Conformal vs confining scenario in SU(2) with adjoint fermions

Abstract

The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling $β= 4/g_0^2 = 2.25$ for values of the bare fermion mass $m_0$ that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near--)conformal and the confining scenario is outlined.

Figures (4)

• Figure 1: Comparative plot of the various observables as a function of $m_\mathrm{PCAC}$. The lines at high PCAC mass show the quenched behavior of the various observables. The horizontal line at $a M = 1$ visually shows the separation between values of masses that are affected by lattice artifacts ($a M > 1$) and values for which the states are below the ultraviolet cutoff ($a M < 1$). Although ideally one wants all the states of interest to be free from lattice artifacts, due to the big separation of the scales, this condition is difficult to accommodate in practice.
• Figure 2: Pseudoscalar mass in units of $\sqrt{\sigma}$ as a function of the pseudoscalar mass in units of $a^{-1}$. Points on the left of the vertical line at $a M = 1$ are expected to be reasonably free from finite lattice spacing effects.
• Figure 3: The ratio of the vector mass $m_V$ over the pseudoscalar mass $m_\mathrm{PS}$ as a function of the pseudoscalar mass. Quenched data at equivalent bare lattice parameters are also shown.
• Figure 4: Comparison of the lightest pseudoscalar and glueball masses in the quenched and in the dynamical theory as a function of the pseudoscalar mass.