectrum and existence of penetrating and long-flying particles.

GeV.ItwasofthisadhocThegoingtoinelasticofthecosmicrayscascadesdevelopments.Itsenergydependenceisnotclearandnumberofmodelspredictthedecreasingenergydependencewhileothermodelsinsistontheincreasingenergybehaviourathighenergies(cf.e.g.[11]).Adoptingsimpleansatzofgeometricalmodelswhereparameterofinelasticityisrelatedtoinelasticoverlapfunctionwecanusethefollowingequationfor K [12]

σel K =4σtot

togetaqualitativeknowledgeontheinelasticityenergydependence.Theestima-tionofinelasticitybasedontheparticularmodelwithantishadowing[7]leadstoincreasingdependenceofinelasticitywithenergytillE 4·107GeV.Inthisre-gioninelasticityreachesmaximumvalue K =1,sinceσel/σtot=1/2andthenstartstodecreaseattheenergieswherethisratiogoesbeyondtheblackdisklimit1/2.Suchqualitativenonmonotonousenergydependenceofinelasticityisthere-sultoftransitiontotheantishadowingscatteringregime.Itisworthnotingthatthemaximumininelasticityenergydependenceiscorrelatedwiththeminimumoftherelativefractionofprotonsinthecosmicrays.

Itshouldbenotedthatthebehaviouroftheratioσel/σtotwhenitgoestounityats→∞d …… 此处隐藏：5745字，全部文档内容请下载后查看。喜欢就下载吧 ……