[Paper Review] Constraints on subleading interactions in beta decay Lagrangian

Adam Falkowski, Martín González‐Alonso+2 more|arXiv (Cornell University)|Dec 14, 2021

Nuclear physics research studies4 citations

TL;DR

This paper develops a comprehensive effective field theory (EFT) framework for nuclear beta decay, systematically matching quark-level interactions to nucleon-level dynamics at the MeV scale. It computes the impact of subleading recoil corrections—arising from pseudoscalar, weak magnetism, and tensor interactions—on differential decay widths, finding 3.5σ experimental evidence for nucleon weak magnetism consistent with isospin symmetry predictions.

ABSTRACT

We discuss the effective field theory (EFT) for nuclear beta decay. The general quark-level EFT describing charged-current interactions between quarks and leptons is matched to the nucleon-level non-relativistic EFT at the O(MeV) momentum scale characteristic for beta transitions. The matching takes into account, for the first time, the effect of all possible beyond-the-Standard-Model interactions at the subleading order in the recoil momentum. We calculate the impact of all the Wilson coefficients of the leading and subleading EFT Lagrangian on the differential decay width in allowed beta transitions. As an example application, we show how the existing experimental data constrain the subleading Wilson coefficients corresponding to pseudoscalar, weak magnetism, and induced tensor interactions. The data display a 3.5 sigma evidence for nucleon weak magnetism, in agreement with the theory prediction based on isospin symmetry.

Motivation & Objective

• To construct a modern effective field theory (EFT) description of nuclear beta decay using non-relativistic EFT at the MeV scale.
• To systematically match quark-level charged-current interactions to nucleon-level EFT, including all beyond-the-Standard-Model (BSM) interactions at subleading order in recoil momentum.
• To compute the impact of all Wilson coefficients in the leading and subleading EFT Lagrangian on differential decay widths in allowed beta transitions.
• To constrain subleading Wilson coefficients—specifically for pseudoscalar, weak magnetism, and induced tensor interactions—using existing experimental data.
• To test the consistency of experimental results with theoretical predictions based on isospin symmetry, particularly for nucleon weak magnetism.

Proposed method

• Formulate a pionless non-relativistic EFT with nucleons and leptons as degrees of freedom, expanding in powers of ∇/m_N to organize recoil corrections.
• Match the quark-level EFT to the nucleon-level EFT at the MeV scale, including all possible BSM interactions at O(∇¹) in the Lagrangian.
• Derive explicit expressions for the differential decay width in allowed beta decays, including linear recoil corrections from vector, axial, scalar, and tensor currents.
• Use the full amplitude expressions to compute observables such as the electron energy spectrum, angular correlations, and asymmetries, including terms linear in nuclear 3-momenta.
• Apply the EFT framework to extract constraints on Wilson coefficients using data from superallowed decays, neutron decay, mirror decays, and pure Fermi correlation measurements.
• Perform a global fit to experimental data to extract bounds on subleading coefficients, particularly for weak magnetism and tensor interactions.

Experimental results

Research questions

• RQ1 How do subleading recoil corrections—arising from pseudoscalar, weak magnetism, and induced tensor interactions—affect the differential decay width in allowed beta transitions?
• RQ2 To what extent do existing experimental data constrain the Wilson coefficients of subleading EFT interactions in beta decay?
• RQ3 Is there experimental evidence for nucleon weak magnetism at the subleading recoil level, and does it agree with isospin symmetry predictions?
• RQ4 How do the subleading corrections modify the angular and energy distributions in beta decay, and can they be distinguished from leading-order SM contributions?
• RQ5 Can the EFT framework consistently incorporate both SM and BSM contributions to beta decay at the MeV scale, enabling constraints on new physics?

Key findings

• The paper provides the first complete calculation of subleading recoil corrections in beta decay EFT, including all possible BSM interactions at O(∇¹).
• Experimental data show 3.5σ evidence for nucleon weak magnetism, in agreement with the theoretical prediction based on isospin symmetry.
• The subleading Wilson coefficients for pseudoscalar, weak magnetism, and induced tensor interactions are constrained using data from superallowed decays, neutron decay, mirror decays, and correlation measurements.
• The differential decay width is computed to linear order in nuclear 3-momenta, with explicit expressions derived for observables such as A, B, and λ_AB asymmetries.
• The analysis confirms that the leading-order EFT formulas of Jackson, Treiman, and Wyld are recovered in the zero-recoil limit, with subleading corrections explicitly quantified.
• The EFT framework successfully unifies SM and BSM contributions to beta decay at the MeV scale, enabling a consistent matching to WEFT and SMEFT.