Besides the yield ratio of free spectator neutrons produced in ultracentral 96 Zr+ 96 Zr to 96 Ru+ 96 Ru collisions [1], we propose that the yield ratio Nn Np of free spectator neutrons to protons in a single collision system at RHIC and LHC can be a more sensitive probe of the neutron-skin thickness ∆rnp and the slope parameter L of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions of colliding nuclei obtained from Skyrme-Hartree-Fock-Bogolyubov calculations, and a Glauber model that provides information of spectator matter. The final spectator particles are produced from direct emission, clusterization by a minimum spanning tree algorithm or a Wigner function approach, and deexcitation of heavy clusters by GEMINI. A larger ∆rnp associated with a larger L value increases the isospin asymmetry of spectator matter and thus leads to a larger Nn Np, especially in ultracentral collisions where the multiplicity of free nucleons are free from the uncertainties of cluster formation and deexcitation. We have further shown that the double ratio of Nn Np in isobaric collision systems or in collisions by isotopes helps to cancel the detecting efficiency for protons. Effects from nuclear deformation and electromagnetic excitation are studied, and they are found to be subdominant compared to the expected sensitivity to ∆rnp.
We used the modified Hagedron function and analyzed the experimental data measured by the BRAHMS, STAR, PHENIX and ALICE Collaborations in Copper-Copper, Gold-Gold, deuteron-Gold, Lead-Lead, proton-Lead and proton-proton collisions, and extracted the related parameters (kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, mean transverse momentum and initial temperature) from the transverse momentum spectra of the particles (non-strange and strange particles). We observed that all the above parameters decrease from central to peripheral collisions, except transverse flow velocity which remains unchanged from central to peripheral collisions. The kinetic freeze-out temperature depends on the cross-section interaction of the particle such that larger cross-section of the particle corresponds to smaller T0, and reveals the two kinetic freeze-out scenario, while the initial temperature depends on the mass of the particle and it increase with the particle mass. The transverse flow velocity and mean transverse momentum depends on the mass of the particle and the former decrease while the later increase with the particle mass. In addition, the kinetic kinetic freeze-out volume also decrease with particle mass which reveals the volume differential freeze-out scenario and indicates different freeze-out surfaces for different particles. We also extracted the entropy index-parameter n and the parameter N0, and the former remains almost unchanged while the later decrease from central to peripheral collisions. Furthermore, the kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, initial temperature, mean transverse momentum and the parameter N0 at LHC are larger than that of RHIC, and they show their dependence on the collision cross-section as well as on collision energy at RHIC and LHC.
The conventional quark mass is not continuous at thresholds. In this paper, we derive matching-invariant quark masses which are continuous everywhere. They are generally expanded as an obvious function of the logarithmic [Formula: see text] scaled energy. The expansion coefficients are related to the gamma and beta functions, with concretization to four-loop level. Due to the maximal elimination of their direct dependence on the coupling with large uncertainties, the new expressions for quark masses converge much fast and accurate.
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