Nucleon Spin-Polarisabilities from Polarisation Observables in Low-Energy Deuteron Compton Scattering

TL;DR

This paper analyzes how polarisation observables in low-energy deuteron Compton scattering depend on nucleon spin polarisabilities, using Chiral Effective Field Theory to identify optimal conditions for extracting these fundamental quantities.

Contribution

It provides a detailed theoretical framework for extracting nucleon spin polarisabilities from polarisation observables in deuteron Compton scattering, including effects of Delta(1232) and rescattering.

Findings

Double-polarised observables can isolate specific spin polarisabilities.

Spin-polarisabilities are accessible at photon energies above 100 MeV.

Low-energy measurements can accurately determine spin-independent polarisabilities.

Abstract

We investigate the dependence of polarisation observables in elastic deuteron Compton scattering below the pion production threshold on the spin-independent and spin-dependent iso-scalar dipole polarisabilities of the nucleon. The calculation uses Chiral Effective Field Theory with dynamical Delta(1232) degrees of freedom in the Small Scale Expansion at next-to-leading order. Resummation of the NN intermediate rescattering states and including the Delta induces sizeable effects. The analysis considers cross-sections and the analysing power of linearly polarised photons on an unpolarised target, and cross-section differences and asymmetries of linearly and circularly polarised beams on a vector-polarised deuteron. An intuitive argument helps one to identify kinematics in which one or several polarisabilities do not contribute. Some double-polarised observables are only sensitive to linear combinations of two of the spin-polarisabilities, simplifying a multipole-analysis of the data. Spin-polarisabilities can be extracted at photon energies \gtrsim 100 MeV, after measurements at lower energies of \lesssim 70 MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from hgrie@gwu.edu.