High Energy Hadronic Interactions and Cosmic Ray Physics G. Mitsuka Solar-Terrestrial Environment Laboratory, Nagoya University Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan Interpretation of observations of ultra-high-energy cosmic rays relies on the knowledge about forward particle productions in hadronic interaction. Especially the choice of the hadronic interaction generator (model) in the Monte Carlo simulations of air shower development significantly affects the simulated results, and accordingly accelerator data on the production of very forward emitted particles are indispensable for constraining the hadronic interaction models. In this paper, recent progress in understanding of high energy hadronic interactions is discussed from the viewpoint of the cosmic ray observations.
1
Introductions
Measurements of the energy spectrum, chemical composition and arrival direction of ultrahigh-energy cosmic rays (E & 1018 eV) are indispensable for understanding their origin and the high energy phenomena occurred in the universe. Huge experiments for observing extensive air showers, E & 1014 eV, have been operated and also provided valuable data so far. However the interpretation of these experimental air shower data to the primary cosmic ray parameters largely relies on our relatively poor knowledge of hadronic interaction in the earth’s atmosphere at the corresponding energy scale. A biggest open problem is the long standing question of the origin and the acceleration mechanism of the galactic cosmic rays 1 . In the “standard” scenario, supernova remnants can be a source of the galactic cosmic rays and the acceleration limit is thought to be Z × 1015 eV where Z is the charge of the primary cosmic ray. This scenario predicts a Z dependence of the cutoff energy for galactic cosmic rays. Determination of the chemical composition above E > 1015 eV is important for confirming the standard scenario. The Pierre Auger Observatory 2 , Telescope Array 3 and HiRes 4 have carried out precise measurements of the shower particles on the ground, however their interpretation highly depends on the choice of hadronic interaction generator employed in the air shower Monte Carlo (MC) simulations. Figures 1 show the Xmax and RMS(Xmax ) distribution as a function of reconstructed cosmic ray energy together with the predictions of MC simulations. It is found that, for example, predicted Xmax varies ∼ 50 g/cm2 for proton primaries and ∼ 30 g/cm2 for iron primaries at 4×1019 eV and such variation propagates into an uncertainty of the determination of chemical composition. Even in other problems, i.e. energy spectrum and arrival direction, cosmic ray studies based on a large number of experimental data could be misinterpreted due to the uncertainty of the hadronic interaction generators in air shower MC simulations. These uncertainties can only be reduced by precise theoretical understanding of hadronic interaction and high energy accelerator experiments in the forward direction.
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230 188 face Detector750(SD) has 1660 water detector stations ar143 331 230 188 143 186 619 457 781 30 998 ranged in a 1.5 km triangular grid and sensitive to the 106 1251 47 Fe 700 shower particles at 1407 the ground. The FD has 27 tele20 Fe scopes overlooking the SD, housed in 5 different stations, 10 recording UV650light emitted in the de-excitation of nitrogen molecules in the atmosphere after10the passage of the 0 10 10 10 80 100 charged particles of a shower. The shower geometry Eis[eV] reE [eV] g/cm-2] constructed from the arrival times of the data. The number Figure 2: !Xmax " (top panel) and RMS (Xmax ) (bottom panel) 70 thethe energy. Data (points) are shown with the ing events recorded of fluorescence emitted proportional to thedistribution en- as a function Figure 1: photons Xmax (left) and isRMS(X obtainedofby measurements by the fluorescence max ) (right) p predictions for proton and iron for several hadronic interaction pared to a detailed detector60 of Augerby Observatory. ergy deposited in the Pierre atmosphere the shower. Measured Using thedata (closed circle) are shown with the predictions for proton models.generators. The number The of events in each is indicated. iron primary cosmic ray for several hadronic interaction number of bin events in eachSystematic energy showerand geometry and correcting for the attenuation of the uncertainties are indicated as a band. 1251 50 1407 998Shaded 781 619 bin is also shown. area indicates the systematic uncertainties. Figures are taken from the Proceedings of 457 light between the shower and the 331 detector, the longitudinal 5 ICRC 2011 . 40 230 188 profile of the shower can be reconstructed. This profile is ector stations ar143 186 fitted to a Gaisser-Hillas function [7] to determine Xmax we require data from at least one SD station, we place an 30 sensitive to the 106 47 and the energy of the shower [8]. dependent on both the energy shower zenith angle and FD has 27 teleThis paper is organized as follows. Section energy 2 discusses howcutmuch high hadron pro20 the distance of the SD station to the reconstructed core so Fe different stations, We follow the analysis in [6].a We consider duction cross already sectionreported can affect determination of the origin of cosmic rays. In Section 3, an 10 the trigger probability of a single station at these energies xcitation of nitroonly showers reconstructed using FD data and that have at application of inclusive photon spectra 4 at the TeV energy scale to air shower simulation is he passage of the least a signal in0 one of the SD stations measured in coinci- is saturated for both proton and iron primaries. 10Instead Section is 10 assigned to the discussion of low-energy pion productions. Finally er geometry is reE [eV] dence.discussed. The geometry for these events is determined with an Finally, requiring that the shower maximum is observed this paper isof"summarized in Section Figure 2: !Xmax (top◦ panel) and aerosol RMS (Xcontent (bottom data. The number max )5. angular uncertainty 0.6 [9]. The in thepanel) means that, for some shower geometries, we could introas a function of the constantly energy. Data (points) shown[10] with the rtional to the enatmosphere is monitored during dataare taking duce a composition dependent bias in our data. This is predictions for proton and iron for several hadronic interaction hower. Using the and only events for which a reliable measurement of the avoided using only geometries for which we are able to 2 Hadron production sectionSystematic models. The number of events in eachcross bin is indicated. attenuation of the aerosoluncertainties optical depth exists areasconsidered. Also the cloud observe the full range of the Xmax distribution. are indicated a band. r, the longitudinal content is monitored nightly of across the array and of periods the end 6744cross eventssection (42% ofon those pass the quality Possible effects an uncertainty hadronAtproduction thethat determination d. This profilewith is excessive cloud coverage are rejected. Furthermore, 18 6 . uncertainty cuts) remain above 10 eV. The systematic of X and RMS(X ) are investigated by R. Ulrich, R. Engel and M. Unger In this max data from maxone SD station, we place an determine Xmax we require at least we reject events with a χ2 /Ndf greater than 2.5 when the in the energy reconstruction of the FD events is 22% The study, artificial modifications are applied to the secondary multiplicity, hadron production cross cut on bothasthe zenith angle 2 profileenergy is fitteddependent to a Gaisser-Hillas, thisshower could indicate the and resolution in X13 is ata the level of 20 g/cm over the enmax section, elasticity and pion charge-ratio in the sibyll model and large number of air showers the of distance the SDThe station the reconstructed core so presence residualofclouds. totaltostatistical uncertainty n [6]. We consider ergy range considered. This resolution is estimated with a 8 , where an artificial modification is formulated as are simulated trigger probability of a single station at these energies a and that haveinat the the reconstruction ofbyXconex max is calculated including the detailed simulation of the detector and cross-checked using is saturated forthe both proton and iron primaries. easured in coinciuncertainties due to geometry reconstruction and to the the difference in the reconstructed X max when one event is f (E,uncertainties fmaximum +observed (f19 observed − 1)F (E), etermined with atmospheric an Finally,conditions. Events with above requiring that the shower is 19 ) = 1 by two or more FD stations (Fig. 1). ( 2 sol content in the 40 g/cm arethat, rejected. We shower also reject events that means for some geometries, wehave could 0 anintroE 5 1 PeV g data taking [10] angle duce between the shower dependent and the telescope smaller a composition bias in our This is PeV) F (E) = data.than (1) log10 (E/1 E > discussion 1 PeV. asurement of the only geometries which we are to 20◦ toavoided accountusing for the difficulties of for reconstructing their 3 Results and logable (10 EeV/1 PeV) 10 d. Also the cloud observe thetheir full range of the Xof distribution. geometry and for high fraction Cherenkov light. Fimax array and periods The factor f19we ) isrequire getting larger as energy E above E > 1 PeV, is max set" as nally, At in order to 6744 reliably determine Xthose that In Fig. 2 we present the updated resultswhile for !X and max themodification end events (42% fof(E, that pass the quality 15 18 this ed. Furthermore, the maximum has been actually observed within the field 1 below 10 eV since energy range has been studied by accelerator based experiments. f19 RMS (Xmax ) using 13 bins of ∆ log E = 0.1 below cuts) remain above 10 eV. The systematic uncertainty 19 19 han 2.5 when the of view theenergy FD. 15979 events pass quality selection. 10of eV and ∆ log Eon=X0.2 An energy in reconstruction of this the FD events is 22% The isofthe the preassigned uncertainty at 10 eV. Impact modifications and RMS(X are maxabove. max )depen2 18 2 could indicate the dent on correction ranging from 3.5 g/cm (at 10 eV) to resolution inFigures X atensure the level 20 data g/cm over the both enAnother set ofin cuts is max usedisto thatofthe sample is found 2. Largest systematic shift Xmax and RMS(X ) is caused by the max 2 19 istical uncertainty −0.3 g/cm (at 7.2 · 10 eV, the highest energy event) has ergy range considered. This resolution is estimated with a unbiased with respect to the cosmic ray composition. Since uncertainty of hadron production cross section indicated by closed circle. For example factor ted including the detailed simulation of the detector and cross-checked been applied to the2data to correct for a small bias observed using ∼ 3 increase of cross section at E = 1019 eV gives −100 g/cm shift in the mean of Xmax for ruction and to the the difference in the reconstructed Xmax when one event is proton primaries, thus they can be misidentified as iron primaries that have smaller Xmax values. certainties above observed by two or more FD stations (Fig. 1). See the original document for detailed discussions about other many observables by air shower vents that have an cope smaller than experiments. constructing their 3 Results and discussion erenkov light. Fi3 Fig. Inclusive photon spectra In 2 we present the updated results for !Xmax " and x we require that d within the field RMS (Xmax ) using 13 bins of ∆ log E = 0.1 below 3 illustrate theabove. impactAnof energy pion productions on air shower development. In left panel, quality selection. 1019 Figures eV and ∆ log E = 0.2 depen2 18 XF distributions of two correction ranging fromdifferent 3.5 g/cmpion (at production 10 eV) to models are presented within 0.01 < XF < 1.0: the data sample is dent 2 19 omposition. Since −0.3 g/cm (at 7.2 · 10 eV, the highest energy event) has been applied to the data to correct for a small bias observed 186
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Figure 2: Impact of uncertainties in hadronic interactions on Xmax and RMS(Xmax ). Left and right panel show the results with proton and iron primaries of the energy 1019.5 eV, respectively. Figures are taken from Phys. Rev. D 83, 054026 (2011) 6 .
ad-hoc model A (open circle) and ad-hoc model B (cross). Model A is supposed to carry out the primary energy into deeper in the atmosphere, while in model B energy is deposited earlier than model A. The number of electrons in air shower simulations with proton primaries with E = 1017 eV are found in the right panel. There are two points to be noted. One is the effect to an absolute energy reconstruction; In case showers are detected at an altitude of 900 g/cm2 , energy can be misidentified by a factor of 1.75 between model A and B due to the difference of number of electrons at the detection level. Second is the effect to a determination of chemical composition using Xmax . Xmax of model A is approximately 650 g/cm2 , while in model B Xmax is ∼ 750 g/cm2 . The difference by ∼ 100 g/cm2 is enough large to lead to a misconstruction of a kind of primary cosmic ray particle. 1e+08
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The Large Hadron Collider forward (LHCf) experiment 9 has been designed to measure the neutral particle (photon, π 0 and neutron) production cross sections at very forward collision angles of LHC proton-proton collisions. Study of inclusive photon spectra by LHCf 10 has been carried out in two pseudorapidity regions, 8.81 < η < 8.99 and η > 10.94, in which photons are dominantly attributed to π 0 decay. Figures 4 show the LHCf measurements and the predictions of several hadronic interaction generators. Different colors show the results from LHCf data (black) and predictions by qgsjet II-03 11 (blue), dpmjet 3.04 12 (red), sibyll 2.1 13 (green), epos 1.99 14 (magenta) and pythia 8.145 15 (yellow). Error bars and gray shaded areas in each plot indicate the experimental statistical and the systematic errors, respectively. The magenta shaded area indicates the statistical error of the MC data set using epos 1.99 as a representative of the other models. Accordingly it is recognized that none of the generators lies within the errors of the LHCf photon spectra over the entire energy range.
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Figure 4: Comparison of the single photon energy spectra between the experimental data and the MC predictions. Top panels show the spectra and the bottom panels show the ratios of MC results to experimental data. Left (right) panel shows the results for the large (small) rapidity range. Figures are taken from Phys. Lett. B 703, 128-134 (2011) 10 .
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Low energy hadronic interaction
The Pierre Auger Observatory has uses muons detected by their ground detectors for reconstructing the primary energy of cosmic ray. The mesons, dominantly pions, that decay into muons at the detection altitude are produced in the relatively low energy interactions (E ∼ 10 − 1000 GeV) that correspond to the last interaction of air shower development. It is known that effects of low energy interactions to the entire uncertainty of the number of muons that can be detected at the ground level are larger than 10 % 16 . It is also reported that the excess of the number of muons at ground level compared to the prediction of air shower simulations causes the systematic uncertainty for the interpretation of the ultra-high-energy measurements. An proposed idea 17 is to enhance the production of (anti-)baryons in hadron-air interactions,
that is implemented in the epos hadronic interaction generator. Modeling of baryon productions in hadron-nucleus and nucleus-nucleus collisions can be tested using the measurements by the NA61/SHINE experiment 18 . The NA61/SHINE experiment aims an understanding of hadron productions in relatively low energy regions (proton beam p < 158 GeV/c). NA61 has taken data since 2007. Analysis of inclusive charged pion production is performed using the 2007 pilot run with p + C interactions at 31 GeV/c, and analysis results are compared with the predictions of low-energy hadronic interaction generators commonly used in air-shower MC simulations. Figures 5 show the charged pion spectra and predictions by fluka 2008 19 , urqmd 1.3.1 20 and venus 4.12 21 that are parts of the corsika air shower simulation library 22 . It is recognized that the best agreement with the NA61 measurements is obtained by the fluka 2008 library.
Figure 5: Charged pion productions in p + C interactions at 31 GeV/c, and simulated results by fluka 2008, urqmd 1.3.1 and venus 4.12. π + productions are shown in the left panel and π − productions are shown in the right panel. Figures are taken from Phys. Rev. C 84, 034604 (2011) 18 .
5
Conclusions
The interpretation of observations of ultra-high-energy cosmic rays owe to knowledge of hadron productions in cosmic ray interaction in the atmosphere. As an example, there still exists a large systematic variation in Xmax and RMS(Xmax ) especially in the energy range E > 1018 eV, and this is responsible for somewhat poor understanding of chemical composition of ultra-high-energy cosmic rays. In this paper, possible reasons for systematic variations in the observables of air shower experiment are investigated within a few tens of GeV to EeV. References 1. 2. 3. 4. 5. 6.
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