Nucleon polarisabilities at and beyond physical pion masses

Harald W. Grießhammer; Judith A. McGovern; Daniel R. Phillips

doi:10.1140/epja/i2016-16139-5

2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A (2016) 52: 139
https://doi.org/10.1140/epja/i2016-16139-5

Regular Article - Theoretical Physics

Nucleon polarisabilities at and beyond physical pion masses

Harald W. Grießhammer¹^*, Judith A. McGovern² and Daniel R. Phillips³

¹ Institute for Nuclear Studies, Department of Physics, The George Washington University, 20052, Washington, DC, USA
² School of Physics and Astronomy, The University of Manchester, M13 9PL, Manchester, UK
³ Department of Physics and Astronomy and Institute of Nuclear and Particle Physics, Ohio University, 45701, Athens, OH, USA

^* e-mail: hgrie@gwu.edu

Received: 23 November 2015
Revised: 28 March 2016
Accepted: 7 April 2016
Published online: 24 May 2016

Abstract

We examine the results of Chiral Effective Field Theory ( $\chi$ EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of ${m_{\pi}}$ . This provides chiral extrapolations for lattice QCD polarisability computations. We include both the leading and subleading effects of the nucleon’s pion cloud, as well as the leading ones of the $\Delta$ (1232)-resonance and its pion cloud. The analytic results are complete at N²LO in the $\delta$ counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as 68% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as ${m_{\pi}}$ approaches about 300 MeV --as has already been seen in other observables. $\chi$ EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $\chi$ EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence.