Comprehensive study of observables in Compton scattering on the nucleon

Abstract

We present an analysis of 13 observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisationtransfer observables are investigated for energies up to the ∆(1232) resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N 4 LO, O(e 2 δ 4 ), for photon energies ω ∼ m π , and so has an accuracy of a few per cent there. At photon energies in the resonance region, it is complete at NLO, O(e 2 δ 0 ), and so its accuracy there is about 20%. We find that for energies from pion-production threshold to about 250 MeV, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pionproduction threshold, 6 observables suffice to reconstruct the Compton amplitude, and above it 11 are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from judith.mcgovern@manchester.ac.uk.

Compton Scattering and Nucleon Polarisabilities: Theory Progress

“…Thus at these energies, a reliable link between the amplitudes and the static polarisability is lost. In our recent paper [9] we explored the sensitivity of various target-beam asymmetries to the spin polarisabilities. As an advertisement for our results we here show the prediction for the asym-PoS(CD2018)009 metry Σ 2x , which involves circularly polarised photons and a target polarised perpendicularly to the scattering plane.…”

“…M1 has been connected to the nucleon electromagnetic mass difference (see references in [9]). The calculation of nucleon polarisabilities is also an aim of lattice QCD, and several groups now have published results, albeit almost all at large pion masses (see references in [10]).…”

“…In this contribution we report on the results of highprecision EFT fits of scalar polarisabilities to current data, and on prospects for the determination of spin polarisabilities. For more details and in particular for more complete references to earlier work the reader is referred to our review [1], and to subsequent papers [6,9,10,11], and another contribution on 3 He in these proceedings [12].…”

“…Circles indicate the approximate location of the data of[4]; their size does not reflect the error bars, nor the size of energy or angle bins. Figure modified from[9].…”

Electromagnetic currents for dressed hadrons

“…This bare expression provides the Powell crosssection [17], but it does not describe more complex experimental data like electric and magnetic polarizibilities (see Refs. [18][19][20] and references therein). However, as with the real Compton scattering tensor for the pion that the corresponding gauge derivatives of both sides of Eq.…”