A dispersion relation for the pion-mass dependence of hadron properties

Abstract

We present a dispersion relation in the pion-mass squared, which static quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of analyticity in the entire complex $m_{\pi }^2$ plane modulo a cut at negative $m_{\pi }^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $\Delta$-isobar properties computed in chiral perturbation theory up to order $p^3$. We outline a method to obtain relations for other mass-dependencies, and illustrate it on a two-loop example.

8 pages, 4 figs

References in corpus (7)

• Electromagnetic excitation of the Delta(1232)-resonance
• Chiral perturbation theory
• Predictive powers of chiral perturbation theory in Compton scattering off protons
• Chiral extrapolation of nucleon magnetic form factors
• Chiral extrapolation of g_A with explicit Delta(1232) degrees of freedom
• $\pi N$ Scattering in the $\Delta (1232)$ Region in an Effective Field Theory
• Manifestly-covariant chiral PT calculation of nucleon Compton scattering

Cited by in corpus (4)

• Octet-baryon axial-vector charges and SU(3)-breaking effects in the semileptonic hyperon decays
• The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses
• Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation
• Background field approach to electromagnetic properties of baryons