First measurement of prompt and non-prompt ${\rm D^{*+}}$ vector meson spin alignment in pp collisions at $\sqrt{s} = 13$ TeV

This letter reports the first measurement of spin alignment, with respect to the helicity axis, for ${\rm D^{*+}}$ vector mesons and their charge conjugates from charm-quark hadronisation (prompt) and from beauty-meson decays (non-prompt) in hadron collisions. The measurements were performed at midrapidity ($|y|<0.8$) as a function of transverse momentum ($p_{\rm T}$) in proton-proton (pp) collisions collected by ALICE at the centre-of-mass energy $\sqrt{s} = 13$ TeV. The diagonal spin density matrix element $\rho_{00}$ of ${\rm D^{*+}}$ mesons was measured from the angular distribution of the ${\rm D^{*+}} \to {\rm D}^0 (\to {\rm K}^{-}\pi^{+}) \pi^+$ decay products, in the ${\rm D^{*+}}$ rest frame, with respect to the ${\rm D^{*+}}$ momentum direction in the pp centre of mass frame. The $\rho_{00}$ value for prompt ${\rm D^{*+}}$ mesons is consistent with $1/3$, which implies no spin alignment. However, for non-prompt ${\rm D^{*+}}$ mesons an evidence of $\rho_{00}$ larger than $1/3$ is found. The measured value of the spin density element is $\rho_{00}=0.455\pm0.022(\text{stat.})\pm0.035(\text{syst.})$ in the $5<p_{\rm T}<20$ GeV/$c$ interval, which is consistent with a PYTHIA 8 Monte Carlo simulation coupled with the EVTGEN package, which implements the helicity conservation in the decay of ${\rm D^{*+}}$ meson from beauty mesons. In non-central heavy-ion collisions, the spin of the ${\rm D^{*+}}$ mesons may be globally aligned with the direction of the initial angular momentum and magnetic field. Based on the results for pp collisions reported in this letter it is shown that alignment of non-prompt ${\rm D^{*+}}$ mesons due to the helicity conservation coupled to the collective anisotropic expansion may mimic the signal of global spin alignment in heavy-ion collisions.


Introduction
The production of hadrons containing heavy quarks, i.e. charm and beauty, has been extensively studied in both lepton and hadron collisions, improving significantly the understanding of the hadronisation mechanism [1][2][3][4][5][6][7][8].However, several aspects of the transition of the heavy quark to the final-state hadron are not yet settled.One of them regards the spin properties of produced particles in the quark hadronisation.In the limit of very large heavy-quark mass (m Q → ∞), the polarisation of heavy-flavour baryons is assumed to be that carried by the heavy valence quark [9].This assumption was studied at LEP in e + e − collisions where the polarisation of Λ 0 b baryons was used to probe the electroweak structure of the Z 0 boson production and decays [10][11][12][13][14].In hadronic collisions, the polarisation of Λ 0 b baryons can arise during the hadronisation process if beauty quarks are produced with a transverse polarisation, as predicted by the heavy-quark effective theory [9,11].At this time, one measurement, performed by the LHCb Collaboration, found no significant polarisation [15].For vector mesons with quantum numbers J P = 1 − , both in lepton and hadron collisions, at least part of the polarisation should arise from the hadronisation process [9].Models based on statistical quantum mechanics considerations [16,17], heavy-quark effective theory [9], or inspired by quantum chromodynamics (QCD) [18] provide very different predictions, from no polarisation, to very large longitudinal or transverse polarisation.This aspect of the hadronisation is typically not accounted for in QCD-inspired Monte Carlo (MC) generators based on the Lund string model [19], such as PYTHIA 8 [20,21], or the clustering model [22], as implemented in HERWIG 7 [23].Measurements of excited B vector meson states in Z 0 decays at LEP did not show any significant polarisation [24,25].For charm vector mesons (D * + ) a longitudinal polarisation was observed by OPAL [26].However, previous measurements in e + e − collisions indicated no significant polarisation for D * + mesons [27][28][29].
The polarisation of vector mesons containing heavy quarks in heavy-ion collisions is of special interest.The initial stages of such collisions, with non-zero impact parameter, are expected to be characterised by a large orbital angular momentum [30] and a strong magnetic field [31][32][33].These initial conditions could influence the produced colour-deconfined matter (called quark-gluon plasma [34,35]).The directions of the angular momentum and the magnetic field in such collisions are perpendicular to the reaction plane (subtended by the beam axis and impact parameter) [36].Theoretical calculations at LHC energies predict the values of the angular momentum to be of the order of 10 7 ℏ [30] and the magnetic field to be about 10 16 T [31-33, 37, 38].While the angular momentum, a conserved quantity in strong interactions, is expected to affect the whole evolution of the collision, the magnetic field is transient in nature and its strength falls steeply with time.Heavy quarks are produced at the initial stages of heavy-ion collisions, in a time scale shorter than the quark-gluon plasma formation time [39] and are sensitive to the large initial magnetic field as well as the angular momentum.In the presence of these initial conditions, charm quarks can be polarised.The quark polarisation is expected to be further transferred to the final-state hadrons during hadronisation and it is predicted to be different in the case of hadronisation in vacuum, or recombination with light quarks from the deconfined medium [36,[40][41][42].Measurements in heavyion collisions indicate that the recombination mechanism is important to describe the production and angular anisotropies of charm hadrons [43][44][45][46][47][48][49][50][51].If observed, a non-zero polarisation of D * + mesons will be a manifestation of the angular momentum and the magnetic field created in heavy-ion collisions.The study of D * + mesons would provide additional information, crucial for the interpretation of the recently measured J/ψ polarisation in Pb-Pb collisions by the ALICE Collaboration [52,53].In fact, the polarisation of D * + and J/ψ mesons have different contributions from the angular momentum and the magnetic field, given the valence light quark present in the D * + meson, which is expected to be less sensitive than the charm quark to the magnetic field.However, the interpretation of experimental data for heavy-ion collisions requires a baseline study in elementary proton-proton (pp) collisions, where such initial conditions are not expected to form.Moreover, in this study, one of the major sources of background is the feed-down contribution of D * + mesons originating from decays of scalar mesons containing a beauty quark, which are observed to be longitudinally polarised by the Belle and LHCb Spin alignment of D * + vector mesons in pp collisions at √ s = 13 TeV ALICE Collaboration Collaborations in e + e − and pp collisions, respectively [54,55].This is a direct consequence of the helicity conservation and the Vector-Axial (V−A) nature of the weak interaction involved in the b → c decay, which leads to left-handed fermion couplings in interactions with W bosons [56,57].It is therefore important to separate contributions to the polarisation from promptly produced mesons and from those originating in beauty-hadron decays.This was not possible in the case of the J/ψ meson in Pb-Pb collisions with LHC Run 2 data, for which only the inclusive polarisation was used as baseline [53].
The polarisation of D * + vector mesons cannot be probed directly as D * + mesons are measured through the parity conserving strong decay D * + → D 0 (→ K − π + )π + .However, experimentally, the spin alignment along the quantisation direction can be studied by measuring the diagonal spin density matrix element (ρ 00 ) of the vector meson.The ρ 00 reflects the probability of finding a vector meson in the state with spin zero out of possible states with spin projection −1, 0, and 1 [58].If the spin of particles is homogeneously distributed, all spin states are expected to be equally probable, thereby yielding ρ 00 = 1/3.The spin alignment is studied by measuring the angular distribution of the decay products of vector mesons.Their decay products are measured with respect to a quantisation axis, which is the vector meson momentum direction (helicity axis) in pp collisions and the perpendicular direction of the reaction plane in heavy-ion collisions.In the latter, these two axes are further correlated through the anisotropic collective expansion which is quantified by coefficients in a Fourier decomposition of the azimuthalangle distribution of final-state particle momenta, with the second-harmonic coefficient v 2 , called elliptic flow [59], being the dominant one [50].The angular distribution of the D * + decay products is expressed where θ * is the angle between the momentum of either the D 0 meson or the pion in the rest frame of the vector meson with respect to the quantisation axis [60].
In this letter, the first measurement of the spin alignment of D * + mesons from charm-quark hadronisation (prompt) and from beauty-hadron decays (non-prompt) at midrapidity is presented as a function of transverse momentum (p T ) in pp collisions at a centre-of-mass energy of √ s = 13 TeV.Based on these measurements, quantitative predictions for the spin distributions of non-prompt D * + meson for a future measurement of the D * + -meson spin alignment in heavy-ion collisions are provided.

Experimental apparatus and data analysis
The analysis was performed using about 1.8 × 10 9 minimum-bias and about 10 9 high-multiplicity triggered pp collisions at √ s = 13 TeV recorded with the ALICE apparatus [61,62], corresponding to an integrated luminosity of L int ≈ 32 nb −1 and L int ≈ 7.7 pb −1 , respectively.The minimum-bias trigger required coincident signals in the two V0 detectors, which are two scintillator arrays covering the pseudorapidity intervals −3.7 < η < −1.7 and 2.8 < η < 5.1 [63].The high-multiplicity trigger selected the 0.17% highest-multiplicity events out of all inelastic collisions with at least one charged particle in the pseudorapidity range |η| < 1, relying on the signal amplitudes of the V0 detectors.Events were further selected offline to remove machine-induced backgrounds [61].They were required to have a reconstructed collision vertex located within ±10 cm from the centre of the detector along the beamline direction to maintain a uniform acceptance.Events with multiple reconstructed primary vertices (pileup) were rejected.Primary vertices were reconstructed from track segments measured with the two innermost layers of the Inner Tracking System (ITS), which consists of six cylindrical layers of silicon detectors [64].The remaining undetected pileup was studied and found to be negligible for this analysis.
The D * + mesons and their charge conjugates were measured at midrapidity (|y| < 0.8) via the D * + → D 0 (→ K − π + )π + decay channel, with branching ratio BR = (2.67 ± 0.03)% [65].The measurement of D * + mesons was based on charged-particle tracks reconstructed with the Time Projection Chamber (TPC) [66] and ITS detectors.The D 0 decay candidates were defined combining pairs of tracks with Spin alignment of D * + vector mesons in pp collisions at √ s = 13 TeV ALICE Collaboration the expected charge combinations.Each track from the decay was required to have |η| < 0.8, p T > 0.3 GeV/c, at least 70 (out of 159) associated space points in the TPC, and a minimum of two hits in the ITS, with at least one in either of the two innermost layers to ensure a good pointing resolution.The D * + -meson candidates were reconstructed by combining D 0 candidates with low-p T tracks (referred to as soft pions) having |η| < 0.8, p T > 50 MeV/c, and at least two hits in the ITS.The analysis was based on the reconstruction of decay-vertex topologies of D 0 mesons displaced from the interaction vertex.In particular, the proper decay length of D 0 mesons of cτ ≈ 123 µm and that of beauty hadrons of cτ ≈ 500 µm were exploited to resolve the D 0 -meson decay vertices.In order to reduce the large combinatorial background and to separate the contribution of prompt and non-prompt D * + mesons, a multiclass classification algorithm based on Boosted Decision Trees (BDTs) was used [67,68].The candidate information used by the BDT algorithm to distinguish among prompt and non-prompt D * + mesons and background candidates was based on i) the distance between the reconstructed D 0 -meson decay vertex and the primary vertex, ii) the D 0 -meson and soft-pion distance of closest approach to the interaction vertex, iii) the cosine of the pointing angle between the D 0 -meson candidate line of flight and its reconstructed momentum vector, and iv) the particle identification (PID) information of the decay tracks.The PID information was provided by the specific energy loss and the flight time of particles measured with the TPC and Time Of Flight (TOF) [69] detectors, respectively.Signal samples of prompt and non-prompt D * + mesons for the BDT training were obtained from MC simulations based on the PYTHIA 8.243 event generator [20,21] with the Monash tune [70] and GEANT 3 package [71] for the propagation of the generated particles through the detector.The background samples were obtained in data from the sideband region of the invariant-mass distribution ∆M = M(Kππ) − M(Kπ).The sideband region was chosen as the invariant-mass interval ∆M > 150 MeV/c 2 , where no D * + signal is present.Independent BDTs were trained for the high-multiplicity and minimum-bias samples in three different p T intervals, i.e. 5 < p T < 7 GeV/c, 7 < p T < 10 GeV/c, and 10 < p T < 20 GeV/c.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 prompt D * + meson, non-prompt D * + meson, or combinatorial background.
The selection based on the probability to be background was optimised to yield a good statistical significance and purity of the signal.By selecting high probability to be prompt or non-prompt D * + mesons, the samples of candidates were further separated to the charm-enhanced (significant contribution of prompt D * + mesons) and the beauty-enhanced (significant contribution of non-prompt D * + mesons) samples.The threshold values were tuned as a function of p T using MC simulations.The fractions of prompt ( f prompt ) and non-prompt ( f non-prompt ) D * + mesons in each sample were evaluated with a data-driven method based on the sampling of the raw yield Y i at different values of the BDT-output score related to the probability of being a non-prompt D * + meson.These fractions can be computed by solving a system of equations that relate raw yields to the corrected yields of prompt (N prompt ) and non-prompt (N non-prompt ) D * + mesons by the product of the geometrical acceptance and the reconstruction and selection (including BDT) efficiency factors (Acc × ε) for prompt and non-prompt D * + mesons.Each equation, obtained for a set of BDT selections i, can be expressed as where δ i is the residual originating from the uncertainties on Y i , (Acc×ε) non-prompt,i , and (Acc×ε) prompt,i .
To define the sets of selections, the BDT-output response related to the probability of a candidate to be a non-prompt D * + meson was sampled monotonically, to obtain n selections ordered in such a way that the i th selected sample was completely included in the (i − 1) th one.The system of equation is then solved via a χ 2 minimisation, which provides as output the corrected yields of prompt (N prompt ) and non-prompt (N non-prompt ) D * + mesons and their covariance matrix.A detailed description of this method is presented in Refs.[72][73][74].For each p T interval, the raw yields of D * + mesons were extracted with a fit to the distribution of the invariant mass ∆M.The distribution was fitted with a combination of the Gaussian function corresponding to the D * + signal and a background function.The shape of the background distribution can be described with the function , where p 0 and p 1 are free parameters and M π is the pion mass.The corresponding Acc × ε factors were obtained with MC simulations analogous to those used for the BDT trainings.Finally, the fraction of (non-)prompt D * + mesons for a given set of selections was computed as A different index " j" is used here to underline the fact that not all of these sets are used for the χ 2 minimisation given by Eq. 2. The uncertainty of f (non-)prompt, j is computed considering the covariance matrix of N prompt and N non-prompt obtained in the χ 2 -minimisation procedure.Figure 1 shows an example of a raw-yield extracted as a function of the BDT selection employed in the minimisation procedure for D * + mesons with 5 < p T < 7 GeV/c in high-multiplicity triggered pp collisions at √ s = 13 TeV.The leftmost data point of the distribution is the raw yield corresponding to the loosest selection on the BDT output related to the candidate probability of being a non-prompt D * + meson, while the rightmost one corresponds to the strictest selection, which is expected to preferentially select non-prompt D * + mesons.The Acc × ε factors obtained for these selections ranged from about 10% to 0.1% for prompt D * + mesons, and from about 30% to 10% for non-prompt D * + mesons.The prompt and non-prompt components are represented by the red and blue filled histograms, respectively, while their sum is depicted by the green histogram.The f prompt factor obtained in the charm-enhanced sample is higher than 90% for both the high-multiplicity and minimum-bias triggered events, while the f non-prompt in the beauty-enhanced sample is ∼ 60% and ∼ 40% almost independent of p T for high-multiplicity and minimum-bias triggered events, respectively.
The raw yields of D * + mesons were extracted in different cos θ * and p T intervals for both the beautyand the charm-enhanced samples.Figure 2  Spin alignment of D * + vector mesons in pp collisions at √ s = 13 TeV ALICE Collaboration impact on the ρ 00 measurement due to the shape of the cos θ * and p T distributions in the MC simulations was studied by weighting the generated MC distributions in order to reproduce the measured cos θ * and p T distributions, and the effect on the Acc × ε values was found to be smaller than 0.1% in the analysed p T intervals.The efficiency and acceptance corrected angular distributions at midrapidity for the selected p T interval in high-multiplicity triggered pp collisions at √ s = 13 TeV are shown in Fig. 3.The left panel of Fig. 3 shows the angular distribution of the charm-enhanced D * + sample and the right panel shows the same but for the beauty-enhanced D * + sample.The absolute value of cos θ * was considered due to the limited size of the analysed sample.The angular distributions were further fitted with the functional form given in Eq. 1 to extract the ρ 00 values for both the charm-and the beauty-enhanced samples in each p T interval.
It was verified with a MC simulation that the ρ 00 parameter linearly depends on the fraction of nonprompt D * + meson in the analysed sample.Hence, a linear fit of the measured ρ 00 parameters obtained for the charm-and beauty-enhanced samples as a function of the f non-prompt was performed to obtain the ρ 00 values for prompt and non-prompt D * + mesons.The charm-and the beauty-enhanced selections used in this analysis provided two samples of independent candidates.Moreover, the samples of candidates in the minimum-bias and high-multiplicity triggered events are statistically independent.Considering that the measured ρ 00 parameter can be decomposed as a linear combination of the prompt and non-prompt components, the four independent measurements corresponding to the charm-and beauty-enhanced samples for both minimum-bias and high-multiplicity events were fitted with a linear function in order to extrapolate it to f non-prompt = 0 and f non-prompt = 1.A similar procedure was adopted in Ref. [75] to measure the elliptic flow of prompt and non-prompt D mesons.With the current data samples it is not possible to perform the linear extrapolation of the ρ 00 parameter independently for the minimum-bias and high-multiplicity collisions, which may have different physical origin, and the reported results are for the combined sample.Figure 4 shows the linear fit of ρ 00 as a function of f non-prompt in 5 < p T < 7 GeV/c.The filled (empty) markers correspond to the measurements performed in the minimum-bias (high-multiplicity) pp collisions.The coloured band represents the 1σ confidence interval obtained from the linear fit.The ρ 00 parameter for prompt and non-prompt D * + mesons is then obtained by evaluating the fit function for f non-prompt = 0 and f non-prompt = 1, respectively.

Systematic uncertainties
There are four major sources of systematic uncertainties in the measurement of ρ 00 for prompt and non-prompt D * + mesons.These uncertainties are related to: i) the signal extraction, ii) the track reconstruction and selection efficiencies, iii) the BDT selection efficiency, and iv) the (non-)prompt fraction estimation.The systematic uncertainty arising from the signal extraction was estimated by varying the invariant-mass fit range, leaving the Gaussian width free in the fit, and using a bin-counting method for the raw-yield extraction.In the bin-counting method the signal yield is extracted by integrating the invariant-mass distribution after subtracting the background estimated from the background fit function.
The systematic uncertainty associated with the track selection and reconstruction efficiency was evaluated by varying the track-quality selection criteria as described in Ref. [76].The systematic uncertainty on the selection efficiency originates from imperfections in the description of the decay kinematics as well as the detector resolution and alignment in the simulation.It was estimated by comparing the ρ 00 parameters obtained for prompt and non-prompt D * + mesons with different BDT selection criteria.The uncertainty associated with the (non-)prompt fraction estimation was evaluated by varying the selection criteria described in Sec. 2, as well as the configuration of the invariant-mass fits.All of the above mentioned variations were performed independently and, assuming they are uncorrelated with each other, added in quadrature to obtain the total systematic uncertainties.systematic uncertainties for the lowest and highest p T intervals, reporting separately the various sources for prompt and non-prompt D * + mesons.The total systematic uncertainty ranges between 2.5% and 3.5% for prompt D * + mesons, and between 6.5% and 8% for non-prompt D * + mesons.These systematic uncertainties were considered as fully correlated as a function of p T .
In order to validate the results of the measurements, an additional analysis was performed with respect to a random quantisation axis (random unit vector direction in 3-dimensional space) which breaks the correlation between the helicity axis and the daughter momentum direction, due to helicity conservation.As expected, the extracted ρ 00 values for both prompt and non-prompt D * + mesons are consistent with 1/3.

Results
Figure 5 shows the ρ 00 values with respect to the helicity axis for prompt and non-prompt D * + mesons as a function of p T in pp collisions at √ s = 13 TeV.The measurements are performed in |y| < 0.8.The ρ 00 values for prompt D * + mesons are consistent with 1/3, while for non-prompt D * + mesons they are significantly larger than 1/3 throughout the studied p T range.The values measured in the three p T intervals were averaged using the corrected yields of prompt and non-prompt D * + mesons as weights.The resulting ρ 00 values in the p T interval between 5 and 20 GeV/c are ρ 00 (prompt D * + ) = 0.324 ± 0.004(stat.)± 0.008(syst.),ρ 00 (non-prompt D * + ) = 0.455 ± 0.022(stat.)± 0.035(syst.).
(5) This finding implies no spin alignment for prompt D * + mesons with a simultaneous non-zero spin alignment of non-prompt D * + mesons in high-energy pp collisions.The evidence of non-prompt D * + -meson spin alignment can be understood as a consequence of helicity conservation in the decay of beauty scalar mesons to vector mesons.Measured ρ 00 values are further compared with the MC event generator PYTHIA 8 + EVTGEN [70,77].The EVTGEN decay package, which conserves the helicity and account for the V−A nature in the decay of beauty mesons, is used in place of the default PYTHIA 8 decayer.In this case, model calculations are found to be in agreement with the extracted ρ 00 values for both prompt and non-prompt D * + mesons, while if the EVTGEN package is not used, the ρ 00 parameter is found to be compatible with 1/3 for both prompt and non-prompt D * + mesons.The measured ρ 00 for non-prompt D * + mesons is qualitatively consistent with the longitudinal polarisation fraction ( f L ) observed by the LHCb collaboration in the B 0 → D * − D * + s decay with respect to a different quantisation axis defined by the B-meson momentum direction [55].The direct comparison between the magnitudes of f L and ρ 00 measured by the LHCb and ALICE Collaborations is not possible due to the different quantisation axis After the validation of the helicity conservation in the H b → D * + + X decays via the comparison with the measurement presented in this letter, the predicted ρ 00 value obtained with PYTHIA 8 and the EVTGEN decay package can be used to estimate the magnitude of the corresponding contribution to the spin alignment in heavy-ion collisions.In particular, the spin alignment of non-prompt D * + meson with respect to the helicity axis can affect the measurements of D * + spin alignment with respect to the reaction plane in heavy-ion collisions.Due to the elliptic flow of the non-prompt D * + mesons [50, 51, [78][79][80] in heavy-ion collisions, the helicity axis is correlated to the direction of the angular momentum and the magnetic field, which are perpendicular to the orientation of the reaction plane [50].In order to obtain a quantitative estimate of this effect for heavy-ion collisions, a combination of PYTHIA 8 and the EVTGEN decay package, which are in good agreement with ALICE measurements as shown in Fig. 5, is used to model the spin alignment of non-prompt D * + -mesons with respect to the helicity axis.Elliptic flow modulations of non-prompt D * + mesons are introduced in the simulation by an appropriate rotation of the D * + and its decay product momentum in the azimuthal plane.Introducing v 2 modulation aligns the momentum direction of non-prompt D * + in the direction perpendicular to the reaction plane.Two different calculations with v 2 values of 0.05 and 0.1 were performed.These values were chosen to mimic measurements reported by the ALICE and ATLAS Collaborations of leptons from beauty-hadron decays for midcentral Pb-Pb collisions [81,82].Figure 6 shows the calculated ρ 00 values for D * + mesons as a function of f non-prompt with respect to the direction perpendicular to the reaction plane.It is found that in the presence of v 2 , helicity conservation in the beauty-meson decay leads to a value of ρ 00 less than 1/3.The opposite direction with respect to 1/3 compared to the measurement presented in this letter is due to the different quantisation axis.In the recombination hadronisation scenario of polarised Spin alignment of D * + vector mesons in pp collisions at √ s = 13 TeV ALICE Collaboration quarks, the expected value of ρ 00 for both the magnetic field and angular momentum is also less than 1/3 [42].Therefore, in the presence of v 2 the spin alignment of non-prompt D * + mesons due to the helicity conservation in beauty-meson decays mimics the signal of global spin alignment, expected due to the presence of large angular momentum and magnetic field in midcentral heavy-ion collisions.In the presence of additional non-flow correlations (i.e.correlations not induced by the collective expansion but rather by decays and jet contributions) [83], this effect can get further enhanced.A sizeable fraction of non-prompt D * + mesons, e.g.f non-prompt = 0.2 [72,74] can give on the order of 5% deviation from the ρ 00 = 1/3.This contribution is not negligible considering the recent J/ψ polarisation measurement in Pb-Pb collisions by the ALICE Collaboration where a deviation up to 10% from the ρ 00 = 1/3 was observed [52].Thanks to the higher luminosity and improved spatial resolution of the upgraded ITS installed in ALICE for the LHC Run 3 [84,85], future measurements with non-prompt charm hadrons of the spin alignment in pp collisions and azimuthal anisotropy in heavy-ion collisions will provide a more accurate baseline for understanding effects induced by the initial angular momentum and magnetic field in non-central heavy-ion collisions.

Summary
The first measurements for prompt and non-prompt D * + meson spin alignment with respect to the helicity axis at midrapidity in pp collisions at √ s = 13 TeV are presented.No spin alignment is observed for the prompt D * + mesons in pp collisions, with measured ρ 00 values being consistent with 1/3.This observation is consistent with previous measurements in e + e − collisions far from the Z 0 resonance and suggests that charm quarks are either produced unpolarised or their polarisation is washed out during the hadronisation process.The measured value for the non-prompt D * + -meson spin density element is ρ 00 = 0.455 ± 0.022(stat.)± 0.035(syst.)in the 5 < p T < 20 GeV/c interval.The measured value is compatible with the prediction from PYTHIA 8 + EVTGEN simulations and is interpreted as an evidence of spin alignment of non-prompt D * + mesons with respect to the helicity axis due to the helicity conservation in beauty-meson decays.Based on the measurements and MC simulations, it was estimated that the spin alignment of the non-prompt D * + mesons in the presence of elliptic flow can mimic the signal of global spin alignment in heavy-ion collisions.The new data presented in this letter provide an important baseline for future spin alignment measurements of D * + vector mesons in heavy-ion collisions, which probe the initial angular momentum and magnetic field.

Figure 1 :
Figure 1: Raw yield as a function of the BDT selection and extracted contributions from prompt and non-prompt D * + mesons with 5 < p T < 7 GeV/c and |y| < 0.8 in the high-multiplicity triggered pp collisions at √ s = 13 TeV.

Figure 4 :
Figure 4: The spin density matrix element (ρ 00 ) as a function of f non-prompt in 5 < p T < 7 GeV/c for charm-and beauty-enhanced samples obtained for minimum-bias and high-multiplicity triggered pp collisions at √ s = 13 TeV.Only statistical uncertainties are shown.The blue line represents the linear fit to the data with the blue band indicating its 1σ confidence interval.

Figure 5 :
Figure 5: The spin density matrix element (ρ 00 ) for prompt and non-prompt D * + mesons as a function of p T in pp collisions at √ s = 13 TeV.Measurements are carried out with respect to the helicity axis at |y| < 0.8.Statistical and systematic uncertainties are represented by bars and boxes, respectively.The measurements are compared with the estimations from the QCD-based MC event generator PYTHIA 8 + EVTGEN [70, 77].Model estimations are shown by colour bands where the width of the band corresponds to the statistical uncertainty in model calculations.

Figure 6 :
Figure6: Model simulation based on the MC event generator PYTHIA 8 + EVTGEN[70,77] for the spin density matrix element (ρ 00 ) for D * + mesons with respect to the direction perpendicular to the reaction plane as a function of f non-prompt .Model simulations are carried out for D * + mesons at midrapidity (|y| < 0.8) with two input values of v 2 .

Table 1 :
Summary of the relative systematic uncertainties on the ρ 00 parameter of prompt and non-prompt D * + mesons for different p T intervals.