Proton energy spectrum with the DAMPE experiment

The DAMPE (DArk Matter Particle Explorer) experiment, in orbit since December 17th 2015, is a space mission whose main purpose is the detection of cosmic electrons and photons up to energies of 10 TeV, in order to identify possible evidence of Dark Matter in their spectra. Furthermore it aims to measure the spectra and the elemental composition of the galactic cosmic rays nuclei up to the energy of hundreds of TeV. The proton analysis and the flux with kinetic energy ranging from 50 GeV up to 100 TeV, at the end of two years of data taking, will be presented and discussed.


Introduction
Cosmic Rays (CRs) with energies up to ∼ 4 PeV (the so called knee of the CRs spectrum [1]) are widely to be believed originated by the strong shock of Supernovae explosions in the Milky Way [2]. CRs are mainly composed of protons, therefore a very precise measurement of the proton flux up to energies of the order of PeV is crucial to understand the mechanism at the origin of their acceleration and the physical basis of the knee.
Starting from energies higher than 30 GeV the energy spectrum of CRs is expected to follow a featureless power-law according to the conventional acceleration models [3]. Recent measurements of proton flux carried out by baloon-and space-borne experiments (ATIC-2 [4], CREAM I-III [5], AMS-02 [6], PAMELA [7]) observed a spectral hardening, that is a deviation from the single powerlaw distribution. Moreover a spectral softening was observed at energies higher than 50 TeV (CREAM I-III [5], NUCLEON [9], ARGO-YBJ [8]).
One of the goals of DAMPE (DArk Matter Particle Explorer) is to investigate with high precision the hardening and the softening fitting a bridge between direct and indirect measurements.

DAMPE detector
The DAMPE detector [10] is composed by four sub-detectors from the top to the bottom: a Plastic Scintillator strip Detector (PSD), a Silicon-Tungsten tracKer-converter (STK), a BGO calorimeter and a NeUtron Detector (NUD).
The PSD measures the absolute value of the charge of incident particles (up to Z≤28), it provides also background rejection for gamma-ray detection. The STK reconstructs the trajectory and gives an independent charge measurement, it also acts as a gamma-ray converter using three tungsten foils a e-mail: antonio.debenedittis@le.infn.it interleaved in the first layers of silicon strips. The BGO calorimeter measures the energy of the particles and provides an electron/hadron discrimination, his depth (about 32 X 0 ) ensures that almost 100% of the energy of electrons and γ-rays is deposited in the calorimeter, and about 40% regarding nuclei [11]. The NUD gives a redundant electron/hadron discrimination using the neutrons produced in BGO by the hadronic showers.

Data analysis
Two years of data taking since the 1st January, 2016 to the 31st December, 2017 are taken in account in this analysis. The operational live time is about 75.5%, the lost time consists of three part: the instrumental dead time, the crossing time of the South Atlantic Anomaly (SAA) region, the time for the on-orbit calibration procedures.

Event selection
In this analysis some pre-selection cuts are applied to satisfy some basilar requests: to ensure that all sub-detectors work in good conditions, the SAA events are excluded; to avoid the effect due to the geomagnetic cut-off, only particles that release E ≥ 20 GeV in the calorimeter are considered; the track of the particle has to be geometrically contained in the detector in order to select particles that are crossing all the sub-detectors. After the pre-selection cuts, only the events passing the High Energy Trigger (HET), that foresees a deposited energy in the first four layers of BGO higher than 230 MeV (∼ 10 MIPs). The HET efficiency ( Fig. 1 left side) is estimated using the Unbias Trigger (which requires that the energy deposited in each of the first two BGO layers has to be ≥ 0.5 MIP): where N unb are the events passing the unbias trigger and N he|unb are those that satisfy also the HET. Moreover only the events with at least a reconstructed track in the STK are selected, and the selected track has to cross all the PSD layers and has to satisfy the STK-BGO match. The track reconstruction efficiency ( Fig. 1 right side) is estimated using a proton sample selected by an independent charge selection based on the reconstructed shower axis in the calorimeter, and it is defined as: where N BGOtrack are the events with a selected track in the calorimeter and N track|BGOtrack are those passing the STK track selection cuts.
Finally the proton candidates are selected by the information coming from the PSD charge distribution for different ranges of BGO energy. The charge recostruction efficiency (Fig. 2) is estimated independently for each PSD layer using the information coming from the first STK layer and from the other PSD layer.

Background
The background for protons is due mainly to mis-identified helium nuclei and electron events. The helium contamination is evaluated applying the template-fit method to the charge distributions obtained from PSD signals and using the MC samples of proton and helium nuclei (Fig. 3 left side). The  helium background is less than 2% up to energies of about 10 TeV; while the electron background, thanks to the high e/p discrimination power, is less than 0.1% (Fig. 3 right side). The helium and electron contamination is taken into account in the systematic uncertainties.

Results and conclusions
The effective acceptance (Fig. 4 left side) is evaluated using a MC sample of pure proton events. It is defined (for the i-th primary energy bin) as: where A gen is the geometrical factor of the MC generation half-sphere, N pass,i and N gen,i are the number of generated events and surviving events respectively.
The right side of Fig. 4 shows the DAMPE preliminary proton flux as a function of kinetic energy, compared with the previous measurements of AMS-02, PAMELA, ATIC-2, CREAM-III. The spectral hardening at E 200 GeV is in agreement with the measurements of AMS-02 and PAMELA. Moreover a softening at energies higher than 10 4 GeV, according to ATIC and CREAM (within the systematic uncertainties) results, has been observed with unprecedent resolution.  The data analysis and the evaluation of systematic uncertainties are still on-going. In the future, with the increase in data sample it is expected to obtain a proton flux up to energies higher than 100 TeV with high precision.