Leading logarithms for the nucleon mass

Abstract

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behaviour of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of $m^{2n+1}{\log }^{(n-1)}({\mu }^2/m^2)$ and $m^{2n+2}{\log }^n({\mu }^2/m^2)$, with $m$ the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral.

24p, misprints corrected, some minor reformulations

References in corpus (6)

• The Massive O(N) Non-linear Sigma Model at High Orders
• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• Leading Chiral Logarithms for Pion Form Factors to Arbitrary Number of Loops
• Breakdown of chiral expansion for parton distributions
• Chiral Inflation of the Pion Radius
• Chiral expansion of nucleon PDF at $x\sim m_{\pi }/M_N$

Cited by in corpus (6)

• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Leading Logarithms of the Two Point Function in Massless O(N) and SU(N) Models to any Order from Analyticity and Unitarity
• Quasi-Renormalizable Quantum Field Theories
• Leading chiral logarithms for the nucleon mass
• Status of Chiral Meson Physics
• Leading logarithms for mesons and nucleons