The nucleon axial-vector coupling beyond one loop

Abstract

We analyze the nucleon axial-vector coupling to two loops in chiral perturbation theory. We show that chiral extrapolations based on this representation require lattice data with pion masses below 300 MeV.

Figures (2)

• Figure 1: Topologies of the one--loop graphs that generate the coefficient of the double log at two--loop order. The hatched square denotes a dimension three insertion proportional to some of the LECs $d_i$.
• Figure 2: The axial-vector coupling as a function of the pion mass. Solid (red) line: $g_0 = 1.2, \bar{d}_{16} = -1.76\,$GeV$^{-2}$, $\gamma_4^f = 50\,$GeV$^{-2}$, $\beta_4^f = 60\,$GeV$^{-4}$, $\alpha_5^f = 20\,$GeV$^{-5}$; Dot-dashed (black) line: $g_0 = 1.1, \bar{d}_{16} = -0.92\,$GeV$^{-2}$, $\gamma_4^f = 40\,$GeV$^{-2}$, $\beta_4^f = 20\,$GeV$^{-4}$, $\alpha_5^f = 50\,$GeV$^{-5}$; Dashed (green) line: $g_0 = 1.0, \bar{d}_{16} = -1.76\,$GeV$^{-2}$, $\gamma_4^f = -50\,$GeV$^{-2}$, $\beta_4^f = \alpha_5^f = 0$. The dotted (violet) line is the complete one-loop result with $g_0 = 1, \bar{d}_{16} = -1.76\,$GeV$^{-2}$ and using the physical values of the nucleon mass and the pion decay constant. The (magenta) circle denotes the physical value of $g_A$ at the physical pion mass and the triangles are the lowest mass data from Ref. Edwards:2005ym.