Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering

Abstract

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $$\{ \alpha _{E1} , \, \beta _{M1}\}_p = \{ 11.2(0.7), \, 3.9(0.7)\} \times 10^{-4}$${αE1,βM1}p={11.2(0.7),3.9(0.7)}×10-4 fm$$^3$$3, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $$ \{ \alpha _{E2} , \, \beta _{M2} \}_p = \{ 17.3(3.9), \, -15.5(3.5)\} \times 10^{-4}$${αE2,βM2}p={17.3(3.9),-15.5(3.5)}×10-4 fm$$^5$$5, $$\{\alpha _{E1u } , \, \beta _{M1u }\}_p = \{ -1.3(1.0), \, 7.1(2.5)\} \times 10^{-4}$${αE1ν,βM1ν}p={-1.3(1.0),7.1(2.5)}×10-4 fm$$^5$$5, and $$ \{ \gamma _{E1E1} , \, \gamma _{M1M1}, \gamma _{E1M2} , \, \gamma _{M1E2} \}_p = \{ -3.3(0.8), \, 2.9(1.5),\, 0.2(0.2), 1.1(0.3) \} \times 10^{-4}$${γE1E1,γM1M1,γE1M2,γM1E2}p={-3.3(0.8),2.9(1.5),0.2(0.2),1.1(0.3)}×10-4 fm$$^4$$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 $$\Sigma _3$$Σ3 and $$\Sigma _{2x}$$Σ2x reproduce the experimental data from LEGS and MAMI. Results for $${ \Sigma }_{2z}$$Σ2z agree with a recent sum rule evaluation in the forward kinematics. The asymmetry $${ \Sigma }_{1z}$$Σ1z 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, the numerical values being $$\{ \alpha _{E1}, \, \beta _{M1}\}_n = \{ 13.7(3.1), \, 4.6(2.7)\} \times 10^{-4}$${αE1,βM1}n={13.7(3.1),4.6(2.7)}×10-4 fm$$^3$$3, $$ \{ \alpha _{E2}, \, \beta _{M2} \}_n = \{ 16.2(3.7), \, -15.8(3.6)\} \times 10^{-4}$${αE2,βM2}n={16.2(3.7),-15.8(3.6)}×10-4 fm$$^5$$5, $$\{\alpha _{E1u }, \, \beta _{M1u }\}_n = \{ 0.1(1.0), \, 7.2(2.5)\} \times 10^{-4}$${αE1ν,βM1ν}n={0.1(1.0),7.2(2.5)}×10-4 fm$$^5$$5, and $$ \{ \gamma _{E1E1}, \, \gamma _{M1M1},\, \gamma _{E1M2}, \, \gamma _{M1E2} \}_n = \{ -4.7(1.1), 2.9(1.5),\, 0.2(0.2),\, 1.6(0.4) \} \times 10^{-4}$${γE1E1,γM1M1,γE1M2,γM1E2}n={-4.7(1.1),2.9(1.5),0.2(0.2),1.6(0.4)}×10-4 fm$$^4$$4. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching the dynamical and static polarisabilities.