Cosmic Ray particle production - citeseerx.ist.psu.edu

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arXiv:hep-ph/9711334v2 17 Nov 1997 1 Cosmic Ray particle production J. Ranft a * a INFN, Lab. Naz. del Gran Sasso, I–67010 Assergi, Italy The status of some popular models to simulate hadronic and nuclear interactions at Cosmic Ray energies is reviewed. The models predict the rise of all the hadronic and nuclear cross sections with energy and a smooth (logarithmic) rise of average multiplicities, rapidity plateaus and average transverse momenta with the energy. Big differences are found between model predictions partly already at energies, where collider data are available. It is argued, that at the highest energies data of the Cosmic Ray cascade can only be reliably interpreted by sampling the cascade using more than one model. The importance is stressed to put more effort into the models and especially a better understanding of the minijet component at the highest energies. Likewise, experimental data on particle production are needed at the highest possible energies, to guide the models. Presented at the International Symposium om Multiparticle Dynamics Frascati, Italy Sept.8 to 12 1997 1. Introduction The extension of models for multiparticle pro- duction in hadron–hadron, hadron–nucleus and nucleus–nucleus collisions to be used for the sim- ulation of the Cosmic Ray cascade up to E lab = 10 21 eV (corresponding to s = 2000 TeV) is needed to prepare for the Auger experiment [1] as well as for a reliable interpretation of present experiments like Agasa [2] and Flys Eye [3], which present data in the EeV energy region. The need for careful comparisons of hadron produc- tion models was stressed at the International Cos- mic Ray Conference in Roma 1995. Following this, such a code comparison in the energy re- gion of interest to the Kaskade experiment [4] was presented by members of the Kaskade exper- iment [5]. From this code comparison it became clear, that already in the knee region of the Cos- mic Ray energy spectrum important differences exist between the models and that these differ- ences might change the interpretation of certain Cosmic Ray results. Here we will discuss the sta- tus of some of these models, discuss the minijet component, present typical comparisons to Col- lider data, present some characteristics of hadron production up to E lab = 10 21 eV and finally com- pare some results obtained simulating the cosmic * Present adress: FIGS and Physics Dept. Uni- versit¨ at Siegen, D–57068 Siegen Germany, e–mail: [email protected] ray cascade using different models. 2. The present status of some event generators used for Cosmic Ray cascade simulations The presently dominant hadron production models used for the simulation of the Cosmic Ray cascade are constructed on the basis of multi- string fragmentation, they use Gribov–Regge and Gribov–Glauber theory, to construct the multi- string production in hadron–hadron and nuclear collisions. Most of the models use minijets as an important mechanism for particle production at high energies. The DPMJET–II event generator based on the two–component Dual Parton Model (DPM) was described in detail [6–8]. The extension of this model up to energies of s = 2000 TeV was reported this year, the resulting model will be refered to as DPMJET–II.3. The extension is done by calculating the minijet component of the model using new parton distribution func- tions, the GRV–LO parton distributions [9] and the CTEQ4 parton distributions [10], which are both available in a larger Bjorken–x range than the MRS(D-) parton distributions, which were the default in DPMJET–II.2. These new par- ton distributions describe the structure function data measured in the last years at the HERA Col- lider. DPMJET–II.3 descibes well minimum bias

Transcript of Cosmic Ray particle production - citeseerx.ist.psu.edu

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1

Cosmic Ray particle production

J. Ranfta∗

aINFN, Lab. Naz. del Gran Sasso, I–67010 Assergi, Italy

The status of some popular models to simulate hadronic and nuclear interactions at Cosmic Ray energies isreviewed. The models predict the rise of all the hadronic and nuclear cross sections with energy and a smooth(logarithmic) rise of average multiplicities, rapidity plateaus and average transverse momenta with the energy.Big differences are found between model predictions partly already at energies, where collider data are available.It is argued, that at the highest energies data of the Cosmic Ray cascade can only be reliably interpreted bysampling the cascade using more than one model. The importance is stressed to put more effort into the modelsand especially a better understanding of the minijet component at the highest energies. Likewise, experimentaldata on particle production are needed at the highest possible energies, to guide the models.

Presented at the International Symposium om Multiparticle Dynamics Frascati, Italy Sept.8 to 12 1997

1. Introduction

The extension of models for multiparticle pro-duction in hadron–hadron, hadron–nucleus andnucleus–nucleus collisions to be used for the sim-ulation of the Cosmic Ray cascade up to Elab =1021 eV (corresponding to

√s = 2000 TeV) is

needed to prepare for the Auger experiment [1]as well as for a reliable interpretation of presentexperiments like Agasa [2] and Flys Eye [3], whichpresent data in the EeV energy region. Theneed for careful comparisons of hadron produc-tion models was stressed at the International Cos-mic Ray Conference in Roma 1995. Followingthis, such a code comparison in the energy re-gion of interest to the Kaskade experiment [4]was presented by members of the Kaskade exper-iment [5]. From this code comparison it becameclear, that already in the knee region of the Cos-mic Ray energy spectrum important differencesexist between the models and that these differ-ences might change the interpretation of certainCosmic Ray results. Here we will discuss the sta-tus of some of these models, discuss the minijetcomponent, present typical comparisons to Col-lider data, present some characteristics of hadronproduction up to Elab = 1021 eV and finally com-pare some results obtained simulating the cosmic

∗Present adress: FIGS and Physics Dept. Uni-

versitat Siegen, D–57068 Siegen Germany, e–mail:

[email protected]

ray cascade using different models.

2. The present status of some eventgenerators used for Cosmic Ray cascadesimulations

The presently dominant hadron productionmodels used for the simulation of the Cosmic Raycascade are constructed on the basis of multi-string fragmentation, they use Gribov–Regge andGribov–Glauber theory, to construct the multi-string production in hadron–hadron and nuclearcollisions. Most of the models use minijets as animportant mechanism for particle production athigh energies.

The DPMJET–II event generator based on thetwo–component Dual Parton Model (DPM) wasdescribed in detail [6–8]. The extension of thismodel up to energies of

√s = 2000 TeV was

reported this year, the resulting model will berefered to as DPMJET–II.3. The extension isdone by calculating the minijet component ofthe model using new parton distribution func-tions, the GRV–LO parton distributions [9] andthe CTEQ4 parton distributions [10], which areboth available in a larger Bjorken–x range thanthe MRS(D-) parton distributions, which werethe default in DPMJET–II.2. These new par-ton distributions describe the structure functiondata measured in the last years at the HERA Col-lider. DPMJET–II.3 descibes well minimum bias

2

hadron and hadron jet production up to presentcollider energies. It is also demonstrated, thatthe model performs as well as the previous oneDPMJET–II.2 for hadron production in hadron–nucleus and nucleus–nucleus colisions. DPMJETis used for the simulation of the Cosmic Ray cas-cade within the HEMAS–DPM code [11] usedmainly for the MACRO experiment [12].

The SIBYLL model [13] is a minijet model andhas been reported to be applicable up to Elab =1020 eV. However, the EHQL [14] parton struc-ture functions used for the calculation of the mini-jet component might , after the HERA experi-ments, no longer be adequate. It is known, that asignificant updating of SIBYLL is planned for thenext year. SIBYLL is the most popular model forsimulating the Cosmic Ray cascade in the USA.

VENUS, a very popular model applied origi-nally for describing heavy ion experiments, is nowthe leading event generator within the CorsikaCosmic Ray cascade code [15]. VENUS is appi-cable up to Elab = 5×1016 eV. It has been re-ported [16], that the introduction of minijets intoVENUS has been planned, this will allow to applyVENUS up to higher energies.

QGSJET [17] is the most popular Russianevent generator used for Cosmic Ray simulations.It is based on the Quark Gluon String (QGS)model, this model is largely equivalent to theDPM. QGSJET also contains a minijet compo-nent and is reported to be applicable up to Elab

= 1020 eV.HPDM [18] is based on parametrizations in-

spired by the DUAL Parton Model. it is reportedto be applicable up to Elab = 1020 eV, however-some of the parametrizations might become un-reliable above Elab = 1017 eV. HPDM was origi-nally used as event generator within the Corsikacascade code.

MOCCA [19] is an empirical model employinga succesive splitting algorihm. It was reportedto be applicable up to Elab = 1020 eV. Since themodel does not contain minijets, its predictionsat the upper energy end might differ significantlyfrom the other models.

In Table 1 we present some characteristics ofthe models. The Gribov–Regge theory is appliedby three of the models. The pomeron intercept

for SIBYLL is equal to one, SIBYLL is a mini-jet model using a critical pomeron, with one softchain pair, all the rise of the cross section resultsfrom the minijets. In the models with pomeronintercept bigger than one, we have also multi-ple soft chain pairs, already the soft pomeronleads to some rise of the cross sections with en-ergy. Minijets are used in three of the models, itis believed, that minijets are necessary to reachthe highest energies. All models contain diffrac-tive events. Secondary interactions between allproduced hadrons and spectators exist only inVENUS, DPMJET has only a formation zoneintranuclear cascade (FZIC) between the pro-duced hadrons and the spectators. Only three ofthe models sample properly nucleus–nucleus col-lisions, the other two models replace this by thesuperposition model, where the nucleus–nucleuscollision is replaced by some hadron–nucleus col-lisions. The residual projectile (and target) nucleiare only given by two of the models.

Table 1. Characteristics of some popular mo-dels for hadron production in Cosmic Ray cas-cades. (VEN = VENUS, QGS = QGSJET, SIB= SIBYLL, HP = HPDM, DPM = DPMJET)

VEN QGS SIB HP DPM

Grib.–Regg. x x x

Pom. ic. 1.07 1.07 1.00 1.05

minijets x x x

Diffr. ev. x x x x x

sec. int. x x

A–A int. x x x

superp. x x

res. nucl. x x

max. E [GeV] 107 1011 1011 108 1012

3

3. The calculation of the minijet compo-nent

The input cross section (before the unitariza-tion procedure applied by the models) for semi-hard multiparticle production (or minijet pro-duction) σh is calculated applying the QCD im-proved parton model, the details (for DPMJET)are given in Ref.[20–25].

σh =∑i,j

∫ 1

0

dx1

∫ 1

0

dx2

∫dt

1

1 + δij

dσQCD,ij

dt

×fi(x1, Q2)fj(x2, Q

2) Θ(p⊥ − p⊥thr) (1)

fi(x, Q2) are the structure functions of partonswith the flavor i and scale Q2 and the sum i, jruns over all possible flavors. To remain in theregion where perturbation theory is valid, a lowp⊥ cut–off p⊥thr

is used for the minijet compo-nent. Since the HERA measurements, the struc-ture functions are known to behave at small xlike 1/xα with α between 1.35 and 1.5. Theminijet production is dominated by very small xvalues, therefore the minijet cross section calcu-lated with the new structure functions rise verysteeply with energy. We found already 1993 [25]with the MRS[D-] structure function [26] at theLHC energy a minijetcross section about 10 timeslarger than the total cross section at this energy.

Such large minijet cross sections are inconsis-tent and wrong: The input minijet cross sec-tions σh, which one puts into the unitarizationscheme are inclusive cross sections normalized tonminijetsσinel, where nminijets is the multiplicityof minijets. The physical processes, which con-tribute to this inclusive cross section are 2 → nparton processes. 2 → n processes give a con-tribution to σh equal to nσ2→n. If one treatsthis huge cross section as σh in the usual wayin the eikonal unitarization scheme one replacesit by n/2 simultaneuos 2 → 2 parton processes,this is the inconsistency. What one should re-ally use in the unitarization, but what we do notknow how to compute reliably at present wouldbe σh =

∑n σ2→n. The way to remove this incon-

sistency is to make in the two component DPMthe threshold for minijet production p⊥thr energydependent in such a way, that at no energy and

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ps [GeV]

�tot GRV94LO 2.�el GRV94LO 2.�inel GRV94LO 2.�tot CTEQ96 2.�el CTEQ96 2.�inel CTEQ96 2.�tot D.-L.�tot data ccccccc ccccccccc c cccc ccc�el data ssss sssss ssss s

�inel data rr r r

Figure 1. Total, inelastic and elastic pp and ppcross sections from DPMJET–II.3 as function ofthe center of mass energy

√s. The model results

obtained using the GRV–LO parton distributions[9] and the CTEQ4 parton distributions [10] arecompared to the Donnachie–Landshoff fit for thetotal cross section [27] and to data [28–30] [31–36]

for no PDF the resulting σh is much bigger thanthe total cross section. Then at least we havea cross section, which is indeed mainly the crosssection of a 2 → 2 parton process at this level, theparton–parton scattering with the largest trans-verse momentum. We can get back to the real2 → n processes and recover the minijets withsmaller transverse momenta via parton shower-ing. One possible form for this energy dependentcut off is [25]:

p⊥thr = 2.5 + 0.12[lg10(√

s/√

s0)]3

[GeV/c],√

s0 = 50GeV. (2)

4

200300400500600700800

0:01 1 100 10000 1e+ 06�p�Air(mb)

Energy E [TeV]

DPMJET p{Air c

c c c c c c c c c c c c c c c c c c cVENUS p{AirSIBYLL p{AirExp. p{Air uu uuu uuuuuuuuuuuuuuu uuuuuu uuuuuuu

Figure 2. The inelastic cross section σp−Air calcu-lated by DPMJET–II.3 (as well as the ones fromVENUS and SIBYLL according to Ref. [5]) asfunction of the laboratory collision energy (from0.02 TeV up to 1.E9 TeV) compared to experi-mental data collected by Mielke et al. [37].

The resulting σh are smaller or not much largerthan the total cross sections resulting after theunitarization for all PDF’s.

There are further features of the minijet com-ponent worth mentioning. One uses as first de-scribed in [24] at p⊥thr the continuity requirementfor the soft and hard chain end p⊥ distributions.Physically, this means, that we use the soft crosssection to cut the singularity in the minijet p⊥distribution. But note, that this cut moves withrising collision energy to higher and higher p⊥values. This procedure has besides cutting thesingularity more attractive features:

(i) The model results (at least as long as we donot violate the consistency requirement describedabove) become somewhat independent from theotherwise arbitrary p⊥ cut–off. This was already

0123456

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Pseudorapidity �uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuueeeeeeeeeee

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeesssssssssssssssssssssssssssssssssssssscccccccc

ccccccccccccccccccccccccccccccccc

rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

b bb bb bbbb bb

bb bb bb bb bb bb bb bb bb bb bb bb bb bb bb

uuuuuuuuuuuuuuuuuu

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eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeFigure 3. Pseudorapidity distributions of chargedhadrons produced in nondiffractive pp collisionsat

√s = 0.2, 0.54, 0.9 and 1.8 TeV. The

DPMJET–II.3 results are compared with datafrom the UA–5 Collaboration [38] and from theCDF Collaboration [39].

demonstrated with DTUJET90 [22] and cut–offsof 2 and 3 GeV/c.

(ii)The continuity between soft and semihardphysics is emphasized, there is no basic differ-ence between soft and semihard chains besides thetechnical problem, that perturbative QCD allowsonly to calculate the semihard component.

(iii) With this continuity in mind we feel freeto call all chain ends, whatever their origin in themodel, minijets, as soon as their p⊥ exceeds acertain value, say 2 GeV/c.

5

4. Comparing the models to data at accel-erator and collider energies

Each model has to determine its free param-eters. This can be done by a global fit to allavailable data of total, elastic, inelastic, and sin-gle diffractive cross sections in the energy rangefrom ISR to collider experiments as well as to thedata on the elastic slopes in this energy range.Since there are some differences in the hard par-ton distribution functions at small x values re-sulting in different hard input cross sections wehave to perform separate fits for each set of par-ton distribution functions. After this stage eachmodel predicts the cross sections also outside theenergy range, where data are available. In Fig. 1we plot for DPMJET–II.3 the fitted cross sectionsobtained with two PDF’s together with the data.Furthermore we compare the total cross sectionsobtained with the popular Donnachie–Landshofffit [27]. For applications in Cosmic Ray cascadesimulations we need in particular the hadron–Aircross section. in Fig.2 we compare data accordingto Mielke et al. [37] with the cross sections ac-cording to three models. At low energies all mod-els are describing these data rather well. At highenergies we observe however small differences bet-ween the models.

At higher energies (and in non-single diffractivepp collisions) there are pseudorapidity distribu-tions from the UA–5 Collaboration [38] and fromthe CDF Collaboration [39]. In Fig.3 a very goodagreement is found of DMJET–II.3 with thesedata. Still very often there is and was always(see Fig.3) a disagreement of the models with theUA–5 data at the highest pseudorapidity values.The models predict systematically more particlesat the largest pseudorapidities of the experiment.This disagreement (if the data would be correct)would of course be of importance, if one is inter-ested in Cosmic Ray cascades, where the particleproduction in the fragmentation region is of maininterest. Fortunately, a new independent mea-surement of the pseudorapidity distribution in thecollider energy range became available recently[40]. In Fig. 4 the comparison with this new datais presented and we find a remarkable agreementwith DPMJET–II.3 in the large pseudorapidity

00:511:522:533:544:55

�8 �6 �4 �2 0 2 4 6 8dNd�

Pseudorapidity �

Harr et al. 630 GeV bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

DPMJET-23 (nsd) uuuuuuuuuu

uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuFigure 4. Pseudorapidity distributions ofcharged hadrons produced in nondiffractive ppcollisions at

√s = 0.63 TeV. The DPMJET–II.3

results are compared with recent data from Harret al. [40]. [41].

region. In Fig.5 we present the comparison (fromRef.[5]) of multiplicity distributions according to5 models with the data from the UA–5 Collabora-tion [38]. Most of the models describe at least thehigh multiplicity tail of the data reasonably well,however the multiplicity distribution occording tothe SIBYLL model is everywhere rather far fromthe data. We turn to collisions with nuclei. InFig. 6 the comparison of DPMJET–II.3 is withthe rapidity distribution of charged hadrons inp-Ar collisions at 200 GeV. In Fig. 6 we com-pare with the rapidity distribution of negativelycharged hadrons in central S–S and S–Ag colli-sions.

At least in models with a minijet componentwe expect good agreement with data on trans-verse momentum distributions. In Fig.8 we com-pare hadron jet production in DPMJET–II.3 withdata from the CDF–Collaboration [44]. The jetsfrom the model are found out of the Monte Carloevents using a jet finding algorithm with the same

6

10-5

10-4

10-3

10-2

10-1

0 20 40 60 80 100 120 140

VENUS

QGSJET

SIBYLL

HDPM

DPMJET

Nch

dN

/dN

ch

UA5

Figure 5. Multiplicity distribution of chargedhadrons from nondiffractive p−p collisions at

√s

= 540 GeV. The data are from the UA–5 Col-laboration [38]. The comparison with 5 models isfrom [5].

parameters like the one used by the experiment.With a minimum bias Monte Carlo event gener-ator it is of course not possible to obtain goodstatistics on the total transverse energy range ofthe experiment. We find good agreement of thejets in the model with the data up to E⊥ = 30GeV/c. The transverse momentum distributionin a large p⊥ region was determined by the UA–1–MIMI Collaboration [45]. In Fig.9 we compareDPMJET–II.3 results with the parametrizationof the data given by this experiment and we finda good agreement.

In Fig.10 we compare average transverse mo-menta as obtained from DPMJET–II.3, QGSJETand SIBYLL as function of the cms energy

√s

with data collected by the UA–1 Collaboration.This plot gives at the same time the DPMJETpredictions for the average transverse momentaup to

√s = 2000 TeV and the predictions of the

two other models up to√

s = 100 TeV. While atenergies where data exist all models agree ratherwell with each other and with the data, we find

0123456

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Rapidity y

Exp. p - Ar uu u u

u u u u u u u u u u u u u u u uDPMJET-23 p - Ar e

eeeeeeeeeeeeeeeeeeeeeeee

Figure 6. Charged particle rapidity distributionfor p–Ar interactions. The DPMJET–II.3 resultsare compared with data [42].

completely different extrapolations to higher en-ergies. We should note, this are just the threemodels with a minijet component. But it seems,that in spite of the minijets the average transversemomentum in QGSJET becomes constant at highenergies, while it continues to rise in DPMJET.For me the rise of the average transverse momen-tum in DPMJET is connected with the fact, thatwith the new parton structure functions since theHERA measurements really the minijets domi-nate very much all of hadron production at highenergy. We can conclude, there are very big dif-ferences in implementing the minijet componentsin the models.

5. Properties of the models in the highestenergy region

In Fig.11 the pseudorapidity distributions forcharged hadrons according to DPMJET–II.3 arepresented for energies between

√s = 1 TeV and

2000 TeV. The width of the distributions in-creases like the logarithm of the energy and also

7

05101520253035404550

0 1 2 3 4 5 6(dNdy )

Rapidity yeeeeeeeeeeeeeeeeeeeeeeeeeeec c c c c c

c c c c c c c c c c c c c c c c c c c c cuuuuuuuuuuuuuuuuuu uuuuuss s s

s s s s s s s s s s s s s s s sFigure 7. Rapidity distribution of negativelycharged hadrons in central S–S ans S–Ag colli-sions. The results of DPMJET–II.3 are comparedwith data from the NA–35 Collaboration [43].

the maximum of the curves rises like the loga-rithm of the energy. If we call the central re-gion around the two maxima the plateau, then wefind the width of this plateau hardly to changewith energy. Fig.12 presents the rise of the to-tal charged multiplicity with the cms energy

√s

according to DPMJET, QGSJET and SIBYLL.we find again, at low energies, where data areavailable, the models agree rather well. DPM-JET and SIBYLL agree in all the energy rangeshown. However, QGSJET above the energy ofthe TEVATRON extrapolates to higher energiesin a completely different way.

In Fig.13 we present for pp anf p–Air collisionsthe energy fractions K for B − B (baryon - an-tibaryon) and charged pion production. The cos-mic ray spectrum–weighted moments in p–A col-lisions are defined as moments of the F (xlab) :

Zp−Ai =

∫1

0

(xlab)γ−1F p−A

i (xlab)dxlab (3)

Here −γ ≃ –1.7 is the power of the integral cos-

0:010:1110100

10 15 20 25 30 35 40 45 50dNdE?�bGeV

Jet transverse energy E?

CDF ee e e e e eDTUJET{97 uuuuuuuuuuuuuuuuuuuuuuu u uuu

Figure 8. The jet transverse energy distri-bution is compared with data from the CDF–Collaboration [44]. The jets are found from themodel events in the pseudorapidity region |η| ≤0.7 using a jet finding algorithm.

mic ray energy spectrum and A represents boththe target nucleus name and its mass number.In Fig.14 we present the spectrum weighted mo-ments for pion production in pp and p–Air colli-sions as function of the cms energy

√s per nu-

cleon. We find all average values characterizinghadron production: the cross sections (Fig.1), theaverage transverse momenta (Fig.10) the chargedmultiplicities (Fig.12), and the moments in Figs.14 and in Fig. 13 to change smoothly with en-ergy in most cases just like the logarithm of theenergy.

Comparison of the models after simulatingthe Cosmic Ray cascade

First we present results of a comparison be-tween the cascade code HEMAS [47] using DP-MJET as event generator and the cascade codeCORSIKA [15] using VENUS as event generator[48]. This comparison has been done for quan-

8

10 2 4 6 8 10 12 14

Ed3�d3pmb/GeV2transverse momentum p?

UA1{MIMI ee e e e e e e e e e e e eDTUJET{97 uuuuuuuuuuuuuuuuuuuuuuuuuu uu

Figure 9. Comparison of transverse momentumcross sections according to DPMJET–II.3 at

√e

= 0.63 TeV with collider data from the UA–1MIMI Collaboration [45]. The experimental dateare represented by the parametrization given bythe Experiment.

tities of interest for the EAS–Top and MACROexperiments in the Gran Sasso Lab. The zenithangle is fixed at 31 degrees (MACRO/EAS-TOPcoincidence direction). The e.m. shower size andmuons above 1 TeV are sampled at 2000 metersa.s.l. (946 g/cm2 slant depth, 810 g/cm2 vert.depth). The calculations were done for primaryprotons, He nuclei and Fe nuclei with energiesbetween 3 and 2000 TeV. Calculated are for eachprimary energy and particle (i) the e.m. showerprofile, (ii)the Log(e.m. size) at EAS-TOP sam-pling depth (946 g/cm2), (iii)the distance muon-shower axis for E > 1 TeV muons, (iv) the muondecoherence for E > 1 TeV muons, (v) the numberof muons per shower and (vi) the energy spec-trum of E > 1 TeV muons. In Figs. 15 to 18we present two of these comparisons. A satis-factory agreement is found in these plots as wellas in all other comparisons at different energiesand with the other primary particles. Next we

00:20:40:60:811:21:4

0:01 0:1 1 10 100 1000< p? >(GeV/c)

ps [TeV]

DPMJET{23 j�j � 2.5 ee e e e e e e e e e e e e e e eQGSJET all j�jSIBYLL all j�jEXP. �=0 u

uuuuuuu uuuuuuFigure 10. Average transverse momenta ofcharged secondaries produced in pp and pp col-lisions calculated from DPMJET, QGSJET andSIBYLL (The latter two as given in Ref.[5]) asfunction of the center of mass energy

√s com-

pared to date collected by the UA–1 Collabora-tion [46].

present two comparisons from the Karlsruhe codecomparison [5]. The distributions choosen in thiscomparison are motivated by the interest of theKASKADE[4] experiment in Karlsruhe. In Fig.19the Muon multiplicity distribution at ground levelis calculated for primary protons of E = 1015 eV.The calculation is done with the CORSIKA cas-cade code using 5 different event generators forthe hadronic interactions. While again VENUSand DPMJET give distributions , which agreevery well, it is found, that SIBYLL gives a verydifferent distribution centered at smaller Muonnumber.

In Figs. 20 and 21 ( The distributions werecalculated using the CORSIKA shower code [5]with 5 different event generators for the hadronicinteractions. ) Fe and p induced showers withenergies of E = 1014 and 1015 eV are plottedin the log10 Nµ –log10 Ne plane (Muon–number

9

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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Figure 11. The development of the pseudora-pidity distribution of charged hadrons producedin inelastic pp collisions in the in the center ofmass energy range between

√s=1 TeV and

√s =

2000 TeV.

–Electron–number plane). The distribution ofevents according to each of the 5 interaction mod-els for each energy and primary perticle is indi-cated by contours. Considering these plots calcu-lated with only one of the models, where Muonnumber is plotted over electron number, the im-pression is, that a simultaneous measurement ofMuon–number and Electron number allows to de-termine the primary energy as well as the compo-sition of the primary component. In these plotswe see, that for instance VENUS and DPMJETagree very well, but the contour according toSIBYLL for Fe projectiles of E = 1015 eV over-laps the VENUS and DPMJET contours for pprojectiles. From these differences between themodels one can conclude, that at present the sys-tematic errors of the cascade calculations (andthis are just the differences obtained using differ-ent models) prevent to identify safely the compo-sition of the primary component from such mea-surements.

050100150200250

0:01 0:1 1 10 100 1000< nch >

ps [TeV]

DPMJET bb b b b b b b b b b b b b b b bQGSJETSIBYLL

Figure 12. Rise of the charged multiplicity in in-elastic pp collisions according to DPMJET–II.3 inthe center of mass energy range between

√s=0.02

TeV and√

s = 2000 TeV. At energies between 1and 100 TeV we plot also the average multiplici-ties according to SIBYLL and QGSJET as givenin Ref.[5].

6. Conclusions

I would like to stress, more efforts are needed toextend the models used to simulate the hadronicinteractions in the C.R. cascade up to the energiesto be explored by the Auger Experiment.

At least at collider energies, where data areavailable, these models should agree among them-selves and with the data. Disagreements to datalike the ones seen in Fig.5 should be removed assoon as discovered.

A much better understanding is needed howto calculate the minijet component. Certainly,the parton structure functions used for calculat-ing the minijet cross sections should correspondto the HERA measurements at small x. But thisis certainly not the only problem. The differencesin the extrapolation to higher energies of quanti-ties like average transverse momenta and charged

10

0:20:250:30:350:40:450:50:550:6

0:01 0:1 1 10 100 1000 10000Ki

Energy ps [TeV]

DPMJET{23 KB� �B p{p uu u u u u u u u u u u u u u u uDPMJET{23 K�+;�� p{p r

r r r r r r r r r r r r r r r rDPMJET{23 KB� �B p{N ee e e e e e e e e e eDPMJET{23 K�+;�� p{N bb b b b b b b b b b b b b b b b

Figure 13. Laboratory energy fractions for B−Band pion production in pp and p–Air collisionsaccording to DPMJET–II.3 as function of the(nucleon–nucleon) cms energy

√s.

multiplicities (see Figs. 10 and 12 ) in the threemodels implementing minijets are huge. Thesedifferences indicate, that much effort is needed toget a better understanding of the minijet compo-nent.

Another question, where models disagree is thepresence at high energy of an important soft com-ponent of hadron production like in the modelswith a supercritical pomeron. In minijet modelsall rise of the cross sections and of particle pro-duction at high energy is only due to the minijets.

There are (even at energies, where collider dataare available, see Fig. 19) large differences be-tween the models after simulating the C.R. cas-cade. We have to interpret these differences asthe systematic errors of the cascade simulation.Such large differences could well prevent the in-terpretation of otherwise very interesting CosmicRay data. In future, C.R. results should alwaysbe interpreted using simulations with some differ-ent models.

It might be dangerous, that at present many of

0:0450:050:0550:060:0650:070:0750:08

0:01 0:1 1 10 100 1000 10000f�+;��

Energy ps [TeV]

DPMJET p{p rr r r r r r r r r r r r r r r rDPMJET p{Air cc c c c c c c c c c c c c c c cFigure 14. Spectrum weighted moments for pionproduction in pp and p–Air collisions as functionof the (nucleon–nucleon) cms energy

√s.

the popular models are based on the same the-oretical foundations (and yet might differ verymuch in their results). To be on the safe side, itwould be usefull to construct models based alsoon widely different theoretical concepts (for in-stance on the string fusion model [49]).

Finally, I would like to stress the need for newmeasurements of hadron production especially atthe highest possible energies. In particular in thefragmentation region so important for the cosmicray cascade, data (like Feynman–x distibutions)from the TEVATRON collider would be highlywelcome.

AcknowledgementsThanks are due to J.Knapp, for providing me

with some of the Figures from the Karlsruhe codecomparison and due to C.Forti for providing mewith the Figures from the 2000 TeV code com-parison.

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11

Figure 15. The distribution of the electron num-ber at the sampling level calculated for 2000 TeVprimary protons.

Figure 16. The distance muon-shower axis for E> 1 TeV muons calculated for 2000 TeV primaryprotons. This distribution is mainly related tothe transverse momentum distribution of pionsand Kaons in the hadronic collisions.

Figure 17. The multiplicity distribution of Muonsat the sampling level

Figure 18. The energy spectrum of E > 1 TeVmuons at the sampling level.

12

10-1

1

3.4 3.6 3.8 4 4.2 4.4

VENUS

QGSJET

SIBYLL

HDPM

DPMJET

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dN

/dlo

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