Analysis of Low-Energy Pion Spectra

Abstract

The transverse mass spectra and the rapidity distributions of π + and π − in Au-Au collisions at 2, 4, 6, and 8 GeV·A by E895 collaboration are fitted using an elliptically expanding fireball model with the contribution from the resonance decays and the final state Coulomb interaction. The ratio of the total number of produced π − and π + is used to fit the data. The resulting freeze-out temperature is rather low(T f < 60 MeV) with large transverse flow and thus resonance contribution is very small. The difference in the shape of mt spectra of the oppositely charged pions are found to be due to the Coulomb interaction of the pions.PACS numbers: 24.10. Pa, Pion production just above the threshold energy is quite different from that at very high energies such as RHIC energy since the ratio of π − to π + at very high energies is one which is not the case at low energies. At just above the threshold energy, pions are produced through the production of ∆ resonances and counting all the possible channels of ∆ decay the difference in the composition of isospins in the colliding nuclei appears as the difference in the numbers of the two oppositely charged pions [1,2,3], whereas at high energies many channels producing pions are open and small asymmetry in the initial isospin does not matter.Other features of the pion spectra at low energies are [1,2,3,4,5,6,7]: (1)The transverse momentum spectra both of the π − and π + seem to have two temperatures. Usually the low temperature component in the low momentum region is attributed to the pions decayed from resonances, especially the delta resonance, while the higher temperature component in the mid-momentum region is the thermal ones. (2) Transverse momentum spectra of π − and π + at very small momentum are different in the sense that the π + spectra is convex in its shape while the π − spectra does not show this behavoir. This difference in low momentum region is due to the Coulomb effect. The hadronic matter formed during the collision has charge which comes from the initially colliding two nuclei and thus the thermal pions escaping from the system experience the Coulomb interaction. The Coulomb interaction of π − may bend the spectrum in the low momentum region upward and thus it is hard to disentangle the contribution from the delta resonance and the Coulomb interaction in the low momentum region. (3) Width of the rapidity spectra of π − and π + are much wider than those from the isotropically expanding thermal model. The wide width may either come from partly transparent nature of the collision dynamics or the ellipsoidal expansion geometry. In order to fit large rapidity width using expanding fireball model one usually needs large longitudinal expansion velocity. * kslee@chonnam.ac.kr Even though all those features mentioned above are not new, calculations with all those features put in together comparing each contributions in detail is hard to find. There are claims that the properties of ∆ resonance are modified inside the hadronic matter formed even at this low ener...