Abstract
We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{\alpha_{E1},\,\beta_{M1}\}_p=\{11.2(0.7),\,3.9(0.7)\}\times10^{-4}$fm$^3$, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{\alpha_{E2},\,\beta_{M2}\}_p=\{17.3(3.9),\,-15.5(3.5)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_p=\{-1.3(1.0),\,7.1(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_p=\{-3.3(0.8),\,2.9(1.5),\,0.2(0.2),\,1.1(0.3)\}\times10^{-4}$fm$^4$. The results for the scalar polarisabilities are in significant disagreement with semi-empirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries $\Sigma_3$ and $\Sigma_{2x}$ reproduce the experimental data from LEGS and MAMI. Results for $\Sigma_{2z}$ agree with a recent sum rule evaluation in the forward kinematics. The asymmetry $\Sigma_{1z}$ near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron: $\{\alpha_{E1},\,\beta_{M1}\}_n=\{13.7(3.1),\,4.6(2.7)\}\times10^{-4}$fm$^3$, $\{\alpha_{E2},\,\beta_{M2}\}_n=\{16.2(3.7),\,-15.8(3.6)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_n=\{0.1(1.0),\,7.2(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_n=\{-4.7(1.1),\,2.9(1.5),\,0.2(0.2),\,1.6(0.4)\}\times10^{-4}$fm$^4$. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.
Highlights
We compare our results with the dispersive calculation of Ref. [38] and the results of the Computational Hadronic Model (CHM) [55,56]
The uncertainty bands in these figures are generated with a similar method to that used for the static polarisabilities, in particular, at low energies these bands are defined by the corresponding uncertainties on the static polarisabilities σ [see Eq (19)]
We have considered low-energy Compton scattering off the nucleon in the framework of manifestly Lorentz-invariant χ PT, extending our previous calculation [13] to the Deltaresonance region
Summary
Following Refs. [12–14], where one can find details such as the relevant χ PT Lagrangians, we consider low-energy Compton scattering in Bχ PT, i.e., a manifestly covariant formulation of χ PT with pion, nucleon and Delta(1232) isobar degrees of freedom; see Ref. [31, Sec. 4] for a review. [12–14], where one can find details such as the relevant χ PT Lagrangians, we consider low-energy Compton scattering in Bχ PT, i.e., a manifestly covariant formulation of χ PT with pion, nucleon and Delta(1232) isobar degrees of freedom; see Ref. Our present calculation of the Compton amplitude follows that of Ref. [13] below photoproduction threshold (and for the static polarisabilities), but improves the treatment of the Delta-excitation near the resonance, as described below Our present calculation of the Compton amplitude follows that of Ref. [13] below photoproduction threshold (and for the static polarisabilities), but improves the treatment of the Delta-excitation near the resonance, as described below
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