Percent-Level Prediction of the Deuteron Magnetic Polarizability

Abstract

Working through next-to-next-to-leading order (NNLO) accuracy in pionless effective field theory, we compute the isovector magnetic-dipole contribution to the scalar deuteron magnetic polarizability. The polarizability follows from detailed balance and a dispersion integral with the two magnetic current counter-terms fixed by the thermal $np\to d\gamma$ rate. The conventional $\rho$ and $Z$ expansion schemes differ by $12.3\%$ at next-to-leading order but agree to $0.165\%$ at NNLO, resulting an apparent scheme dependence and supplying an independent convergence diagnostic. We obtain ${\beta }_{M0}^{(M{1}_v)}=0.0789\pm 0.0010{\mathrm{fm}}^3$, a $1.3\%$ uncertainty, compared with $4.9\%$ previously.

10 pages, 1 figure