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

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 $m_π^2$ plane modulo a cut at negative $m_π^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $Δ$-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.

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