Third-order spin polarizabilities of the nucleon

Abstract

We study the structure-constant (polarizability) coefficients of the spin-dependent terms of the nucleon Compton scattering amplitude which are third order in the frequency of the incoming photon. It is shown that these spin-polarizability coefficients can be related to sums of products of electromagnetic transition moments of the nucleon, involving the electric and magnetic dipoles, the electric and magnetic quadrupoles, and the charge electric and magnetic dipole mean-square radii. Three sum rules involving products of the electric dipole transition moments emerge from the calculation. PACS numberk): 13.60.F~

Compton scattering and the spin structure of the nucleon at low energies

“…We note that the nucleon Born contributions up to O(ǫ 3 ) (Fig.1) do not contribute to the polarizabilities as defined in Eqs. (13)(14)(15)(16)(17)(18)) but provide the model-independent LETs of current algebra discussed in section 2. The (anomalous) contributions from neutral pion exchange (Fig.2a) are also excluded here and can be found in Appendix A.…”

“…in Eqs. (13,14) enter in the unpolarized cross section at the same order as the spin-polarizabilities and are very poorly known at this point. Nevertheless, we want to point out that the significant difference in magnitude between γ (p) 0 and γ (p) π can be easily explained once one connects these two different linear combinations of the four spin-polarizabilities with the underlying physics using ChPT.…”

Virtual Compton Scattering—Generalized Polarizabilities of Nucleons and Pions

“…Relations between the GPs at |q| = 0 and the four spin-dependent RCS polarizabilities γ i of Ref. [20] were discussed in [12]:…”

Implementation of general background electromagnetic fields on a periodic hypercubic lattice

“…In particular, spin-dependent structure parameters beyond the magnetic moment can show up at low orders in the weak-field strength if one allows the spatial and/or temporal derivatives of the background fields to be nonvanishing. Among such quantities are spin polarizabilities of nucleons [23,39], and the quadrupole moment of hadrons and nuclei with spin, s ≥ 1 [15]. Moreover, nonuniform background fields do not constrain one to the static limit of EM form factors, and by injecting energy and momentum into the system, provide a means to directly evaluate the corresponding off-forward hadronic matrix elements of the EM current from a response to the background fields [40], with different systematic uncertainties than other methods.…”