High Energy Hadronic Interactions and 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 sig- nificantly 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 ultra- 18 high-energy cosmic rays (E & 10 eV) are indispensable for understanding their origin and the high energy phenomena occurred in the universe. Huge experiments for observing extensive air 14 showers, E & 10 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 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. P. FACAL SAN LUIS et al. THE DISTRIBUTION OF SHOWER MAXIMA OF UHECR AIR SHOWERS ] 2 EPOSv1.99 60 data: RMS=19±1.1 g/cm2 QGSJET01 p 850 SIBYLL2.1 MC: RMS=19±0.1 (stat.) +2 (syst.) g/cm2 QGSJETII -1

50 > [g/cm events

max 800

40

47 186 106 750 143 331 230 188 30 619 457 998 781 1251 700 1407 Fe 20

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18 19 0 10 10 P. FACAL SAN LUIS et al. THE DISTRIBUTION-80 -60OFSHOWER -40 -20 0 MAXIMA 20 40 60 OF UHECR 80 100 AIR SHOWERS E [eV] -2 ] ΔX / 2 [g/cm ] ]

2 max EPOSv1.99 2 2 70 60 data: RMS=19±1.1 g/cm Figure 1: The resolutionQGSJET01 of Xmax obtained using events recordedp SIBYLL2.1 +2 2 850 p MC: RMS=19±0.1 (stat.) (syst.) g/cm simultaneously from twoQGSJETII FD stations, compared to a detailed -1 60 ) [g/cm 50 > [g/cm events Monte Carlo simulation. max max 800 50 1251 1407 998 781 619 457 40

face Detector (SD) has 1660 water detector143 stations ar- RMS(X 331 230 188 30 619 457 143 186 998 781 30 ranged in a 1.5 km triangular grid and sensitive to the 106 1251 47 700 1407 Fe 20 shower particles at the ground. The FD has 27 tele- 20 scopes overlooking the SD, housed in 5 different stations, Fe 10 recording UV650 light emitted in the de-excitation of nitro- 10

gen molecules in the18 atmosphere after the19 passage of the 0 0 10 10 1018 1019 -80 -60 -40 -20 0 20 40 60 80 100 charged particles of a shower. The shower geometryE is [eV] re- E [eV] -2

ΔXmax/ 2 [g/cm ] ] constructed2 from the arrival times of the data. The number Figure 2: Xmax (top panel) and RMS (Xmax) (bottom panel) 70 ! " Figure 1: The resolution of Xmax obtained using events recordedof fluorescenceFigure 1: photonsXmax (left) emitted and is RMS( proportionalXmax) (right) to the distribution en- as a function obtained of by the the energy. measurements Data (points) by theare shown fluorescence with the simultaneously from two FD stations, compared to a detailed p predictions for proton and iron for several hadronic interaction ergy depositeddetector60 ofin the Pierreatmosphere Auger by Observatory. the shower. Measured Using the data (closed circle) are shown with the predictions for proton ) [g/cm Monte Carlo simulation. and iron primary cosmic ray for several hadronic interactionmodels. generators. The number Theof events number in each of bin events is indicated. in each Systematic energy shower geometrymax and correcting for the attenuation of the 50 1251 uncertainties are indicated as a band. 1407 998 781 619 bin is also shown. Shaded457 area indicates the systematic uncertainties. Figures are taken from the Proceedings of light between the shower and the331 detector, the longitudinal 5 40 ICRC 2011 . profile of the shower can be reconstructed.230 188 This profile is

face Detector (SD) has 1660 water detector stations ar- RMS(X 143 186 fitted to a Gaisser-Hillas30 function [7] to determine Xmax we require data from at least one SD station, we place an ranged in a 1.5 km triangular grid and sensitive to the 106 shower particles at the ground. The FD has 27 tele-and the energy of the shower [8]. 47 energy dependent cut on both the shower zenith angle and This20 paper is organized as follows. Section 2 discusses how much high energy hadron pro- the distance of the SD station to the reconstructed core so scopes overlooking the SD, housed in 5 different stations,We followduction the analysis cross alreadysection reported can affect in [6]. a We determination considerFe of the origin of cosmic rays. In Section 3, an recording UV light emitted in the de-excitation of nitro-only showers10 reconstructed using FD data and that have at the trigger probability of a single station at these energies application of inclusive photon spectra 4 at the TeV energy scale to air shower simulation is gen molecules in the atmosphere after the passage of theleast a signal in0 one of the SD stations measured in coinci- is saturated for both proton and iron primaries. discussed.10 Instead18 Section is1019 assigned to the discussion of low-energy productions. Finally charged particles of a shower. The shower geometry is re-dence. The geometry for these events is determined withE [eV] an Finally, requiring that the shower maximum is observed constructed from the arrival times of the data. The number Figurethis paper 2: Xmax is summarized(top panel) and inRMS Section (Xmax) 5.(bottom panel) angular uncertainty! of" 0.6◦ [9]. The aerosol content in the means that, for some shower geometries, we could intro- of fluorescence photons emitted is proportional to the en-atmosphereas a function is monitored of the constantly energy. Data during (points) data are taking shown [10] with theduce a composition dependent bias in our data. This is ergy deposited in the atmosphere by the shower. Using the predictions for proton and iron for several hadronic interaction and onlymodels.2 events Hadron The for number which production of events a reliable in each crossmeasurement bin is indicated. section of Systematic the avoided using only geometries for which we are able to shower geometry and correcting for the attenuation of theaerosoluncertainties optical depth are indicated exists are as considered. a band. Also the cloud observe the full range of the Xmax distribution. light between the shower and the detector, the longitudinal content is monitoredPossible effects nightly ofacross an uncertaintythe array and ofperiods hadronAt production the end 6744 cross events section (42% of on those the that determination pass the quality profile of the shower can be reconstructed. This profile is with excessive cloud coverage are rejected. Furthermore, cuts) remain above 1018 eV.Thesystematicuncertainty6 fitted to a Gaisser-Hillas function [7] to determine X weof requireXmax and data from RMS(2 atX leastmax one) are SD investigated station, we place by an R. Ulrich, R. Engel and M. Unger . In this maxwe reject events with a χ /Ndf greater than 2.5 when the in the energy reconstruction of the FD events is 22% The and the energy of the shower [8]. energystudy, dependent artificial cut modifications on both the shower are applied zenith angle to the and secondary multiplicity, hadron production cross profile is fitted to a Gaisser-Hillas, as this could indicate the resolution in X13 is at the level of 20 g/cm2 over the en- thesection, distance elasticity of the SD and station pion to charge-ratio the reconstructed in the coresibyll so model maxand a large number of air showers We follow the analysis already reported in [6]. We considerpresence of residual clouds. The total statistical uncertainty ergy range considered. This resolution is estimated with a theare trigger simulated probability by conex of a single8, where station an at artificialthese energie modifications is formulated as only showers reconstructed using FD data and that havein at the reconstruction of Xmax is calculated including the detailed simulation of the detector and cross-checked using least a signal in one of the SD stations measured in coinci-uncertaintiesis saturated due to for the both geometry proton and reconstruction iron primaries. and to the the difference in the reconstructed Xmax when one event is dence. The geometry for these events is determined withatmospheric an Finally, conditions. requiring that Events the showerwithf(E, uncertainties f maximum19) = 1is above + observed (f19 observed1)F (E by), two or more FD stations (Fig. 1). 2 − angular uncertainty of 0.6◦ [9]. The aerosol content in the40 g/cmmeansare that, rejected. for some We showeralso reject geometries, events that we have could( an intro- 0 E 5 1 PeV atmosphere is monitored constantly during data taking [10]angleduce between a composition the shower dependent and the telescope biasF (E in) oursmaller = data. than Thislog ( isE/1 PeV) (1) 10 E > 1 PeV. and only events for which a reliable measurement of the20◦ toavoided account using for the only difficulties geometries of for reconstructing which we are theirlog able10(10 to3Resultsanddiscussion EeV/1 PeV) aerosol optical depth exists are considered. Also the cloudgeometryobserve and for the their full range high fraction of the X ofmax Cherenkovdistribution. light. Fi- content is monitored nightly across the array and periodsnally,At inThe order the modification end to 6744 reliably events determine factor (42%f of(XE, thosemax f19we that) is require pass getting the that quality largerIn Fig. as energy 2 we presentE above the updatedE > 1 PeV, results while for X ismax set asand 15 18 ! " with excessive cloud coverage are rejected. Furthermore,the maximumcuts)1 below remain has 10 been aboveeV actually since10 eV this observed.Thesystematicuncertainty energy within range the has field beenRMS studied (Xmax by) using accelerator 13 bins based of ∆log experiments.E =0.1 belowf19 we reject events with a χ2/Ndf greater than 2.5 when the 19 19 of viewinis of the the the energy preassigned FD. 15979 reconstruction events uncertainty pass of this the FDquality at 10events selection.eV. is 22% Impact The10 of modificationseV and ∆logE on=0Xmax.2 above.and RMS( An energyXmax) depen- are profile is fitted to a Gaisser-Hillas, as this could indicate the 2 2 18 Anotherresolutionfound set of in cuts in FiguresX ismax usedis to 2. at ensure the Largest level that of thesystematic 20 datag/cm sampleover shift isthe bothen-dent oncorrectionXmax and ranging RMS( fromX 3.5maxg)/ iscm caused(at 10 byeV) the to presence of residual clouds. The total statistical uncertaintyunbiasedergy with range respect considered. to the cosmic This resolution ray composition. is estimated Since with a0.3g/cm2 (at 7.2 1019 eV, the highest energy event) has uncertainty of hadron production cross section− indicated by closed· circle. For example factor in the reconstruction of Xmax is calculated including the detailed simulation of the detector and cross-checked19 usinbeeng applied to the2 data to correct for a small bias observed uncertainties due to the geometry reconstruction and to the 3 increase of cross section at E = 10 eV gives 100 g/cm shift in the mean of Xmax for the∼ difference in the reconstructed Xmax when one event is − proton primaries, thus they can be misidentified as iron primaries that have smaller X values. atmospheric conditions. Events with uncertainties above observed by two or more FD stations (Fig. 1). max 40 g/cm2 are rejected. We also reject events that have an See the original document for detailed discussions about other many observables by air shower angle between the shower and the telescope smaller than experiments. 20◦ to account for the difficulties of reconstructing their 3Resultsanddiscussion geometry and for their high fraction of Cherenkov light. Fi- 3 Inclusive photon spectra nally, in order to reliably determine Xmax we require that In Fig. 2 we present the updated results for X and ! max" the maximum has been actually observed within the field RMS (Xmax) using 13 bins of ∆logE =0.1 below of view of the FD. 15979 events pass this quality selection. 1019 FigureseV and ∆ 3 illustratelogE =0 the.2 above. impact An of energy pion productions depen- on air shower development. In left panel, Another set of cuts is used to ensure that the data sample is dentXF distributions correction ranging of two from different 3.5 g/cm pion2 (at production1018 eV) to models are presented within 0.01 < XF < 1.0: unbiased with respect to the cosmic ray composition. Since 0.3g/cm2 (at 7.2 1019 eV, the highest energy event) has been− applied to the data· to correct for a small bias observed 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 2 composition using Xmax. Xmax of model A is approximately 650 g/cm , 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

1 Vertical shower σ 1 d

F0.1 inela ad-hoc A ad-hoc A σ 1e+07 d dX ad-hoc B ad-hoc B F X

0.01 Number of Electrons Number

1e+06 200 300 400 500 600 700 800 900 1000 0.01 0.1 1 XF Vertical Depth (g/cm2 )

Figure 3: (Left) XF distributions of two different pion production models. Open circle and cross indicate the ad-hoc model A and B, respectively. (Right) The number of electrons in air shower simulation based on ad-hoc model A (open circle) and B (cross). Figures are taken from the TDR of the LHCf experiment 9. The forward (LHCf) experiment 9 has been designed to measure the neutral particle (photon, π0 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 π0 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.

10-3 10-3 /GeV /GeV -4 -4 ine 10 LHCf s=7TeV ine 10 LHCf s=7TeV Gamma-ray like Gamma-ray like 10-5 ° 10-5 ° η > 10.94, ∆φ = 360 8.81 < η < 8.99, ∆φ = 20 Events/N Events/N

10-6 10-6

10-7 10-7

-1 -1 10-8 Data 2010, ∫ Ldt=0.68+0.53nb 10-8 Data 2010, ∫ Ldt=0.68+0.53nb Data 2010, Stat. + Syst. error Data 2010, Stat. + Syst. error DPMJET 3.04 DPMJET 3.04 -9 -9 10 QGSJET II-03 10 QGSJET II-03 SIBYLL 2.1 SIBYLL 2.1 EPOS 1.99 EPOS 1.99 10-10 10-10 PYTHIA 8.145 PYTHIA 8.145

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0 0 500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500 Energy[GeV] Energy[GeV]

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.

4 Low energy hadronic interaction

The Pierre Auger Observatory has uses muons detected by their ground detectors for re- constructing the primary energy of cosmic ray. The mesons, dominantly , 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.

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