Towards quantitative precision in the chiral crossover: Masses and fluctuation scales

Abstract

We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is important for the correct relative weight of quantum, thermal and density fluctuations. Hence, it governs the location of phase boundaries as well as the phase structure of QCD. The identification of the correct physics scales is also primarily important for the correct adjustment of the parameters of effective models for low-energy QCD. It is shown that subject to an appropriate definition of the latter, all these scales agree at vanishing temperature, while they deviate from each other at finite temperature.

In-medium spectral functions of vector- and axial-vector mesons from the functional renormalization group

“…by including non-trivial wavefunction renormalizations in the gradient expansion of the effective action. It has been shown in [54], that this reduces the difference between curvature and pole masses, especially for the light mesons. Phenomenologically viable spectral functions also require the inclusion of the feedback of the vector mesons themselves as well as baryonic degrees of freedom, both of which have been neglected here.…”

Chiral mirror-baryon-meson model and nuclear matter beyond mean-field approximation

“…Beyond mean-field, pole masses in present truncations for two-point functions are typically considerably closer to such onsets than curvature masses as well. To completely resolve this discrepancy, and to reduce the unnaturally large differences between curvature and pole masses, one has to include wave-function renormalization beyond the LPA [51].…”

Physics and the choice of regulators in functional renormalisation group flows

“…Strictly speaking this asks for the evaluation of the poles and cuts of the theory in a real time formulation. For the scalar and Yukawa-type theories explicitly discussed in the present work it has been shown in [35] that the real-time pole masses and the imaginary time curvature masses are very similar in advanced approximations. For the present purpose these subtleties are not relevant and we define the inverse gap as the maximum of the imaginary time propagator,…”

“…It has been shown in [35] for relativisitic Yukawa systems that this approximation of the full frequencyand momentum-dependence already captures well the full dependence. We expect this to be also the case in the present non-relativistic case.…”

“…Note in this context that Fig. 9 gives us the full information of the relative size of the integrands in the length of the flow in (35): for a given V ′′ > 0 the related ω diverges with 1 k 2 phys . This is easily confirmed with the explicit computation of the length, summarised in Fig.…”