The cosmic ray proton plus helium energy spectrum measured by the ARGO-YBJ experiment in the energy range 3-300 TeV
ARGO-YBJ Collaboration, B. Bartoli, P. Bernardini, X.J. Bi, Z. Cao, S. Catalanotti, S.Z. Chen, T.L. Chen, S.W. Cui, B.Z. Dai, A. D'Amone, Danzengluobu, I. De Mitri, B. D'Ettorre Piazzoli, T. Di Girolamo, G. Di Sciascio, C.F. Feng, Zhaoyang Feng, Zhenyong Feng, Q.B. Gou, Y.Q. Guo, H.H. He, Haibing Hu, Hongbo Hu, M. Iacovacci, R. Iuppa, H.Y. Jia, Labaciren, H.J. Li, C. Liu, J. Liu, M.Y. Liu, H. Lu, L.L. Ma, X.H. Ma, G. Mancarella, S.M. Mari, G. Marsella, S. Mastroianni, P. Montini, C.C. Ning, L. Perrone, P. Pistilli, P. Salvini, R. Santonico, G. Settanta, P.R. Shen, X.D. Sheng, F. Shi, A. Surdo, Y.H. Tan, P. Vallania, S. Vernetto, C. Vigorito, H. Wang, C.Y. Wu, H.R. Wu, L. Xue, Q.Y. Yang, X.C. Yang, Z.G. Yao, A.F. Yuan, M. Zha, H.M. Zhang, L. Zhang, X.Y. Zhang, Y. Zhang, J. Zhao, Zhaxiciren, Zhaxisangzhu, X.X. Zhou, F.R. Zhu, Q.Q. Zhu
PPreprint submitted to Phys. Rev. D
The cosmic ray proton plus helium energy spectrum measured bythe ARGO–YBJ experiment in the energy range 3–300 TeV
B. Bartoli,
1, 2
P. Bernardini,
3, 4
X.J. Bi, Z. Cao, S. Catalanotti,
1, 2
S.Z. Chen, T.L. Chen, S.W. Cui, B.Z. Dai, A. D’Amone,
3, 4
Danzengluobu, I. De Mitri,
3, 4
B. D’EttorrePiazzoli,
1, 2
T. Di Girolamo,
1, 2
G. Di Sciascio, C.F. Feng, Zhaoyang Feng, ZhenyongFeng, Q.B. Gou, Y.Q. Guo, H.H. He, Haibing Hu, Hongbo Hu, M. Iacovacci,
1, 2
R. Iuppa,
9, 12
H.Y. Jia, Labaciren, H.J. Li, C. Liu, J. Liu, M.Y. Liu, H. Lu, L.L. Ma, X.H. Ma, G. Mancarella,
3, 4
S.M. Mari,
13, 14, ∗ G. Marsella,
3, 4
S. Mastroianni, P. Montini,
13, 14, † C.C. Ning, L. Perrone,
3, 4
P. Pistilli,
13, 14
P. Salvini, R. Santonico,
9, 12
G. Settanta, P.R. Shen, X.D. Sheng, F. Shi, A. Surdo, Y.H. Tan, P. Vallania,
16, 17
S. Vernetto,
16, 17
C. Vigorito,
16, 17
H. Wang, C.Y. Wu, H.R. Wu, L. Xue, Q.Y. Yang, X.C. Yang, Z.G. Yao, A.F. Yuan, M. Zha, H.M. Zhang, L. Zhang, X.Y. Zhang, Y. Zhang, J. Zhao, Zhaxiciren, Zhaxisangzhu, X.X. Zhou, F.R. Zhu, and Q.Q. Zhu (ARGO–YBJ Collaboration) Dipartimento di Fisica dell’Universit`a di Napoli “Federico II”,Complesso Universitario di Monte Sant’Angelo, via Cinthia, 80126 Napoli, Italy. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli,Complesso Universitario di Monte Sant’Angelo, via Cinthia, 80126 Napoli, Italy. Dipartimento Matematica e Fisica ”Ennio De Giorgi”,Universit`a del Salento, via per Arnesano, 73100 Lecce, Italy. Istituto Nazionale di Fisica Nucleare,Sezione di Lecce, via per Arnesano, 73100 Lecce, Italy. Key Laboratory of Particle Astrophysics,Institute of High Energy Physics, Chinese Academy of Sciences,P.O. Box 918, 100049 Beijing, P.R. China. Tibet University, 850000 Lhasa, Xizang, P.R. China. Hebei Normal University, Shijiazhuang 050016, Hebei, P.R. China. Yunnan University, 2 North Cuihu Rd.,650091 Kunming, Yunnan, P.R. China. Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata, a r X i v : . [ h e p - e x ] M a r ia della Ricerca Scientifica 1, 00133 Roma, Italy. Shandong University, 250100 Jinan, Shandong, P.R. China. Southwest Jiaotong University, 610031 Chengdu, Sichuan, P.R. China. Dipartimento di Fisica dell’Universit`a di Roma “Tor Vergata”,via della Ricerca Scientifica 1, 00133 Roma, Italy. Dipartimento di Matematica e Fisica dell’Universit`a “Roma Tre”,via della Vasca Navale 84, 00146 Roma, Italy. Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre,via della Vasca Navale 84, 00146 Roma, Italy. Istituto Nazionale di Fisica Nucleare,Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy. Istituto Nazionale di Fisica Nucleare,Sezione di Torino, via P. Giuria 1, 10125 Torino, Italy. Dipartimento di Fisica dell’Universit`a di Torino,via P. Giuria 1, 10125 Torino, Italy. (Dated: October 13, 2018)
Abstract
The ARGO–YBJ experiment is a full–coverage air shower detector located at the YangbajingCosmic Ray Observatory (Tibet, People’s Republic of China, 4300 m a.s.l.). The high altitude,combined with the full–coverage technique, allows the detection of extensive air showers in a wideenergy range and offer the possibility of measuring the cosmic ray proton plus helium spectrumdown to the TeV region, where direct balloon/space–borne measurements are available. The de-tector has been in stable data taking in its full configuration from November 2007 to February2013. In this paper the measurement of the cosmic ray proton plus helium energy spectrum ispresented in the region 3 −
300 TeV by analyzing the full collected data sample. The resultingspectral index is γ = − . ± .
01. These results demonstrate the possibility of performing anaccurate measurement of the spectrum of light elements with a ground based air shower detector. ∗ Corresponding author: [email protected] † Corresponding author: [email protected] . INTRODUCTION Cosmic rays are ionized nuclei reaching the Earth from outside the solar system. Manyexperimental efforts have been devoted to the study of cosmic ray properties. In the lastdecades many experiments were focused on the identification of cosmic ray sources and onthe understanding of their acceleration and propagation mechanisms. Despite a very largeamount of data collected so far, the origin and propagation of cosmic rays are still underdiscussion. Supernova remnants (SNRs) are commonly identified as the source of galacticcosmic rays since they could provide the amount of energy needed in order to accelerateparticles up to the highest energies in the Galaxy. The measurement of the diffuse gamma–ray radiation in the energy range 1 −
100 GeV supports these hypotheses on the origin andpropagation of cosmic rays [1]. Moreover the TeV gamma–ray emission from SNRs, detectedby ground–based experiment, can be related to the acceleration of particles up to ∼
100 TeV[2, 3]. A very detailed measurement of the energy spectrum and composition of primarycosmic rays will lead to a deeper knowledge of the acceleration and propagation mechanisms.Since the energy spectrum spans a huge energy interval, experiments dedicated to the studyof cosmic ray properties are essentially divided into two broad classes. Direct experimentsoperating on satellites or balloons are able to measure the energy spectrum and the isotopiccomposition of cosmic rays on top of the atmosphere. Due to their reduced detector activesurface and the limited exposure time the maximum detectable energy is limited up to fewTeV. New generation instruments, capable of long balloon flights, have extended the energymeasurements up to ∼
100 TeV. All the information concerning cosmic rays above 100 TeVis provided by ground–based air shower experiments. Air shower experiments are able toobserve the cascade of particles produced by the interaction between cosmic rays and theEarth’s atmosphere. Ground based experiments detect extensive air showers produced byprimaries with energies up to 10 eV, however they do not allow an easy determination ofthe abundances of individual elements and the measurement of the composition is thereforelimited only to the main elemental groups. Moreover, due to a lack of a model–independentenergy calibration, the determination of the primary energy relies on the hadronic interactionmodel used in the description of the shower’s development.The ARGO–YBJ experiment is a high–altitude full–coverage air shower detector which wasin full and stable data taking from November 2007 up to February 2013. As described in3ection II, the detector is equipped with a digital and an analog readout systems workingindependently in order to study the cosmic ray properties in the energy range 1 − TeV,which is one of the main physics goals of the ARGO–YBJ experiment. The high space–time resolution of the digital readout system allows the detection of showers produced byprimaries down to few TeV, where balloon–borne measurements are available. The analogreadout system was designed and built in order to detect showers in a very wide rangeof particle density at ground level and to explore the cosmic ray spectrum up to the PeVregion. In 2012 a first measurement of the cosmic ray proton plus helium (light component)spectrum obtained by analyzing a small sample collected during the first period of datataking with the detector in its full configuration (by using the digital readout informationonly) has been presented [4].In this paper we report the analysis of the full data sample collected by the ARGO–YBJexperiment in the period from January 2008 to December 2012 and the measurement ofthe light component energy spectrum of cosmic rays in the energy range 3 −
300 TeV byapplying an unfolding procedure based on the bayesian probabilities. The analysis of theanalog readout data and the corresponding cosmic ray spectrum up to the PeV energy regionis in progress and will be addressed in a future paper.
II. THE ARGO-YBJ EXPERIMENT
The ARGO–YBJ experiment (Yangbajing Cosmic Ray Observatory, Tibet, P.R. China.4300 m a.s.l.) is a full–coverage detector made of a single layer of Resistive Plate Chambers(RPCs) with ∼
93% active area [5, 6], surrounded by a partially instrumented guard ringdesigned to improve the event reconstruction. The detector is made of 1836 RPCs, arrangedin 153 clusters each made of 12 chambers. The digital readout consists of 18360 pads eachsegmented in 8 strips. A dedicated procedure was implemented to calibrate the detector inorder to achieve high pointing accuracy [7]. The angular and core reconstruction resolutionare respectively 0 . ◦ and 5 m for events with at least 500 fired pads [8, 9]. The installation ofthe central carpet was completed in June 2006. The guard ring was completed during spring2007 and connected to the data acquisition system [10] in November 2007. A simple triggerlogic based on the coincidence between the pad signals was implemented. The detectorhas been in stable data taking in its full configuration for more than five years with a4rigger threshold N pad = 20, corresponding to a trigger rate of about 3 . ,which correspond to primaries up to a few hundreds of TeV. In order to extend the detectoroperating range and investigate energies up to the PeV region each RPC has been equippedwith two large size electrodes called Big Pads [11]. Each Big Pad provide a signal whoseamplitude is proportional to the number of particles impinging the detector surface. Theanalog readout system allows a detailed measurement of showers with particle density atground up to more than 10 particles / m . III. DATA ANALYSISA. Unfolding of the cosmic ray energy spectrum
As widely described in [4, 12], the determination of the cosmic ray spectrum startingfrom the measured space–time distribution of charged particles at ground level is a classicalunfolding problem that can be dealt by using the bayesian technique[13]. In this frameworkthe detector response is represented by the probability P ( M j | E i ) of measuring a multiplicity M j due to a shower produced by a primary of energy E i . The estimated number of events ina certain energy bin E i is therefore related to the number of events measured in a multiplicitybin M j by the equation ˆ N ( E i ) ∝ (cid:88) j N ( M j ) P ( E i | M j ) (1)where η ij is constructed by using the Bayes theorem P ( E i | M j ) = P ( M j | E i ) P ( E i ) (cid:80) k P ( M j | E k ) P ( E k ) . (2)The values of the probability P ( M j | E i ) are evaluated by means of a Monte Carlo simulationof the development of the shower and of the detector response. The quantity P ( E i | M j )represents the probability that a shower detected with multiplicity M j has been producedby a primary of energy E i . The values of P ( M j | E i ) are evaluated by means of an iterative5rocedure starting from a prior value P (0) ( E i ), in which in the n –th step P ( n ) ( E i ) is replacedby the updated value P ( n +1) ( E i ) = ˆ N ( n ) ( E i ) (cid:80) k ˆ N ( n ) ( E k ) , (3)where ˆ N ( n ) ( E i ) is evaluated in the n -th step according to eq. 1. As initial prior P (0) ( E i ) ∼ E − . was chosen, the effect of using different prior distributions has been evaluated asnegligible. The iterative procedure ends when the variation of all ˆ N ( E i ) in two consecutivesteps are evaluated as negligible, namely less than 0.1 %. Typically the convergence isreached after 3 iterations. B. Air shower and detector simulations
The development of the shower in the Earth’s atmosphere has been simulated by usingthe CORSIKA (v. 6980) code [14]. The electromagnetic component are described by theEGS4 code [15, 16], while the high energy hadronic interactions are reproduced by QGSJET-II.03 model [17, 18]. Low energy hadronic interactions are described by the FLUKA package[19, 20]. Showers produced by Protons, Helium, CNO nuclei and Iron have been generatedwith a spectral index γ = − . − . × ) TeV. About 5 × showers have been generated in the zenith angle range 0–45 degrees and azimuth angle range0-360 degrees. Showers were sampled at the Yangbajing altitude and the shower core wasrandomly distributed over an area of (250 × centered on the detector. The resultingCORSIKA showers have been processed by a GEANT3 [21] based code in order to reproducethe detector response, including the effects of time resolution, RPC efficiency, trigger logic,accidental background produced by each pad and electronic noise. C. Event selection
The ARGO-YBJ experiment was in stable data taking in its full configuration for morethan five years: more than 5 × events have been recorded and reconstructed. Severaltools have been implemented in order to monitor the detector operation and reconstructionquality. The detector control system (DCS) [22] continuously monitors the RPC current, thehigh voltage distribution, the gas mixture and the environmental conditions (temperature,6ressure, humidity). In this work the analysis of events collected during the period 2008–2012 is presented. Data and simulated events have been selected according to a multi–stepprocedure in order to obtain high quality events and to ensure a reliable and unbiasedevaluation of the bayesian probabilities. The first step concerns the run selection: in orderto obtain a sample of high–quality runs, the working condition of the detector and thequality of the reconstruction procedure have been analyzed by using the criteria describedbelow. • At least 128 clusters out of 130 must be active and connected to the DAQ and triggersystems. This criterium selects runs taken with almost the whole apparatus in datataking, discarding the runs that can bias the analysis because of the switched–offclusters. • Only runs with a duration T (cid:62) • The value of the trigger rate for each run must stay within the range 3 . − . • To monitor the quality of the event reconstruction the mean value of the unnormalised χ obtained by fitting the shower front must be less than 135 ns (see figure 1). Nearlyall runs that have ¯ χ >
135 ns encountered some sort of problems.In figure 1 the distribution of the trigger rate and the ¯ χ of the reconstruction procedureare reported. The procedure described above selects a data sample of about 3 × events,corresponding to a live time of about 24000 hours.The following selection criteria (fiducial cuts) have been applied to both Monte Carlo andexperimental data in order to improve the quality of the reconstruction and to obtain thebest estimation of the bayesian probabilities. • Only events with reconstructed zenith angles ϑ R (cid:54) ◦ have been considered. Theresulting solid angle Ω is about 1.13 sr.7 ate [kHz]2.5 3 3.5 4 4.5 E n t r i e s / b i n χ [ ns ]
90 100 110 120 130 140 150 160 170 180 E n t r i e s / b i n FIG. 1. Distribution of the trigger rate (top) and of the unnormalised ¯ χ (bottom) of all the runscollected by the ARGO–YBJ experiment (black lines). The resulting 2008-2012 sample selectedaccording to the criteria described in section III is also reported (dashed red lines) • The measured shower multiplicity M had to be in the range 150 (cid:54) M (cid:54) × . Thisselection cut was introduced in order to reduce bias effects in the estimation of thebayesian probabilities that are mainly located at the edges of the simulated energyrange. Moreover the highest multiplicity cut avoid saturation effects of the digitalreadout system. • The cluster with the highest multiplicity had to be contained within an area of about40 ×
40 m centered on the detector. This cut was applied in order to reject eventswith their true shower core position located outside the detector surface.In order to select showers induced by proton and helium nuclei the following criterium hasbeen used. • Density cut: the average particle density ( ρ in ) measured by the central area (20 innerclusters) of the detector must be higher than the particle density ( ρ out ) measured by8
60 -40 -20 0 20 40 60-60-40-200204060
X[m] Y [ m ] en t r i e s / b i n FIG. 2. Distribution of reconstructed core positions of showers selected by applying the criteriadescribed in section III C. The boxes represent the clusters layout.
Log(E/GeV) R a t e [ H z ] -3 -2 -1 Simulated spectrumAfter fiducial cutsDensity cutLight ComponentHeavy Component
FIG. 3. Energy distribution of all Monte Carlo events (black) and of those surviving the fiducialcuts (blue) and the density cut (green and red) described in section III C according to the H¨orandelmodel [23]. the outermost area (42 outer clusters): ( ρ in > . ρ out ). This selection criteria basedon the lateral particle distribution was introduced in order to discard events producedby nuclei heavier than helium. In fact, in showers induced by heavy primaries thelateral distribution is wider than in light–induced ones. By applying this criterionon events with the core located in a narrow area around the detector center, showersmainly produced by light primaries have been selected. The contamination of elementsheavier than helium does not exceed few %, as discussed in section IV A 4.9 nergy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Energy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Energy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Energy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Energy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Energy [GeV] ] - G e V - s r - s - F l u x [ m -11 -10 -9 -8 -7 -6 -5 -4 Full sample
FIG. 4. The light component spectrum measured by the ARGO–YBJ experiment by using datataken in each year of the period 2008–2012 and the full 2008–2012 data sample. The power–lawfit of each spectrum is also reported (red lines).
In figure 2 the coordinates of the reconstructed core position of the events surviving theselection criteria described above are reported. The plot shows that the contribution ofevents located outside an area of 40 ×
40 m is negligible. In figure 3 the event rate obtainedby using the H¨orandel model for input spectra and isotopic composition [23] and survivingthe selection criteria described above is reported as a function of energy for both protonplus helium (light component) and heavier elements (heavy component). The plot showsthat the selected sample is essentially made of light nuclei. IV. THE LIGHT COMPONENT SPECTRUM
The analysis was performed on the sample selected by the criteria described in sectionIII. Simulated events have been sorted in 16 multiplicity bins and 13 energy bins in orderto minimize the statistical error and to reduce bin migration effects. The Monte Carlodata sample was analyzed in order to evaluate the probability distribution P ( M | E ) and the10nergy resolution which turns out to be about 10% for energies below 10 TeV and of theorder of 5% at energies of about 100 TeV. The multiplicity distribution extracted from datahas been unfolded according to the procedure described in section III A. Results are reportedin figure 4 for each year of data taking and also for the full sample. In order to investigatethe stability of the detector over a long period the analysis was performed separately on thedata samples collected during each solar year in the period 2008–2012. The values of theproton plus helium flux measured at 50 TeV are reported in table I. A power–law fit has beenperformed on the measured spectrum of each year and of the full data sample, the resultingspectral indices are reported in figure 5. Both the spectral indices and the flux values arein very good agreement between them, demonstrating the long–period reliability and thestability of the detector. The spectral index γ = − . ± .
01, obtained by analyzing the fulldata sample, is in good agreement with the one measured by using a smaller data samplecollected in the first months of 2008 [4] which was not corrected by the contamination fromheavier nuclei (see section IV A 4).In table II and figure 6 the flux obtained by analyzing the full data sample is reported.The spectrum covers a wide energy range, spanning about two orders of magnitude and isin excellent agreement with the previous ARGO–YBJ measurement. Statistical errors areof the order of 1 ‰ , more than 10 events have been selected in the highest energy region,while at the lowest energies more than 10 events have been selected. Systematic errorsare discussed in the next section. The ARGO–YBJ data are in good agreement with theCREAM proton plus helium spectrum [24]. At energies around 10 TeV and 50 TeV thefluxes differ by about 10% and 20% respectively. This means that the absolute energy scaledifference of the two experiments is within 4% and 6%. The uncertainty on the absoluteenergy scale has been evaluated by exploiting the Moon shadow tool at a level of 10% forenergies below 30 TeV [8]. At present the ARGO–YBJ experiment is the only ground–baseddetector able to investigate the cosmic ray energy spectrum in this energy region. A. Systematic uncertainties
A study of possible systematic effects has been performed. Four main sources of system-atic uncertainties on the flux measurement have been considered in this work: variation ofthe selection cuts, reliability of the detector simulation, different interaction models, con-11 Y ea r FIG. 5. Spectral indices of the power–law fit of the light component spectrum measured by an-alyzing the data sample collected in the period 2008–2012. The spectral index obtained in aprevious analysis of the ARGO–YBJ data is shown as 2008* [4] . The error bars represent thetotal uncertainty.TABLE I. Proton plus helium flux measured at 5 . × GeV..Year Flux ± tot. error [m − s − sr − GeV − ]2008 (4 . ± . × − . ± . × − . ± . × − . ± . × − . ± . × − tamination by heavy elements.
1. Selection criteria
The fiducial selection criteria have been fine tuned in order to obtain an unbiased evalu-ation of the bayesian probabilities, leading to the best estimation of the cosmic ray protonplus helium energy spectrum. A possible source of systematic error is related to the valuesof the fiducial cuts on observables used in the event selection procedure. The uncertainty12
ABLE II. Light component energy spectrum measured by the ARGO–YBJ experiment by usingthe full 2008–2012 data sample in each energy bin.Energy Range Energy Flux ± total error[GeV] [GeV] [m − s − sr − GeV − ]3 . × − . × . × (2 . ± . × − . × − . × . × (1 . ± . × − . × − . × . × (4 . ± . × − . × − . × . × (1 . ± . × − . × − . × . × (7 . ± . × − . × − . × . × (3 . ± . × − . × − . × . × (1 . ± . × − . × − . × . × (5 . ± . × − . × − . × . × (2 . ± . × − . × − . × . × (8 . ± . × − . × − . × . × (3 . ± . × − . × − . × . × (1 . ± . × − . × − . × . × (6 . ± . × − on the measured spectrum has been estimated by applying large variations (about 50 %)to the fiducial cuts and turns out to be of about 3%. The bins located at the edges of themeasured energy range are affected by an uncertainty of about ±
2. Reliability of the detector simulation
A systematic effect could arise from inaccuracies in the simulation of the detector re-sponse. The quality of the simulated events has been estimated by comparing the distri-bution of the observables obtained by applying the same selection criteria to Monte Carlosimulations and the data sample collected in each different year. As an example in figure 7the multiplicity distribution obtained from the Monte Carlo events is reported with the mul-tiplicity distribution of the data. The ratio between the two distributions is also reported13 nergy [GeV] ] . G e V - s r - s - [ m . E · F l u x ARGO-YBJ - P+HeARGO-YBJ - P+He (2012)CREAM - P+HePamela - PPamela - HeHorandel - P+HeGaisser-Stanev-Tilav - P+He
FIG. 6. The proton plus helium spectrum measured by the ARGO–YBJ experiment using the full2008–2012 data sample. The error bars represent the total uncertainty. Previous measurementperformed by ARGO–YBJ in a narrower energy range by analyzing a smaller data sample is alsoreported (blue squares) [4]. The green inverted triangles represent the sum of the proton andhelium spectra measured by the CREAM experiment [24]. The proton (stars) and helium (emptystars) spectra measured by the PAMELA experiment [25] are also shown. The light componentspectra according to the Gaisser-Stanev-Tilav (dashed–dotted line) [26] and H¨orandel (dashed line)[23] models are also shown. showing a good agreement between the two distributions. The contribution to the totalsystematic uncertainty due to the reliability of the detector simulation has been evaluatedby using the unfolding probabilities and turns out to be about ±
3. Hadronic interaction models
In order to estimate effects due to the particular choice of the high energy hadronicinteraction model in Monte Carlo simulations, a dataset has been generated by using theSIBYLL 2.1 model [27, 28]. These data have been compared with the QGSJET datasetused in this analysis. In figure 8 the ratio between the multiplicity distributions obtained byusing QGSJET model and the one obtained by using SIBYLL is reported as a function ofprimary energy. The plot shows that the variation of the multiplicity distributions obtained14 R a t e [ H z ] -4 -3 -2 -1 Log(M) D a t a / M C FIG. 7. Multiplicity distributions of the events selected by the criteria described in section III C.Values for data and Monte Carlo (black solid line) are reported. The ratio between data and MonteCarlo is shown in the lower panel.
Log(E/GeV)3 3.5 4 4.5 5 5.5
Log ( M Q / M S ) -0.2-0.15-0.1-0.0500.050.10.150.2 FIG. 8. Ratio between the multiplicity distributions obtained from QGSJET and SIBYLL basedMonte Carlo simulations. with the two hadronic models is of few percents, giving a negligible effect on the measuredflux. 15 . Contamination of heavier elements
A possible systematic effect relies in the contamination of elements heavier than Helium.The selection criterion based on the particle density rejects a large fraction of showers pro-duced by heavy primaries, as shown in figure 3. The fraction of heavier elements, estimatedby using the QGSJET–based simulations according to the H¨orandel model [23], is reducedand can be considered as negligible at energies up to 100 TeV. In the lower energy bins thecontamination is about 1%, whereas in the bins below 100 TeV the contamination does notexceed few % and in the higher energy bins it is about 10%. The unfolding procedure hasbeen set up in order to take into account the amount of heavier nuclei passing the selectioncriteria. The contribution of this effect is therefore not included in the total systematicuncertainty.
5. Summary of systematic errors
The total systematic uncertainty was determined by quadratically adding the individualcontributions. The results are affected by a systematic uncertainty of the order of ±
5% inthe central bins, while the edge bins are affected by a larger systematic uncertainty less than ± V. CONCLUSIONS
The ARGO–YBJ experiment was in operation in its full and stable configuration for morethan five years: a huge amount of data has been recorded and reconstructed. The peculiarcharacteristics of the detector, like the full–coverage technique, high altitude operation andhigh segmentation and spacetime resolution, allow the detection of showers produced byprimaries in a wide energy range from a few TeV up to a few hundreds of TeV. Showersdetected by ARGO–YBJ in the multiplicity range 150 − −
300 TeV) energy range. The relation between the shower sizespectrum and the cosmic ray energy spectrum has been established by using an unfoldingmethod based on the Bayes theorem. The unfolding procedure has been performed on thedata collected during each year and on the full data sample. The resulting energy spectrumspans the energy range 3 −
300 TeV, giving a spectral index γ = − . ± .
01, which is in very16ood agreement with the spectral indices obtained by analyzing the sample collected duringeach year, therefore demonstrating the excellent stability of the detector over a long period.The resulting spectral indices are also in good agreement with the one obtained by analyzingthe first data taken with the detector in its full configuration [4]. Special care was devotedto the determination of the uncertainties affecting the measured spectrum. The uncertaintyon the results is due to systematic effects of the order of ±
5% in the central energy bins.This measurement demonstrates the possibility to explore the cosmic ray properties down tothe TeV region with a ground–based experiment, giving at present one of the most accuratemeasurement of the cosmic ray proton plus helium energy spectrum in the multi–TeV region.
ACKNOWLEDGMENTS
This work is supported in China by NSFC (Contract No. 101201307940), the ChineseMinistry of Science and Technology, the Chinese Academy of Science, the Key Laboratory ofParticle Astrophysics, CAS, and in Italy by the Istituto Nazionale di Fisica Nucleare (INFN),and Ministero dell’Istruzione, dell’Universit`a e della Ricerca (MIUR). We also acknowledgethe essential support of W.Y. Chen, G. Yang, X.F. Yuan, C.Y. Zhao, R. Assiro, B. Biondo,S. Bricola, F. Budano, A. Corvaglia, B. D’Aquino, R. Esposito, A. Innocente, A. Mangano,E. Pastori, C. Pinto, E. Reali, F. Taurino and A. Zerbini, in the installation, debugging, andmaintenance of the detector. [1] M. Ackerman et al. , Astrophys. J. , 3 (2012).[2] F. A. Aharonian et al. , Nature , 75 (2004).[3] F. A. Aharonian et al. , Astron. Astrophys. , 235 (2007).[4] B. Bartoli et al. , Phys. Rev. D , 092005 (2012).[5] G. Aielli et al., Nucl. Instrum. Meth. A562 , 92 (2006).[6] G. Aielli et al., Nucl. Instrum. Meth.
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