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

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Summary

Compton scattering in Bχ PT

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

Power counting
Complete NLO calculation in the Delta-region
Remarks on higher-order Delta contributions
Summary
Decompositions of the Compton amplitude
Definitions
Proton
Neutron
Dynamical polarisabilities and multipoles
Results
Polarised observables for the proton
Conclusion
E N ω2B MN
Full Text
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