Deconfinement transition within the Curci-Ferrari model -- Renormalization scale and scheme dependences

Abstract

We analyze the confinement/deconfinement transition of pure Yang-Mills theories within the framework of the center-symmetric Landau gauge supplemented by a Curci-Ferrari mass term that models the effect of the associated Gribov copies in the infrared. In addition to providing details for earlier one-loop calculations in that framework, we explore how the results depend on the renormalization scale and/or on the renormalization scheme. We find that the predicted values for the transition temperatures of SU($2$) and SU($3$) Yang-Mills theories are similar in both schemes and are little sensitive to the renormalization scale $μ$ over a wide range of values including the standard range $\smash{μ\in[πT,4πT]}$. These values are also close both to those obtained from a minimal sensitivity principle and to those of lattice simulations, especially in the SU($3$) case. These results further confirm the good behavior of perturbative calculations within the Curci-Ferrari model and support the adequacy of the latter as an effective description of Yang-Mills theories in the infrared. We perform a similar analysis for the spinodal temperatures in the SU($3$) case and for the Polyakov loop, the order parameter associated to the breaking of center symmetry.

Figures (7)

• Figure 1: Running of the expansion parameter ${\lambda={g^2N}/{16\pi^2}}$ in the considered renormalization schemes for SU(2) (transparent) and SU(3) (dark). The thin vertical lines mark the values of the renormalization scale at which this parameter goes above $1$.
• Figure 2: SU($2$) transition temperature as a function of the renormalization scale $\mu$ in both the IR-safe and VM renormalization schemes. The conic band represents the region ${\mu\in [\pi T,4\pi T]}$, with the dashed line representing the central value ${\mu=2\pi T}$. The black dots correspond to the values obtained from a "minimum sensitivity" principle ${dT_c/d\mu=0}$.
• Figure 3: SU($3$) higher spinodal temperatures as a function of the renormalization scale $\mu$ in both the IR-safe and VM renormalization schemes. For each, the colored band represents the temperature interval between the two spinodals. The conic band represents the region ${\mu\in [\pi T,4\pi T]}$, with the dashed line representing the central value ${\mu=2\pi T}$. The black dots correspond to the values obtained from a "minimum sensitivity" principle ${dT_{\rm hsp}/d\mu=0}$.
• Figure 4: SU($3$) transition temperature as a function of the renormalization scale $\mu$ in both the IR-safe and VM renormalization schemes. The conic band represents the region ${\mu\in [\pi T,4\pi T]}$, with the dashed line representing the central value ${\mu=2\pi T}$. The black dots correspond to the values obtained from a "minimum sensitivity" principle ${dT_c/d\mu=0}$.
• Figure 5: SU(2) and SU(3) Polyakov loops as a function of the rescaled temperature $T/T_c$ and the renormalization scale ${\mu\in[\pi T,4\pi T]}$. The regions spanned by taking $\mu$ between $\pi T$ and $4\pi T$ are shaded in.