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arXiv · 1703.10564

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

Ferenc Niedermayer·Peter Weisz
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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 ($χ$PT) 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 $χ$PT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using $χ$PT with dimensional regularization, we determine the $χ$PT 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 $χ$PT result in terms vanishing like $1/\ell$ for $\ell=L_t/L_s\to\infty$. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant.

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Ferenc Niedermayer, Peter Weisz. 2017-06-20. Isospin susceptibility in the O($n$) sigma-model in the delta-regime. https://doi.org/10.1007/jhep06(2017)150

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