Isospin susceptibility in the O(n) sigma-model in the delta-regime

Abstract We compute the isospin susceptibility in an effective O(n) scalar field theory (in d = 4 dimensions), to third order in chiral perturbation theory (χPT) in the delta-regime using the quantum mechanical rotator picture. This is done in the presence of an additional coupling, involving a parameter η, describing the effect of a small explicit symmetry breaking term (quark mass). For the chiral limit η = 0 we demonstrate consistency with our previous χPT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using χPT with dimensional regularization, we determine the χPT expansion for η to third order. The behavior of the shape coefficients for long tube geometry obtained here might be of broader interest. The susceptibility calculated from the rotator approximation differs from the χPT result in terms vanishing like 1/ℓ for ℓ = L t /L s → ∞. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant.

Abstract licence: CC BY

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