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Radiative Corrections to Neutron Beta Decay and (Anti)Neutrino-Nucleon Scattering from Low-Energy Effective Field Theory

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Abstract

We study radiative corrections to neutron beta decay and low-energy (anti)neutrino-nucleon scattering within a top-down effective field theory approach. As it was recently shown, a few electromagnetic and electroweak low-energy coupling constants in heavy-baryon chiral perturbation theory are yet to be determined. Performing matching to the four-fermion effective field theory, we relate these low-energy constants to correlation functions of vector and axial-vector currents. Such relations allow us to explicitly clarify scheme dependence for radiative corrections to neutron decay and low-energy charged-current (anti)neutrino scattering, provide a robust prediction of leading in the electromagnetic coupling constant contributions, and achieve a clear separation between short-distance and long-distance contributions.

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Notes

  1. The same ultraviolet divergences appear in the static limit of the (anti)neutrino-nucleon scattering [17, 24,25,26].

  2. For evaluation of low-energy QED diagrams in the conventional to \(\chi \textrm{PT}\) \(\overline{\textrm{MS}}\) scheme [13, 16], we substitute \(\hat{C}_{V,A}\).

  3. Coincidentally, the same constant term \(-11/8\) is obtained in Ref. [49].

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Acknowledgements

I acknowledge many useful discussions and validations with Emanuele Mereghetti, Vincenzo Cirigliano, Richard Hill, and Wouter Dekens, and useful correspondence with Bastian Kubis. I thank Emanuele Mereghetti and Wouter Dekens for reading this manuscript. This work is supported by the US Department of Energy through the Los Alamos National Laboratory and by LANL’s Laboratory Directed Research and Development (LDRD/PRD) program under projects 20210968PRD4 and 20210190ER. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). FeynCalc [51, 52], LoopTools [53], and Mathematica [54] were extremely useful in this work.

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  1. Theoretical Division,T-2, MS B283, LANL, Los Alamos, 87545, USA

    Oleksandr Tomalak

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Tomalak, O. Radiative Corrections to Neutron Beta Decay and (Anti)Neutrino-Nucleon Scattering from Low-Energy Effective Field Theory. Few-Body Syst 64, 23 (2023). https://doi.org/10.1007/s00601-023-01802-3

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