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Measurement of the proton air cross section using hybrid data of the Pierre Auger Observatory [Elektronische Ressource] / von Ralf Matthias Ulrich

162 pages
Measurementoftheproton-aircrosssectionusinghybriddataofthePierreAugerObservatoryZurErlangungdesakademischenGradeseinesDOKTORSDERNATURWISSENSCHAFTENvonderFakulta¨tfu¨rPhysikderUniversita¨t(TH)KarlsruhegenehmigteDISSERTATIONvonDipl.-Phys. RalfMatthiasUlrichausBasel(Schweiz)Tagdermu¨ndlichenPru¨fung: 21.12.2007Referent: Prof. J.Blu¨merKorreferent: Prof. G.QuastALT XEAbstractThe subject of this thesis is the measurement of the proton-air cross section at ultra highenergy with hybrid data of the Pierre Auger Observatory. Based on a critical review of theshortcomings of previous air shower measurements, a new analysis method is developed.Thisanalysis methodtakesintoaccount themostimportantandrelevantexperimentalandair shower physics effects. The impact of a changed cross section extrapolation on the re-sulting air shower development is considered in addition to its more obvious effect on thedistributionofshowerstartingpoints. Furthermore,detectoracceptanceeffectsareexplicitlyincludedinthereconstructionansatz,whichallowsustousealmostthecompletedatasetintheanalysis. Systematicuncertaintiesontheresultingcrosssectionsarethoroughlystudiedand quantified. Assuming a proton dominated composition, the analysis is applied to hy-briddataofthePierreAugerObservatory. Theobtainedcrosssectionis,withinthestatisticalandsystematicuncertainties,inagreementwithpredictionsfromhadronicinteractionmod-18.4elsupto10 eV.Athigherenergiestheresultingcrosssectionincreasesrapidly.
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Measurementoftheproton-aircrosssection
usinghybriddataofthe
PierreAugerObservatory
ZurErlangungdesakademischenGradeseines
DOKTORSDERNATURWISSENSCHAFTEN
vonderFakulta¨tfu¨rPhysikderUniversita¨t(TH)
Karlsruhe
genehmigte
DISSERTATION
vonDipl.-Phys. RalfMatthiasUlrich
ausBasel(Schweiz)
Tagdermu¨ndlichenPru¨fung: 21.12.2007
Referent: Prof. J.Blu¨mer
Korreferent: Prof. G.QuastALT XEAbstract
The subject of this thesis is the measurement of the proton-air cross section at ultra high
energy with hybrid data of the Pierre Auger Observatory. Based on a critical review of the
shortcomings of previous air shower measurements, a new analysis method is developed.
Thisanalysis methodtakesintoaccount themostimportantandrelevantexperimentaland
air shower physics effects. The impact of a changed cross section extrapolation on the re-
sulting air shower development is considered in addition to its more obvious effect on the
distributionofshowerstartingpoints. Furthermore,detectoracceptanceeffectsareexplicitly
includedinthereconstructionansatz,whichallowsustousealmostthecompletedatasetin
theanalysis. Systematicuncertaintiesontheresultingcrosssectionsarethoroughlystudied
and quantified. Assuming a proton dominated composition, the analysis is applied to hy-
briddataofthePierreAugerObservatory. Theobtainedcrosssectionis,withinthestatistical
andsystematicuncertainties,inagreementwithpredictionsfromhadronicinteractionmod-
18.4elsupto10 eV.Athigherenergiestheresultingcrosssectionincreasesrapidly. Finallythe
proton-air cross section is converted to a proton-proton cross section using Glauber theory
andlimitsontheelasticscatteringslopearederived.
Bestimmung des Wechselwirkungsquerschnittes von Protonen mit Luft mittels
Hybrid-DatendesPierreAugerObservatoriums
In dieser Arbeit werden Hybrid-Daten des Pierre Auger Observatoriums verwendet, um
den Wechselwirkungsquerschnitt von Protonen mit Kernen der Luft bei ultra-hoher En-
ergiezubestimmen. BasierendaufeinerAnalysederSchwachpunktefru¨hererLuftschauer-
Messmethodenwirdein neuerRekonstruktionsansatzentwickelt. Dieserberu¨cksichtigtex-
plizit diewichtigstenexperimentellensowiephysikalischenEffekte. DerEinflusseinerver-
a¨ndertenExtrapolationdesWechselwirkungsquerschnittesaufdieLuftschauer-Entwicklung
wirdebensoberu¨cksichtigtwiederEinflussaufdieVerteilungderLuftschauer-Startpunkte.
Daru¨ber hinaus wird die Akzeptanz des Detektors direkt in der Rekonstruktionsmethode
beru¨cksichtigt, wodurch fast der komplette Datensatz fu¨r die Analyse verwendet werden
kann. SystematischeUnsicherheitendesresultierendenWechselwirkungsquerschnitteswer-
denim Detailuntersuchtundquantifiziert. Die Hybrid-DatendesPierreAugerObservato-
riums werden unter der Annahme einer proton-dominierten Zusammensetzung der kos-
mischenStrahlunganalysiert. DerresultierendeWechselwirkungsquerschnittist,innerhalb
18.4der statistischen und systematischenUnsicherheiten, bis zu einer Energie von 10 eV mit
denVorhersagenvonhadronischenWechselwirkungsmodellenkompatibel. Beiho¨hererEn-
ergie nehmen die resultierendenWechselwirkungsquerschnittejedoch sehr schnell zu. Ab-
schliessendwird derProton-Luft-WechselwirkungsquerschnittmittelsderGlauber-Theorie
indenProton-Proton-WechselwirkungsquerschnittkonvertiertundeswerdenEinschra¨nkun-
gendesSteigungsparametersderelastischenStreuungabgeleitet.
iiiContents
1 Introduction 1
2 Cosmicrays,extensiveairshowersandhighenergyhadronicinteractions 3
2.1 Overviewofcosmicrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Extensiveairshowerphenomenology . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Hadronicinteractionmodels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Low-energymodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 High-energymodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Proton-aircrosssectionmeasurementsusingcosmicraydata . . . . . . . . . . 26
2.7 Glaubertheoryandproton-protoncrosssection . . . . . . . . . . . . . . . . . 35
3 PierreAugerObservatory 41
3.1 Experimentalsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
line3.2 Off softwareframework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Hybrideventreconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Hybriddetectorsimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Anovelmethodtoderivetheproton-aircrosssection 73
4.1 Motivationof X asobservable . . . . . . . . . . . . . . . . . . . . . . . . . . 73max
4.2 Impactofmasscompositionandhadronicinteractionfeaturesonairshowers 74
4.3 ParameterizationoftheX -distribution . . . . . . . . . . . . . . . . . . . . . 84max
4.4 ShowerdevelopmentandtheΔX -distribution . . . . . . . . . . . . . . . . . . 861
4.5 Invisiblecrosssection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Fittingrangeandstability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.7 Comparisontopreviousmeasurementstechniques. . . . . . . . . . . . . . . . 95
4.8 Primarycomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5 Dataanalysis 101
5.1 Hybriddataselectionandqualitycuts . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Hybrid X -resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104max
5.3 Detectoracceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4 Protonhypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Proton-aircrosssection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.6 Systematicuncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.7 Discussionoftheresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6 Summary 131
References 135
Appendix 143
A Fasthybridsimulations 143
iiiB ΔX-parameterizations 148
B.1 Energydependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
B.2 Crosssectiondependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
C Fitsofthecross-sectionanalysis 154
C.1 AnalysisbasedonSIBYLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
C.2 AnalysisbasedonQGSJET01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
iv1 Introduction
In the early years, elementary particle physics began with the observation of cosmic rays
and cosmic ray induced air showers. Many discoveries are directly linked to the analysis
of cosmic ray interactions, like the finding of positrons [1], muons [2] and pions [3, 4, 5].
Following these early discoveries based on cosmic rays, accelerators were built for preci-
sionstudies. Thiswasleadingtohugeachievementsinunderstandingfundamentalparticle
physicsandtotheformulationoftheextremelysuccessfulstandardmodelofelementarypar-
ticlephysics. Allphysicssofardiscoveredatacceleratorscanbedescribedverywellwithin
thisframework(forexample [6,7]). Mainly thedifficulty tounifythecouplingconstantsof
allelementaryforcesathighenergyandthegeneralproblemtodescribegravityaretheory-
motivated arguments that require physics beyond the standard model. Again, it is only
astro- and astroparticle physics, which are currently providing experimental evidence for
theexistenceofsuchphysics. Namely,theobservationofthenon-vanishingmassofneutri-
nos[8,9]andtherequiredexistenceofdarkmatter[10].
Furthermore man-made accelerators are limited in their maximum energy, on the other
hand astroparticle physics can provide observations of the most extreme environments in
theuniverseandevenprobeultra-highenergyphysicsdirectly. Forexample,theextragalac-
ticpropagationofcosmicraysatultra-high energiesissensitivetoviolations oftheLorentz
invariance of space-time [11, 12] as well as new particle physics. Moreover, by the obser-
vation of the highest energy cosmic rays it is also possible to study hadronic interactions
directlyatenergiesfarlarger,thananyEarth-basedacceleratorisabletoreach.
With the Pierre Auger Observatory there is the first time a detectoravailable, which al-
lowsustodohighprecisionstudiesofcosmicraysatultra-highenergies[13]. Thisismainly
duetothehybriddetectordesign,combiningagroundbasedairshowerarraywiththedata
of telescopedetectors,which observetheshowerdevelopmentwithin theatmosphere. The
2enormous size of the Auger detectorof more than 3000km allows us to gather high event
statisticsalreadyafterthefirstfewyearsofoperationdespiteof theextremelysmallcosmic
ray flux at these energies. This is ideal for studying cosmic ray properties like their origin,
butalsotostudyhadronicinteractionsatultra-highenergies.
The aim of this thesis is the first measurement of the proton-air cross section based on
thehybriddataofthePierreAugerObservatorycollectedsofar.
As a starting point methodical studies of previous attempts to measure the proton-air
cross section using air shower data are studied, unveiling the common scheme, on which
they are all founded on. The principal shortcoming, which is inherent to all of them, is
pointedout.
Basedonthesefundamentalstudiesanovelmethodtoderivetheproton-aircrosssection
from air showerdatais developed. Compared topreviousmethodstomeasuretheproton-
aircrosssection,twomainimprovementsaretobepointedout. Firstly,notonlytheobvious
exponential dependence of the fluctuation of the shower starting point from the cross sec-
tionareconsidered,butalsotheequallyimportantimpactofachangingcrosssectiononthe
subsequent air shower development. Secondly, the acceptance of the detection and recon-
structionprocessisstudiedcarefullyandisincorporateddirectlywithinthepresentedcross
sectionanalysis.
1This could only be achieved by developing a detailed detector simulation for hybrid
events that allows us to study the impact of the detection and reconstruction process on
the final observables. Special attentionis paid to enhance the generalunderstandingof the
Augerdetectorandtoimprovethereconstructionalgorithms,withanemphasisontheprop-
agationofuncertaintiesintothefinallyusedquantities.
The fundamental necessity to utilize Monte Carlo simulations to relate any air shower
based observation to properties of the primary cosmic ray particle introduces an inherent
model-dependence. The new method to measure the proton-air cross section developed
in this thesis fully accounts for the existing model-dependence and reduces it as much as
possible. Estimates of the systematic uncertainties induced by the model-dependence are
presented,whichapplyalsotootherairshowerbasedcross-sectionmeasurements.
Othergeneralsourcesofsystematicuncertaintiesarethoroughlystudied. Firstandfore-
most this is the unknown mass composition of cosmic rays at ultra-high energies. This in-
cludestheimpactofapossiblecontributionofveryhighenergygamma-rays.
After application of the new method to the data of the Pierre Auger Observatory and
the extraction of the proton-air cross section at ultra-high energy, the results are converted
intopredictionsforthecorrespondingproton-protoncrosssectionbyutilizing Glauber the-
ory. The implications of the measurement, for example, on the expected interaction char-
acteristics at the LHC, but also on the interpretation of cosmic ray data in terms of mass
compositionarediscussed.
22 Cosmicrays,extensiveairshowersandhighenergyhadronicin-
teractions
2.1 Overviewofcosmicrays
Afteralmost100yearsofresearchcosmicrayphysicsisremainingtobeanexcitingfieldand
thecurrentactivityisprobablylargerthaneverbefore[14]. Recenthighqualityobservations
are uncovering more and more of the mysteries associated to the existence of cosmic rays.
It seems very likely that cosmic rays up to the highest energies will fit seamlessly into the
framework of astro and particle physics. This implies important improvements in under-
standing our cosmic environment as well as ultra-high energy interactions during the next
years. SincethesecosmicraysareparticleswithmacroscopicenergiesofuptoseveralJoules
(16EeV∼1J),thiswillbeamajorstepforparticlephysics.
Thecurrentlyfavoredtheoriestoexplainthephenomenaofcosmicraysarefoundedon
the assumption of charged particle acceleration at collisionless magnetic shock fronts and
the propagation as well as confinement of charged particles within the galactic and extra-
Equivalent c.m. energy s [GeV]pp
2 3 4 510 10 10 10
HiRes IIATIC KASCADE (SIBYLL 2.1)
34 PROTON Fly’s eye stereoKASCADE-Grande (prel.)10
RUNJOB Auger 2007
3310
3210
fixed target (p-A)
HERA ( -p) LHC
RHIC (p-p)
Tevatron
3110
12 13 14 15 16 17 18 19 2010 10 10 10 10 10 10 10 10
Energy [eV/particle]
Figure 2.1: Cosmic ray energy spectrum as measured by many experiments over a wide range in
2.7energy[15,16,17,18,19,20,21]. Theenergyspectrumismultipliedby E toremovetheenormous
slope over∼15 orders in magnitude of the flux. In this representation the structures of the energy
spectrumcanbeseenveryclear: thekneeatseveralPeV,theanklearound∼3EeVandthecutoff above
∼50EeV.WhiletheloweraxisreflectstheenergyoftheprimarycosmicraynucleiE ,theupperaxislab
denotes the corresponding center-of-mass energy per nucleon. Some typical energies, which can be
accessedbyaccelerators,areemphasized.
3
g
2.7 -2 1.7
-1 -1
Scaled flux E J(E) [m sec sr eV ]Fe4 BLANCA HEGRA (Airobicc)
CACTI Mt. Lian Wang
DICE SPASE/VULCAN3.5
Fly's Eye ? Tunka-25
Haverah Park Yakutsk Mg
3 HiRes/MIA
?HiRes
N
?2.5
? ?? Be? ??2 ? ? ?? ? ?? ??
1.5
He
1
direct: JACEE
0.5 RUNJOB
H0
CASA-MIA direct: JACEE Fe4
Chacaltaya RUNJOB
EAS-TOP + MACRO
3.5 EAS-TOP (e/m)
HEGRA (CRT) Mg
? SPASE/AMANDA3
?
? N
2.5
Be?
?2 ? ?
1.5
He
1
KASCADE (nn)
KASCADE (h/m
0.5 KASCADE (e/m) QGSJET
KASCADE (e/m) SIBYLL
H0
4 5 6 7 8 9 10
10 10 10 10 10 10 10
Energy E [GeV]
0
Figure2.2: Meanlogarithmic massofthe primarycosmic raycomposition asderivedfromobserva-
tionsoftheshowermaximum(toppanel)orofelectrons,muonsandhadronsatgroundlevel(bottom
panel). Directmeasurementsareincludedinbothplots. Forthereferencessee[22].
galacticenvironment. Thestochasticnatureoftheaccelerationandpropagationprocessesis
generatingthepower-law-likeshapeoftheenergyspectrumasitisobservedonEarth,start-
ingfromthesolarmodulationcutoffat∼GeVuptothehighenergycutoffaround∼ 50EeV.
2.7Figure 2.1 showsthe cosmic ray particle flux, multiplied by E in order to compensatefor
the enormous steepness of the spectrum. Several distinct features of the energy spectrum
are instantly visible, commonly associated by the eye-catching analogy to the anatomy of
a human leg. In addition, Figure 2.2 summarizes the available data on the mass composi-
tionofthehighenergycosmicrayfluxarrivingatEarth. Theuncertaintiesintheassociated
analysesarebecominglargerwithincreasingenergyandthereforetherearelargesystematic
errorsassociatedtoanyabsolutemeasurementofthemasscompositionatultra-highenergy.
However, there are indications for two transitions within the data, where the mass compo-
sitionchangesrapidly,firstaround∼PeVfromlighttoheavierandthenat∼EeVbackfrom
heaviertolighterprimaryparticles.
4
˜CAC¯G5G¯G¯GA5G¯G˜G¯G¯GAdAdRd˘d˜dRd˜d˜d¯˘¯˘¯˘¯˘A˘A˘AGAGAGRG˜CCC˜C¯¯A¯˜¯˜¯˜¯˜¯˜¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯A¯A¯A˜A˜A˜A˜A˜A˜R˜R5RC¯˜d˜5CG˜5˜55
Mean logarithmic mass <ln A> Mean logarithmic mass <ln A>
˜˜
˜˜
˜˜