Nucleon polarizabilities revisited: insights from the Bernabéu-Ericson-Ferro Fontan-Tarrach sum rule
Abstract
We present a complete dispersive evaluation of the Bernabéu-Ericson-Ferro Fontan-Tarrach (BEFT) sum rule for the nucleon dipole polarizability difference αE1−βM1. The analysis is based on hyperbolic dispersion relations, which separate the s- and t-channel contributions without double counting and are particularly suited to backward real Compton scattering. This framework makes it possible to precisely determine the polarizability difference from independent dispersive input rather than from fits to low-energy Compton scattering data. The s-channel part is updated with modern single-pion photoproduction multipoles and model estimates of non-πN inelastic channels. For the t-channel, we use contemporary dispersive input for γγ→ππ/KK̅It=0 together with Roy-Steiner equation solutions for ππ/KK̅It=0→ NN̅, and we extend the calculation to the isovector πη/KK̅It=1 channel associated with the a0(980). The resulting treatment resolves the long-standing puzzle of earlier BEFT evaluations driven by the scalar-isoscalar two-pion channel and gives a controlled estimate of the subleading isovector contribution. Combining the resulting BEFT values with the Baldin sum rule, we obtain, in units of 10−4 fm3, αE1p=11.17(52), βM1p=2.84(52), αE1n=12.18(59), βM1n=3.03(59). For the proton, these values provide a benchmark with a precision comparable to state-of-the-art dispersive and chiral effective field theory extractions. For the neutron, whose polarizabilities are much less directly constrained experimentally, the result provides an independent dispersive benchmark with an uncertainty comparable to that of the proton.
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BibTeX
@misc{cao2026nucleon,
title = {{Nucleon polarizabilities revisited: insights from the Bernabéu-Ericson-Ferro Fontan-Tarrach sum rule}},
author = {Xiong-Hui Cao and Ling-Yun Dai and Feng-Kun Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34276},
eprint = {2610.34276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34276},
}
RIS
TY - UNPB
TI - Nucleon polarizabilities revisited: insights from the Bernabéu-Ericson-Ferro Fontan-Tarrach sum rule
AU - Xiong-Hui Cao
AU - Ling-Yun Dai
AU - Feng-Kun Guo
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34276
UR - https://arxiv.org/abs/2610.34276
AB - We present a complete dispersive evaluation of the Bernabéu-Ericson-Ferro Fontan-Tarrach (BEFT) sum rule for the nucleon dipole polarizability difference α_E1−β_M1. The analysis is based on hyperbolic dispersion relations, which separate the s- and t-channel contributions without double counting and are particularly suited to backward real Compton scattering. This framework makes it possible to precisely determine the polarizability difference from independent dispersive input rather than from fits to low-energy Compton scattering data. The s-channel part is updated with modern single-pion photoproduction multipoles and model estimates of non-πN inelastic channels. For the t-channel, we use contemporary dispersive input for γγ→ππ/KK̅_I_t=0 together with Roy-Steiner equation solutions for ππ/KK̅_I_t=0→ NN̅, and we extend the calculation to the isovector πη/KK̅_I_t=1 channel associated with the a_0(980). The resulting treatment resolves the long-standing puzzle of earlier BEFT evaluations driven by the scalar-isoscalar two-pion channel and gives a controlled estimate of the subleading isovector contribution. Combining the resulting BEFT values with the Baldin sum rule, we obtain, in units of 10^−4 fm^3, α_E1^p=11.17(52), β_M1^p=2.84(52), α_E1^n=12.18(59), β_M1^n=3.03(59). For the proton, these values provide a benchmark with a precision comparable to state-of-the-art dispersive and chiral effective field theory extractions. For the neutron, whose polarizabilities are much less directly constrained experimentally, the result provides an independent dispersive benchmark with an uncertainty comparable to that of the proton.
ER -