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Register a new userChiral Lagrangians with $Delta(1232)$ to one loop
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We construct the Lorentz-invariant chiral Lagrangians up to the order $mathcal{O}(p^4)$ by including $Delta(1232)$ as an explicit degree of freedom. A full one-loop investigation on processes involving $Delta(1232)$ can be performed with them. For the $piDeltaDelta$ Lagrangian, one obtains 38 independent terms at the order $mathcal{O}(p^3)$ and 318 independent terms at the order $mathcal{O}(p^4)$. For the $pi NDelta$ Lagrangian, we get 33 independent terms at the order $mathcal{O}(p^3)$ and 218 independent terms at the order $mathcal{O}(p^4)$. The heavy baryon projection is also briefly discussed.
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An updated and extended analysis of the quark mass dependence of the nucleons 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.
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