Transverse momentum spectra and nuclear modification factors of charged particles in Xe-Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV

Transverse momentum ($p_{\rm T}$) spectra of charged particles at mid-pseudorapidity in Xe-Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV measured with the ALICE apparatus at the Large Hadron Collider are reported. The kinematic range $0.15<p_{\rm T}<50$ GeV/$c$ and $|\eta|<0.8$ is covered. Results are presented in nine classes of collision centrality in the 0-80% range. For comparison, a pp reference at the collision energy of $\sqrt{s}$ = 5.44 TeV is obtained by interpolating between existing \pp measurements at $\sqrt{s}$ = 5.02 and 7 TeV. The nuclear modification factors in central Xe-Xe collisions and Pb-Pb collisions at a similar center-of-mass energy of $\sqrt{s_{\rm NN}}$ = 5.02 TeV, and in addition at 2.76 TeV, at analogous ranges of charged particle multiplicity density $\left\langle\rm{d}N_{\rm ch}/\rm{d}\eta\right\rangle$ show a remarkable similarity at $p_{\rm T}>10$ GeV/$c$. The centrality dependence of the ratio of the average transverse momentum $\left\langle p_{\rm{T}}\right\rangle$ in Xe-Xe collisions over Pb-Pb collision at $\sqrt{s}$ = 5.02 TeV is compared to hydrodynamical model calculations.


Introduction
Transverse momentum (p T ) spectra of charged particles carry essential information about the high-density deconfined state of strongly-interacting matter commonly denoted as quark-gluon plasma, that is formed in high-energy nucleus-nucleus (A-A) collisions [1]. Relativistic hydrodynamics is able to model the evolution of this medium [2,3].
At low to intermediate p T , typically in the range of up to 10 GeV/c, charged particle production is governed by the collective expansion of the system, which is observed in the shapes of singleparticle transverse-momentum spectra [4,5] and multi-particle correlations [2]. However, there is presently an intense debate as to whether the strikingly similar signatures observed in small collision systems (pp and p-A) are also of hydrodynamical origin [6][7][8][9][10][11][12][13][14]. A key ingredient of calculations in relativistic hydrodynamics is the initial energy density [2,15,16]. The number of produced particles and the volume of the medium are approximately proportional to the number of nucleons N part that participate in the collision [17][18][19]. Thus, the particle density per unit volume is roughly independent of N part . As a consequence, particle spectra at small transverse momentum should be similar in nucleus-nucleus collisions, independently of the mass number, when compared at similar values of N part [20].
At high p T , typically above 10 GeV/c, particles originate from parton fragmentation and are sensitive to the amount of energy loss that the partons suffer when propagating in the medium. In a simplified model, the energy loss depends on the number of scattering centers, which is roughly proportional to the energy density, and on the path length that the parton propagates in the medium [21]. For elastic collisions, the dependence is linear, while for medium induced gluon radiation, it is quadratic [22]. A description of experimental data lies in between those [23].
For hard processes, the production yield N AA in nucleus-nucleus (A-A) collisions is expected to scale with the average nuclear overlap function T AA when compared to the production cross section σ pp in pp collisions. In the absence of nuclear effects, the nuclear modification factor R AA (p T ) = 1 T AA · dN AA (p T )/dp T dσ pp (p T )/dp T (1) equals unity. The average nuclear overlap function is defined as the average number of binary nucleon-nucleon collisions N coll per inelastic nucleon-nucleon cross section and is estimated via a Glauber model calculation [24]. At the Large Hadron Collider (LHC), particle production is observed to be strongly suppressed in Pb-Pb collisions by a factor of up to 7-8 around p T = 6-7 GeV/c with a linear decrease at higher p T but still a substantial suppression even above 100 GeV/c [5,25].
The LHC produced for the first time collisions of xenon nuclei at a center-of-mass energy of √ s NN = 5.44 TeV during a pilot run with 6 hours of stable beams in October 2017. This allows for studying the dependence of particle production on the collision system size where xenon neatly bridges the gap between data from pp, p-Pb and Pb-Pb collisions. Here, the atomic mass numbers are A = 129 for xenon, and A = 208 for lead with half-density radii of the nuclear-charge distribution of r = (5.36 ± 0.1) fm and (6.62 ± 0.06) fm, respectively [24,26]. The parameters of the nuclear-charge density distribution for 129 Xe are not yet measured but were extrapolated from neighboring isotopes and are thus less precisely known than for 208 Pb. While 208 Pb is a spherical nucleus, 129 Xe has a deformation parameter of β 2 = (0.18 ± 0.02).
The ITS is comprised of six cylindrical layers of silicon detectors with radii between 3.9 and 43.0 cm. The two innermost layers, with average radii of 3.9 cm and 7.6 cm, are equipped with Silicon Pixel Detectors (SPD); the two intermediate layers, with average radii of 15.0 cm and 23.9 cm, are equipped with Silicon Drift Detectors (SDD) and the two outermost layers, with average radii of 38.0 cm and 43.0 cm, are equipped with double-sided Silicon Strip Detectors (SSD). The large cylindrical TPC has an active radial range from about 85 to 250 cm and an overall length along the beam direction of 500 cm. It covers the full azimuth in the pseudorapidity range |η| < 0.9 and provides track reconstruction with up to 159 points along the trajectory of a charged particle as well as particle identification via the measurement of specific energy loss dE/dx.
The collision vertex is determined using reconstructed particle trajectories in the TPC including hits in the ITS. All collisions with a reconstructed vertex position within ±10 cm along the beam direction from the nominal interaction point are accepted. The collision centrality is defined as the percentile of the hadronic cross section corresponding to the measured charged R AA of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration particle multiplicity. The centrality determination is based on the sum of the amplitudes of the V0A and V0C signals [18,19]. Averaged quantities characterizing a centrality class such as the number of participants N part , the number of binary collisions N coll , and the nuclear overlap function T AA are calculated as the average over all events in this class by fitting the experimental distribution with a Glauber Monte Carlo model that employs negative binomial distributions to model multiplicity production [18, 19] (see Table 1). The analysis is restricted to the 0-80% centrality range in order to ensure that effects of trigger inefficiency and contamination by electromagnetic processes are negligible.

Track selection
Primary charged particles within the kinematic range |η| < 0.8 and 0.15 < p T < 50 GeV/c are measured. Here, primaries are defined as all charged particles with a proper lifetime τ larger than 1 cm/c that are either produced directly in the primary beam-beam interaction, or from decays of particles with τ smaller than 1 cm/c, excluding particles produced in interactions with the detector material [31]. The track selection is optimized for best track quality and minimum contamination from secondary particles. The selection criteria are identical to those of the previous analysis of Pb-Pb collisions at √ s NN = 5.02 TeV [5] except for the following changes in the parameterization on the transverse momentum dependence. The geometrical track length in the TPC fiducial volume [29] is L/cm > 130 − (p T / GeV/c) −0.7 , and the distance of closest approach to the primary vertex in the transverse plane is |DCA xy |/cm < 0.0119+0.049 (p T / GeV/c) −1 . These changes reflect differences in particle tracking due to the reduced magnetic field. In order to reject fake tracks that contaminate the spectrum, especially at high p T , another selection is introduced: the uncertainty in the reconstructed p T as estimated from the covariance matrix of the track fit must be less than ten times the standard deviation, when averaged over all tracks at that momentum.

Corrections
The doubly-differential transverse momentum spectra in Xe-Xe collisions are normalized by the number of events N ev in each centrality class, and are given by R AA of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration where N rec ch is the raw yield of reconstructed primary charged particles in each interval of pseudorapidity and transverse momentum (∆η, ∆p T ). The symbols α(∆p T ) and ε(∆p T ) are the correction factors for detector acceptance and tracking efficiency, respectively. The correction due to the finite transverse-momentum resolution in the reconstruction of primary charged particles is denoted by δ p T (∆p T ). The efficiencies for trigger, event vertex reconstruction and tracking are estimated using Monte Carlo simulations with HIJING [32] as the event generator and GEANT3 [33] for particle propagation and simulation of the detector response. The trigger and vertex selections are fully efficient for the whole centrality range used in the analysis. Contamination from secondary charged particles, i.e. from weak decays and interactions in the detector material, is subtracted from the raw spectrum by employing a data driven method [5]. Reconstructed trajectories of primary charged particles point to the collision vertex, while charged particles from weak decays and particles generated in the detector material preferentially point away from it. In order to distinguish between primary and secondary particles, the distance of closest approach to the collision vertex in radial direction, DCA xy , is used. A multitemplate function that consists of templates for primary particles, secondary particles produced from weak decays and secondary particles from interactions in the detector material is fitted to the DCA xy distributions in each p T interval.
The primary charged particle reconstruction efficiency is obtained from the Monte Carlo simulation. As discussed in detail in [5], this efficiency depends on the relative abundances of the various primary particles species. These relative abundances are adjusted in the simulation using a data-driven re-weighting procedure. The particle composition in Xe-Xe collisions is not yet known. However, bulk particle production scales with the average charged particle multiplicity density, dN ch /dη , independently of the collision system [34]. In Xe-Xe collisions, The acceptance times tracking efficiency for charged pions, charged kaons and (anti-)protons for 5% most central Xe-Xe collisions is shown in Fig. 1 as a function of the particle transverse momentum and compared to 10-20% Pb-Pb collisions at √ s NN = 5.02 TeV. The two centrality classes have similar multiplicity densities. The particular shape with a dip at p T ∼ 0.4 GeV/c arises from the geometrical length selection that is especially visible for pions. This dip corresponds to particles that cross the TPC sector boundaries under small angles. The decrease at low values of p T is due to curling trajectories in the magnetic field which do not reach the required minimum track length in the TPC. In Pb-Pb collisions, the magnetic field was set to B = 0.5 T, which results in the dip being positioned around 1 GeV/c. At large p T , above 7 GeV/c, the tracking efficiency is reduced by an increased local track density, i.e. high p T particles are preferentially produced within jets, leading to a slight decrease in the track finding performance.
The transverse momentum of primary charged particles is reconstructed from the track curvature as measured by the ITS and the TPC [38]. The finite momentum resolution modifies the reconstructed charged-particle spectrum and is estimated by the corresponding covariance matrix element of the Kalman fit. The relative p T resolution, σ (p T )/p T , depends on the momentum and amounts to approximately 4.5% at p T = 0.15 GeV/c, it shows a minimum of 1.5% around p T = 1.0 GeV/c, and increases linearly for larger p T , approaching 9.3% at 50 GeV/c. The centrality dependence of the relative p T resolution is negligible. To account for the finite p T resolution, correction factors to the spectra for p T > 10 GeV/c are determined using an unfolding procedure [39]. At transverse momenta below 10 GeV/c, these corrections are negligible. The p T dependent correction factors are applied to the measured p T spectrum and depend slightly on collision centrality because of the change in the slope of the spectrum, especially at high p T . The correction factor δ p T deviates from unity by less than 1% below p T = 15 GeV/c for all centrality classes, and by up to 3% (4%) in 0-5% (70-80%) central collisions above 15 GeV/c.

pp reference at √ s = 5.44 TeV
The p T -differential cross section in pp collisions at √ s = 5.44 TeV is needed to measure the corresponding nuclear modification factor. As there are no measurements of pp collisions at this energy, a reference is obtained by interpolating pp references [5,39] as measured at √ s = 5.02 TeV and √ s = 7 TeV assuming a power-law dependence in each The statistical uncertainties of the pp reference are interpolated between the references at √ s = 5.02 TeV and 7 TeV assuming also a power-law dependence and are assigned to the interpolated reference. This interpolation method [39] is based on the observation that the cross section at a fixed transverse momentum approximately scales with collision energy like a power law.
As an alternative approach, the scaling of the measured cross section at √ s = 5.02 TeV to √ s = 5.44 TeV by using the ratio of spectra at those two energies obtained with the PYTHIA 8 (Monash tune) event generator [40] is studied. The ratio of the pp references at √ s = 5.44 TeV from the power-law interpolation and at √ s = 5.02 TeV is shown in Fig. 2 together with results obtained with the alternative method. The spectrum is harder at higher collision energy, with a small change in the total cross section of 4% below 1 GeV/c and an increase of about 10% at transverse momenta above 10 GeV/c.

Systematic uncertainties
For the total systematic uncertainty, all contributions are added in quadrature and are summarized in Table 2.   The effect of the selection of events based on the vertex position is studied by comparing the fully corrected p T spectra obtained with alternative vertex selections corresponding to ± 5 cm, and ± 20 cm. The difference in the fully corrected p T spectra is less than 0.3% for central R AA of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration collisions and less than 0.5% for peripheral collisions.
In order to test the description of the detector response and the track reconstruction in the simulation, all criteria for track selection are varied within the ranges as described in the previous publication [5]. A full analysis is performed by varying one selection criterion at a time. The maximum change in the corrected p T spectrum is then considered as systematic uncertainty.
The overall systematic uncertainty related to track selection is obtained from summing up all individual contributions quadratically and it amounts to 0.6-3.0%, depending on p T and centrality.
The systematic uncertainty on the secondary-particle contamination is estimated by varying the fit model using two templates, i.e. for primaries and secondaries, or three templates, i.e. primaries, secondaries from interactions in the detector material and secondaries from weak decays of K 0 s and Λ, as well as varying the fit ranges. The maximum difference between data and the two-component-template fit is summed in quadrature together with the difference between results obtained from the two-and three-component-template fits. The systematic uncertainty due to the contamination from secondaries is decreasing with increasing p T . It dominates at low p T with values up to 4% and is negligible above 2 GeV/c. The systematic uncertainty on the primary particle composition is taken from [5]. An additional uncertainty is estimated by assuming the particle composition from a neighboring dN ch /dη range to the matched one in the Pb-Pb analysis and is added quadratically. The sum peaks around 3 GeV/c with a maximum of 5% (less than 2%) for the 0-5% (70-80%) centrality class.
In order to estimate the systematic uncertainty due to the tracking efficiency, the track matching between the TPC and the ITS information in data and Monte Carlo is compared after scaling the fraction of secondary particles obtained from the fits to the DCA xy distributions [5]. The difference in the TPC-ITS track-matching efficiency between data and simulation is assigned to the corresponding systematic uncertainty (see Table 2). It amounts to 2% in central collisions, and up to 3.5% in peripheral collisions.
The material budget in ALICE at η ≈ 0 amounts to (11.4 ± 0.5)% in radiation lengths for primary charged particles that have sufficient track length in the TPC [38]. A difference in the amount of detector material leads to different amounts of secondary particles that are produced. After the subtraction of the contribution due to secondaries using the three-component DCA xy fits, the differences on the secondary correction factor is negligible. A variation of the material budget within above limits leads to a p T dependent systematic uncertainty on the tracking efficiency of 0.1-0.3%.
The uncertainty due to the finite p T resolution is estimated using the azimuthal dependence of the 1/p T spectra for positively and negatively charged particles. The relative shift of the spectra for oppositely charged particles along 1/p T determines the size of uncertainty for a given angle. The RMS of the 1/p T shift as distributed over the full azimuth is used as an additional increase of the p T resolution. The uncertainty due to the finite p T resolution is significant only at the highest momentum bin and amounts to 0.5% (0.9%) for the 0-5% (70-80%) centrality class.
The uncertainty due to the centrality determination is estimated by changing the fraction of the visible cross section (90.0 ± 0.5)%. The uncertainty is estimated from the variation of the resulting p T spectra and amounts to ∼ 0.1% and ∼ 3.2% for central (0-5%) and peripheral (70-80%) collisions, respectively. R AA of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration The systematic uncertainty of the pp reference at √ s = 5.44 TeV has two contributions, which are added quadratically. For each p T interval, the systematic uncertainty of the pp references at √ s = 5.02 TeV and √ s = 7 TeV are interpolated to √ s = 5.44 TeV by using a power-law. This corresponds to interpolating between the upper and lower boundaries of the experimental data points as given by their systematic uncertainties. It assumes full correlation of systematic uncertainties at both energies.
The difference between the interpolated reference and the one using the PYTHIA 8 event generator is assigned as the other contribution to the systematic uncertainty in the pp reference, in each p T interval. The systematic uncertainty in the pp reference has a minimum of 2.2% around 1 GeV/c and reaches its maximum of 7.7% at the highest momentum bin. The systematic uncertainty of the pp reference spectrum is dominated by the interpolation uncertainty, especially at momenta above 10 GeV/c. In the most-peripheral collisions, the p T spectrum is similar to that of pp collisions and exhibits a power law behavior that is characteristic of hard-parton scattering and vacuum fragmentation. With increasing collision centrality, the p T differential cross section is progressively depleted above 5 GeV/c.  In order to determine the nuclear modification factor R AA , the interpolated p T -differential cross R AA of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV ALICE Collaboration section is scaled by the average nuclear overlap function T AA . The resulting nuclear modification factor as a function of transverse momentum is shown in Fig. 4 for nine centrality classes. The overall normalization uncertainties for R AA are indicated by vertical bars around unity. The uncertainties of the pp reference and the centrality determination are added in quadrature. The latter is larger for Xe-Xe collisions than for Pb-Pb because of the less precisely known nuclearcharge-density distribution of the deformed 129 Xe and the resulting larger relative uncertainty in T AA [18,19]. The nuclear modification factor exhibits a strong centrality dependence with a minimum around p T = 6-7 GeV/c and an almost linear rise above. In particular, in the 5% most central collisions, at the minimum, the yield is suppressed by a factor of about 6 with respect to the scaled pp reference. The nuclear modification factor reaches a value of 0.6 at the highest measured transverse-momentum interval of 30-50 GeV/c. For comparison, the nuclear modification factor R AA in Pb-Pb collisions at √ s NN = 5.02 TeV is shown in Fig. 4 as open circles for the same centrality classes as Xe-Xe. In both collision systems, a similar characteristic p T dependence of R AA is observed. In Pb-Pb collisions, the suppression of high-momentum particles is apparently stronger for the same centrality class but still in agreement with Xe-Xe collisions within uncertainties.

Results
Nuclear modification factors from Xe-Xe and Pb-Pb collisions and their ratios at similar ranges of dN ch /dη are shown in Fig. 5. In 5% most central Xe-Xe collisions, the nuclear modifi-  4) for the 0-5% (10-20%) centrality class in Xe-Xe (Pb-Pb) collisions [30], and thus they deviate significantly, where a remarkable similarity in R AA is found between both collision system. ln the 30-40% Xe-Xe (40-50% Pb-Pb) centrality class, again agreement is found within uncertainties at also similar values of N part of 82 ± 4 (86 ± 2). These findings of matching nuclear modification factors at similar ranges of dN ch /dη are in agreement with results from the study of fractional momentum loss of high-p T partons at RHIC and LHC energies [41].
A comparison of the nuclear modification factors as a function of dN ch /dη in Xe-Xe and Pb-Pb collisions for three different regions of p T (low, medium, and high) is shown in Fig. 6  Pb collisions at √ s NN = 5.02 and 2.76 TeV when compared at identical ranges in dN ch /dη , for dN ch /dη > 400. This holds both at low momentum where the hydrodynamical expansion of the medium dominates the spectrum and at high momentum, where parton energy loss inside the medium drives the spectral shape. At dN ch /dη < 400, the values of R AA still agree within rather large uncertainties.
In a simplified radiative energy loss scenario when assuming identical thermalization times [42,43], the average energy loss ∆E is proportional to the density of scattering centers in the medium, which in turn is proportional to the energy density ε, and to the square of the path length L of the parton in the medium, ∆E ∝ ε · L 2 [22]. The energy density can be estimated from the average charged-particle multiplicity density [44] per transverse area, ε ∝ dN ch /dη /A T . In central collisions, the initial transverse area A T is related to the radius r of the colliding nuclei, A T = π · r 2 [22]. Therefore, the comparison of the measured R AA values in the two colliding systems could enable a test of the path length dependence of medium-induced parton energy loss.
To further address bulk production, the average transverse momentum p T in the range from 0-10 GeV/c is derived. The spectra are extrapolated down to p T = 0 by fitting a Hagedorn function in the range 0.15 GeV/c < p T < 1 GeV/c. The relative fraction of the extrapolated particle yield amounts to 8% (11%) for the 0-5% (70-80%) centrality class. Statistical uncertainties in p T are negligible. Systematic uncertainties are estimated by varying each source of systematic uncertainty in the spectra at a time, by varying the fit range to 0.15 GeV/c < p T < 0.5 GeV/c, by changing the interpolation range to 0-0.2 GeV/c, and by assuming a constant yield below 0.15 GeV/c. All contributions are then added quadratically. The relative systematic uncertainty is 1.2% (1.1%) for the 0-5% (70-80%) centrality class.
The average transverse momentum is presented in the top panel of Fig. 7 for Xe-Xe collisions at √ s = 5.44 TeV (squares) and Pb-Pb collisions at √ s = 5.02 TeV (diamonds) for nine centrality classes. An increase of p T with centrality is visible in both collision systems and is attributed to the increasing transverse radial flow. The bottom panel of Fig. 7 shows the ratios of p T in both collision systems. The ratio is flat within uncertainties but allows for relative variations of up to two percent. Comparison to results from hydrodynamical calculations [42] are shown by the hashed areas for pions, kaons and protons. The calculations assume a boost-invariant longitudinal expansion of the medium. The initial density profile is taken from the T R ENTo model with parameter p = 0 and is determined over the transverse plane a few million times. Each initial density profile is then numerically evolved by means of the viscous relativistic hydrodynamical code V-USPHYDRO with an equation of state from lattice QCD calculations with three quark flavors and physical quark masses. The hydrodynamic evolution starts at τ 0 = 0.6 fm/c and stops when the temperature drops below 150 MeV, at which point the fluid transforms into hadrons. Hadronic rescatterings are neglected. While the calculations are not able to predict absolute particle spectra, predictions are made for the relative difference in p T between both collision systems in order to study the system size dependence. The predicted trend of a larger p T in 5% most central Xe-Xe collision and continuously lower values towards the 40-50% centrality class are consistent with the data.

Summary
Transverse momentum spectra and nuclear modification factors of charged particles in Xe-Xe collisions at √ s NN = 5.44 TeV in the kinematic range 0.15 < p T < 50 GeV/c and |η| < 0.8 are reported for nine centrality classes, in the 0-80% range. A pp reference at √ s = 5.44 TeV is obtained by the interpolation of the existing spectra at √ s = 5.02 and 7 TeV. When comparing nuclear modification factors at similar ranges of averaged charged particle multiplicity densities, a remarkable similarity between central Xe-Xe collisions and Pb-Pb collisions at a similar center-of-mass energy of √ s NN = 5.02 TeV and at 2.76 TeV is observed. The comparison of the measured R AA values in the two colliding systems could provide insight on the path length dependence of medium-induced parton energy loss. The observed scaling of the nuclear modification factor with the charged particle multiplicity density still holds at dN ch /dη < 400 within rather large uncertainties. The centrality dependence of the ratio of the average transverse momentum p T in Xe-Xe collisions over Pb-Pb collisions is flat within uncertainties but allows for relative variations of up to two precent. Predictions from hydrodynamical calculations that take into account the significantly different geometries of both collision systems are consistent [10] CMS Collaboration, S. Chatrchyan et al., "Multiplicity and transverse-momentum dependence of two-and four-particle correlations in pPb and PbPb collisions," Phys. Lett        [21] J. Bjorken, "Energy loss of energetic Partons in quark -gluon plasma: possible extinction of high p T jets in hadron -hadron collisions," Tech. Rep. FERMILAB-PUB-82-059-T, Fermilab, 1982. http://lss.fnal.gov/archive/preprint/fermilab-pub-82-059-t.shtml.