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

In the limit of N_f massless quarks, a significant feature of the fundamental theory of strong interactions, known as Quantum ChromoDynamics (QCD), is its chiral symmetry. This means that the Lagrangian of the theory is invariant under the transformations within the chiral group G = U(1)_V x U(1)_A x SU(N_f)_V x SU(N_f)_A. Although at zero temperature this symmetry is anomalously and spontaneously broken down to its vectorial subgroup U(1)_V x SU(N_f)_V, lattice QCD simulations indicate that above a critical temperature, T_c, thermal fluctuations lead to a partial restoration of the chiral symmetry group U(1)_V x SU(N_f)_V x SU(N_f)_A, while the fate of the U(1)_A symmetry still remains a subject of active research. To model the chiral symmetry breaking and its restoration at finite temperature, we make use of an effective Lagrangian approach. In particular, extending the results obtained in previous works, we perform an analysis of the extended linear sigma model by studying the scalar and pseudoscalar meson mass spectrum above T_c in the realistic case with N_f=2+1 light (but not massless) quark flavors. This is done while maintaining exact SU(2)_V isospin symmetry, meaning 0 < m_u = m_d << m_s. The predictions of the model are then critically compared with the results from lattice QCD simulations available in the literature.