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Study of the scalar and pseudoscalar meson mass spectrum above the QCD chiral phase transition, using an effective Lagrangian approach

Giulio Cianti, Enrico Meggiolaro

TL;DR

This paper uses the extended linear sigma model ($EL_ ext_sigma$) to study the scalar and pseudoscalar meson mass spectrum above the chiral transition in a realistic $N_f=2+1$ QCD setup. By solving stationary-point conditions and diagonalizing the mass Hessian, it derives the temperature-dependent spectrum, including mixing in the $ ext{σ}$–$ ext{σ}$ and $ ext{η}$–$ ext{η}$ sectors, with explicit roles for the U(1)_A anomaly via the parameter $k$. The authors compare predictions to lattice QCD screening masses, extract constraints on the anomalous couplings $kar{ extσ}_2$ and $kar{ extσ}_s$, and find evidence that U(1)_A breaking persists above $T_c$, with the effective anomaly coupling increasing with temperature in the explored range. They also derive a consistency condition relating quark masses to meson masses and test it against lattice data, noting good agreement for $T o$172 MeV and deviations near $T_c$, motivating further model refinements and lattice investigations.

Abstract

In this work, expanding on previous analyses, we employ an effective Lagrangian approach to investigate the mass spectrum of scalar and pseudoscalar mesons at finite temperature, above the (pseudo-)critical temperature $T_c$, in a "realistic" $N_f = 2 + 1$ flavor scenario with degenerate $up$ and $down$ quarks and a heavier $strange$ quark: $0 < m_u = m_d \ll m_s$. The model's predictions are then critically compared with available lattice QCD results (where meson screening masses are extracted from chiral susceptibilities, which correspond to two-point correlation functions of suitable interpolating operators), looking, in particular, for signatures of the breaking of the $U(1)$ axial symmetry above $T_c$.

Study of the scalar and pseudoscalar meson mass spectrum above the QCD chiral phase transition, using an effective Lagrangian approach

TL;DR

This paper uses the extended linear sigma model () to study the scalar and pseudoscalar meson mass spectrum above the chiral transition in a realistic QCD setup. By solving stationary-point conditions and diagonalizing the mass Hessian, it derives the temperature-dependent spectrum, including mixing in the – and – sectors, with explicit roles for the U(1)_A anomaly via the parameter . The authors compare predictions to lattice QCD screening masses, extract constraints on the anomalous couplings and , and find evidence that U(1)_A breaking persists above , with the effective anomaly coupling increasing with temperature in the explored range. They also derive a consistency condition relating quark masses to meson masses and test it against lattice data, noting good agreement for 172 MeV and deviations near , motivating further model refinements and lattice investigations.

Abstract

In this work, expanding on previous analyses, we employ an effective Lagrangian approach to investigate the mass spectrum of scalar and pseudoscalar mesons at finite temperature, above the (pseudo-)critical temperature , in a "realistic" flavor scenario with degenerate and quarks and a heavier quark: . The model's predictions are then critically compared with available lattice QCD results (where meson screening masses are extracted from chiral susceptibilities, which correspond to two-point correlation functions of suitable interpolating operators), looking, in particular, for signatures of the breaking of the axial symmetry above .
Paper Structure (10 sections, 78 equations, 8 figures)

This paper contains 10 sections, 78 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The meson mass spectrum of the $EL_\sigma$ model in the "ideal" $N_f=2+1$ case
  3. The meson mass spectrum of the $EL_\sigma$ model in the "realistic" $N_f=2+1$ case
  4. Study of the potential and the stationary-point conditions above $T_{c}$
  5. The squared mass matrix and the spectrum of the theory
  6. Comparison with lattice simulation results
  7. Extrapolated value of $k\bar{\sigma}_2$ and $k\bar{\sigma}_s$
  8. Other relevant quantities
  9. A consistency condition for the model
  10. Summary of the results, comments and conclusions

Figures (8)

  • Figure 1: Extrapolated value of $k\bar{\sigma}_2$.
  • Figure 2: Extrapolated value of $k\bar{\sigma}_s$.
  • Figure 3: Anomalous contributions to $\Delta_{\kappa K}$ (on the left) and $\Delta_{\delta\pi}$ (on the right).
  • Figure 4: Extrapolated value of $\frac{k^2}{\lambda_{\pi}^2}$. The two figures have been divided because of the central value variability spanning over three orders of magnitude and the compatibility of the data with zero.
  • Figure 5: Extrapolated value of $k B_m m_l$.
  • ...and 3 more figures