Measurement of beauty-strange meson production in Pb–Pb collisions at √sNN = 5.02 TeV via non-prompt Ds+ mesons

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Measurement of beauty-strange meson production in Pb–Pb collisions at √sNN = 5.02 TeV via non-prompt Ds+ mesons © 2022 the Authors Published version ALICE Collaboration ALICE Collaboration. (2023). Measurement of beauty-strange meson production in Pb–Pb collisions at √sNN = 5.02 TeV via non-prompt Ds+ mesons. Physics Letters B, 846, Article 137561. https://doi.org/10.1016/j.physletb.2022.137561 2023 Physics Letters B 846 (2023) 137561 Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Measurement of beauty-strange meson production in Pb–Pb collisions at √sNN =5.02 TeV via non-prompt D+ smesons .ALICE Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 25 May 2022 Received in revised form 7 October 2022 Accepted 8 November 2022 Available online 19 September 2023 Editor: M. Doser Dataset link: https:// www.hepdata .net /record /ins2071181 The production yields of non-prompt D+ smesons, namely D+ smesons from beauty-hadron decays, were measured for the first time as a function of the transverse momentum (pT) at midrapidity (|y| <0.5) in central and semi-central Pb–Pb collisions at a centre-of-mass energy per nucleon pair √sNN =5.02 TeV with the ALICE experiment at the LHC. The D+ smesons and their charge conjugates were reconstructed from the hadronic decay channel D+ s→φπ+, with φ→K−K+, in the 4 <pT<36 GeV/cand 2 <pT< 24 GeV/cintervals for the 0–10% and 30–50% centrality classes, respectively. The measured yields of non-prompt D+ smesons are compared to those of prompt D+ sand non-prompt D0mesons by calculating the ratios of the production yields in Pb–Pb collisions and the nuclear modification factor RAA. The ratio between the RAA of non-prompt D+ sand prompt D+ smesons, and that between the RAA of non-prompt D+ sand non-prompt D0mesons in central Pb–Pb collisions are found to be on average higher than unity in the 4 <pT<12 GeV/cinterval with a statistical significance of about 1.6 σand 1.7 σ, respectively. The measured RAA ratios are compared with the predictions of theoretical models of heavy-quark transport in a hydrodynamically expanding QGP that incorporate hadronisation via quark recombination. ©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3. 1. Introduction A transition from ordinary nuclear matter to a colour-deconfined medium called quark–gluon plasma (QGP) is predicted to occur at a very high temperature and energy density by quantum chromodynamics (QCD) calculations on the lattice [1–3], and is supported by several measurements in ultrarelativistic heavy-ion collisions at the SPS, RHIC, and LHC [4–11]. In such collisions, charm and beauty quarks are mainly produced in hard scattering processes that occur before the formation of the QGP. Hence, they are effective probes of the entire system evolution. While the system undergoes a hydrodynamic expansion, they interact with the medium constituents via elastic [12–14] and inelastic [15,16]scatterings. These interactions imply that charm and beauty quarks exchange energy and momentum with the medium constituents, causing high-momentum quarks to lose part of their energy while traversing the QGP. The in-medium energy loss is commonly studied via the measurement of the nuclear modification factor, RAA(pT)=1 TAA×dNAA/dpT dσpp/dpT,(1) where dNAA/dpTis the transverse-momentum (pT) differential production yield in nucleus–nucleus collisions, dσpp/dpTthe pT- E-mail address: alice -publications @cern .ch. differential cross section in proton–proton (pp) collisions, and TAAis the average of the nuclear overlap function [17]. Several measurements of charm and beauty hadrons in Pb–Pb [18–30] and Au–Au [31–33] collisions show a strong suppression of the production yield at intermediate and high pT(pT>4–5 GeV/c) in heavy-ion collisions compared to pp collisions, suggesting a substantial energy loss of heavy quarks in the QGP. The comparison of the RAA of light, charm, and beauty hadrons indicates that the energy loss is sensitive to the colour charge and the parton mass. In particular, the RAA of beauty hadrons is observed to be larger than that of charm hadrons [21,24]. For pT>5–6 GeV/c, where radiative processes are expected to dominate the energy loss, the smaller suppression is attributed mainly to the so-called “dead cone” effect [34,35], which suppresses the gluon radiation at angles smaller than θ≈mQ/EQ, where mQis the mass of the quark and EQits energy. Instead, low-pTheavy quarks experience a “Brownian motion”, which consists of a diffusion process occurring via multiple elastic interactions with low-momentum transfer [36]. Owing to the larger mass, beauty quarks diffuse less than charm quarks and have a longer relaxation time, which is expected to be proportional to the quark mass. Measurements of the heavy-flavour hadron production and azimuthal anisotropies can be exploited to constrain the spatial diffusion coefficient Dsvia the comparison with theoretical models based on the heavy-quark transport in a hydrodynamically expanding QGP [18,37]. https://doi.org/10.1016/j.physletb.2022.137561 0370-2693/©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3. ALICE Collaboration Physics Letters B 846 (2023) 137561 A precise description of the hadronisation process in the hot nuclear matter is crucial to understand the transport properties of the QGP [38]. The hadronisation mechanism of low and intermediate-pTheavy quarks is expected to be sensitive to the presence of a colour-deconfined medium, which could enable hadron formation via quark recombination in addition to the vacuum-like fragmentation. This leads to an enhancement of the production yield of heavy-flavour hadrons with strange-quark content relative to those of non-strange hadrons in Pb–Pb collisions compared to pp collisions, caused by the abundant production of strange–antistrange quark pairs in the QGP [11,39,40]. Recent measurements of the production of prompt D+ smesons, i.e. D+ s mesons originating from the charm-quark hadronisation or decays of excited charm-hadron states, by the STAR [41] and ALICE [19,42] Collaborations suggest a relevant role of the recombination mechanism in the charm-quark hadronisation. Similar studies in the open-beauty sector, conducted by the CMS Collaboration via the measurement of the B0 s-meson production relative to that of B+mesons, show a hint of enhanced production of strange over non-strange mesons [26,43]. However, no firm conclusions can be drawn within the current uncertainties. Complementary information about the heavy-quark hadronisation in presence of the medium is provided by the measurements of charm baryons and charmonia in heavy-ion collisions [20,27,44–47]. Recently, the production of heavy-flavour hadrons containing strange quarks was also investigated in high-multiplicity pp collisions [48,49], following the observation of an enhanced production of strange and multi-strange hadrons with increasing charged-particle multiplicity in the light-flavour sector [50]. In this Letter, the measurement of the production of D+ smesons originating from beauty-hadron decays (non-prompt) is reported for central (0–10%) and semicentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair √sNN =5.02 TeV. Nonprompt D+ smesons provide information about the diffusion and the energy loss of beauty quarks in the QGP. In addition, together with the measurement of non-prompt D0mesons, they have the potential to reveal the beauty-quark hadronisation mechanisms in the QGP, since in pp collisions about 50% of non-prompt D+ s mesons are produced in B0 sdecays [51,52]. Therefore, the nonprompt D+ spT-differential production yield and RAA are compared with those of prompt D+ sand non-prompt D0mesons, as well as with theoretical models based on beauty-quark transport in the QGP. 2. Experimental apparatus and analysis technique The D+ s-mesons were reconstructed from their hadronic decays with the ALICE central barrel detectors, which cover the full azimuth in the pseudorapidity interval |η| <0.9 and are embedded in a large solenoidal magnet providing a uniform 0.5Tmagnetic field parallel to the beam direction. Charged-particle trajectories are reconstructed from their hits in the Inner Tracking System (ITS) [53] and the Time Projection Chamber (TPC) [54]. Particle identification (PID) is provided via the measurement of the specific ionisation energy loss dE/dxin the TPC and of the flight time of the particles from the interaction point to the Time-Of-Flight detector (TOF) [55]. The reconstruction of the interaction vertex and of the decay vertices of charmand beauty-hadron decays relies on the precise determination of the track parameters in the vicinity of the interaction point provided by the ITS. The data sample of Pb–Pb collisions used in the analysis was collected with the ALICE detector in 2018, during LHC Run 2. Three trigger classes were considered: minimum bias, central, and semicentral, all based on the signals in the two scintillator arrays of the V0 detector [56], which covers the full azimuth in the pseudorapidity intervals −3.7 <η<−1.7(V0C) and 2.8 <η<5.1(V0A). Background events due to the interaction of one of the beams with residual gas in the vacuum tube and other machine-induced backgrounds were rejected offline using the timing information provided by the V0 and the neutron Zero Degree Calorimeters (ZDC) [57]. Only events with a primary vertex reconstructed within ±10 cm from the centre of the detector along the beam-line direction were considered in the analysis. Collisions were classified into centrality intervals, defined in terms of percentiles of the hadronic Pb–Pb cross section, based on the V0 signal amplitude as described in detail in Ref. [58]. The measurement of non-prompt D+ s-meson production was carried out for central (0–10%) and semicentral (30–50%) collisions. The number of events considered for the analysis is about 100 ×106and 85 ×106in the 0–10% and 30–50% centrality intervals, corresponding to integrated luminosities Lint of (130.5 ±0.5)μb−1and (55.5 ±0.2)μb−1, respectively [59]. The average values of the nuclear overlap function, TAA, for the considered central and semicentral event intervals were estimated via Glauber-model [60] simulations anchored to the V0 signal amplitude distribution, and are (23.26 ±0.17)mb−1and (3.92 ±0.06) mb−1[17,59], respectively. The D+ smesons and their charge conjugates were reconstructed via the D+ s→φπ+→K−K+π+decay channel with branching ratio BR =(2.24 ±0.08)%[51]. The analysis was based on the reconstruction of decay-vertex topologies displaced from the interaction vertex. For prompt mesons, the separation between the interaction point and the D+ sdecay vertex is governed by the mean proper decay length cτof D+ smesons, which is about 151 μm[51]. The decay vertices of non-prompt D+ smesons on average are more displaced than those of prompt D+ smesons due to the large mean proper decay lengths of beauty hadrons (cτ≃450 μm[51]). Therefore, by exploiting the selection of displaced decay-vertex topologies, it is possible to separate non-prompt D+ smesons from the combinatorial background and from prompt D+ smesons. D+ s-meson candidates were built combining triplets of tracks with the proper charge signs, each with |η| <0.8, at least 70 (out of a maximum of 159) crossed TPC pad rows, a track fit quality χ2/ndf <1.25 in the TPC (where ndf is the number of degrees of freedom involved in the track fit procedure), and a minimum of two (out of a maximum of six) hits in the ITS, with at least one in either of the two innermost layers, which provide the best pointing resolution. Moreover, at least 50 clusters available for particle identification in the TPC were required, and only tracks with pTabove 0.6(0.4)GeV/cwere considered for central (semicentral) collisions. These track selection criteria limit the D+ s-meson acceptance in rapidity, which drops steeply to zero for |y| >0.5 at low pTand for |y| >0.8at pT>5GeV/c. Thus, only D+ smeson candidates within a pT-dependent fiducial acceptance region, |y| <yfid(pT), were selected. The yfid(pT)value was defined as a second-order polynomial function, increasing from 0.5 to 0.8 in the transverse-momentum range 0 <pT<5GeV/c, and as a constant term, yfid =0.8, for pT>5GeV/c. Similarly to other recent D-meson measurements by the ALICE Collaboration [19,21,52], Boosted Decision Trees (BDT) algorithms were employed to reduce the large combinatorial background and to separate the contribution of prompt and nonprompt D+ smesons through a multiclass classification. In particular, the implementation of the BDT algorithm provided by the XGBoost [61,62]library was used. Background samples for the BDT training were extracted from the sidebands of the candidate invariant mass distributions in the data, namely from the 1.72 < M(KKπ) <1.83 GeV/c2and 2.01 <M(KKπ) <2.12 GeV/c2regions. Applying these selections, candidates belonging to D+→K−K+π+ decays are rejected. Signal samples of prompt and non-prompt D+ s mesons were obtained from Monte Carlo (MC) simulations. The MC samples were built by simulating Pb–Pb collisions with the HIJING 1.36 [63]event generator in order to describe the charged2 ALICE Collaboration Physics Letters B 846 (2023) 137561 particle multiplicity and detector occupancy. To enrich the sample of prompt and non-prompt D-meson signals, additional ccand bb-quark pairs were injected into each HIJING event using the PYTHIA 8.243 event generator [64,65]with Monash tune [66]. The D+ smesons were forced to decay into the hadronic channel of interest for the analysis. The generated particles were then propagated through the apparatus using the GEANT3 transport code [67]. Detailed descriptions of the detector response, the geometry of the apparatus and the conditions of the luminous region, including their evolution with time during the data taking period, were included in the simulation. Before the BDT training, loose kinematic and topological selections were applied to the D+ s-meson candidates together with the particle identification of decay-product tracks. The D+ s-meson candidate information provided to the BDTs, as an input for the models to distinguish among prompt and non-prompt mesons and background candidates, was mainly based on the displacement of the tracks from the primary vertex, the distance between the D+ s-meson decay vertex and the primary vertex, the D+ s-meson impact parameter, and the cosine of the pointing angle between the D+ s-meson candidate line of flight (the vector connecting the primary and secondary vertices) and its reconstructed momentum vector. In addition, the absolute difference between the reconstructed K+K−invariant mass and the PDG average mass for the φmeson [51] and variables related to the PID of decay tracks were also included. Independent BDTs were trained in the different pTintervals of the analysis and for the different centrality intervals. Subsequently, they were applied to the real data sample in which the type of candidate is unknown. The BDT outputs are related to the candidate probability to be a non-prompt D+ smeson or combinatorial background. Selections on the BDT outputs were optimised to obtain a high non-prompt D+ smeson fraction while maintaining a reliable signal extraction from the candidate invariant mass distributions. The D+ s-meson candidates were selected by requiring a high probability to be non-prompt D+ smesons and a low probability to be combinatorial background. The raw yield of D+ smesons, including both particles and antiparticles, was extracted from binned maximum-likelihood fits to the invariant mass (M) distributions in transverse-momentum intervals 4 <pT<36 GeV/cand 2 < pT<24 GeV/cfor the 0–10% and the 30–50% centrality intervals, respectively. The fit function was composed of a Gaussian for the description of the signal and an exponential term for the background. An additional Gaussian was used to describe the peak due to the decay D+→K−K+π+, with a branching ratio of (9.68 ±0.18) ×10−3[51], present at a lower invariant mass value than the D+ s-meson signal peak. To improve the stability of the fits, the width of the D+ s-meson signal peak was fixed to the value extracted from a data sample dominated by prompt candidates, which is characterised by a signal extraction with higher statistical significance. As an example, the invariant mass distribution for the 4 <pT<6GeV/cinterval in central Pb–Pb collisions, together with the result of the fit and the estimated non-prompt fraction is reported in Fig. 1. The measured raw yield, although dominated by non-prompt candidates, still contains a residual contribution of prompt D+ smesons which satisfy the BDT-based selections. The procedure used to calculate the fraction of non-prompt candidates present in the extracted raw yield is described below. The statistical significance of the observed signals varies from about 4 to 11 depending upon the pTand centrality intervals. The corrected pT-differential yields of non-prompt D+ smesons were computed for each pTinterval as Fig. 1. Invariant mass distribution of non-prompt D+ scandidates and their charge conjugates in the 4 <pT<6GeV/cinterval for central Pb–Pb collisions. The blue solid line shows the total fit function and the red dashed line the combinatorialbackground contribution. The values of the mean (μ), width (σ), and raw yield (S) of the signal peak are reported together with their statistical uncertainties resulting from the fit. The fraction of non-prompt candidates in the measured raw yield is reported with its statistical and systematic uncertainties. dN dpT    |y|<0.5=1 2×1 pT × fnon-prompt(pT)×ND+D,raw(pT)  |y|<yfid(pT) cy(pT)×(Acc ×ε)non-prompt(pT)×BR ×Nevt . (2) The raw-yield values ND+D,raw were divided by a factor of two and multiplied by the non-prompt fraction fnon-prompt to obtain the charge-averaged yields of non-prompt D+ smesons. Furthermore, they were divided by the acceptance-times-efficiency correction factor of non-prompt D+ smesons (Acc ×ε)non-prompt, the BR of the decay channel, the width of the pTinterval pT, the correction factor for the rapidity coverage cy, and the number of analysed events Nevt. The correction factor for the rapidity acceptance cy was defined as the ratio between the generated D-meson yield in y =2 yfid(pT)and that in |y| <0.5. It was computed with FONLL perturbative QCD calculations [68,69]as in Refs. [18,19]. The (Acc ×ε)correction factor was obtained from MC simulations, using samples not employed in the BDT training. The D+ s-meson pTdistributions from simulations were reweighed in order to mimic the realistic shapes in the determination of the (Acc ×ε)factor, which depends on pT. In particular, weights were applied to the pTdistributions of prompt D+ smesons and of beauty-hadron mother particles in case of non-prompt D+ smesons. These weights were defined to reproduce the shapes given by FONLL calculations multiplied by the RAA of prompt D+ smesons and B mesons predicted by the TAMU [70,71]model. The TAMU model implements the charmand beauty-quark transport inside a strangeness-rich QGP, and it reasonably reproduces the prompt D-meson measurements at low pT[18,19]. The (Acc ×ε)factors as a function of pTfor prompt and non-prompt D+ smesons in the 0–10% and 30–50% centrality intervals are displayed in Fig. 2, along with the ratios of the non-prompt to prompt factors. The prompt D+ s-meson acceptance times efficiency is smaller than that of non-prompt D+ smesons by a factor varying from 5 to 20 depending on pTand centrality. This is expected since the selections 3 ALICE Collaboration Physics Letters B 846 (2023) 137561 Fig. 2. Acceptance-times-efficiency factors for prompt and non-prompt D+ smesons as a function of pTin the 0–10% and 30–50% centrality intervals, together with their ratios (bottom panel). applied to obtain the non-prompt enriched sample strongly suppress the prompt D+ s-meson efficiency. Instead, the acceptance is the same for prompt and non-prompt mesons. In central collisions, the prompt D+ s-meson suppression increases with increasing pT. The opposite trend is observed in semicentral collisions, since less stringent selections on the BDT outputs are necessary to extract the non-prompt D+ s-meson signal due to the lower yield. The fraction fnon-prompt of non-prompt D+ smesons in the extracted raw yield was estimated with a data-driven procedure based on the construction of data samples with different abundances of prompt and non-prompt candidates. These samples were built by varying the selection on the BDT output related to the candidate probability to be a non-prompt D+ smeson. Starting from the values of raw yield and acceptance times efficiency of prompt and non-prompt D+ smesons obtained for each sample, the corrected yield of prompt and non-prompt D+ smesons and the fnon-prompt fraction were calculated. This data-driven technique does not depend on theoretical calculations of heavy-quark production and interaction with the QGP constituents, and it is described in detail in Ref. [52]. The fnon-prompt fractions obtained as a function of pT in central and semicentral Pb–Pb collisions are reported in Fig. 3, together with their statistical and systematic uncertainties. The determination of the systematic uncertainty on the fnon-prompt fraction is described in Section 3. The fnon-prompt values vary between about 0.72 (0.56) and 0.82 (0.70) in the 0–10% (30–50%) centrality interval as a function of transverse momentum. The fnon-prompt is observed to be on average lower in semicentral collision with respect to central collisions. This difference is expected as in the 30–50% centrality interval less stringent BDT selections were applied compared to 0–10% centrality interval. The non-prompt D+ s-meson nuclear modification factor, RAA, was computed according to Eq. (1). The measurement of the pTdifferential cross section of non-prompt D+ smesons at midrapidity (|y| <0.5) in pp collisions at √s=5.02 TeV from Ref. [52], which covers the transverse-momentum interval 2 <pT<12 GeV/c, was used as the reference for the RAA computation. For pT>12 GeV/c, an extrapolated pp reference was obtained from FONLL calculations of the beauty-hadron cross section and by using PYTHIA 8 to describe the decay kinematics of beauty hadrons to D+ smesons, for more details see Ref. [52]. The resulting predictions were then scaled to match the measured values at lower transverse momenta. Fig. 3. Fraction of non-prompt D+ smesons in the extracted raw yield as a function of pTin the 0–10% and 30–50% centrality intervals. The vertical bars (boxes) report the statistical (systematic) uncertainties. The total systematic uncertainty on the pp reference is +38 −28%for all the extrapolated pTintervals. The procedures for the pTextrapolation and the systematic uncertainty estimation are the same as in Ref. [72]. 3. Systematic uncertainties The following sources of systematic uncertainty were considered for the production yield and RAA estimation: (i) the raw-yield extraction, (ii) track reconstruction efficiency, (iii) non-prompt D+ smeson fraction, (iv) BDT selection efficiency, (v) PID selection efficiency, (vi) relative abundances of beauty-hadron species in the MC simulation, and (vii) shapes of the simulated pT-differential distributions. The resulting systematic uncertainties on the nonprompt D+ s-meson yield and RAA in representative pTintervals are summarised in Table 1. In the RAA computation, the systematic uncertainties on the pp measurement were treated as uncorrelated from the ones on the Pb–Pb corrected yields, except for the uncertainty on the BR (3.6%) [51] which cancels in the RAA and was considered only in the pT-differential production yield. The normalisation uncertainty on the RAA includes the uncertainty on the integrated luminosity in pp collisions (2.1% [73]), the uncertainty on the TAAestimation, 0.7% (1.5%) for the 0–10% (30–50%) centrality interval [17], and the one related to the centrality-interval definition. This last contribution is due to the uncertainty on the fraction of the hadronic cross section used in the Glauber fit to determine the centrality. It was estimated to be < 0.1% and 2% for the 0–10% and 30–50% centrality intervals, respectively [72]. The systematic uncertainty on the raw-yield extraction was estimated by adopting several fit configurations changing the background fit function (linear and parabolic), the upper and lower fit limits, and the bin size of the invariant mass spectrum. The sensitivity to the line shape of the D+ speak was tested by comparing the raw-yield values from the fits with those obtained by counting the candidates in the invariant mass region of the signal after subtracting the background estimated from the side bands. The systematic uncertainty on the track reconstruction efficiency accounts for possible discrepancies between data and MC in the ITS–TPC prolongation efficiency and in the selection efficiency due to track-quality criteria in the TPC. The per-track systematic uncertainties were estimated by varying the track-quality selection criteria and by comparing the prolongation probability of the 4 ALICE Collaboration Physics Letters B 846 (2023) 137561 Table 1 Systematic uncertainties on the measurement of the non-prompt D+ s-meson corrected yield and RAA in the 0–10% and 30–50% centrality intervals for representative transverse-momentum intervals. Centrality interval 0–10% 30–50% pT(GeV/c)4–6 12–16 2–4 12–16 Yield extraction 5% 5% 10% 5% Tracking efficiency 13% 13% 11% 12% Non-prompt fraction 6% 6% 5% 6% Selection efficiency 8% 5% 10% 5% PID efficiency negl. negl. negl. negl. Bhadrochemistry 1% 1% 1% 1% MC pTshape 10% 8% 15% 2% Centrality limits < 0.1% 2% TAA0.7% 1.5% Lpp int 2.1% Branching ratio 3.6% TPC tracks to the ITS hits in data and simulations. They were then propagated to the non-prompt D+ smesons via their decay kinematics. The systematic uncertainties on the non-prompt D+ s-meson fraction and the BDT selection efficiency are due to possible discrepancies between data and MC in the distributions of the variables used in the BDT-model training (i.e. the D+ s-meson decayvertex topology, kinematic, and PID variables). The former was computed by varying the configuration and the number of BDT selections employed in the data-driven method described in Sec. 2. In particular, wider and narrower intervals of the probability to be non-prompt D+ smesons, and smaller and larger step sizes between the chosen BDT selections were considered. For each configuration, the non-prompt D+ s-meson fraction was recomputed. The systematic uncertainty related to the BDT selection efficiency was studied by repeating the entire analysis varying the selection criteria based on the BDT outputs. The uncertainty for this source of systematic uncertainty was assigned considering the RMS and the shift of the corrected yield obtained by varying the BDT selection with respect to the reference one. Analogously, the systematic uncertainty on the PID selection efficiency relative to the loose selection on the PID variables applied before the BDT ones was also considered. This source was evaluated in the prompt D+ s-meson analysis [19], and it was found to be negligible for the adopted PID strategy. The selection efficiency of non-prompt D+ smesons originating from the decay of different beauty-hadron species can differ because of the different lifetime of the parent hadron and the different decay kinematics. Consequently, an imperfect description in the MC simulation of the beauty-hadron composition might result in a bias in the estimation of the D-meson efficiencies. This is especially important for D+ smesons, which receive significant contributions from all the three ground-state B-meson species (B+, B0, and B0 s). The PYTHIA 8 event generator describes the measurements of different B-meson species in pp collisions [52], however in heavy-ion collisions an enhanced production of strange over non-strange B mesons is expected compared to the one observed in pp collisions. Nevertheless, since no precise measurement of B0 smeson production down to low momentum is available in Pb–Pb collisions, the relative abundances present in PYTHIA 8 were used without applying any reweighting. The systematic uncertainty introduced by this assumption was estimated by reweighting the B0 s contribution present in the MC enhanced by a factor 2 as predicted by the TAMU model [70]. The systematic uncertainty was assigned considering the variation between the production yield estimated using the enhanced B0 scontribution and the default one. The systematic uncertainty due to the shape of the pTdistributions of D+ smesons and beauty hadrons in the MC simulations was Fig. 4. Prompt and non-prompt D+ smeson production yield in central and semicentral Pb–Pb collisions at √sNN =5.02 TeV. The prompt D+ sresults are taken from Ref. [19]and scaled by a factor 10 for visibility. The vertical bars (boxes) report the statistical (systematic) uncertainties. evaluated by applying different weights to the pTdistributions of prompt D+ smesons and of beauty-hadron mother particles in case of non-prompt D+ smesons. As an alternative to the TAMU model, the shape resulting from the LIDO model [74]was considered. The main difference between the TAMU and LIDO model derives from the fact that the former includes the enhanced production of the B0 smesons, unlike the latter. An additional variation of the shape of the pTdistributions of prompt D+ smesons was included considering the results from Ref. [19]. The systematic uncertainty was assigned considering the variation of the corrected yield compared to the default case. 4. Results Fig. 4shows the pT-differential production yield of prompt and non-prompt D+ smesons in central and semicentral Pb–Pb collisions at √sNN =5.02 TeV. The measured prompt D+ s-meson production yields were taken from Ref. [19] and scaled by a factor 10 for visibility. Fig. 5reports the ratios of the production yield of non-prompt to prompt D+ s(left panel) and non-prompt D+ sto non-prompt D0[21] (right panel) in central and semicentral Pb–Pb collisions, as well as in pp collisions [52]. Computing these ratios helps to further investigate the effects of the QGP medium on the hadron formation mechanism. To get an indication of the B0 s-meson pT probed by non-prompt D+ smesons, a simulation with PYTHIA 8 was performed. As an example, the mean pTdistribution of B0 s mesons decaying to D+ smesons with 4 <pT<6GeV/chas a mean of about 8.8GeV/cand an RMS of about 3.1GeV/c. The non-prompt to prompt D+ s-meson ratio ranges between about 0.05 and 0.20 and increases with increasing pTup to pT=10 GeV/c. At higher momentum the slope of the ratios seems to reduce, even though no firm conclusions can be drawn with the current uncertainties. On the other hand, the non-prompt D+ sto non-prompt D0 ratio shows an almost flat trend around 0.2 in the pTrange of the measurement. The ratios computed in pp and semicentral Pb–Pb 5 ALICE Collaboration Physics Letters B 846 (2023) 137561 Fig. 5. The pT-differential production yield of non-prompt D+ smesons divided by those of prompt D+ smesons (left panel) and non-prompt D0mesons (right panel) for the 0–10% and 30–50% centrality intervals in Pb–Pb collisions at √sNN =5.02 TeV from Refs. [19,21]compared with those in pp collisions at the same centre-of-mass energy from Ref. [52]. collisions are compatible within the uncertainties. A hint of enhancement compared to pp collisions with a significance of 1.7σ, where σindicates the sum in quadrature of statistical and systematic uncertainties, is found by performing a weighted average of the non-prompt D+ s/D0values in the 4 <pT<12 GeV/cinterval for the 0–10% centrality class. The inverse of the squared sum of the relative statistical and pT-uncorrelated systematic uncertainties was used as weight in the average. All the systematic uncertainties, except for those on the raw-yield extraction, were considered as fully correlated in pT. This hint of a larger non-prompt D+ s/D0yield ratio is consistent with an enhanced production of strange-beauty mesons in heavy-ion collisions compared to pp collisions, as expected in a scenario in which beauty quarks hadronise via recombination with surrounding quarks in the strangenessenriched QGP medium. In the transverse-momentum interval 4 < pT<12 GeV/c, also the non-prompt to prompt D+ s-meson ratio in the 0–10% centrality class shows a mild enhancement with respect to pp collisions with a significance of 1.6σ. The RAA of non-prompt D+ smesons was computed according to Eq. (1), where the pp reference was obtained from the measurement published in Ref. [52]. To study the effects of the QGP medium on the resulting momentum spectra and the hadronisation mechanism of beauty quarks, the nuclear modification factor measured for the non-prompt D+ smesons was compared to that of prompt D+ s[19] and non-prompt D0[21]mesons measured at the same centre-of-mass energy per nucleon pair. The prompt and non-prompt D+ sRAA are compared in the topand bottom-left panels of Fig. 6for the 0–10% and 30–50% centrality class, respectively. Analogously, the comparison between the nuclear modification factor of non-prompt D+ sand non-prompt D0 mesons is reported in the right panels of the same figure. The RAA of prompt and non-prompt D mesons shows a decreasing trend with increasing pTup to a minimum of about 0.2 (0.4) around 10 GeV/cin the 0–10% (30–50%) centrality class. In the lowest pT intervals, the RAA increases up to unity. In particular, the central values of the non-prompt D+ sRAA are higher with respect to those of prompt D+ sand non-prompt D0in the 0–10% centrality class for pT<6GeV/c, even though they are compatible within uncertainties. This possible difference between prompt and non-prompt D+ s RAA would be consistent with the different loss of energy experienced by charm and beauty quarks traversing the QGP. In fact, the effect due to the different decay kinematics of charm and beauty hadrons is found to be negligible, as discussed in Ref. [21]. Instead, the difference between non-prompt D+ sand D0mesons could result from the hadronisation via recombination and the presence of a strangeness-rich environment. In semicentral collisions, no separation among the RAA of prompt D+ s, non-prompt D+ s, and non-prompt D0is observed within the measurement uncertainties. The RAA measurements were compared with the predictions of the TAMU model [70]. In the TAMU model, the heavy-quark transport is described via the Langevin equation and the hadronisation can occur both via recombination with light quarks from the medium, which is the dominant mechanism at low pT, or via fragmentation, which becomes more important at high pT. The TAMU predictions are shown in Fig. 6. The uncertainty band for prompt D+ smesons is due to the modification of the parton distribution functions in Pb nuclei, which is neglected for the beauty-quark production. The TAMU model qualitatively describes the pTtrend of the non-prompt D+ s-meson RAA, although it overestimates the measurements. In the left and right panels of Fig. 7, the nuclear modification factors of non-prompt D+ smesons divided by that of prompt D+ s mesons and non-prompt D0mesons are shown, respectively. The measurements in both centrality intervals are compared with the predictions of the TAMU model. In the 0–10% centrality class, the non-prompt D+ sto prompt D+ sRAA ratio suggests a hint of enhancement with a statistical significance of 1.6σin the 4 <pT< 12 GeV/cinterval, which is by construction the same of that reported for the corresponding yield ratio. The RAA ratio is consistent with a larger energy loss for the charm quark with respect to the beauty quark due to its smaller mass, as already suggested by the results shown in Fig. 6. No hint for a ratio of the RAA larger than unity is observed in semicentral collisions. Considering the measurement uncertainties, TAMU predictions qualitatively describe the results for central collisions. At variance, for semicentral collisions the TAMU model overestimates the RAA ratio values. The measurements of the non-prompt D+ sto non-prompt D0RAA ratio suggest a possible enhancement with respect to unity in the 4 <pT<12 GeV/cinterval for central collisions, as reported for the yield ratio. In this case, the rise at low pTmight be a consequence of the abundance of strange quarks thermally produced in the QGP and the dominance of the hadronisation via recombination in this range of momentum. The TAMU model describes the data within the experimental uncertainties. 6 ALICE Collaboration Physics Letters B 846 (2023) 137561 Fig. 6. Left panels: prompt (Ref. [19]) and non-prompt D+ s-meson RAA in central (top) and semicentral (bottom) Pb–Pb collisions at √sNN =5.02 TeV. Right panels: nonprompt D+ s-and D0-meson (Ref. [21]) RAA in central (top) and semicentral (bottom) Pb–Pb collisions at √sNN =5.02 TeV. The experimental results are compared with the predictions of the TAMU model [70]. Statistical (bars), systematic (boxes), and normalisation (shaded box around unity) uncertainties are shown. Fig. 7. The RAA of non-prompt D+ smesons divided by the one of prompt D+ smesons [19](left panel) and non-prompt D0mesons [21](right panel) for the 0–10% and 30–50% centrality intervals in Pb–Pb collisions at √sNN =5.02 TeV. The measurements are compared with TAMU model predictions [70]. Statistical (bars) and systematic (boxes) uncertainties are shown. 5. Conclusions In this Letter, the first measurement of the non-prompt D+ smeson production at midrapidity in Pb–Pb collisions at √sNN = 5.02 TeV was reported. The non-prompt D+ s-meson production yield was measured between 4 and 36 (2 and 24) GeV/cin the 0–10% (30–50%) centrality interval. These measurements were compared to the ones performed for prompt D+ sand non-prompt D0mesons at the same centre-of-mass energy. The production yield was employed to compute the non-prompt D+ s-meson RAA, which was compared with the RAA of prompt D+ sand non-prompt D0mesons. The non-prompt D+ sRAA shows a significant pTdependence. A minimum at intermediate transverse momentum (pT≈10 GeV/c) around 0.2 (0.4) in central (semicentral) collisions, and a mild increase with decreasing pT, with RAA reaching (close to) unity at 7 ALICE Collaboration Physics Letters B 846 (2023) 137561 pT≈4–6 (2–4)GeV/cin the 0–10% (30–50%) centrality interval are reported. The TAMU model, which implements the parton inmedium energy loss through collisional processes as well as the beauty-quark hadronisation both via fragmentation and recombination, describes the pTtrend of the RAA. However, it overestimates the measurements. Further comparisons were performed between prompt and non-prompt D+ sas well as non-prompt D0 mesons by computing the ratios of their production yields and RAA. These ratios suggest the presence of an enhancement of non-prompt D+ smesons compared to prompt D+ s(non-prompt D0) mesons in central collisions in the 4 <pT<12 GeV/cinterval, with a significance of 1.6σ(1.7σ). The increase is consistent with expectations for the overall effect of the energy-loss mechanism and the hadronisation-process modification in presence of the colour-deconfined medium. The recent upgrade of the ALICE apparatus will greatly enhance the physics potential of the experiment in the LHC Run 3 datataking period, allowing for more precise measurements of the nonprompt D+ s-meson production in heavy–ion collisions. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability This manuscript has associated data in a HEPData repository at: https://www.hepdata .net /record /ins2071181. Acknowledgements The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundac¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; The Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency -BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia y Tecnología (CONACYT), through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Académico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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A 757 (2005) 102–183, arXiv:nucl -ex /0501009. 8 ALICE Collaboration Physics Letters B 846 (2023) 137561 44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 45 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 46 Indian Institute of Technology Bombay (IIT), Mumbai, India 47 Indian Institute of Technology Indore, Indore, India 48 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 49 INFN, Sezione di Bari, Bari, Italy 50 INFN, Sezione di Bologna, Bologna, Italy 51 INFN, Sezione di Cagliari, Cagliari, Italy 52 INFN, Sezione di Catania, Catania, Italy 53 INFN, Sezione di Padova, Padova, Italy 54 INFN, Sezione di Pavia, Pavia, Italy 55 INFN, Sezione di Torino, Turin, Italy 56 INFN, Sezione di Trieste, Trieste, Italy 57 Inha University, Incheon, Republic of Korea 58 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 60 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 61 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 62 Institute of Space Science (ISS), Bucharest, Romania 63 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 64 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 65 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 66 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 67 iThemba LABS, National Research Foundation, Somerset West, South Africa 68 Jeonbuk National University, Jeonju, Republic of Korea 69 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 70 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 71 KTO Karatay University, Konya, Turkey 72 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 73 Lawrence Berkeley National Laboratory, Berkeley, CA, United States 74 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 75 Nagasaki Institute of Applied Science, Nagasaki, Japan 76 Nara Women’s University (NWU), Nara, Japan 77 National and Kapodistrian University of Athens, School of Science, Department of Physics, Athens, Greece 78 National Centre for Nuclear Research, Warsaw, Poland 79 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 80 National Nuclear Research Center, Baku, Azerbaijan 81 National Research and Innovation Agency -BRIN, Jakarta, Indonesia 82 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 83 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands 84 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 85 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-ˇ Rež, Czech Republic 86 Oak Ridge National Laboratory, Oak Ridge, TN, United States 87 Ohio State University, Columbus, OH, United States 88 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia 89 Physics Department, Panjab University, Chandigarh, India 90 Physics Department, University of Jammu, Jammu, India 91 Physics Department, University of Rajasthan, Jaipur, India 92 Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan 93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 95 Physik Department, Technische Universität München, Munich, Germany 96 Politecnico di Bari and Sezione INFN, Bari, Italy 97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 98 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 99 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 100 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 101 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 102 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 103 Suranaree University of Technology, Nakhon Ratchasima, Thailand 104 Technical University of Košice, Košice, Slovak Republic 105 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 106 The University of Texas at Austin, Austin, TX, United States 107 Universidad Autónoma de Sinaloa, Culiacán, Mexico 108 Universidade de São Paulo (USP), São Paulo, Brazil 109 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 110 Universidade Federal do ABC, Santo Andre, Brazil 111 University of Cape Town, Cape Town, South Africa 112 University of Houston, Houston, TX, United States 113 University of Jyväskylä, Jyväskylä, Finland 114 University of Kansas, Lawrence, KS, United States 115 University of Liverpool, Liverpool, United Kingdom 116 University of Science and Technology of China, Hefei, China 117 University of South-Eastern Norway, Kongsberg, Norway 118 University of Tennessee, Knoxville, TN, United States 119 University of the Witwatersrand, Johannesburg, South Africa 120 University of Tokyo, Tokyo, Japan 121 University of Tsukuba, Tsukuba, Japan 122 University Politehnica of Bucharest, Bucharest, Romania 123 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 15 ALICE Collaboration Physics Letters B 846 (2023) 137561 124 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 125 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000, Strasbourg, France 126 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France 127 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 128 Università degli Studi di Foggia, Foggia, Italy 129 Università del Piemonte Orientale, Vercelli, Italy 130 Università di Brescia, Brescia, Italy 131 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 132 Warsaw University of Technology, Warsaw, Poland 133 Wayne State University, Detroit, MI, United States 134 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany 135 Wigner Research Centre for Physics, Budapest, Hungary 136 Yale University, New Haven, CT, United States 137 Yonsei University, Seoul, Republic of Korea 138 Zentrum für Technologie und Transfer (ZTT), Worms, Germany 139 Affiliated with an institute covered by a cooperation agreement with CERN 140 Affiliated with an international laboratory covered by a cooperation agreement with CERN IDeceased. II Also at: Max-Planck-Institut für Physik, Munich, Germany. III Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy. IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy. VAlso at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India. VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland. VII Also at: An institution covered by a cooperation agreement with CERN. 16