Vacuum structure of vector mesons in QCD

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.

Figure 1

The running of the different strong couplings in comparison to the one-loop running.

Figure 2

The RG flows of the scalar and vector yukawa couplings ${\overline{h}}_{S,k}$, ${\overline{h}}_{V,k}$. The thick and thin lines correspond to different initial values of the couplings at different initial scales.

Figure 3

Renormalized masses (33) as a function of the RG scale. Masses in the shaded area are larger than the cutoff scale and, therefore, decoupled from the dynamics.

Figure 4

Effective propagators (a9) of the matter fields as a function of the RG scale. They are a measure for the effective strength of the fluctuations of the fields.

Figure 5

The renormalized mass of the $\rho$ meson, $M_{\rho ,k}$, as a function of the RG scale. We see that it first decreases with increasing $k$, before it starts increasing for $k\gtrsim M_{\pi }$.

Figure 6

Scalar and vector wave function renormalization as function of the RG scale. We normalized them to be 1 at the IR scale $k=30\mathrm{MeV}$.

Figure 7

Bare masses of the mesons, $m_{\varphi }^2=Z_{\varphi ,k}{M}_{\varphi ,k}^2$, see (10) and (33). Note that we normalized the wave function renormalizations to be 1 in the IR at $k=20\mathrm{MeV}$ here.

Figure 8

The RG flow of the vector-vector and vector-scalar meson couplings ${\overline{g}}_{1–5,k}$. The thick and thin lines correspond to different initial values of the couplings at different initial scales. Vector meson dominance would imply (34).