Precision Sum Rule for Nucleon Isovector Polarizabilities and the Proton-Neutron Mass Difference
Abstract
The precision of the electromagnetic proton-neutron mass difference δmQED extracted from the Cottingham formula hinges on a subtraction function whose low-energy normalization S̅(0) is fixed by the isovector combination of the proton and neutron polarizabilities, (αE1−βM1)p−n. We derive a dispersive sum rule for this combination in terms of s-channel photoabsorption cross sections and the product of t-channel γγ→πη/KK̅It=1 and πη/KK̅It=1→ NN̅ amplitudes, without invoking Reggeon dominance. Combining empirical pion-photoproduction multipoles with coupled-channel Muskhelishvili-Omnès representations of the scalar-isovector πη/KK̅ amplitudes, we obtain (αE1−βM1)p−n=−0.82(33)×10−4 fm3, fixing its sign and reducing the uncertainty by one order of magnitude compared with the previously known value. This result yields S̅(0)=−0.56(28) GeV−2, leading to δmQED=0.75+0.02−0.04 MeV, substantially more precise than previous Cottingham determinations. The negative S̅(0) also provides a low-energy test of Reggeon dominance in the subtraction function.
Related
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BibTeX
@misc{cao2026precision,
title = {{Precision Sum Rule for Nucleon Isovector Polarizabilities and the Proton-Neutron Mass Difference}},
author = {Xiong-Hui Cao and Ling-Yun Dai and Feng-Kun Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15154},
eprint = {2609.15154},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15154},
}
RIS
TY - UNPB
TI - Precision Sum Rule for Nucleon Isovector Polarizabilities and the Proton-Neutron Mass Difference
AU - Xiong-Hui Cao
AU - Ling-Yun Dai
AU - Feng-Kun Guo
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2609.15154
UR - https://arxiv.org/abs/2609.15154
AB - The precision of the electromagnetic proton-neutron mass difference δm_QED extracted from the Cottingham formula hinges on a subtraction function whose low-energy normalization S̅(0) is fixed by the isovector combination of the proton and neutron polarizabilities, (α_E1−β_M1)^p−n. We derive a dispersive sum rule for this combination in terms of s-channel photoabsorption cross sections and the product of t-channel γγ→πη/KK̅_I_t=1 and πη/KK̅_I_t=1→ NN̅ amplitudes, without invoking Reggeon dominance. Combining empirical pion-photoproduction multipoles with coupled-channel Muskhelishvili-Omnès representations of the scalar-isovector πη/KK̅ amplitudes, we obtain (α_E1−β_M1)^p−n=−0.82(33)×10^−4 fm^3, fixing its sign and reducing the uncertainty by one order of magnitude compared with the previously known value. This result yields S̅(0)=−0.56(28) GeV^−2, leading to δm_QED=0.75^+0.02_−0.04 MeV, substantially more precise than previous Cottingham determinations. The negative S̅(0) also provides a low-energy test of Reggeon dominance in the subtraction function.
ER -