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Being used in the fixed-target mode, the multi-TeV LHC proton and lead beams allow for studies of heavy-flavour hadroproduction with unprecedented precision at backward rapidities, far negative Feynman-x, using conventional detection techniques. At the nominal LHC energies, quarkonia can be studied in detail in p+p, p+d, and p+A collisions at sNN≃115 GeV and in Pb + p and Pb + A collisions at sNN≃72 GeV with luminosities roughly equivalent to that of the collider mode that is up to 20 fb−1 yr−1 in p+p and p+d collisions, up to 0.6 fb−1 yr−1 in p+A collisions, and up to 10 nb−1 yr−1 in Pb + A collisions. In this paper, we assess the feasibility of such studies by performing fast simulations using the performance of a LHCb-like detector.

We outline the many quarkonium-physics opportunities offered by a multi-purpose fixed-target experiment using the p and Pb Large Hadron Collider (LHC) beams extracted by a bent crystal. This provides an integrated luminosity of 0.5 fb −1 per year on a typical 1 cm-long target. Such an extraction mode does not alter the performance of the collider experiments at the LHC. With such a high luminosity, one can analyse quarkonium production in great details in pp , pd and pA collisions at GeV and at GeV in Pb A collisions. In a typical pp ( pA ) run, the obtained quarkonium yields per unit of rapidity are 2–3 orders of magnitude larger than those expected at RHIC and about, respectively, 10(70) times larger than for ALICE. In Pb A , they are comparable. By instrumenting the target-rapidity region, the large negative- x F domain can be accessed for the first time, greatly extending previous measurements by Hera-B and E866. Such analyses should help resolving the quarkonium-production controversies and clear the way for gluon PDF extraction via quarkonium studies. The nuclear target-species versatility provides a unique opportunity to study nuclear matter and the features of the hot and dense matter formed in Pb A collisions. A polarised proton target allows the study of transverse-spin asymmetries in J / ψ and production, providing access to the gluon and charm Sivers functions.

We outline the case for heavy-ion-physics studies using the multi-TeV lead LHC beams in the fixed-target mode. After a brief contextual reminder, we detail the possible contributions of AFTER@LHC to heavy-ion physics with a specific emphasis on quarkonia. We then present performance simulations for a selection of observables. These show that Υ ( n S ) , J / ψ and ψ ( 2 S ) production in heavy-ion collisions can be studied in new energy and rapidity domains with the LHCb and ALICE detectors. We also discuss the relevance to analyse the Drell–Yan pair production in asymmetric nucleus–nucleus collisions to study the factorisation of the nuclear modification of partonic densities and of further quarkonium states to restore their status of golden probes of the quark–gluon plasma formation.

We report on the opportunities for spin physics and Transverse-Momentum Dependent distribution (TMD) studies at a future multi-purpose fixed-target experiment using the proton or lead ion LHC beams extracted by a bent crystal. The LHC multi-TeV beams allow for the most energetic fixed-target experiments ever performed, opening new domains of particle and nuclear physics and complementing that of collider physics, in particular that of RHIC and the EIC projects. The luminosity achievable with AFTER@LHC using typical targets would surpass that of RHIC by more that 3 orders of magnitude in a similar energy region. In unpolarised proton-proton collisions, AFTER@LHC allows for measurements of TMDs such as the Boer-Mulders quark distributions, the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using the polarisation of hydrogen and nuclear targets, one can measure transverse single-spin asymmetries of quark and gluon sensitive probes, such as, respectively, Drell-Yan pair and quarkonium production. The fixed-target mode has the advantage to allow for measurements in the target-rapidity region, namely at large x↑ in the polarised nucleon. Overall, this allows for an ambitious spin program which we outline here.

The first measurement at midrapidity (| y | < 0 . 5) of the production yield of the strange-charm baryons$${\\Xi }_{\\text{c}}^{+}$$and$${\\Xi }_{\\text{c}}^{0}$$as a function of transverse momentum ( p T ) in different charged-particle multiplicity classes in proton-proton collisions at$$\\sqrt{s}=13$$TeV with the ALICE experiment at the LHC is reported. The$${\\Xi }_{\\text{c}}^{+}$$baryon is reconstructed via the$${\\Xi }_{\\text{c}}^{+}\\to {\\Xi }^{-}{\\pi }^{+}{\\pi }^{+}$$decay channel in the range 4 < p T < 12 GeV /c , while the$${\\Xi }_{\\text{c}}^{0}$$baryon is reconstructed via both the$${\\Xi}_{\\text{c}}^{0}\\to {\\Xi}^{-}{\\pi }^{+}$$and$${\\Xi}_{\\text{c}}^{0}\\to {\\Xi}^{-}{\\text{e}}^{+}{\\nu }_{\\text{e}}$$decay channels in the range 2 < p T < 12 GeV /c . The baryon-to-meson$$\\left({\\Xi}_{\\text{c}}^{0,+}/{\\text{D}}^{0}\\right)$$and the baryon-to-baryon$$\\left({\\Xi}_{\\text{c}}^{0,+}/{\\Lambda}_{\\text{c}}^{+}\\right)$$production yield ratios show no significant dependence on multiplicity. In addition, the observed yield ratios are not described by theoretical predictions that model charm-quark fragmentation based on measurements at e + e − and e − p colliders, indicating differences in the charm-baryon production mechanism in pp collisions. A comparison with different event generators and tunings, including different modelling of the hadronisation process, is also discussed. Moreover, the branching-fraction ratio of$${\\text{BR}}\\left({\\Xi}_{\\text{c}}^{0}\\to {\\Xi }^{-}{\\text{e}}^{+}{\\nu }_{\\text{e}}\\right)/{\\text{BR}}\\left({\\Xi}_{\\text{c}}^{0}\\to {\\Xi }^{-}{\\pi }^{+}\\right)$$is measured as 0.825 ± 0.094 (stat.) ± 0.081 (syst.). This value supersedes the previous ALICE measurement, improving the statistical precision by a factor of 1.6.

Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum$$(\\langle {p}_{\\text{T}}\\rangle )$$of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in$$\\langle {p}_{\\text{T}}\\rangle $$with respect to the relative change in the average charged-particle density$$(\\langle \\text{d}{N}_{\\text{ch}}/\\text{d}\\eta \\rangle )$$measured at mid-rapidity. This study reports the event-average$$\\langle {p}_{\\text{T}}\\rangle $$of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle$$([{p}_{\\text{T}}])$$distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5 . 02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum is tested. The measured$${c}_{\\text{s}}^{2}$$is found to strongly depend on the exploited centrality estimator and ranges between 0 . 1146±0 . 0028 (stat . )±0 . 0065 (syst . ) and 0 . 4374±0 . 0006 (stat . )±0 . 0184 (syst . ) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event [ p T ] distribution.

The first measurement of prompt D *+ -meson spin alignment in ultrarelativistic heavy-ion collisions with respect to the direction orthogonal to the reaction plane is presented. The spin alignment is quantified by measuring the element ρ 00 of the diagonal spin-density matrix for prompt D *+ mesons with 4 < p T < 30 GeV /c in two rapidity intervals, | y | < 0 . 3 and 0 . 3 < | y | < 0 . 8, in central (0–10%) and midcentral (30–50%) Pb–Pb collisions at$$\\sqrt{{s}_{\\text{NN}}}={5}.0{2}$$TeV. Evidence of spin alignment ρ 00 > 1 / 3 has been found for p T > 15 GeV /c and 0 . 3 < | y | < 0 . 8 with a significance of 3 . 1 σ . The measured spin alignment of prompt D *+ mesons is compared with the one of inclusive J / ψ mesons measured at forward rapidity (2 . 5 < y < 4).

The momentum-differential invariant cross sections of π 0 and η mesons are reported for pp collisions at$$\\sqrt{s}$$= 13 TeV at midrapidity ( |y| < 0 . 8). The measurement is performed in a broad transverse-momentum range of 0 . 2 < p T < 200 GeV/ c and 0 . 4 < p T < 60 GeV/ c for the π 0 and η , respectively, extending the p T coverage of previous measurements. Transverse-mass-scaling violation of up to 60% at low transverse momentum has been observed, agreeing with measurements at lower collision energies. Transverse Bjorken x ( x T ) scaling of the π 0 cross sections at LHC energies is fulfilled with a power-law exponent of n = 5 . 01 ± 0 . 05, consistent with values obtained for charged pions at similar collision energies. The data are compared to predictions from next-to-leading order perturbative QCD calculations, where the π 0 spectrum is best described using the CT18 parton distribution function and the NNFF1.0 or BDSS fragmentation function. Expectations from PYTHIA8 and EPOS LHC overestimate the spectrum for the π 0 and are not able to describe the shape and magnitude of the η spectrum. The charged-particle multiplicity dependent π 0 and η p T spectra show the expected change of the spectral shape, characterized by a flatter slope with increasing multiplicity. This is demonstrated across a broad transverse-momentum range and up to events with a charged-particle multiplicity exceeding five times the mean value in minimum bias collisions. The η/π 0 ratio depends on the charged-particle multiplicity for p T < 4 GeV/ c . PYTHIA8 and EPOS LHC qualitatively explain this behavior with an increasing contribution from the feed-down of heavier particles to the π 0 spectrum.

Correlations in azimuthal angle extending over a long range in pseudorapidity between particles, usually called the “ridge” phenomenon, were discovered in heavy-ion collisions, and later found in pp and p–Pb collisions. In large systems, they are thought to arise from the expansion (collective flow) of the produced particles. Extending these measurements over a wider range in pseudorapidity and final-state particle multiplicity is important to understand better the origin of these long-range correlations in small collision systems. In this Letter, measurements of the long-range correlations in p–Pb collisions at$$ \\sqrt{s_{\\textrm{NN}}} $$s NN = 5 . 02 TeV are extended to a pseudorapidity gap of ∆ η ~ 8 between particles using the ALICE forward multiplicity detectors. After suppressing non-flow correlations, e.g., from jet and resonance decays, the ridge structure is observed to persist up to a very large gap of ∆ η ~ 8 for the first time in p–Pb collisions. This shows that the collective flow-like correlations extend over an extensive pseudorapidity range also in small collision systems such as p–Pb collisions. The pseudorapidity dependence of the second-order anisotropic flow coefficient, v 2 ( η ), is extracted from the long-range correlations. The v 2 ( η ) results are presented for a wide pseudorapidity range of –3 . 1 < η < 4 . 8 in various centrality classes in p–Pb collisions. To gain a comprehensive understanding of the source of anisotropic flow in small collision systems, the v 2 ( η ) measurements are compared with hydrodynamic and transport model calculations. The comparison suggests that the final-state interactions play a dominant role in developing the anisotropic flow in small collision systems.

A newly developed observable for correlations between symmetry planes, which characterize the direction of the anisotropic emission of produced particles, is measured in Pb–Pb collisions at$$\\sqrt{s_\\text {NN}}$$s NN  = 2.76 TeV with ALICE. This so-called Gaussian Estimator allows for the first time the study of these quantities without the influence of correlations between different flow amplitudes. The centrality dependence of various correlations between two, three and four symmetry planes is presented. The ordering of magnitude between these symmetry plane correlations is discussed and the results of the Gaussian Estimator are compared with measurements of previously used estimators. The results utilizing the new estimator lead to significantly smaller correlations than reported by studies using the Scalar Product method. Furthermore, the obtained symmetry plane correlations are compared to state-of-the-art hydrodynamic model calculations for the evolution of heavy-ion collisions. While the model predictions provide a qualitative description of the data, quantitative agreement is not always observed, particularly for correlators with significant non-linear response of the medium to initial state anisotropies of the collision system. As these results provide unique and independent information, their usage in future Bayesian analysis can further constrain our knowledge on the properties of the QCD matter produced in ultrarelativistic heavy-ion collisions.