Subthreshold pion production within a transport description of central Au + Au collisions

Abstract

Mapping out the equation of state (EOS) of nuclear matter is a long standing problem in nuclear physics. Recent emphasis is onto the density dependence of the symmetry energy, with experiments needing dedicated symmetry-energy observables. Towards the latter goal, we employ pBUU transport model [1] to simulate pion production in heavy ion collision (HIC). We find that the net pion yield tests the momentum dependence of nuclear mean field (MF). In exploring the sensitivity of pion observables to the symmetry energy at higher than normal densities, we find that our calculations of pion ratios contradict, at some level, predictions from both IBUU [2] and ImIQMD [3] models. We propose to employ the pion ratio in the high-energy tail of spectra in future experiments, to distinguish between different variants of high-density symmetry energy.

Cross-checking the symmetry energy at high densities

“…Treatment of Delta dynamics in transport models is not so straightforward such as the competing effects of the mean fields and △ thresholds. To understand quantitatively the symmetry energy effect on pion production, it is important to include the isospin-dependent pion in-medium effects [23][24][25]. And recent work of MSU group [54] demonstrates that the ratio of π's spectra is more sensitive than the ratio of integrated yields because the latter gives ambiguous result since it does not distinguish π's messenger of high density from the rest.…”

“…With great efforts, the nuclear symmetry energy and its slope around saturation density of nuclear matter from 28 analysis of terrestrial nuclear laboratory experiments and astrophysical observations have been roughly pinned down [15], while recent interpretations of the FOPI and FOPI-LAND experimental measurements by different groups made the symmetry energy at supra-saturation densities fall into chaos [16][17][18][19][20][21][22]. It does not seem to be clarified why the nuclear symmetry energy at supra-saturation densities is so uncertain, maybe the effects of pion inmedium effects [23][24][25], the isospin dependence of inmedium nuclear strong interactions [26], the short-range tensor force [27,28] are some factors.…”

Effect ofΔpotential on theπ−/π+ratio in heavy-ion collisions at intermediate energies

“…. It thus provides more opportunities and enhances our confidences to study the symmetry energy although there are still many uncertain factors, such as the effects of pion potential [15,16], the isospin dependence of inmedium nuclear strong interactions [17], the short-range tensor force [18,19] and the π − N − ∆ dynamics [20][21][22].…”

“…Fortunately, more related experiments are currently underway or being planed at several advanced radioactive ion beam facilities such as CSR/China [10], FRIB/USA [11], GSI/Germany [12], RIKEN/Japan [13], or KoRIA/Korea [14]. It thus provides more opportunities and enhances our confidences to study the symmetry energy although there are still many uncertain factors, such as the effects of pion potential [15,16], the isospin dependence of inmedium nuclear strong interactions [17], the short-range tensor force [18,19] and the π − N − ∆ dynamics [20][21][22].…”

Symmetry potential of theΔ(1232)resonance and its effects on theπ−/π+ratio in heavy-ion collisions near the pion-prod

“…Unfortunately, several model analyses [13][14][15][16][17][18] of some existing data have so far been inconclusive. Realizing the importance of thoroughly understanding all aspects of the π − N − ∆ dynamics in isospin-asymmetric matter especially since several experiments measuring the π − /π + ratio are cur- * Email: Bao-An.Li@Tamuc.edu rently underway at RIKEN [19] and NIRS [20] besides those planned at other facilities [21,22], significant efforts have been made recently in studying effects of the in-medium pion production threshold [23], pion meanfield [24][25][26][27], electromagnetic field [28], neutron-skin [29] and nucleon-nucleon short-range correlation [30,31] on pion production mostly at intermediate energies above the pion production threshold of about 300 MeV/A. Extending these efforts, we report here results of a study on effects of the completely unknown symmetry (isovector) potential of the ∆(1232) resonance on both the total and differential π − /π + ratios in heavy-ion collisions at beam energies from 100 to 1000 MeV/A within an isospin-dependent transport model IBUU [12].…”