Vacuum structure of vector mesons in QCD

Abstract

We study the chiral dynamics of vector mesons in two-flavor QCD in vacuum by utilizing a functional renormalization group approach. This allows us to capture the dynamical transition from the quark-gluon phase at high energies to the hadronic phase at low energies without the necessity of model parameter tuning. We use this to analyze the scaling of vector meson masses towards the chiral symmetry breaking scale, the decoupling of the mesons at high energies and the validity of vector meson dominance.

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

“…In this section we will present a simple low-energy model of two-flavor QCD that captures the main features relevant for the description of the ρ and a 1 meson which is based on an previous work concerning the description of vector mesons in QCD [16]. In that work the connection of the effective action with QCD is given by successively integrating out quantum fluctuations starting from QCD at high energies.…”

“…Furthermore, it has been shown in [16] that the vector mesons are always decoupled from the dynamics of the system in Euclidean space time. Our computation of the spectral functions uses the solution of the Euclidean system as input and therefore vectormeson self-interactions do not play a role for this input.…”

“…In QCD, the scale of meson formation emerges dynamically and is not introduced by hand. To capture this transition within a unified framework, one can use dynamical hadronization as put forward for QCD in [43,44] and applied to vector mesons in the vacuum in [16]. Since we are only interested in the low-energy effective theory here, we postpone a treatment within full QCD to future work.…”

“…To study chiral symmetry and its breaking pattern in more detail, the gauge concept of Sakurai was extended to the chiral symmetry group SU (2) L × SU (2) R as a local gauge symmetry, where the a 1 meson as chiral partner of the ρ meson also appears as a gauge boson [14] thus leading to the 'gauged linear sigma model'. Another possibility is to impose a global chiral symmetry rather than a local one [15][16][17].…”

“…In this paper we present first results for the ρ and a 1 meson spectral functions from the FRG based on the gauged linear sigma model, inspired by [16]. We derive flow equations for the real-time two-point functions of ρ and a 1 mesons which are obtained from their Euclidean counterparts via an analytic continuation on the level of the flow equations [27,[40][41][42].…”