Using Effective Field Theory to analyse low-energy Compton scattering data from protons and light nuclei

Abstract

Compton scattering from protons and neutrons provides important insight into the structure of the nucleon. For photon energies up to about 300 MeV, the process can be parameterised by six dynamical dipole polarisabilities which characterise the response of the nucleon to a monochromatic photon of fixed frequency and multipolarity. Their zero-energy limit yields the well-known static electric and magnetic dipole polarisabilities α E1 and β M 1 , and the four dipole spin polarisabilities. The emergence of full lattice QCD results and new experiments at MAMI (Mainz), HIγS at TUNL, and MAX-Lab (Lund) makes this an opportune time to review nucleon Compton scattering. Chiral Effective Field Theory (χEFT) provides an ideal analysis tool, since it encodes the well-established low-energy dynamics of QCD while maintaining an appropriately flexible form for the Compton amplitudes of the nucleon. The same χEFT also describes deuteron and 3 He Compton scattering, using consistent nuclear currents, rescattering and wave functions, and respects the low-energy theorems for photon-nucleus scattering. It can thus also be used to extract useful information on the neutron amplitude from Compton scattering on light nuclei. We summarise past work in χEFT on all of these reactions and compare with other theoretical approaches. We also discuss all proton experiments up to about 400 MeV, as well as the three modern elastic deuteron data sets, paying particular attention to the precision and accuracy of each set. Constraining the ∆(1232) parameters from the resonance region, we then perform new fits to the proton data up to ω lab = 170 MeV, and a new fit to the deuteron data. After checking in each case that a two-parameter fit is compatible with the respective Baldin sum rules, we obtain, using the sum-rule constraints in a one-parameter fit, α (p) E1 = 10.7 ± 0.3(stat) ± 0.2(Baldin) ± 0.8(theory), β (p) M 1 = 3.1 ∓ 0.3(stat) ± 0.2(Baldin) ± 0.8(theory), for the proton polarisabilities, and α (s) E1 = 10.9 ± 0.9(stat) ± 0.2(Baldin) ± 0.8(theory), β (s)M 1 = 3.6 ∓ 0.9(stat) ± 0.2(Baldin) ± 0.8(theory), for the isoscalar polarisabilities, each in units of 10 −4 fm 3 . Finally, we discuss plans for polarised Compton scattering on the proton, deuteron, 3 He and heavier targets, their promise as tools to access spin polarisabilities, and other future avenues for theoretical and experimental investigation.

Baryons as relativistic three-quark bound states

“…There has been much recent interest in a precision determination of the nucleon's polarisabilities, which is reflected in a number of reviews on the topic [441,[638][639][640][641][642][643]. The electric polarisability α and magnetic polarisability β tell us how the nucleon responds to an external electromagnetic field, with current PDG values α = 11.2(4) × 10 −4 fm 3 and β = 2.5(4) × 10 −4 fm 3 for the proton [9].…”

“…In the forward limit this is particularly relevant for determining the subtraction function c 2 (η, 0) that appears in the dispersion relations and is related to the magnetic polarisability; see our comments on the proton radius puzzle below. The role of chiral effective field theory and its application to Compton scattering is discussed in the recent reviews [641,643].…”

First extraction of the scalar proton dynamical polarizabilities from real Compton scattering data

“…(6) are the same as in Eqs. (2) and (3), provided that the (α,β) L 4,5 coefficients are replaced by the coefficients (α,β) 4,5 in Eq. (8).…”

“…We used two different data sets, i.e., all the available experimental data for the unpolarized cross sections below pion-production threshold, denoted as FULL data set 1 (for a total of 150 data points) [26,[31][32][33][34][36][37][38][39][40][41][42], and the data set given by the TAPS experiment alone (55 data points) [26], which is, by far, the most comprehensive available subset. "Improved" data sets have been defined in recent fits of RCS observables, by discarding some data points from different experiments [4,20,43]. Here we do not apply any selection to the data, and we postpone a more detailed discussion of the statistical consistency of the different data subsets to a future work [44], entirely devoted to the extraction of the static scalar dipole polarizabilities from data.…”

“…(9). This feature allows us to reduce the overall number of fit parameters with respect to the extended-χ 2 procedure, with a normalization factor for each data set left as free parameters [4]. (ii) The fact that any error distribution of the experimental data can be easily implemented.…”