Search

Jet-associated deuteron production in $pp$ collisions at $\sqrt{s}=13$ TeV and $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV is studied in the coalescence model by using the phase-space information of proton and neutron pairs from a multiphase transport (AMPT) model at the kinetic freezeout. In the low transverse momentum ($p_T$) region $p_T/A < 1.5$ GeV/$c$, where $A$ is the mass number of a nucleus, the in-jet coalescence factor $B_2^\text{In-jet}$ for deuteron production, given by the ratio of the in-jet deuteron number to the square of the in-jet proton number, is found to be larger than the coalescence factor $B_2$ in the medium perpendicular to the jet by a factor of about 10 in $pp$ collisions and of 25 in $p-$Pb collisions, which are consistent with the ALICE measurements at the LHC. Such large low-momentum enhancements mainly come from coalescence of nucleons inside the jet with the medium nucleons. Coalescence of nucleons inside the jet dominates deuteron production only at the higher $p_T$ region of $p_T/A\gtrsim 4$ GeV/$c$, where both the yield ratio $d/p$ of deuteron to proton numbers and the $B_2$ are also significantly larger in the jet direction than in the direction perpendicular to the jet due to the strong collinear correlation among particles produced from jet fragmentation. Studying jet-associated deuteron production in relativistic nuclear collisions thus opens up a new window to probe the phase-space structure of nucleons inside jets.

Particles of non-zero spin produced in non-central heavy-ion collisions are expected to be polarized along the direction perpendicular to the reaction plane because of their spin-orbit interactions in the produced matter, and this has indeed been observed for many hyperons and vector mesons. Here, we show that the hypertriton ($^3_\Lambda\text{H}$), which is the lightest hypernucleus, is also polarized in these collisions. Using the coalescence model based on the kinetic freezeout baryons for light (hyper-)nuclei production, we find that the angular distribution of the decay product of polarized $^3_\Lambda\text{H}$ is highly sensitive to the spin configuration of its wavefunction, providing a novel way to determine its spin structure. We also predict the beam energy dependence of $^3_\Lambda\text{H}$ and ${^3_{\bar{\Lambda}}}\overline{\rm H}$ polarizations in heavy-ion collisions from a few GeV to several TeV based on the measured $\Lambda$ and $\bar{\Lambda}$ polarizations. We further discuss the possibility of studying the spin correlations among nucleons and $\Lambda$ hyperons in the produced hadronic matter from the measured $^3_\Lambda\text{H}$ polarization in non-central heavy-ion collisions., Comment: 6 pages, 2 figures

The production of light nuclei in isobaric $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions, ranging from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV, are studied using the string melting version of A Multi Phase Transport (AMPT) model in combination with a coalescence approach to light nuclei production. From the calculated yields, transverse momentum $p_{T}$ spectra, and rapidity dependences of light nuclei $p$, $n$, $d$, $t$, ${}^{3}$He, we find that the Ru+Ru/Zr+Zr ratios for the yields of these particles exceed unity with the inclusion of a quadrupole deformation $\beta_{ 2 }$ and octupole deformation $\beta_{ 3 }$ as well as the neutron skins. We also find that heavier particles have a larger deviation from unity. Furthermore, we find that as the collision energy increases, the influence of isospin effects on the production of light nuclei in isobar collisions gradually decreases, while the influence of nuclear structure becomes more significant, particularly evident from the energy dependence of the deuteron ratio, which is unaffected by isospin effects., Comment: 9 pages, 5 figures

Understanding the properties of hypernuclei helps to constrain the interaction between hyperon and nucleon, which is known to play an essential role in determining the properties of neutron stars. Experimental measurements have suggested that the hypertriton ($^3_\Lambda \text{H}$), the lightest hypernucleus, exhibits a halo structure with a deuteron core encircled by a $\Lambda$ hyperon at a distance of about 10 fm. This large $\Lambda-d$ distance in $^3_\Lambda \text{H}$ wave function is found to cause a suppressed $^3_\Lambda \text{H}$ yield and a softening of its transverse momentum ($p_T$) spectrum in relativistic heavy-ion collisions. Within the coalescence model based on nucleons and $\Lambda$ hyperons from a microscopic hybrid hydro model with a hadronic afterburner for nuclear cluster production in Pb-Pb collisions at $\sqrt{s_{NN}}$= 5.02 TeV, we show how this softening of the hypertriton $p_T$ spectrum appears and leads to a smaller mean $p_T$ for $^3_\Lambda \text{H}$ than for helium-3 ($^3$He). The latter is opposite to the predictions from the blast-wave model which assumes that $^3_\Lambda \text{H}$ and $^3$He are thermally produced at the kinetic freeze-out of heavy-ion collisions. The discovered quantum mechanical softening of the (anti-)hypertriton spectrum can be experimentally tested in relativistic heavy-ion collisions at different collision energies and centralities and used to obtain valuable insights into the mechanisms for light (hyper-)nuclei production in these collisions., Comment: 6 pages, 4 figures

The strange dibaryons $p\Omega$ ($^5\rm{S}_2$) and $\Omega\Omega$ ($^1\rm{S}_0$) are likely bound, existing either in molecular states like the deuteron or as more exotic compact six-quark states. Here, we investigate the production of these two dibaryons in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV at the CERN Large Hadron Collider (LHC) within a covariant coalescence model, which employs a blast-wave-like parametrization for the phase-space configurations of constituent particles at freeze-out. For the molecular states, the $p\Omega$ and $\Omega\Omega$ are produced via $p$-$\Omega$ and $\Omega$-$\Omega$ coalescence, respectively, while for the six-quark states, they are formed through $uudsss$ and $ssssss$ coalescence. We find that the yield ratio $N_{p\Omega}/N_{\Omega}$ and $N_{\Omega\Omega}/N_{\Omega}$ have a distinct centrality dependence between the molecular and multi-quark states, thus offering a promising way for distinguishing the two states. Our results suggest that the measurements of $p\Omega$ and $\Omega\Omega$ production in relativistic heavy-ion collisions can shed light on their internal structures., Comment: 6 pages, 3 figures

We develop a kinetic approach to the production of light nuclei up to mass number $A$ $\leqslant$ $4$ in intermediate-energy heavy-ion collisions by including them as dynamic degrees of freedom. The conversions between nucleons and light nuclei during the collisions are incorporated dynamically via the breakup of light nuclei by a nucleon and their inverse reactions. We also include the Mott effect on light nuclei, i.e., a light nucleus would no longer be bound if the phase-space density of its surrounding nucleons is too large. With this kinetic approach, we obtain a reasonable description of the measured yields of light nuclei in central Au+Au collisions at energies of $0.25$ - $1.0A~\rm GeV$ by the FOPI collaboration. Our study also indicates that the observed enhancement of the $\alpha$-particle yield at low incident energies can be attributed to a weaker Mott effect on the $\alpha$-particle, which makes it more difficult to dissolve in nuclear medium, as a result of its much larger binding energy., Comment: 6 pages, 4 figures

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

Like nucleosynthesis during the early universe, light nuclei are also produced in relativistic heavy-ion collisions. Although the deuteron ($d$) yields in these collisions can be well described by the statistical hadronization model (SHM), which assumes that particle yields are fixed at a common chemical freezeout near the phase boundary between the quark-gluon plasma and the hadron gas, the recently measured triton ($^3\text{H}$) yields in Au+Au collisions at $\sqrt{s_{NN}}=7.7-200$ GeV are overestimated systematically by this model. Here, we develop a comprehensive kinetic approach to study the effects of hadronic re-scatterings, such as $\pi NN\leftrightarrow\pi d$ and $\pi NNN\leftrightarrow\pi ^3\text{H}~(^3\text{He})$, on $d$, $^3\text{H}$, and $^3\text{He}$ production in these collisions. We find that these reactions have little effects on the deuteron yield but reduce the $^3\text{H}$ and $^3\text{He}$ yields by about a factor of 1.8 from their initial values given by the SHM. This finding helps resolve the overestimation of triton production in the SHM and provides the evidence for hadronic re-scattering effects on nucleosynthesis in relativistic heavy-ion collisions., Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:2106.12742

Using a relativistic transport model to describe the evolution of the quantum chromodynamic matter produced in Au+Au collisions at $\sqrt{s_{NN}}=3-200$ GeV, we study the effect of a first-order phase transition in the equation of state of this matter on the yield ratio $N_tN_p/ N_d^2$ ($tp/d^2$) of produced proton ($p$), deuteron ($d$), and triton ($t$). We find that the large density inhomogeneities generated by the spinodal instability during the first-order phase transition can survive the fast expansion of the subsequent hadronic matter and lead to an enhanced $tp/d^2$ in central collisions at $\sqrt{s_{NN}}=3-5$ GeV as seen in the experiments by the STAR Collaboration and the E864 Collaboration. However, this enhancement subsides with increasing collision centrality, and the resulting almost flat centrality dependence of $tp/d^2$ at $\sqrt{s_{NN}}=3$ GeV can also be used as a signal for the first-order phase transition., Comment: 6 pages, 3 figures

Using the nucleon coalescence model based on kinetic freeze-out nucleons from the hybrid model of MUSIC hydrodynamics and UrQMD hadronic transport, we study the production of anti-deuteron and its event-by-event fluctuation in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. We find a clear suppression of the anti-deuteron to antiproton yield ratio in peripheral collisions, which is in accordance with the measurements from the ALICE Collaboration. Also found is a Poissonian event-by-event fluctuation of the anti-deuteron multiplicity distribution in all collision centralities, which is different from the prediction of a simple coalescence model calculation that assumes all antiproton and antineutron pairs to have the same probability to form anti-deuterons. We further find a small negative correlation between the anti-deuteron and antiproton multiplicity distributions as a result of the baryon conservation., Comment: 5 pages, 5 figures

Understanding the production mechanism of light (anti-)nuclei in high-energy nuclear collisions and cosmic rays has been a long-standing problem in nuclear physics. In the present study, we develop a stochastic method to solve the relativistic kinetic equations for light nuclei production from many-body reactions with the inclusion of their finite sizes. The present approach gives an excellent description of the deuteron and helium-3 data from central Au+Au (Pb+Pb) collisions at $\sqrt{s_{\rm NN}}$ $=$ $200~\rm GeV$ ($2.76~\rm TeV$). It can also naturally explain their suppressed production in $pp$ collisions at 7 TeV as a result of their finite sizes., Comment: 7 pages, 3 figures

Using the nucleon coalescence model based on kinetic freeze-out nucleons from the 3D MUSIC+UrQMD and the 2D VISHNU hybrid model with a crossover equation of state, we study the multiplicity dependence of deuteron ($d$) and triton ($t$) production from central to peripheral Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7, 14.5, 19.6, 27, 39, 62.4 and 200 GeV and Pb+Pb at $\sqrt{s_\mathrm{NN}}=2.76$ TeV, respectively. It is found that the ratio $N_t N_p/N_d^2$ of the proton yield $N_p$, deuteron yield $N_d$ and triton yield $N_t$ exhibits a scaling behavior in its multiplicity dependence, i.e., decreasing monotonically with increasing charged-particle multiplicity. A similar multiplicity scaling of this ratio is also found in the nucleon coalescence calculation based on kinetic freeze-out nucleons from a multiphase transport (AMPT) model. The scaling behavior of $N_t N_p/N_d^2$ can be naturally explained by the interplay between the sizes of light nuclei and the nucleon emission source. We further argue that the multiplicity scaling of $N_t N_p/N_d^2$ can be used to validate the production mechanism of light nuclei, and the collision energy dependence of this yield ratio can further serve as a baseline in the search for the QCD critical point in relativistic heavy-ion collisions., Comment: 9 pages, 5 figures

The machine-learning techniques have shown their capability for studying phase transitions in condensed matter physics. Here, we employ the machine-learning techniques to study the nuclear liquid-gas phase transition. We adopt an unsupervised learning and classify the liquid and gas phases of nuclei directly from the final state raw experimental data of heavy-ion reactions. Based on a confusion scheme which combines the supervised and unsupervised learning, we obtain the limiting temperature of the nuclear liquid-gas phase transition. Its value $9.24\pm0.04~\rm MeV$ is consistent with that obtained by the traditional caloric curve method. Our study explores the paradigm of combining the machine-learning techniques with heavy-ion experimental data, and it is also instructive for studying the phase transition of other uncontrollable systems, like QCD matter., Comment: 9 pages, 8 figures, 1 table; Physical Review Research, in press (2020)

Using the nucleon coalescence model, which can naturally take into account the correlations in the nucleon density distribution, we study the effects of QCD critical point on light nuclei production in relativistic heavy-ion collisions. We find that the yield ratio $N_tN_p/N_d^2$ of proton ($p$), deuteron ($d$) and triton ($t$) increases monotonically with the nucleon density correlation length, which is expected to increase significantly near the critical point in the QCD phase diagram. Our study thus demonstrates that the yield ratio $N_tN_p/N_d^2$ can be used as a sensitive probe of the QCD critical phenomenon. We further discuss the relation between the QCD phase transitions in heavy-ion collisions and the possible non-monotonic behavior of \pdt~in its collision energy dependence., Comment: 6 pages, 1 figure

Using a transport model that includes a first-order chiral phase transition between the partonic and the hadronic matter, we study the development of density fluctuations in the matter produced in heavy ion collisions as it undergoes the phase transition, and their time evolution in later hadronic stage of the collisions. Using the coalescence model to describe the production of deuterons and tritons from nucleons at the kinetic freeze out, we find that the yield ratio $ N_\text{t}N_\text{p}/ N_\text{d}^2$, where $N_\text{p}$, $N_\text{d}$, and $N_\text{t}$ are, respectively, the proton, deuteron, and triton numbers, is enhanced if the evolution trajectory of the produced matter in the QCD phase diagram passes through the spinodal region of a first-order chiral phase transition., Comment: 12 pages, 6 figures

Based on an improved multiphase transport (AMPT) model, which gives a good description of proton production with a smooth quark matter to hadronic matter transition in relativistic heavy ion collisions, we study deuteron and triton production from the coalescence of nucleons at the kinetic freezeout of these collisions. For Au+Au collisions at center-of-mass energies $\sqrt{s_\text{NN}}$ from 7.7 GeV to 200 GeV available at the Relativistic Heavy Ion Collider (RHIC), we find that the yield ratio $N_\text{t}N_\text{p}/N_\text{d}^2$ of proton, deuteron\com{,} and triton is essentially a constant as a function of collision energy. Our result confirms the expectation that without a first-order quark to hadronic matter phase transition in the produced matter or its approach to the critical point of the QCD matter, this yield ratio does not show any non-monotonic behavior in its collision energy dependence., Comment: 5 pages, 2 figures

We study the critical point in the QCD phase diagram in the Nambu-Jona-Lasino (NJL) model by including a scalar-vector coupled interaction. We find that varying the strength of this interaction, which has no effect on the vacuum properties of QCD, can significantly affect the location of the critical point in the QCD phase diagram, particularly the value of the cirtical temperature. This provides a convenient way to use the NJL-based transport or hydrodynamic model to extract information about the QCD phase diagram from relativistic heavy-ion collisions., Comment: 8 pages, 4 figures

We resolve the difference in the yield ratio $\rm S_3$ = $\rm \frac{N_{^3_{\Lambda}H}/N_\Lambda}{N_{^3He}/N_p}$ measured in Au+Au collisions at $\rm \sqrt{s_{NN}}$ = 200 GeV and in Pb-Pb collisions at $\rm \sqrt{s_{NN}}$ = 2.76 TeV by adopting a different treatment of the weak decay contribution to the proton yield in Au+Au collisions at $\rm \sqrt{s_{NN}}$ = 200 GeV. We then use the coalescence model to extract information on the $\Lambda$ and nucleon density fluctuations at the kinetic freeze-out of heavy ion collisions. We also show from available experimental data that the yield ratio $\rm S_2$ = $\rm \frac{N_{^3_{\Lambda}H}}{N_\Lambda N_ d}$ is a more promising observable than $\rm S_3$ for probing the local baryon-strangeness correlation in the produced medium., Comment: 15 pages, 2 figures, 3 tables, submitted for publication

We develop for charmed hadron production in relativistic heavy-ion collisions a comprehensive coalescence model that includes an extensive set of $s$ and $p$-wave hadronic states as well as the strict energy-momentum conservation, which ensures the boost invariance of the coalescence probability and the thermal limit of the produced hadron spectrum. By combining our hadronization scheme with an advanced Langevin-hydrodynamics model that incorporates both elastic and inelastic energy loss of heavy quarks inside the dynamical quark-gluon plasma, we obtain a successful description of the $p_\mathrm{T}$-integrated and differential $\Lambda_c/D^0$ and $D_s/D^0$ ratios measured at RHIC and the LHC. We find that including the effect of radial flow of the medium is essential for describing the enhanced $\Lambda_c/D^0$ ratio observed in relativistic heavy-ion collisions. We also find that the puzzling larger $\Lambda_c/D^0$ ratio observed in Au+Au collisions at RHIC than in Pb+Pb collisions at the LHC is due to the interplay between the effects of the QGP radial flow and the charm quark transverse momentum spectrum at hadronization. Our study further suggests that charmed hadrons have larger sizes in medium than in vacuum., Comment: 6 pages, 5 figures

By analyzing the available data on strange hadrons in central Pb+Pb collisions from the NA49 Collaboration at the Super Proton Synchrotron (SPS) and in central Au+Au collisions from the STAR Collaboration at the Relativistic Heavy-Ion Collider (RHIC) in a wide collision energy range from $\sqrt{s_{\rm NN}}$ = 6.3 GeV to 200 GeV, we find a possible non-monotonic behavior in the ratio $\mathcal{O}_\text{K-$\Xi$-$\phi$-$\Lambda$}$= $\frac{N(K^+)N(\Xi^-)}{N(\phi)N(\Lambda)}$ of $K^+$, $\Xi^-$, $\phi$, and $\Lambda$ yields as a function of $\sqrt{s_{\rm NN}}$. Based on the quark coalescence model, which can take into account the effect of quark density fluctuations on hadron production, a possible non-monotonic behavior in the dependence of the strange quark density fluctuation on $\sqrt{s_{NN}}$ is obtained. This is in contrast to the coalescence model that does not include quark density fluctuations and also to the statistical hadronization model as both fail to describe even qualitatively the collision energy dependence of the ratio $\mathcal{O}_\text{K-$\Xi$-$\phi$-$\Lambda$}$. Our findings thus suggest that the signal and location of a possible critical endpoint in the QCD phase diagram, which is expected to result in large quark density fluctuations, can be found in the on-going Bean Energy Scan program at RHIC., Comment: 7 pages, 3 tables and 1 figure

Light nuclei production is sensitive to the baryon density fluctuations and can be used to probe the QCD phase transition in relativistic heavy-ion collisions. In this work, we studied the production of proton, deuteron, triton in central Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5, 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV from a transport model (JAM). Based on the coalescence production of light nuclei, we calculated the energy dependence of rapidity density $dN/dy$ and particle ratios ($d/p$, $t/p$, and $t/d$). More importantly, the yield ratio $N_{{t}} \times N_{{p}} / N_{{d}}^{2}$, which is sensitive to the neutron density fluctuations, shows a flat energy dependence and cannot describe the non-monotonic trend observed by the STAR experiment. Based on the nucleon coalescence, this work can provide constraint and reference to search for the QCD critical point and/or first order phase transition with light nuclei production in future heavy-ion collision experiments., Comment: 5 pages, 4 figures

Based on the framework of an extended multiphase transport model with mean-field potentials in both the partonic phase and the hadronic phase, we explain the elliptic flow difference between $\pi^+$ and $\pi^-$ in the beam-energy scan program at the relativistic heavy-ion collider by incorporating the vector-isovector potential for quarks and antiquarks with different isospins. It is found that the isospin splitting of pion elliptic flow favors a strong vector-isovector interaction, and thus serves as a probe of the quark matter equation of state as well as the QCD phase structure at finite baryon and isospin chemical potentials., Comment: 6 pages, 6 pages

We study the production of charmed hadrons $D^{0}$ and $\Lambda_c^+$ in relativistic heavy-ion collisions using an improved quark coalescence model. In particular, we extend the usual coalescence model by letting a produced hadron to have the same velocity as the center-of-mass velocity of coalesced constituent quarks during hadronization to take into account the effect of collective flow in produced quark-gluon plasma. This results in a shift of charmed resonances of higher masses to larger transverse momenta ($p_T^{}$). Requiring all charm quarks of very low $p_T^{}$ to be converted to hadrons via coalescence and letting charm quarks not undergoing coalescence to hadronize by independent fragmentation, we obtain a good description of the measured yield ratio $\Lambda_c^+/D^0$ as a function of $p_T^{}$ in $\text{Au} + \text{Au}$ collisions at $\sqrt{s_{NN}}^{}=200$~GeV by the STAR Collaboration at the Relativistic Heavy Ion Collider., Comment: 7 pages, 5 figures

We show that the recently observed suppression of the yield ratio of deuteron to proton and of helium-3 to proton in p+p collisions compared to those in p+Pb or Pb+Pb collisions by the ALICE Collaboration at the Large Hadron Collider (LHC) can be explained if light nuclei are produced from the coalescence of nucleons at the kinetic freeze-out of these collisions. This suppression is attributed to the non-negligible sizes of deuteron and helium-3 compared to the size of the nucleon emission source in collisions of small systems, which reduces the overlap of their internal wave functions with those of nucleons. The same model is also used to study the production of triton and hypertriton in heavy-ion collisions at the LHC. Compared to helium-3 in events of low charged particle multiplicity, the triton is less suppressed due to its smaller size and the hypertriton is even more suppressed as a result of its much larger size., Comment: 6 pages and 2 figures

Using a covariant quark coalescence model combined with a blast-wave-like analytical parametrization for (anti-)strange quark phase-space freeze-out configuration, we extract information on strange quark freeze-out dynamics in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV by fitting the measured transverse momentum spectra and elliptic flows ($v_2$) of $\phi$ mesons and $\Omega$ baryons. We find that although both the measured and calculated $v_2$ of $\phi$ and $\Omega$ satisfy the number-of-constituent-quark (NCQ) scaling, the NCQ-scaled $v_2$ is significantly smaller than the $v_2$ of strange quarks, implying that the NCQ-scaled $v_2$ of $\phi$ and $\Omega$ cannot be simply identified as the $v_2$ of strange quarks at hadronization. Meanwhile, our results indicate that the covariant quark coalescence model can nicely describe the spectra and elliptic flows of $\phi$ and $\Omega$ simultaneously, suggesting the coalescence mechanism is still valid for $\phi$ and $\Omega$ production in Pb+Pb collisions at LHC energies., Comment: 7 pages, 3 figures, 1 table. Some results updated and discussions added. Accepted version to appear in PRC

It is generally believed that the quark-hadron transition at small values of baryon chemical potentials $\mu_B$ is a crossover but changes to a first-order phase transition with an associated critical endpoint (CEP) as $\mu_B$ increases. Such a $\mu_B$-dependent quark-hadron transition is expected to result in a double-peak structure in the collision energy dependence of the baryon density fluctuation in heavy-ion collisions with one at lower energy due to the spinodal instability during the first-order phase transition and another at higher energy due to the critical fluctuations in the vicinity of the CEP. By analyzing the data on the $p$, d and $^3$H yields in central heavy-ion collisions within the coalescence model for light nuclei production, we find that the relative neutron density fluctuation $\Delta \rho_n=\langle(\delta \rho_n)^2\rangle/\langle \rho_n\rangle^2$ at kinetic freeze-out indeed displays a clear peak at $\sqrt{s_{NN}}=8.8$ GeV and a possible strong re-enhancement at $\sqrt{s_{NN}}=4.86$ GeV. Our findings thus provide a strong support for the existence of a first-order phase transition at large $\mu_B$ and its critical endpoint at a smaller $\mu_B$ in the temperature versus baryon chemical potential plane of the QCD phase diagram., Comment: 7 pages, 2 figures, 1 table. Significantly expanded to include some details and discussions. Accepted version to appear in PLB

We show that the Atiyah-Singer index theorem of Dirac operator can be directly proved in the canonical formulation of quantum mechanics, without using the path-integral technique. This proof takes advantage of an algebraic isomorphism between Clifford algebra and exterior algebra in small $\tau$ (high temperature) limit, together with simple properties of quantum mechanics of harmonic oscillator. Compared to the proof given by heat kernel, we try to prove this theorem more quantum mechanically.

Based on the coalescence model for light nuclei production, we show that the yield ratio $\mathcal{O}_\text{p-d-t} = N_{^3\text{H}} N_p / N_\text{d}^2$ of $p$, d, and $^3$H in heavy-ion collisions is sensitive to the neutron relative density fluctuation $\Delta n= \langle (\delta n)^2\rangle/\langle n\rangle^2$ at kinetic freeze-out. From recent experimental data in central Pb+Pb collisions at $\sqrt{s_{NN}}=6.3$~GeV, $7.6$~GeV, $8.8$~GeV, $12.3$~GeV and $17.3$~GeV measured by the NA49 Collaboration at the CERN Super Proton Synchrotron (SPS), we find a possible non-monotonic behavior of $\Delta n$ as a function of the collision energy with a peak at $\sqrt{s_{NN}}=8.8$~GeV, indicating that the density fluctuations become the largest in collisions at this energy. With the known chemical freeze-out conditions determined from the statistical model fit to experimental data, we obtain a chemical freeze-out temperature of $\sim 144~$MeV and baryon chemical potential of $\sim 385~$MeV at this collision energy, which are close to the critical endpoint in the QCD phase diagram predicted by various theoretical studies. Our results thus suggest the potential usefulness of the yield ratio of light nuclei in relativistic heavy-ion collisions as a direct probe of the large density fluctuations associated with the QCD critical phenomena., Comment: 6 pages, 1 figure, 2 tables. Correlations between neutron and proton density fluctuations considered and presentation improved. Accepted version to appear in PLB

Based on a covariant coalescence model with a blast-wave-like parametrization for the phase-space configuration of constituent particles at freeze-out, we derive an approximate analytical formula for the yields of clusters produced in relativistic heavy-ion collisions. Compared to previous existing formulae, the present work additionally considers the contributions from the longitudinal dimension in momentum space, the relativistic corrections and the finite size effects of the produced clusters relative to the spatial distribution of constituent particles at freeze-out. The new analytical coalescence formula provides a useful tool to evaluate the yield of produced clusters, such as light nuclei from nucleon coalescence and hadrons from quark coalescence, in heavy-ion collisions. As a first application of the new analytical formula, we explore the strangeness population factor $S_3 = ^3_{\Lambda}$H/($^3$He$\times \Lambda/$p) based on nucleon/$\Lambda$ coalescence as well as the production of exotic hadrons based on quark coalescence, in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The results are compared with the predictions from other models., Comment: 12 pages, 0 figures, 3 tables. Discussions added. Accepted version to appear in PRC

We study the production of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$ exotic states in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC via both hadron and quark coalescence within a covariant coalescence model with a blast-wave-like parametrization for the phase-space configurations of constituent particles at freezeout. In the hadron coalescence, the two states are considered as molecular states while they are considered as six-quark states in the quark coalescence.For $\overline{\Lambda \text{n}}$, we find that the yields of both molecular and six-quark states are much larger than the experimental upper-limits. For $\Lambda\Lambda$, while the molecule-state yield is much larger than the experimental upper-limits, the six-quark-state yield could be lower than the upper-limits. The higher molecule-state yields are mainly due to the large contribution of short-lived strong resonance decays into (anti-)nucleons and (anti-)$\Lambda$ which can significantly enhance the molecule-state yields of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$ via hadron coalescence. Our results suggest that the current experimental measurement at LHC cannot exclude the existence of the $\Lambda\Lambda$ as an exotic six-quark state, and if $\Lambda\Lambda$ is a six-quark state, it is then on the brink of being discovered., Comment: 6 pages, 4 figures, 2 tables. Minor modifications. Accepted version to appear in PRC

We have studied the properties of hot and dense quark matter based on the 3-flavor Nambu-Jona-Lasinio (NJL) model as well as its Polyakov-loop extension (pNJL) with scalar-isovector and vector-isovector couplings. Provided a considerable large isospin asymmetry or isospin chemical potential, isospin splittings of constituent mass, chiral phase transition boundary, and critical point for $u$ and $d$ quarks can be observed for positive isovector coupling constants but are suppressed for negative ones. The quark matter symmetry energy decreases with the increasing isovector coupling constant, and is mostly enhanced in the pNJL model than in the NJL model. A positive scalar-isovector coupling constant is more likely to lead to an unstable isospin asymmetric quark matter. The isovector coupling has been further found to affect particle fractions as well as the equation of state in hybrid stars. Possible effects on the isospin properties of quark matter have also been discussed if the strangeness sector is further broken among the flavor symmetry., Comment: 12 pages, 11 figures, significantly revised, version to appear in Phys. Rev. D

In the framework of the quark combination, we derive the yield formulas and study the yield ratios of the hidden-charm pentaquark states in ultra-relativistic heavy ion collisions. We propose some interesting yield ratios which clearly exhibit the production relationships between different hidden-charm pentaquark states. We show how to employ a specific quark combination model to evaluate the yields of exotic $P_c^+(4380)$, $P_c^+(4450)$ and their partners on the basis of reproducing the yields of normal identified hadrons, and execute the calculations in central Pb+Pb collisions at $\sqrt{s_{NN}}= 2.76$ TeV as an example.

We show that the measured yield ratio $^3_{\Lambda}$H/$^3$He ($^3_{\overline{\Lambda}}\overline{\text{H}}$/$^3\overline{\text{He}}$) in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV can be understood within a covariant coalescence model if (anti-)$\Lambda$ particles freeze out earlier than (anti-)nucleons but their relative freezeout time is closer at $\sqrt{s_{NN}}=2.76$ TeV than at $\sqrt{s_{NN}}=200$ GeV. The earlier (anti-)$\Lambda$ freezeout can significantly enhance the yield of (anti)hypernucleus $^4_{\Lambda}$H ($^4_{\overline{\Lambda}}\overline{\text{H}}$), leading to that $^4_{\overline{\Lambda}}\overline{\text{H}}$ has a comparable abundance with $^4\overline{\text{He}}$ and thus provides an easily measured antimatter candidate heavier than $^4\overline{\text{He}}$. The future measurement on $^4_{\Lambda}$H ($^4_{\overline{\Lambda}}\overline{\text{H}}$) would be very useful to understand the (anti-)$\Lambda$ freezeout dynamics and the production mechanism of (anti)hypernuclei in relativistic heavy-ion collisions., Comment: 7 pages, 4 figures, 2 tables. Significantly expanded to include some details and discussions. Accepted version to appear in PRC

Combining the covariant coalescence model and a blast-wave-like analytical parametrization for (anti-)nucleon phase-space freezeout configuration, we explore light (anti-)nucleus production in central Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Using the nucleon freezeout configuration (denoted by FO1) determined from the measured spectra of protons (p), deutrons (d) and $^{3}$He, we find the predicted yield of $^{4}$He is significantly smaller than the experimental data. We show this disagreement can be removed by using a nucleon freezeout configuration (denoted by FO2) in which the nucleons are assumed to freeze out earlier than those in FO1 to effectively consider the effect of large binding energy value of $^{4}$He. Assuming the binding energy effect also exists for the production of $^5\text{Li}$, $^5\overline{\text{Li}}$, $^6\text{Li}$ and $^6\overline{\text{Li}}$ due to their similar binding energy values as $^{4}$He, we find the yields of these heavier (anti-)nuclei can be enhanced by a factor of about one order, implying that although the stable (anti-)$^6$Li nucleus is unlikely to be observed, the unstable (anti-)$^5$Li nucleus could be produced in observable abundance in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV where it may be identified through the p-$^4\text{He}$ ($\overline{\text{p}}$-$^4\overline{\text{He}}$) invariant mass spectrum. The future experimental measurement on (anti-)$^5\text{Li}$ would be very useful to understand the production mechanism of heavier antimatter., Comment: 8 pages, 2 figures, 3 tables. Typos fixed and one ref added. Accepted version to appear in PLB

Isospin-violating dark matter (IVDM), which couples differently with protons and neutrons, provides a promising mechanism to ameliorate the tension among recent direct detection experiments. Assuming DM is non-interacting bosonic asymmetric IVDM, we investigate how the existence of old neutron stars limits the DM-proton scattering cross-section $\sigma_{\rm p}$, especially the effects of the isospin violating DM-nucleon interactions and the symmetry energy in the equation of state of isospin asymmetric nuclear matter. Our calculations are completely based on general relativity and especially the structure of neutron stars is obtained by solving the Tolman-Oppenheimer-Volkoff equations with nuclear matter equation of state constrained by terrestrial experiments. We find that, by considering the more realistic neutron star model rather than a simple uniform neutron sphere as usual, the $\sigma_{\rm p}$ bounds from old neutron stars can be varied by more than an order of magnitude depending on the specific values of the DM neutron-to-proton coupling ratio $f_{\rm n}/f_{\rm p}$, and they can be further varied by more than a factor of two depending on the density dependence of the symmetry energy. In particular, we demonstrate that the observed nearby isolated old neutron star PSR B1257+12 can set a very strong limit on $\sigma_{\rm p}$ for low-mass DM particles ($ \le 20 \, {\rm GeV}$) that reaches a sensitivity beyond the current best limits from direct detection experiments and disfavors the DM interpretation of previously-reported positive experimental results, including the IVDM., Comment: 14 pages, 5 figures, 2 tables. Constraint from realistic neutron star added, and for low-mass non-interacting bosonic asymmetric DM, it reaches a sensitivity beyond the current best limits from direct detection experiments and disfavors the DM interpretation of previously-reported positive experimental results, including the isospin-violating dark matter. Accepted version to appear in ApJ