Mean-Field Expansion, Regularization Issue, and Multi-Quark Functions in Nambu–Jona-Lasinio Model

In this paper, the results of the investigation of multi-quark equations in the Nambu–Jona-Lasinio (NJL) model in the mean-field expansion are presented. The multi-quark functions have been considered up to the third order of expansion. One of the purposes of our computations is the study of corrections of higher orders to parameters of the model. The important problem of the application of the NJL model is regularization. We compare the NJL model with 4-dimensional cutoff regularization and the dimensionally analytical regularization. We also discuss so-called “predictive regularization„ in the NJL model, and a modification of this regularization, which is free of the Landau pole, is proposed. To calculate the high-order corrections, we use the Legendre transform method in the framework of bilocal-source formalism, which allows one effectively to take into consideration the symmetry constraints. A generalization of the mean-field expansion for other types of multi-quark sources is also discussed

Multiplicity dependence of light (anti-)nuclei production in p–Pb collisions at sNN=5.02 TeV

The measurement of the deuteron and anti-deuteron production in the rapidity range −1 < y < 0 as a function of transverse momentum and event multiplicity in p–Pb collisions at √sNN = 5.02 TeV is presented. (Anti-)deuterons are identified via their specific energy loss dE/dx and via their time-of- flight. Their production in p–Pb collisions is compared to pp and Pb–Pb collisions and is discussed within the context of thermal and coalescence models. The ratio of integrated yields of deuterons to protons (d/p) shows a significant increase as a function of the charged-particle multiplicity of the event starting from values similar to those observed in pp collisions at low multiplicities and approaching those observed in Pb–Pb collisions at high multiplicities. The mean transverse particle momenta are extracted from the deuteron spectra and the values are similar to those obtained for p and particles. Thus, deuteron spectra do not follow mass ordering. This behaviour is in contrast to the trend observed for non-composite particles in p–Pb collisions. In addition, the production of the rare 3He and 3He nuclei has been studied. The spectrum corresponding to all non-single diffractive p-Pb collisions is obtained in the rapidity window −1 < y < 0 and the pT-integrated yield dN/dy is extracted. It is found that the yields of protons, deuterons, and 3He, normalised by the spin degeneracy factor, follow an exponential decrease with mass number

First study of the two-body scattering involving charm hadrons

This Letter presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$ and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within (1.1-1.5)$\sigma$. Considering an attractive nucleon(N)$\overline{\mathrm{D}}$ strong interaction, in contrast to most model predictions which suggest an overall repulsive interaction, slightly improves the level of agreement. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in [-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel

Constraining hadronization mechanisms with Λc+\rm \Lambda_{\rm c}^{+}/D0^0 production ratios in Pb-Pb collisions at sNN=5.02\sqrt{s_{\rm NN}} = 5.02 TeV

The production of prompt $\rm \Lambda_{\rm c}^{+}$ baryons at midrapidity ($|y|<0.5$) was measured in central (0-10%) and mid-central (30-50%) Pb-Pb collisions at the center-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector. The $\rm \Lambda_{\rm c}^{+}$ production yield, the $\rm \Lambda_{\rm c}^{+}$/D$^0$ production ratio, and the $\rm \Lambda_{\rm c}^{+}$ nuclear modification factor $R_{\rm AA}$ are reported. The results are more precise and more differential in transverse momentum ($p_{\rm T}$) and centrality with respect to previous measurements. The $\rm \Lambda_{\rm c}^{+}$/D$^0$ ratio, which is enhanced with respect to the pp measurement for $4< p_{\rm T} < 8$ GeV/$c$, is described by theoretical calculations that model the charm-quark transport in the quark-gluon plasma and include hadronization via both coalescence and fragmentation mechanisms

Forward rapidity J/ψ production as a function of charged-particle multiplicity in pp collisions at s \sqrt{s} = 5.02 and 13 TeV

The production of J/ψ is measured as a function of charged-particle multiplicity at forward rapidity in proton-proton (pp) collisions at center-of-mass energies $\sqrt{s}$ = 5.02 and 13 TeV. The J/ψ mesons are reconstructed via their decay into dimuons in the rapidity interval (2.5 < y < 4.0), whereas the charged-particle multiplicity density (dN$_{ch}$/dη) is measured at midrapidity (|η| < 1). The production rate as a function of multiplicity is reported as the ratio of the yield in a given multiplicity interval to the multiplicity-integrated one. This observable shows a linear increase with charged-particle multiplicity normalized to the corresponding average value for inelastic events (dN$_{ch}$/dη/〈dN$_{ch}$/dη〉), at both the colliding energies. Measurements are compared with available ALICE results at midrapidity and theoretical model calculations. First measurement of the mean transverse momentum (〈p$_{T}$〉) of J/ψ in pp collisions exhibits an increasing trend as a function of dN$_{ch}$/dη/〈dN$_{ch}$/dη〉 showing a saturation towards high charged-particle multiplicities

Measurement of inclusive J/ψ\psi pair production cross section in pp collisions at s=13\sqrt{s} = 13 TeV

International audienceThe production cross section of inclusive J/$\psi$ pairs in pp collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV is measured with ALICE. The measurement is performed for J/$\psi$ in the rapidity interval $2.5 0$. The production cross section of inclusive J/$\psi$ pairs is reported to be $10.3 \pm 2.3 {\rm (stat.)} \pm 1.3 {\rm (syst.)}$ nb in this kinematic interval. The contribution from non-prompt J/$\psi$ (i.e. originated from beauty-hadron decays) to the inclusive sample is evaluated. The results are discussed and compared with data

Production of K∗(892)0^{*}(892)^{0} and ϕ(1020)\phi(1020) in pp and Pb-Pb collisions at sNN=5.02\sqrt{s_{\rm NN}} = 5.02 TeV

The production of K$^{*}(892)^{0}$ and $\phi(1020)$ mesons in proton-proton (pp) and lead-lead (Pb-Pb) collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV has been measured using the ALICE detector at the Large Hadron Collider (LHC). The transverse momentum ($p_{\mathrm{T}}$) distributions of K$^{*}(892)^{0}$ and $\phi(1020)$ mesons have been measured at midrapidity $(|y| 8$ GeV$/c$, the $R_{\rm AA}$ values of K$^{*}(892)^{0}$ and $\phi(1020)$ are below unity and observed to be similar to those of pions, kaons, and (anti)protons. The $R_{\rm AA}$ values at high $p_{\mathrm T}$ for K$^{*}(892)^{0}$ and $\phi(1020)$ mesons are in agreement within uncertainties for $\sqrt{s_\mathrm{NN}} = 5.02$ and 2.76 TeV

Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at s=13\boldsymbol{\sqrt{{\textit s}}}=13 TeV

Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at $\sqrt{s}$ = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-(∆η ∼ 0) and long-range (1.6 < |∆η| < 1.8) in pseudorapidity are extracted on the near-side (∆φ ∼ 0). They are reported as a function of transverse momentum (p$_{T}$) in the range 1 < p$_{T}$< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-p$_{T}$ leading particles or jets for varying p$_{T}$ thresholds. The results demonstrate that the long-range “ridge” yield, possibly related to the collective behavior of the system, is present in events with high-p$_{T}$ processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the p$_{T}$ dependency, while overestimating the event-scale dependency

Production of muons from heavy-flavour hadron decays at high transverse momentum in Pb–Pb collisions at sNN\sqrt{s_{\rm NN}} = 5.02 and 2.76 TeV

Measurements of the production of muons from heavy-flavour hadron decays in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 and 2.76 TeV using the ALICE detector at the LHC are reported. The nuclear modification factor $R_{AA}$ at $\sqrt{s_{\rm NN}}$ = 5.02 TeV is measured at forward rapidity (2.5 7 GeV/c). The $R_{AA}$ shows an increase of the suppression of the yields of muons from heavy-flavour hadron decays with increasing centrality. A suppression by a factor of about three is observed in the 10% most central collisions. The $R_{AA}$ at $\sqrt{s_{\rm NN}}$ = 5.02 TeV is similar to that at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. The precise $R_{AA}$ measurements have the potential to distinguish between model predictions implementing different mechanisms of parton energy loss in the high-density medium formed in heavy-ion collisions. They place important constraints for the understanding of the heavy-quark interaction with the hot and dense QCD medium

Measurement of the lifetime and Λ\Lambda separation energy of Λ3H^{3}_{\Lambda}\mathrm H

The most precise measurements to date of the $^{3}_{\Lambda}\mathrm H$ lifetime $\tau$ and $\Lambda$ separation energy ${\rm B}_{\Lambda}$ are obtained using the data sample of Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV collected by ALICE at the LHC. The $^{3}_{\Lambda}\mathrm H$ is reconstructed via its charged two-body mesonic decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow$ $^3$He + $\pi^-$ and the charge-conjugate process). The measured values $\tau = [253 \pm 11 \text{ (stat.)} \pm 6 \text{ (syst.)}]$ ps and ${\rm B}_{\Lambda}= [72 \pm 63 \text{ (stat.)} \pm 36 \text{ (syst.)}]$ keV are compatible with predictions from effective field theories and conclusively confirm that the $^{3}_{\Lambda}\mathrm H$ is a weakly-bound system.The most precise measurements to date of the HΛ3 lifetime τ and Λ separation energy BΛ are obtained using the data sample of Pb-Pb collisions at sNN=5.02  TeV collected by ALICE at the LHC. The HΛ3 is reconstructed via its charged two-body mesonic decay channel (HΛ3→He3+π- and the charge-conjugate process). The measured values τ=[253±11(stat)±6(syst)]  ps and BΛ=[102±63(stat)±67(syst)]  keV are compatible with predictions from effective field theories and confirm that the HΛ3 structure is consistent with a weakly bound system.The most precise measurements to date of the $^{3}_{\Lambda}\mathrm H$ lifetime $\tau$ and $\Lambda$ separation energy ${\rm B}_{\Lambda}$ are obtained using the data sample of Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV collected by ALICE at the LHC. The $^{3}_{\Lambda}\mathrm H$ is reconstructed via its charged two-body mesonic decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow$$^3$He + $\pi^-$ and the charge-conjugate process). The measured values $\tau = [253 \pm 11 \text{ (stat.)} \pm 6 \text{ (syst.)}]$ ps and ${\rm B}_{\Lambda}= [102 \pm 63 \text{ (stat.)} \pm 67 \text{ (syst.)}]$ keV are compatible with predictions from effective field theories and confirm that the $^{3}_{\Lambda}\mathrm H$ structure is consistent with a weakly-bound system