Electromagnetic effects in the pion dispersion relation at finite temperature

Abstract

We investigate the charged-neutral difference in the pion self-energy at finite temperature T. Within chiral perturbation theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T ¼ 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to OðT 2 Þ ∼ OðM 2 π Þ. Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a 1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being OðT 2 M 2 π =M 2 R Þ with M R the involved resonance masses.

Thermal behaviors of light scalar resonances at low temperatures

“…As pointed out in Ref. [35] , in addition to the right-hand cut above the threshold, the G(s) FT also includes left-hand cuts along the real axis below the threshold. We do not expect that the thermal left-hand cuts will play relevant roles in the determination of the resonance poles in this work.…”

Degeneracy Patterns of Chiral Companions at Finite Temperature

“…Within ChPT this reduction was observed when implementing NLO amplitudes [102,106]. In fact, the current algebra result does not show this trend [99] nor the LO ChPT amplitudes in the more recent Reference [107] where the pion mass always increases. This result for m π (T) is fully consistent with the one using the SU f (2) IAM in Reference [106] at zero pion chemical potential, which is added to the same panel of Figure 5 under the label "IAM SU(2) ChPT".…”

Heating triangle singularities in heavy ion collisions

“…At even higher T , the structure seems to Table 1 Input meson thermal masses and widths [30][31][32] for increasing temperatures, all in GeV. We exclude m π , practically constant and with modification of unclear sign [33][34][35]. We are not currently aware of a detailed computation of the K * width, so we use a crude estimate of order Γ K * (T = 0) × (1 + n π (T ) + n K (T )) disappear altogether (and is not made visible even changing m A ).…”