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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.19062 |
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| _version_ | 1866918510216609792 |
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| author | Nguyen, Ha S. Vanasse, Jared |
| author_facet | Nguyen, Ha S. Vanasse, Jared |
| contents | The Helium-3 (${}^3\mathrm{He}$) magnetic moment and Gamow-Teller (GT) matrix element in triton (${}^3\mathrm{H}$) $β$-decay are calculated in pionless effective field theory ($\mathrm{EFT}(/\!\!\!π)$) to next-to-leading order (NLO). Coulomb corrections are included perturbatively to $\mathcal{O}(α)$ in this framework and should naively be $αM_n/p^*\!\!\sim\!8\%$ corrections, where $p^*\!\!\sim\!88.5$ MeV is related to the three-nucleon binding momentum. Fitting the two-nucleon iso-vector magnetic current low-energy constant (LEC), $L_1$, to the ${}^3\mathrm{H}$ magnetic moment and the two-nucleon iso-scalar magnetic current LEC, $L_2$, to the deuteron magnetic moment we find the NLO ${}^3\mathrm{He}$ magnetic moment in units of nuclear magnetons is -2.130 and the surprisingly small $\mathcal{O}(α)$ correction is 0.00335, $\approx\!0.18\%$ of the LO $\mathrm{EFT}(/\!\!\!π)$ prediction. The leading-order (LO) GT matrix element for ${}^3\mathrm{H}$ $β$-decay is 0.9806 while again it has a surprisingly small $\mathcal{O}(α)$ Coulomb correction of $-0.000740$, $\approx\!0.08\%$ of the LO $\mathrm{EFT}(/\!\!\!π)$ prediction. At NLO we calculate the GT matrix element of ${}^3\mathrm{H}$ $β$-decay, including the $\mathcal{O}(α)$ Coulomb correction, in terms of the two-nucleon axial current LEC $l_{1,A}$. Fitting $l_{1,A}$ to the ${}^3\mathrm{H}$ half-life we make a prediction for the proton-proton fusion reduced matrix element of $Λ(0)=2.776(331)$. Finally, we attempt to explain the unusually small size of the $\mathcal{O}(α)$ corrections by investigating the Wigner-SU(4) expansion of these observables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_19062 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coulomb Corrections to Three-Nucleon Moments Nguyen, Ha S. Vanasse, Jared Nuclear Theory The Helium-3 (${}^3\mathrm{He}$) magnetic moment and Gamow-Teller (GT) matrix element in triton (${}^3\mathrm{H}$) $β$-decay are calculated in pionless effective field theory ($\mathrm{EFT}(/\!\!\!π)$) to next-to-leading order (NLO). Coulomb corrections are included perturbatively to $\mathcal{O}(α)$ in this framework and should naively be $αM_n/p^*\!\!\sim\!8\%$ corrections, where $p^*\!\!\sim\!88.5$ MeV is related to the three-nucleon binding momentum. Fitting the two-nucleon iso-vector magnetic current low-energy constant (LEC), $L_1$, to the ${}^3\mathrm{H}$ magnetic moment and the two-nucleon iso-scalar magnetic current LEC, $L_2$, to the deuteron magnetic moment we find the NLO ${}^3\mathrm{He}$ magnetic moment in units of nuclear magnetons is -2.130 and the surprisingly small $\mathcal{O}(α)$ correction is 0.00335, $\approx\!0.18\%$ of the LO $\mathrm{EFT}(/\!\!\!π)$ prediction. The leading-order (LO) GT matrix element for ${}^3\mathrm{H}$ $β$-decay is 0.9806 while again it has a surprisingly small $\mathcal{O}(α)$ Coulomb correction of $-0.000740$, $\approx\!0.08\%$ of the LO $\mathrm{EFT}(/\!\!\!π)$ prediction. At NLO we calculate the GT matrix element of ${}^3\mathrm{H}$ $β$-decay, including the $\mathcal{O}(α)$ Coulomb correction, in terms of the two-nucleon axial current LEC $l_{1,A}$. Fitting $l_{1,A}$ to the ${}^3\mathrm{H}$ half-life we make a prediction for the proton-proton fusion reduced matrix element of $Λ(0)=2.776(331)$. Finally, we attempt to explain the unusually small size of the $\mathcal{O}(α)$ corrections by investigating the Wigner-SU(4) expansion of these observables. |
| title | Coulomb Corrections to Three-Nucleon Moments |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2605.19062 |