The interplay between the electromagnetic and the muonic longitudinal profile at production

0.37 MB·English

by  Ruben Conceição

ISVHECRI2012willbesetbythepublisher
DOI:willbesetbythepublisher
(cid:13)c Ownedbytheauthors,publishedbyEDPSciences,2013
The interplay between the electromagnetic and the muonic longitudinal pro-
file at production
RubenConceição1,a,SofiaAndringa1,LorenzoCazon1,andMárioPimenta1,2
1LIP,Av.EliasGarcia,14-1,1000-149Lisboa,Portugal
2DepartamentodeFísica,IST,Av.RoviscoPais,1049-001Lisboa,Portugal
3
1
0 Abstract.Theelectromagneticandthemuoniclongitudinalprofileatproductionenclosureimportantinforma-
2
tionabouttheprimaryparticleandthehadronicinteractionsthatruletheshowerdevelopment. Infact,these

n twoprofilesprovidetwodifferentinsightsoftheshower: theelectromagneticcomponentgivesameasurement
a oftheenergyandthestrengthoftheneutralpionchannel; whilethemuonicprofile,beingintimatelyrelated
J withthechargedmesonsdecays,canbeusedasadirectprobeforthehighenergyhadronicinteractions.

3 Inthisworkweexploretheinterplaybetweentheelectromagneticandmuonicprofiles,byanalysingtheirphe-
nomenologicbehaviourfordifferentprimarymassesandenergies,zenithangles,andalsodifferenthighenergy

] hadronicinteractionmodels.Wehavefoundthatthemuoniclongitudinalprofileatproductiondisplaysuniver-
h
salfeaturessimilartowhatisknownfortheelectromagneticone. Moreover,weshowthatbothprofileshave
p
- newprimarymasscompositionvariableswhicharefairlyindependentofthehighenergyhadronicinteraction
p model.
e Finally we discuss how the information in the electromagnetic and the muonic longitudinal profile can be
h
combinedtobreakthedegeneracybetweentheprimarymasscompositionandthehighenergyhadronicphysics.
[

1
v
7 1 Introduction arefittedtotheavailableacceleratordataandextrapolated
0 severalordersofmagnitudetotheUHECRsenergies.This
5 The Ultra High Energy Cosmic Rays (UHECRs) are the impliesthatthedeterminationoftheUHECRsmasscom-
0 most energetic particles known. And yet its origin and positionislinkedtotheunderstandingoftheshowerphys-
.
1 composition remains a mystery although they were dis- icalmechanisms,inparticulartothehadronicinteractions
0 covered half a century ago. The reason for this resides descriptions.
3 on the difficultyof theirdetection. Since theirflux atthe
Muons are a fundamental tool to assess the high en-
1
highest energies is very low the only way to detect them
: ergyhadronicinteractionmodelsastheyareproducedes-
v is byobservingthehugecascadesofsecondaryparticles,
sentially from chargedmesons (secondaryproductsfrom
Xi known as Extensive Air Showers (EAS), that are created hadronic interactions). Moreover, a large fraction of the
by the interaction of these cosmic rays with the atmo-
r muonscanreachthegroundduetoalowinteractioncross-
a spheremolecules.
sectionandarelativelylargedecaytime. Recentanalyses,
TheEAScanbedetectedbysamplingthechargedpar-
thatusethemuonarrivaltime,areabletoreconstructthe
ticlesthatarriveatthegroundor,in moonlessnights,the
muonlongitudinalprofileatproductionatultrahighener-
shower longitudinal profile can be sampled through the
gies[1],providinganadditionalinsightoftheshower.
collectionofthefluorescencelightproducedastheshower
Thephenomenologicalbehaviourofthemuoniclongi-
developsintotheatmosphere.Thelattermeasurement,al-
tudinalprofileatproductionanditsrelationwiththeelec-
though with a duty cycle of around 10%, provides a di-
tromagneticshowerprofileisthemainfocusofthiswork.
rect measurementof the electromagnetic shower compo-
Moreover,we show, atthe endofthispaper,howseveral
nentdevelopment.
shower observables may be combined to disentangle the
While the arrival direction of the UHECRs can be
masscompositionfromthehadronicinteractionmodels.
easilyobtainedbytheexperimentaltechniquesaforemen-
The paper is organised as follow: in section 2 the
tioned,thedeterminationofthenatureoftheprimarypar-
muoniclongitudinalprofileatproductionispresentedand
ticle is much more difficult. In fact, the shower observ-
themainobservables,namelyX ,arediscussed. When-
ables connected to the type of particle are also sensitive max
everrelevantthefeaturesofthisprofilewillbecompared
tothephysicalinteractionsthatrulestheshowerdevelop-
to the ones found in the electromagnetic profile; In sec-
ment. Moreover, the hadronic interactions at high ener-
tion 3 we show that the muonicprofile shape exhibitsan
giesaredescribedthroughphenomenologicalmodelsthat
universal behaviour and its correlation with the shape of
ae-mail:[email protected] theelectromagneticprofileisassessed;Insection(sec.4)
ISVHECRI2012
×103
-1]g 150 ax 0.25
2 m µXm
c d
µdN [dX 100 dN/ 0.2
vt
Ne 0.15
1/
50
0.1
0 0.05
0 200 400 600 800 1000 1200
X [g cm-2]
0
400 500 600 700 800
Figure 1. Muon production shower profiles as a function of Xµ [g cm-2]
depth(X),forproton(red)andiron(blue)primariesatE =1019 max
eV.Inthispicture100showersforeachprimaryareshown,both
generatedwithQGSJet-II.03andwithθ=40◦. Figure 2. Xmµax distributions of muon production longitudinal
profilesfor different primaries andhadronic interactionmodels
- the red lines are for proton and the blue ones for iron pri-
maries. Thedistributionsgenerated withQGSJet-II areshown
we show how hadronic interaction models can be distin- asfulllineswhiletheonesgeneratedwithEPOSaredisplayed
guishindependentlyofprimarymasscompositionscenar- withdashedlines.
ios, through the combination of different shower observ-
ables. Finally,someconclusionsaredrawninsection5.
results are displayed as full lines and EPOS1.99 [7] as
dashedlines).
2 Longitudinalshowerprofiles
Aninterestingcorrelationtolookatistheonebetween
theXµ andXe.m.,inanevent-by-eventbasis. Thisprofile
To study the true1 MuonicProductionDepth profile (on- max max
isshowninFig.3forproton(inred)andiron(inblue)in-
wards referred as MPD profile) we have used Conex [3] ducedshowers,bothgeneratedwithQGSJet-II.Theelec-
simulations(formoredetailswereferthereaderto[4]).
tromagneticmaximumis reachedaround200gcm2 later
TheMPD2 profileforprotoninducedshowers(inred)
than the muonic profile maximum. On average, there is
and iron primaries (in blue) at E = 1019 eV is shown in
acorrelationbetweentheelectromagneticandthemuonic
Fig.1.Comparedtoprotonshowers,ironinitiatedshowers
X .Itdependsslightlyontheprimarymasscomposition
max
havemoremuons,whichisreadilyseenbylookingatthe
and it was checked to be nearly independentof hadronic
maximum of the profile3, Nµ . Moreover, the height of
max interactionmodels.
themaximumfluctuatesmoreforprotoninducedshowers
The difference between electromagnetic and muonic
than for iron showers. This is a distinct feature from the
X , shown as an inset plot of Fig. 3, also changes be-
electromagneticprofilethat,havingitsNe.m. relatedtothe max
max tweenprimaries−byaround30gcm2intheaveragesep-
shower energy, has essentially the same maximum value
aration−whichmeansthatalthoughrelated,thetwopro-
for both proton and iron shower, whereas the fluctuation
files give some independent information. This quantity,
levelisoftheorderof5%. Xe.m.−Xµ , is veryinterestingas itis byconstructionin-
max max
The second featureworth noticingis the depthof the
dependentofthefirstinteractionpoint,whichmeansthat
shower maximum, Xmµax, and the corresponding distribu- itshouldnotbeaffectedbysuddenchangesintheprimary
tionwhichcanbeseeninmoredetailinFig.2. Hereone
cross-sectionassuggestedin[8].
can see that the behaviour of this observable follows the
onefoundintheelectromagneticprofile.TheXµ ofpro-
max
toninducedshowersaredeeperandfluctuatemorethanin 3 Universality of the longitudinalprofile
ironshowers. Thisobservableissensitivetobothprimary shape
masscompositionandhadronicinteractionphysics,being
thedifferencebetweenprotonandironbiggerthanthedif- InFig.4theprofilesshowninFig.1areexpressedinX′ ≡
ferencefordifferenthadronicmodels(QGSJet-II.03[5,6] X − X and N′ ≡ N/N . In these variables one can
max max
seethattheobtainedshapeisratheruniversal,similarlyto
1theexperimentsmeasuretheapparent-MPD,whichdependsonthe whathappenstotheelectromagneticprofile.
pointofobservation, asthetruedistribution hastobeconvoluted with
Takingadvantageofthisuniversalityitcanbeusefulto
themuonspropagation.Byitsturn,themuonpropagationdependsofthe
distancetravelledbythemuons,theirenergy,amongothers. Thetrans- usetheaverageshapeinordertodeterminethetwomain
formationoftheapparent-MPDintothetrue-MPDisdescribedin[2]. parameters from a fit with a reduced set of data. More-
2notethatinConexthereisanenergythresholdformuonsof1GeV.
over,therecanbeextrainformationontheaverageshape
3inthispapertheindexµande.m.willbeusedtoaddress tovari-
similartowhathappensintheelectromagneticprofile[9].
ablesrelated withtheMPDprofileandtheelectromagnetic profile, re-
spectively. In fact, it was found that iron showers have a broader
ISVHECRI2012
2] N’ 1
-g cm800 dN/dx1/Nevt0.2 RLRL µµ 00 22..4466225588..7711
[

x
µ ma700 0.1 0.5 RR ee ..mm 00....22777755
X LL 223333..33
0
180 200220 240 260 280
Xme.amx.-Xmµax [g cm-2]
600
0
-400 -200 0 200 400 600 800 1000
500 X’ [g cm-2]
Figure5. Average shower profilesfor proton primariesatE =
400 1019 eV, with QGSJet-II, in (X′,N′) coordinates. Comparison
600 700 800 900 betweenelectromagnetic(inred)andmuonic(inblue)shapefea-
Xe.m. [g cm-2] tures.ThelinescorrespondtofitsusingaGaisser-Hillasfunction
max
(2parameters). Thefitresultsaregivenintheplotfortheelec-
tromagnetic(e.m.)andmuonic(µ)profiles.
Figure3. Relationbetweenmuonproduction Xµ andelectro-
max
magneticXe.m.,forE=1019eVshowers.Thedifferencebetween
max
thetwoX areshownintheinsetplots.Thedependenceonpri-
max
marymassisshown(protonisthered(full)lineandirontheblue
(dashed)line,bothgeneratedwithQGSJet-II). m.
e.
R
0.3
µNX 0.2
dd 1
1 µNmax
0.1
0.5 0
260 280
Lµ [g cm-2]
0
-600 -400 -200 0 200 400 600
X - Xµ [g cm-2]
max Figure6.Correlationbetweentheelectromagneticprofileshape
(characterized by Re.m.) and the muon production profile shape
Figure 4. Muon production shower profiles from proton (red)
(representedbyLµ). Theresultsareshownforproton(red/full)
and iron (blue) primaries, in (X′,N′) coordinates. The same
andiron(blue/dashed)inducedshowers,atE=1019eV,andwith
showersusedtobuildFig.1areusedhere. QGSJet-II.Theshadedareashowstheregionwithinonesigma.
halfmeanwidthandtheriseoftheprofilehappensfaster
magnetic profile. In fact, it is worth noting that the full
thanforprotoninducedshowers. Theimpactofdifferent
profiledescriptionisbetterachievedfortheMPDprofile.
hadronicinteractionmodelsintheshapewasfoundtobe
Thisisdueto the factthatthe energydepositprofile(the
verysmall[4].
profilethatisseenbythefluorescencedetectorandisin-
Thisquasi-universalshapeiscomparedtotheelectro-
timately related with the electromagneticshower compo-
magneticshapein Fig.5. TheMPD profilehasa steeper
nent)containsintheend-tailanon-negligiblecontribution
growthandismoreasymmetric,withrespecttotheshower
from muonsthat is not accountedby the Gaisser−Hillas.
maximum.BothprofileswerefittedwithaGaisser−Hillas
Nevertheless, it is interesting to note that both distribu-
function, written in terms of a Gaussian width L and a
tions,havingdifferentdevelopmentmechanisms,sharethe
parameter R, which is related with the asymmetry of the
samekindofstructure.
showerwithrespecttotheshowermaximum[9],suchthat,
Throughthe study of the shape parameters (R,L) we
RX′ R−2 X′ were able to conclude that, similarly to what happened
N′ = 1+ exp − . (1) with the electromagnetic profile, one of the parameters
L ! LR!
retains almost all information on the type of primary al-
We conclude that the MPD profile can be well de- lowing the other one to be fixed. However, while in the
scribed with the same function as used for the electro- e.m. caseitwasLe.m. that,beingrelatedtotheshoweren-
ISVHECRI2012
ergy,couldbefixed,intheMPDprofileitisLµthatshows
×106
more capabilities to distinguish between proton and iron
〉
µ
induced showers. Note that Lµ is proportionalto the in- N
〈 Fe
tegraloftheMPDprofilewhichattainsinformationabout 40
thetotalnumberofmuonsproducedduringtheshowerde-
N
velopment. 35 EPOS1.99
Having a single shape variable to characterise each He
profile, Lµ and Re.m., the correlation between the shape
30 p
oftheMPDandtheelectromagneticprofilecanbeeasily
drawn. The relation between the shapes of the two pro-
QGSJet-II.03
filesforeachindividualeventcanbeseeninfig. 6. Here, 25
(Le.m.,Rµ) were fixed to its correspondingaverage values SIBYLL2.1
of the combined proton and iron distributions. The cor- 20
700 750 800
relation is rather strong in the most populated region of
〈Xe.m.〉
(Re.m.,Lµ). Moreover,itis almostindependentofthe pri- max
marymasscomposition,makingitveryusefulforhybrid
analysis. Indeed,wheneveroneoftheprofilesismeasured Figure7.Averagenumberofmuonsversusaverageelectromag-
neticXe.m.forE=1019eVshowers.Eachsinglepointintheplot
accurately a prediction of the other profile shape can be max
representsaprimarymasscompositionscenario. Theresultsare
established allowing, in this way to perform consistency
shown for three distinct hadronic interaction models: QGSJet-
teststotheshowerdescription.
II.03(inblack); EPOS1.99(inred) andSIBYLL2.1(ingreen).
ForEPOSthepuremasscompositionscenariosaremarkedwith
blackcrossesandthelabelbelowidentifiesthespecie.
4 Constraining Hadronic Interaction
Models
The most interesting feature of this plot is that while
Finally, in this section we want to pointout some strate-
the problem is degenerate when N and Xe.m. are in-
gies on how to disentangle the mass composition from µ max
the hadronic interaction models uncertainty. For this, it terpretedalone, here the hadronicDintEeractio(cid:10)nmo(cid:11)delscan
be distinguished independentlyof any mass composition
isusefultointroducethetwo-dimensionalplotswherethe
scenario,provided,ofcourse,thattheexperimentalresolu-
twofirstmomentaofXe.m.distribution,namely Xe.m. and
max max tionsarebetterthantheseparationbetweenmodels.More-
RMS(Xme.amx.), are plotted for each mass compo(cid:10)sition(cid:11)sce- over,thesekindofanalysesareimportanttoconstrainthe
narioatafixedenergy[10,11]. Inthesekindofplotseach
allowed phase space for hadronicinteractionmodels, in-
pointrepresentsapossiblescenarioandbyconsideringthe
creasinginthiswayourknowledgeabouttheshower.
possible primary mass combinations we are, in a sense,
probing the phase space for a given hadronic interaction
model. 5 Conclusions
Here, we want to extend this concept and combine
twoobservables,thataresensitivetoboththehadronicin- The muon production longitudinal profile of air showers
teraction models and primary mass composition: the av- givesnewprimarymasscompositionvariableswhichare
erage total number of muons produced in the shower4, fairlyindependentofthehighenergyhadronicinteraction
N , and the average electromagneticshower maximum model: the Xµ andtheshapevariableLµ. Thenormali-
µ max
dDeptEh, Xe.m. . The resulting plot is shown in Fig. 7 for sation ofthe profilegivesalso access to thetotal number
max
three di(cid:10)stinct(cid:11)hadronic interaction models: QGSJet-II.03 of produced muons, which is known to be an important
(in black); EPOS1.99 (in red) and SIBYLL2.1 [12] (in variable, both for primary composition and high energy
green). Letusnowevaluatetheresultsofasinglemodel, hadronicinteractionmodelstudies.
namely EPOS. The most extreme point at the left repre- The MPD profile can be described using the param-
sentsascenariowithpureironasmasscomposition,while eterisation that is used for the electromagnetic profile.
thepointattherightisforascenariowherethereareonly Moreover,itsshapedisplaysanuniversalbehaviourwhen
protons. The pure helium and nitrogen scenario are also expressedintermsofX′andN′.
markedforthecaseofEPOS.Theremainingreddotsare Combining the information of the muonic longitudi-
the results for bimodal mass composition scenario from nal profile at productionwith the electromagneticprofile
one pure element to another. Inside of this contour are willgiverisetoextravariables,sensitivetotheshowerde-
alltheremainingcomplexmasscompositioncombination velopmentcharacteristics. Thesewillleadtoamorepre-
amongstthefourspecies:p,He,N,Fe. cise understanding of the shower development. In fact,
we have shownthat alreadysome constrainson hadronic
4thisquantityisobtainedperformingtheintegraloftheMPDprofile interaction models can be applied, independently of any
uptothemaximum. Inthisway,weobtainaquantitywhichispropor- mass composition scenarios, through the combination of
tional tothetotal numberofmuonsintheshowerwithoutanyground
the average electromagneticshower maximumdepth and
effects. Forafixedzenithanglethenumberofmuonsatgroundgives
similarresults. theaveragenumberofmuonsproducedintheshower.
ISVHECRI2012
Withthehighernumberofavailableobservables,using [3] T.Bergmannetal.,Astropart.Phys.26,420(2007),
profileswhichareindependentofthedetectionconditions astro-ph/0606564
andmoredirectlyrelatedtothehadroniccascade,cosmic [4] S. Andringa, L. Cazon, R. Conceição, M. Pimenta,
rays become increasingly useful for the study of particle Astropart.Phys.35,821(2012),1111.1424
physicsatthehighestenergies. [5] S. Ostapchenko, Phys.Rev. D74, 014026 (2006),
hep-ph/0505259
Acknowledgments [6] S. Ostapchenko, Phys.Lett. B636, 40 (2006),
hep-ph/0602139
WewouldliketothankJ.Alvarez-Muñizforcarefulread-
[7] K. Werner, F.M. Liu, T. Pierog, Phys.Rev. C74,
ingthemanuscript. ThisworkispartiallyfundedbyFun-
044902(2006),hep-ph/0506232
daçãoparaaCiênciaeTecnologia(CERN/FP11633/2010
[8] R. Conceição, J. Dias de Deus, M. Pimenta,
and SFRH/BPD/73270/2010), and fundings of MCTES
Nucl.Phys.A888,58(2012),1107.0912
throughPOPH-QREN-Tipologia4.2,Portugal,andEuro-
[9] S. Andringa, R. Conceição, M. Pimenta, As-
peanSocialFund.
tropart.Phys.34,360(2011)
[10] J.Linsley,Proc.19thICRC6,1(1985)
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