Table Of ContentConstraining pion interactions at very high energies
by cosmic ray data
6 Sergey Ostapchenko1,2 and Marcus Bleicher1,3
1
1
0 Frankfurt Institute for Advanced Studies, 60438 Frankfurt am Main, Germany
2 2D.V. Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia
b 3Institute for Theoretical Physics, Goethe-Universitat, 60438 Frankfurt am Main, Germany
e
F
February 29, 2016
6
2
Abstract nuclear compositionofultra-highenergycosmic
]
h rays (UHECRs). The primary CR composition
p
We demonstrate that a substantial part of is the keyobservablefordiscriminating between
-
p the present uncertainties in model predictions different astrophysical models for the origin of
e for the average maximum depth of cosmic ray- the UHECRs and is of utmost importance for
h
induced extensive air showers is related to very revealing the nature of UHECR sources (for re-
[
high energy pion-air collisions. Our analysis cent reviews, see [1, 2]).
2 shows that the position of the maximum of
Typically, one chooses between two main ex-
v
the muon production profile in air showers is
7 perimental procedures [3, 4]. In the first case,
strongly sensitive to the properties of such in-
6 onedealswiththeinformationobtainedbyscin-
teractions. Therefore, the measurements of the
5 tillation detectors positioned at ground. The
6 maximal muon production depth by cosmic ray
energy of the primary particle is reconstructed
0 experiments provide a unique opportunity to
from the measured lateral density of charged
1. constrain the treatment of pion-air interactions
particles (mostly, electrons and positrons)while
0 at very high energies and to reduce thereby
the particle type is inferred from the relative
6 model-relateduncertainties for the showermax-
fraction of muons, comparedto all chargedpar-
1
imum depth.
: ticles at ground. Alternatively, one may study
v
the longitudinal EAS development by measur-
i
X 1 Introduction ing fluorescence light produced by excited air
r moleculesatdifferentheightsintheatmosphere.
a
Here dedicated fluorescence telescopes are em-
Experimental studies of high energy cosmic
ployed. Inthe latter case,the primaryenergy is
rays (CRs) are traditionally performed using
related to the total amount of fluorescence light
extensive air shower (EAS) techniques: the
emitted. Inturn,theparticletypemaybedeter-
properties of the primary CR particles are re-
minedfromthemeasuredpositionoftheshower
constructed from measured characteristics of
nuclear-electromagnetic cascades induced by maximum Xmax – the depth in the atmosphere
(in g/cm2), where the number of ionizing parti-
their interactions in the atmosphere. This nat-
cles reaches its maximal value.
urally implies the importance of detailed Monte
Carlosimulationsofthe EAS development,par- Not surprisingly, the observables used to de-
ticularly, of its backbone – the cascade of nu- termine the primary particle type – the lateral
clear interactions of both, the primary particles muon density and the EAS maximum position
and of the secondary hadrons produced. Thus, Xmax – appear to be very sensitive to details of
the very success of these experimental studies highenergyhadronicinteractions[5]. Morepre-
depends crucially on the accuracy of the mod- cisely, Xmax depends strongly on the properties
eling of hadron-air collisions at high energies. of the primary particle interaction with air nu-
This is especially so for measurements of the clei: the inelastic cross section and the forward
1
spectraofsecondaryhadronsproduced. Inturn, andQGSJET[11,12]models.1 Particularlysur-
the EAS muon content is formed in a multistep prising is the difference between the QGSJET-
cascadeprocess,drivenmostlybyinteractionsof II-04 and EPOS-LHC predictions as both mod-
secondary pions and, to a smaller extent, kaons els havebeen recentlyupdatedusingLHC data.
withair. Here,wearegoingtodemonstratethat Thus, the question arises if the analysis of Ref.
presentmodelpredictionsfortheaverageshower [8]wasnotgeneralenoughorthepositionofthe
maximum depth also depend noticeably on the shower maximum depends on some other char-
model treatment of pion-air collisions. More- acteristicsofhadronicinteractions,notwellcon-
over, due to a reduction of uncertainties related strained by present LHC data.
to the description of very high energy proton- To reveal the interaction features which are
proton and proton-nucleus interactions, caused responsible for the above-discussed differences
by a more reliable model calibration with the in Xmax predictions, we are going to employ
data of the Large Hadron Collider (LHC), the a “cocktail” model approach: using QGSJET-
treatmentofpion-nucleuscollisionsbecomesthe II-04 to describe some selected interactions of
dominant source of model uncertainty concern- hadrons in the atmospheric cascades or some
ing Xmax predictions. We will demonstrate how particular features of the primary interaction,
this can be constrainedby measurements of the while treatingthe restwithoneofthe othertwo
maximalmuonproductiondepth inairshowers. models.2 As the first step, we apply QGSJET-
II-04 to determine the position of the primary
particle interaction in the atmosphere and to
2 Uncertainties of model describe the production of secondary nucleons
in this interaction; all other characteristics of
predictions for X
max the first proton-air collision and all the subse-
quent interactions of secondary hadrons in the
By far, the most suitable EAS parameter for cascadearetreatedusingEPOS-LHC.This way
studying primary CR compositionis the shower we check the sensitivity of the calculated Xmax
maximum depth Xmax. Apart from the possi- to the model differences concerning the proton-
bility to measure it reliably by modern air flu- aircrosssectionandthepredictednucleonspec-
orescence detectors, the uncertainties of the re- tra, which thus comprise the effects of the in-
spectivemodelpredictionshavebeengreatlyre- elastic diffraction. The obtained Xmax shown
duced with the start of LHC. Especially, the by the blue dotted-dashed line in Fig. 1 (left)
precise measurements of the total and elastic differs from the original EPOS-LHC results by
2
proton-proton cross sections by the TOTEM notmorethan5g/cm ,whichiswellwithinthe
and ATLAS experiments [6, 7] provided strong uncertainty range obtained in Ref. [8].
constraints for the models. Another potential Next, we apply QGSJET-II-04 to describe all
source of uncertainty for Xmax is related to its the characteristics of the primary interaction,
sensitivity to the rate of inelastic diffraction whiletreatingtherestofthehadroncascadeus-
in proton-proton and proton-nucleus collisions. ing EPOS-LHC. The obtained Xmax shown by
Diffraction largely dominates the shape of the thebluedashedlineinFig.1(left)isshiftedfur-
very forwardspectra for secondary particle pro- thertowardstheQGSJET-II-04resultsbyupto
duction, which in turn makes a strong impact 5 g/cm2. This additional shift is explained by
on the longitudinal EAS development. This has somewhat harder spectra of secondary mesons,
beeninvestigatedinRef.[8]intheframeworkof most importantly, of secondary pions in EPOS-
the QGSJET-II-04 model [9], in view of recent LHC, compared to QGSJET-II-04. Here we
studiesofdiffractionatLHC.Theobtainedchar- actually observe an important change in the
acteristic uncertainty for Xmax amounted to 10
g/cm2, being thus comparable to the accuracy 1Here and in the following the calculations of EAS
developmentareperformedusingtheCONEXcode[13].
of the shower maximum measurements. 2We restrict our analysis to the case of proton-
However, present differences between various initiated air showers: For average characteristics of
calculations of Xmax are substantially larger,as nucleus-induced EAS, the “superposition” model works
quite well [11, 14, 15]. E.g., for the energy dependence
illustratedinFig.1(left)withthecorresponding
of Xmax foriron-and proton-induced EAS,therelation
results of the QGSJET-II-04, EPOS-LHC [10], XmFeax(E0)=Xmpax(E0/56)holdstoagoodaccuracy.
2
2m) 800 p-induced EAS 2m) 600 p-induced EAS
g/c g/c
(max (max EPOS-LHC
X EPOS-LHC Xµ 550
750
500
700 QGSJET QGSJET
450
17 18 19 17 18 19
10 10 10 10 10 10
E (eV) E (eV)
0 0
Figure 1: Primary energy dependence of Xmax (left) and of Xmµax for Eµ ≥ 1 GeV (right) for
proton-initiated vertical EAS, calculated using the EPOS-LHC, QGSJET-II-04, and QGSJET
models (respectively topblue, middle red,andbottom greensolidlines), orapplying mixedmodel
descriptions, as explained in the text (dashed, dotted-dashed, and dotted lines).
physics of the hadronic cascade in the atmo- of the difference, as is illustrated by the green
sphere. At lower energies, there is a very pro- dotted-dashed line in Fig. 1 (left), obtained by
nounced “leading nucleon” effect, i.e. most en- usingQGSJET-II-04bothfortheprimaryinter-
ergetic secondary particles in proton-air colli- action and for the inelastic cross sections for all
sions are typically protons or neutrons (pro- the secondary hadron-air collisions in the cas-
duced either directly or via decays of hyperons cade. In turn, applying QGSJET-II-04 to de-
andresonances). Ontheotherhand,inthevery scribealsopionandkaonspectrainpion-aircol-
high energy limit the energy loss of leading nu- lisionsproducesanadditional35−50%effect,as
cleons is noticeably higher and the most ener- shown by the green dotted line in Fig. 1 (left).
getic secondary hadron may well be a pion or In case of EPOS-LHC, the remaining ≃ 35%
a kaon, which results in a stronger sensitivity difference with the QGSJET-II-04 results is
of Xmax calculations to the corresponding pro- both due to a copious production of baryon-
ductionspectra. We alsorepeatthe samecalcu- antibaryon pairs in pion- and kaon-air colli-
lation describing secondary hadron interactions sionsandduetoharder(anti-)baryonspectrain
in the cascade with QGSJET, the results be- EPOS-LHC[16]. Thesefeaturesleadtoaslower
ing plotted by the green dashed line in Fig. 1 energy dissipation from the hadronic cascade,
(left). In this case, the difference with the pure hence, to an elongation of the shower profile.
QGSJET-based calculation does not exceed 3 Indeed, if we apply QGSJET-II-04 to describe
g/cm2,whichisduetothefactthatforwardpar- boththeprimaryinteractionandtheproduction
ticle spectra in proton-air collisions are rather ofnucleonsandantinucleonsinallthesecondary
similar in QGSJET and QGSJET-II-04. pion- and kaon-air collisions, while treating the
Thus, there remain large differences between restwithEPOS-LHC,theobtainedXmax shown
th e two dashed lines in Fig. 1 (left) and the bythebluedottedlineinFig.1(left)practically
results of QGSJET-II-04, which arise from the coincides with the QGSJET-II-04 results.
model treatments of pion- and kaon-air interac- Let us now determine the energy range of
tions. In the particular case of QGSJET, this pion- and kaon-air collisions which are most
amounts to 10 − 13 g/cm2, i.e. to ≃ 80% of relevant for the above-discussed model depen-
the difference between QGSJET and QGSJET- dence of Xmax calculations. To this end, we ap-
II-04, and is mainly related to the larger pion- ply QGSJET-II-04 to treat all hadronic inter-
air cross section and softer production spectra actions in the cascade above some “transition”
for secondary mesons, predicted by QGSJET. energy Etrans, while describing hadron-air colli-
Thelargercrosssectionisresponsiblefor≃20% sions at E < Etrans using either EPOS-LHC or
3
2X (g/cm) max 820 p-induced EAS (E 0 = 1019 eV E)POS-LHC 2X (g/cm) maxµ 600 p-induced EAS (E 0 = 1019 eV E)POS-LHC
800
QGSJET-II-04
QGSJET-II-04 550
780
QGSJET
QGSJET
500
13 15 17 19 13 15 17 19
10 10 10 10 10 10 10 10
E (eV) E (eV)
trans trans
Figure 2: Etrans-dependence of Xmax (left) and of Xmµax for Eµ ≥ 1 GeV (right) for proton-
initiated verticalEAS of energy1019 eV, calculatedusing QGSJET-II-04for hadronic interactions
at E > Etrans and applying EPOS-LHC or QGSJET at E < Etrans - respectively blue and green
dotted lines. The predictions of the QGSJET-II-04, EPOS-LHC, and QGSJET models are shown
by the red solid, blue dashed, and green dotted-dashed lines respectively.
QGSJET. The obtained dependence of the cal- ing other characteristics of very high energy
culatedXmaxonEtransforthetwocasesisshown EAS. Recently, the Pierre Auger experiment
in Fig. 2 (left) by respectively blue and green measured the maximal muon production depth
dotted lines for E0 = 1019 eV. Not surprisingly, inEAS,Xmµax –thedepthintheatmosphere(in
themodeldifferencesforthepredictedXmax are g/cm2), where the rate of muon production via
duetoveryhighenergypion-andkaon-airinter- decays of pions and kaons reaches its maximal
actions, which is reflected in the strong Etrans- value [17]. In particular, one observed a strong
dependence in the corresponding energy range. contradiction between the results of EAS sim-
Indeed,asthelongitudinalchargedparticlepro- ulations with EPOS-LHC and the experimen-
file in EAS is dominated by the contribution of tal data: the measured Xµ was substantially
max
electronsandpositrons,Xmaxmaybeinfluenced smaller than predicted by that model, even if
bypion-andkaon-airinteractionsonlyinthebe- the heaviest primary CRs were considered.
ginning of the hadronic cascade, before most of There are both similarities and differences
the energy of the primary particle is channelled concerning the relation of Xmax and Xmµax to
into secondary electromagnetic cascades. the properties of hadron-air collisions. Obvi-
ously, both characteristics are sensitive to the
3 Relation to maximal muon position X0 of the primary particle interaction
intheatmosphere,whichdependsontherespec-
production depth tive inelastic cross section: fluctuations of X0
shiftthewholecascadeupwardsanddownwards
As demonstrated in Section 2, a large part of in the atmosphere and thus do so for Xmax and
th e model uncertainty for the predicted Xmax Xmµ ax for a particular shower. However, in con-
is related to the treatment of pion-air collisions trast to Xmax, Xmµax is much less sensitive to
at very high energies. As no accelerator exper- hadron production in the primary interaction.
iments with a very high energy pion beam are The EAS muon content rather depends on the
foreseen, this may constitute a serious obstacle multistep hadronic cascade in which the num-
forimprovingthe accuracyofXmax calculations ber ofpionsandkaonsincreasesinanavalanche
andthus mayhamperfurther progressinexper- way until the probabilities for their decays be-
imental studies of UHECR composition. come comparable to the ones for interactions.
However,the treatment of pion-nucleus inter- Forchargedpions,thishappenswhentheirener-
actions can be constrained indirectly by study- gies approach the corresponding critical energy,
4
Eπ± ≃80GeV[18]. Themaximumofthemuon thisismainlycausedbysomewhatlargerinelas-
crit
production profile is close to this turning point. tic pion- and kaon-air cross sections and softer
As a consequence, Xµ is very sensitive to meson spectra predicted by that model. The
max
the forwardspectral shape of secondary mesons first effect is responsible for ≃ 25% of the dif-
in pion-air collisions: producing in each cascade ference between QGSJET and QGSJET-II-04.
step a meson of a slightly higher energy would This is illustrated by the green dotted-dashed
mean that a larger number of cascade branch- line inFig.1(right),whichisobtainedapplying
ings is required for reaching the critical energy, QGSJET-II-04 to describe both the primary in-
with the result that the maximum of the muon teraction and the inelastic cross sections for all
productionprofilewillbeobserveddeeperinthe the secondary hadron-air collisions in the cas-
atmosphere. A similar effect may be produced cade, while treating hadron production in sec-
by a smaller pion-air cross section as this would ondary hadron-air interactions with QGSJET.
increase the pion mean free pass and thereby Onthe other hand,using QGSJET-II-04results
elongate the muon production profile. However, also for the pion and kaon spectra in pion-air
thereisanotherpotentialmechanismwhichmay collisions produces an additional ≃ 60% effect
influence model predictions for Xµ , namely, a which thus covers the most of the difference of
max
copious production of baryon-antibaryon pairs the two models’ predictions for Xµ , as shown
max
in pion-air interactions. Indeed, (anti-)nucleons by the green dotted line in Fig. 1 (right).
do not decay,3 hence, they continue to interact In turn, the largest part of the difference be-
even when their energies fall below 100 GeV, tween EPOS-LHC and QGSJET-II-04 (≃ 35−
producing additional generations of secondary 40%)isduetothecopiousproductionofbaryon-
hadrons in the cascade. Muons emerging from antibaryonpairsinthe formermodel. Thisis il-
decays of secondary pions and kaons created in lustrated by the blue dotted-dashed line in Fig.
interactions of such low energy (anti-)nucleons 1 (right), which is obtained applying QGSJET-
contribute to the elongation of the muon pro- II-04 to describe both the primary interaction
duction profile and give rise to larger values of and the production of nucleons and antinucle-
Xmµax. It is noteworthy that the respective ef- onsinallthesecondarypion-aircollisions,while
fect is noticeable if (and only if) the yield of treating the rest with EPOS-LHC. The remain-
baryon-antibaryon pairs in pion-air collisions is ing≃30−35%differencebetweenthetwomod-
comparable to the one of secondary pions. els isdue to harderspectraofsecondarymesons
For the calculated Xmµax (for muon ener- in EPOS-LHC for pion- and kaon-air interac-
gies Eµ ≥ 1 GeV), we observe substantially tions. Indeed, usingQGSJET-II-04resultsboth
stronger model dependence than for Xmax, as fortheprimaryinteractionandforhadronspec-
demonstrated in Fig. 1 (right). To reveal the tra in pion- and kaon-air collisions, we obtain
physicsbehind,weusethesame“cocktail”model the energy dependence of Xµ , shown by the
max
approach as in Section 2. First, we apply blue dotted line in Fig. 1 (right), which is very
QGSJET-II-04 to describe all the characteris- close to the pure QGSJET-II-04 calculation.
ticsoftheprimaryinteraction,whiletreatingthe
Finally, let us check the energyrangeof pion-
rest of the hadron cascade using either EPOS- and kaon-air collisions which impact Xµ . As
max
LHC or QGSJET, the results shown respec-
in Section 2, we apply QGSJET-II-04 to treat
tively by the blue and green dashed lines in hadronic interactions at E > Etrans, while de-
Fig. 1 (right). As expected, the obtained Xmµax scribinghadron-aircollisionsatE <Etransusing
deviates only slightly from the original model
either EPOS-LHC or QGSJET. The obtained
caanldcudlaastihoends:blutheelindeiffsedroeenscenobteetwxceeeendt7hge/scomli2d, dependenceofXmµaxonEtransforthetwocasesis
shown in Fig. 2 (right) by respectively blue and
whilebeingevensmallerforQGSJET(solidand greendottedlinesforE0 =1019 eV.Similarlyto
dashed green lines). Indeed, the bulk of the the Xmax case, the range of relevant pion- and
differences between the model predictions for
kaon-aircollisionsextendstoveryhighenergies,
Xmµax is due to secondary (mostly pion-air) in- as reflected by the observed Etrans-dependence
teractions in the cascade. In case of QGSJET, of the calculated Xµ . On the other hand,
max
3Life time of relativistic neutrons exceeds by many this energy range is significantly broader than
ordersofmagnitudethetimescaleforEASdevelopment. in the case ofXmax because allthe stagesofthe
5
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