[Paper Review] Consistent description of angular correlations in $β$ decay for Beyond Standard Model physics searches

L. Hayen, A. R. Young|arXiv (Cornell University)|Sep 23, 2020

Nuclear physics research studies7 citations

TL;DR

This paper provides a unified theoretical framework for calculating angular correlations in β decay, integrating nuclear structure effects, radiative corrections, and experimental geometry to enable precision searches for Beyond Standard Model physics. It resolves inconsistencies in prior treatments by standardizing corrections across different experimental setups, significantly improving the sensitivity to exotic scalar and tensor currents via Fierz interference terms at the per-mille level.

ABSTRACT

Measurements of angular correlations between initial and final particles in $β$ decay remain one of the most promising ways of probing the Standard Model and looking for new physics. As experiments reach unprecedented precision well into the per-mille regime, proper extraction of results requires one to take into account a great number of nuclear structure and radiative corrections in a procedure which becomes dependent upon the experimental geometry. We provide here a compilation and update of theoretical results which describe all corrections in the same conceptual framework, point out pitfalls and review the influence of the experimental geometry. Finally, we summarize the potential for new physics reach.

Motivation & Objective

• To resolve inconsistencies in theoretical treatments of angular correlations in β decay across different experimental analyses.
• To provide a consistent, unified description of higher-order corrections—nuclear structure, radiative, and recoil effects—for precision measurements.
• To clarify the impact of experimental geometry on correlation measurements, especially in high-precision settings.
• To enable more robust comparisons between experimental results by standardizing theoretical inputs.
• To enhance sensitivity to new physics, particularly exotic scalar and tensor currents, via accurate modeling of Fierz interference terms.

Proposed method

• Adopts the Behrens-Bühring formalism as a consistent framework for expressing weak matrix elements in β decay, enabling systematic inclusion of nuclear structure effects.
• Translates form factors between the Behrens-Bühring and Walecka-Breit frame formalisms, ensuring compatibility with existing experimental analyses.
• Incorporates radiative corrections using the Sirlin and Holstein formalisms, including phase-space and recoil corrections up to O(α) and O(1/M).
• Derives explicit expressions for correlation coefficients (e.g., $A_{\beta}$, $a_{\beta\nu}$) in terms of nuclear matrix elements and effective couplings.
• Reconciles differing sign conventions in literature by standardizing definitions of $F^{V}_{0}$, $F^{A}_{0}$, $F^{V}_{\sigma}$, and $F^{A}_{\sigma}$ relative to Holstein’s conventions.
• Applies corrections for kinematic recoil and finite nuclear mass effects a posteriori in the Breit frame, ensuring consistency with experimental kinematics.

Experimental results

Research questions

• RQ1 How can theoretical corrections in β decay angular correlations be consistently unified across different experimental geometries and nuclear systems?
• RQ2 What is the impact of nuclear structure effects and radiative corrections on the measurement of $A_{\beta}$ and $a_{\beta\nu}$ at the per-mille precision level?
• RQ3 How do different formalisms (Behrens-Bühring, Walecka, Holstein) compare in their treatment of weak matrix elements, and what are the necessary translation factors?
• RQ4 To what extent do recoil and finite-mass corrections affect the interpretation of angular correlation coefficients in high-precision experiments?
• RQ5 How can the Fierz interference term $b_F$ be reliably extracted to probe new physics beyond the Standard Model?

Key findings

• The paper establishes a consistent translation between the Behrens-Bühring and Walecka-Breit frame formalisms, with explicit relations between form factors (e.g., $V_0 = a$, $A_{10} = -c$) that resolve long-standing inconsistencies.
• It identifies that the Jerusalem group’s analysis (Glick-Magid et al., 2016) omits crucial recoil corrections, which must be added a posteriori to maintain consistency with the Breit frame formalism.
• The leading-order expressions for correlation coefficients (e.g., $A_{\beta} \propto -c$, $a_{\beta\nu} \propto b$) are derived with full inclusion of phase-space and recoil corrections.
• The Fierz interference term $b_F$ is expressed in terms of effective couplings $\epsilon_S$, $\epsilon_T$, and nuclear matrix elements, enabling direct sensitivity to new physics at scales $\Lambda \gtrsim \text{TeV}$.
• The standardization of form factor definitions ensures that commonly quoted ratios like $b/Ac$ and $d/Ac$ remain invariant across formalisms, preserving comparability of experimental results.
• The framework enables a unified treatment of $\beta$-asymmetry and $\beta$-$\nu$ correlation measurements, reducing systematic uncertainties and enhancing sensitivity to exotic scalar and tensor currents.