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

Vadim Lensky; Judith A. McGovern; Vladimir Pascalutsa

doi:10.1140/epjc/s10052-015-3791-0

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2015) 75: 604
https://doi.org/10.1140/epjc/s10052-015-3791-0

Regular Article - Theoretical Physics

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

Vadim Lensky¹^,2^,3^,4^*, Judith A. McGovern⁴ and Vladimir Pascalutsa¹

¹ Institut für Kernphysik and PRISMA Cluster of Excellence, Johannes Gutenberg Universität Mainz, 55128, Mainz, Germany
² Institute for Theoretical and Experimental Physics, 117218, Moscow, Russia
³ National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Moscow, Russia
⁴ Theoretical Physics Group, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK

^* e-mail: lensky@itep.ru

Received: 16 October 2015
Accepted: 10 November 2015
Published online: 19 December 2015

Abstract

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{ \alpha _{E1} , \, \beta _{M1}\}_p = \{ 11.2(0.7), \, 3.9(0.7)\} \times 10^{-4}$ fm $$^3$$ , and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{ \alpha _{E2} , \, \beta _{M2} \}_p = \{ 17.3(3.9), \, -15.5(3.5)\} \times 10^{-4}$ fm $$^5$$ , $\{\alpha _{E1\nu } , \, \beta _{M1\nu }\}_p = \{ -1.3(1.0), \, 7.1(2.5)\} \times 10^{-4}$ fm $$^5$$ , and $\{ \gamma _{E1E1} , \, \gamma _{M1M1}, \gamma _{E1M2} , \, \gamma _{M1E2} \}_p = \{ -3.3(0.8), \, 2.9(1.5),\, 0.2(0.2), 1.1(0.3) \} \times 10^{-4}$ 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, the numerical values being $\{ \alpha _{E1}, \, \beta _{M1}\}_n = \{ 13.7(3.1), \, 4.6(2.7)\} \times 10^{-4}$ fm $$^3$$ , $\{ \alpha _{E2}, \, \beta _{M2} \}_n = \{ 16.2(3.7), \, -15.8(3.6)\} \times 10^{-4}$ fm $$^5$$ , $\{\alpha _{E1\nu }, \, \beta _{M1\nu }\}_n = \{ 0.1(1.0), \, 7.2(2.5)\} \times 10^{-4}$ fm $$^5$$ , and $\{ \gamma _{E1E1}, \, \gamma _{M1M1},\, \gamma _{E1M2}, \, \gamma _{M1E2} \}_n = \{ -4.7(1.1), 2.9(1.5),\, 0.2(0.2),\, 1.6(0.4) \} \times 10^{-4}$ fm $$^4$$ . The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching the dynamical and static polarisabilities.