The data-driven Bayesian model averaging is a rigorous statistical approach to combining multiple models for a unified prediction. Compared with the individual model, it provides more reliable information, especially for problems involving apparent model dependence. In this work, within both the non-relativistic Skyrme energy density functional and the nonlinear relativistic mean field model, the effective proton-neutron chemical potential difference <math><mi>Δ</mi><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>pn</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> of neutron-rich nuclei is found to be strongly sensitive to the symmetry energy <math><msub><mrow><mi>E</mi></mrow><mrow><mi>sym</mi></mrow></msub><mo>(</mo><mi>ρ</mi><mo>)</mo></math> around <math><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn></math>, with <math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub></math> being the nuclear saturation density. Given discrepancies on the <math><mi>Δ</mi><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>pn</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math>-<math><msub><mrow><mi>E</mi></mrow><mrow><mi>sym</mi></mrow></msub><mo>(</mo><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn><mo>)</mo></math> correlations between the two models, we carried out a Bayesian model averaging analysis based on Gaussian process emulators to extract the symmetry energy around <math><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn></math> from the measured <math><mi>Δ</mi><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>pn</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> of 5 doubly magic nuclei $^{48}$Ca, $^{68}$Ni, $^{88}$Sr, $^{132}$Sn and $^{208}$Pb. Specifically, the <math><msub><mrow><mi>E</mi></mrow><mrow><mi>sym</mi></mrow></msub><mo>(</mo><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn><mo>)</mo></math> is inferred to be <math><msub><mrow><mi>E</mi></mrow><mrow><mi>sym</mi></mrow></msub><mo>(</mo><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn><mo>)</mo><mo>=</mo><msubsup><mrow><mn>25.6</mn></mrow><mrow><mo>−</mo><mn>1.3</mn></mrow><mrow><mo>+</mo><mn>1.4</mn></mrow></msubsup><mspace width="0.2em"></mspace><mrow><mi>MeV</mi></mrow></math> at 1σ confidence level. The obtained constraints on the <math><msub><mrow><mi>E</mi></mrow><mrow><mi>sym</mi></mrow></msub><mo>(</mo><mi>ρ</mi><mo>)</mo></math> around <math><mn>2</mn><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mn>3</mn></math> agree well with microscopic predictions and results from other isovector indicators.

China

Mengying Qiu

Bao-Jun Cai

Lie-Wen Chen

Cen-Xi Yuan

Zhen Zhang

Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei

Using the isospin-dependent relativistic Vlasov-Uehling-Uhlenbeck (RVUU) model, we study charged pion (<math><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></math>) production in Au+Au collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo></math> 2.4 GeV. By fitting the density dependence of the Δ resonance production cross section in nuclear medium to reproduce the experimental <math><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></math> multiplicities measured by the HADES Collaboration, we obtain a good description of the rapidity distributions and transverse momentum spectra of <math><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></math> in collisions at various centralities. Some shortcomings in the description of <math><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></math> production may indicate the need for including the strong potential on <math><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></math> in RVUU, which is at present absent. We also calculate the proton rapidity distribution in the most central collisions and compare with the coalescence invariant proton rapidity distribution extracted from preliminary HADES data.

United States

Kyle Godbey

Jeremy W. Holt

Che Ming Ko

Charged pion production from Au + Au collisions at GeV in the relativistic Vlasov-Uehling-Uhlenbeck model

The exotic resonant states <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4457</mn><mo>)</mo></math> are studied using the constrained phase-space coalescence model plus the parton and hadron cascade (paciae) model in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn></math>, 13 TeV, respectively. The pentaquark states, the nucleuslike states, and the hadronic molecular states are considered as their possible structures based on the <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>p</mi><mrow><mo>(</mo><mover><mi>p</mi><mo>¯</mo></mover><mo>)</mo></mrow></math> bound state. The predictions about the yield, the normalized <math><msub><mi>p</mi><mi>T</mi></msub></math>-differential yield, and the normalized rapidity-differential yield are presented for the aforementioned scenarios. The results indicate a hierarchy of the yields for different possible structures; they are all on the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>. These predictions can be tested by future experimental measurements.

Chun-hui Chen

Yi-Long Xie

Hong-ge Xu

Dai-Mei Zhou

Zhi-Lei She

Gang Chen

Exotic states <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn></math>, 13 TeV

We study the thermodynamic properties of asymmetric quark matter, large mass quark stars (QSs), and proto-quark stars (PQSs) within the quasiparticle model. Considering the effects of temperature within quasiparticle model can significantly influence the EOS and the entropy of strange quark matter (SQM), quark fractions in SQM, as well as the tidal deformability and the maximum mass of PQSs along the star evolution line. Our results indicate that the recent discovered heavy compact stars PSR J0348+0432, MSR J0740+6620, PSR J2215+5135, and especially the GW190814’s secondary component  $$m_2$$  <math> <msub> <mi>m</mi> <mn>2</mn> </msub> </math>   can be well described as QSs within the quasiparticle model. The tidal deformability for the QSs describing the heavy compact stars is extremely large, which can not well describe GW170817 as QSs, and the effects of the temperature in the heating process along the star evolution will further increase the tidal deformability and the maximum mass of PQSs.

Peng-Cheng Chu

Yao-Yao Jiang

He Liu

Xiao-Min Zhang

Xiao-Hua Li

Quark star matter at finite temperature in a quasiparticle model

A dynamically constrained phase-space coalescence model and PACIAE model are used to predict the exotic resonant state  $$Z_c^{\pm }(3900)$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>±</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   yield in pp collisions at  $$\sqrt{s} = 1.96, 7$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>1.96</mn> <mo>,</mo> <mn>7</mn> </mrow> </math>   and 13 TeV, respectively, which are estimated to be around  $$10^{-6}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </math>   to  $$10^{-5}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math>   based on the  $$J/\psi \pi ^{\pm }$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <msup> <mi>π</mi> <mo>±</mo> </msup> </mrow> </math>   bound state in the decay chain of b hadrons. The energy dependence of the transverse momentum distributions and rapidity distributions with  $$|y|&lt;6$$  <math> <mrow> <mo>|</mo> <mi>y</mi> <mo>|</mo> <mo>&lt;</mo> <mn>6</mn> </mrow> </math>   and  $$p_{T}&lt;10$$  <math> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>&lt;</mo> <mn>10</mn> </mrow> </math>   GeV/c are also calculated for  $${Z_c^{+}(3900)}$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $${Z_c^{-}(3900)}$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>  . The production of  $${Z_c^{+}(3900)}$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   and its anti-particle  $${Z_c^{-}(3900)}$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   are found to be quite similar to each other.

Liang Zheng

Hong-Ge Xu

Yu-Liang Yan

Ben-Hao Sa

The study of exotic state  $$Z_c^{\pm }(3900)$$  <math> <mrow> <msubsup> <mi>Z</mi> <mi>c</mi> <mo>±</mo> </msubsup> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>   decaying to  $$J/\psi \pi ^{\pm }$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <msup> <mi>π</mi> <mo>±</mo> </msup> </mrow> </math>   in the pp collisions at  $$\sqrt{s}$$  <math> <msqrt> <mi>s</mi> </msqrt> </math>   = 1.96, 7, and 13 TeV

In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at <math><mi>E</mi><mo>/</mo><mi>A</mi><mo>=</mo><mn>270</mn><mtext> MeV</mtext></math> with the SπRIT Time Projection Chamber. While individual pion multiplicities are measured to 4% accuracy, those of the charged pion multiplicity ratios are measured to 2% accuracy. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron and proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for still better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.

G. Jhang

J. Estee

J. Barney

G. Cerizza

Japan

M. Kaneko

South Korea

J.W. Lee

W.G. Lynch

T. Isobe

M. Kurata-Nishimura

T. Murakami

C.Y. Tsang

M.B. Tsang

R. Wang

D.S. Ahn

Germany

L. Atar

T. Aumann

H. Baba

K. Boretzky

Poland

J. Brzychczyk

N. Chiga

N. Fukuda

Croatia

I. Gasparic

B. Hong

A. Horvat

K. Ieki

N. Inabe

Y.J. Kim

T. Kobayashi

Y. Kondo

P. Lasko

H.S. Lee

Y. Leifels

J. Łukasik

J. Manfredi

A.B. McIntosh

P. Morfouace

T. Nakamura

N. Nakatsuka

S. Nishimura

R. Olsen

H. Otsu

P. Pawłowski

K. Pelczar

D. Rossi

H. Sakurai

C. Santamaria

H. Sato

H. Scheit

R. Shane

Y. Shimizu

H. Simon

Netherlands

A. Snoch

A. Sochocka

Z. Sosin

T. Sumikama

H. Suzuki

D. Suzuki

H. Takeda

S. Tangwancharoen

H. Toernqvist

Y. Togano

Z.G. Xiao

S.J. Yennello

J. Yurkon

Y. Zhang

Italy

Maria Colonna

Romania

Dan Cozma

Paweł Danielewicz

Hannah Elfner

Natsumi Ikeno

Justin Mohs

Dmytro Oliinychenko

Akira Ono

Jun Su

Yong Jia Wang

Hermann Wolter

Jun Xu

Ying-Xun Zhang

Symmetry energy investigation with pion production from Sn+Sn systems

We put a stringent constraint on the isovector nuclear interactions in the Skyrme-Hartree-Fock model from the centroid energy <math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msub></math> of the isovector giant dipole resonance in $^{208}$Pb as well as its electric polarizability <math><msub><mrow><mi>α</mi></mrow><mrow><mi>D</mi></mrow></msub></math>. Using the Bayesian analysis method, <math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi>α</mi></mrow><mrow><mi>D</mi></mrow></msub></math> are found to be mostly determined by the nuclear symmetry energy <math><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub></math> at about <math><msup><mrow><mi>ρ</mi></mrow><mrow><mo>⋆</mo></mrow></msup><mo>=</mo><mn>0.05</mn></math> fm$^{−3}$ and the isovector nucleon effective mass <math><msubsup><mrow><mi>m</mi></mrow><mrow><mi>v</mi></mrow><mrow><mo>⋆</mo></mrow></msubsup></math> at the saturation density. At 90% confidence level, we obtain <math><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub><mo>(</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mo>⋆</mo></mrow></msup><mo>)</mo><mo>=</mo><msubsup><mrow><mn>16.4</mn></mrow><mrow><mo>−</mo><mn>0.9</mn></mrow><mrow><mo>+</mo><mn>1.0</mn></mrow></msubsup></math> MeV and <math><msubsup><mrow><mi>m</mi></mrow><mrow><mi>v</mi></mrow><mrow><mo>⋆</mo></mrow></msubsup><mo>/</mo><mi>m</mi><mo>=</mo><msubsup><mrow><mn>0.79</mn></mrow><mrow><mo>−</mo><mn>0.06</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup></math>.

Jia Zhou

Wen-Jie Xie

Bao-An Li

Constraining isovector nuclear interactions with giant resonances within a Bayesian approach

We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of $^{208}$Pb shows a strong dependence on the in-medium nucleon-nucleon cross section <math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>NN</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math>. A very large medium reduction of <math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>NN</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> is needed to reproduce the measured value of the GDR width of $^{208}$Pb at the Research Center for Nuclear Physics in Osaka, Japan.

Rui Wang

Yu-Gang Ma

Constraining the in-medium nucleon-nucleon cross section from the width of nuclear giant dipole resonance

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the long time large deviation function, found to agree with previous works using completely different techniques. Unexpected similarities with stationary large deviations of TASEP with periodic and open boundaries are discussed. Two additional applications are given. (i) Our method is generalized to study the linear statistics of the Airy point process, i.e. of the GUE edge eigenvalues. We obtain the generating function of the cumulants of the empirical measure to a high order. The second cumulant is found to match the result in the bulk obtained from the Gaussian free field by Borodin and Ferrari [1,2], but we obtain systematic corrections to the Gaussian free field (higher cumulants, expansion towards the edge). This also extends a result of Basor and Widom [3] to a much higher order. We obtain large deviation functions for the Airy point process for a variety of linear statistics test functions. (ii) We obtain results for the counting statistics of trapped fermions at the edge of the Fermi gas in both the high and the low temperature limits.

France

Alexandre Krajenbrink

Pierre Le Doussal

Sylvain Prolhac

Systematic time expansion for the Kardar–Parisi–Zhang equation, linear statistics of the GUE at the edge and trapped fermions

Based on the phase-space distributions of freeze-out nucleons and Λ hyperons from a blast-wave model, we study hypertriton production in the coalescence model. Including both the coalescence of Λ with proton and neutron as well as with deuteron, which is itself formed from the coalescence of proton and neutron, we study how the production of hypertriton is affected if nucleons and deuterons are allowed to stream freely after freeze-out. Using central Pb+Pb collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></math> as an example, we find that this only reduces slightly the hypertriton yield, which has a value consistent with the experimental data, even if the volume of the system has expanded to a size similar to the freeze-out volume for a hyertriton if its dissociation cross section by pions in the system is given by its geometric size. Our results thus suggest that the hypertriton yield in relativistic heavy ion collisions is essentially determined at the time when nucleons and deuterons freeze out, although it still undergoes reactions with pions.

Hypertriton production in relativistic heavy ion collisions