Chiral extrapolation of g_A with explicit Delta(1232) degrees of freedom

TL;DR

The paper investigates the quark-mass dependence of the nucleon axial coupling $g_A$ and its connection between lattice QCD results and the physical point. It shows that standard pion–nucleon chiral EFT at ${\cal O}(p^4)$ cannot interpolate lattice data, whereas the Small Scale Expansion with explicit $\Delta(1232)$ degrees of freedom provides a successful description across a broad range of $m_\pi$, with convergence most reliable for $m_\pi$ below the Delta–nucleon scale $\Delta$. The fits to LHPC and RBCK lattice data yield consistent parameters (e.g., $g_A^0\approx 1.22$, $c_A\approx 1.5$, $\Delta\approx 271$ MeV) and indicate that $g_A$ is dominated by Delta-related dynamics as reflected in the Adler– Weisberger framework. The work also shows that expanding the SSE result in $m_\pi$ is well-behaved up to $\sim 300$ MeV but becomes problematic beyond that, highlighting the need to keep the Delta explicit and to pursue higher-order corrections and finite-volume analyses for robust extrapolations.

Abstract

An updated and extended analysis of the quark mass dependence of the nucleon's axial vector coupling constant g_A is presented in comparison with state-of-the-art lattice QCD results. Special emphasis is placed on the role of the Delta(1232) isobar. It is pointed out that standard chiral perturbation theory of the pion-nucleon system at order p^4 fails to provide an interpolation between the lattice data and the physical point. In constrast, a version of chiral effective field theory with explicit inclusion of the Delta(1232) proves to be successful. Detailed error analysis and convergence tests are performed. Integrating out the Delta(1232) as an explicit degree of freedom introduces uncontrolled errors for pion masses m_pi >~ 300 MeV.

Figures (12)

• Figure 1: Diagrams contributing to the quark mass dependence of $g_A$ up to order $p^3$ in Baryon Chiral Perturbation Theory. The wiggly line denotes an external isovector axial-vector field, interacting with a nucleon (solid line). The first graph to the left encodes the relevant counterterms.
• Figure 2: Graph contributing to nucleon field renormalization at order $p^3$.
• Figure 3: Diagrams contributing to $g_A$ at the next-to-leading one-loop level. The triangle denotes a vertex appearing in ${\cal{L}}_{\pi N}^{(2)}$. The wiggly line represents an external axial vector field.
• Figure 4: Graph contributing to the nucleon $Z$-factor at order $p^4$. The square denotes a vertex from ${\cal{L}}_{\pi N}^{(2)}$ involving $c_1$, $c_2$ and $c_3$.
• Figure 5: Data base of lattice QCD results for the pion mass dependence of $g_A$ provided by the RBCK RBCK, QCDSF newQCDSF and LHPC negele collaborations. Also shown is the ${\cal O}(p^4)$ result for $g_A(m_\pi)$ in Heavy Baryon $\chi$PT, with the physical point included as a constraint. The band reflects the uncertainty on the input values of the low-energy constants involved.