Radiative Corrections to Superallowed Beta Decays Resolve Discrepancies with Ultrasoft Loop Corrections of up to 0.03%

Superallowed beta decays serve as a crucial test of the Standard Model of particle physics, yet precise determination of fundamental parameters requires increasingly accurate theoretical calculations, and a team led by Òscar L. Crosas from Universität Zürich and Emanuele Mereghetti from PSI Center for Neutron and Muon Sciences now delivers a significant advance in this field. The researchers calculate previously neglected radiative corrections arising from interactions within the nucleus, employing a sophisticated theoretical framework to account for the subtle effects of these processes. Their calculations reveal that these corrections, while small, are not negligible, inducing a relative change to the decay rate ranging from one to two parts per thousand depending on the specific nucleus, and will therefore impact the precision with which fundamental constants like the weak mixing angle can be determined. By reducing theoretical uncertainties, this work paves the way for even more stringent tests of the Standard Model and a more accurate understanding of the fundamental forces governing the universe.

Scientists study systems with a heavy-particle effective field theory that systematically describes the interactions of low-energy photons with nuclei. They calculate two-loop virtual and one-loop real-virtual amplitudes by reducing complex integrals to a set of master integrals, which they solve analytically using a variety of techniques. These techniques are applicable to other calculations in nuclear physics.

Precision Calculation of Vud from Neutron Decay

Scientists are performing a highly precise calculation of the parameter Vud, a fundamental component of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, using neutron beta decay. This requires extremely accurate calculations of all relevant radiative corrections and theoretical uncertainties, employing state-of-the-art techniques in perturbative quantum chromodynamics, effective field theory, and numerical integration. The research utilizes a comprehensive theoretical framework, incorporating heavy quark effective theory and chiral perturbation theory to systematically account for strong interactions, and relies on renormalization group methods and perturbative techniques to achieve high precision. The research also incorporates precise measurements and theoretical modeling of the neutron lifetime and beta spectrum, alongside the determination of the axial form factor. Results demonstrate that ultrasoft loops induce a relative correction to the decay rate ranging from 1. 3×10⁻³ in the decay of Carbon-10 to 4. 6×10⁻³ in the decay of Cobalt-54. This correction significantly impacts the extraction of Vud at the permille level, improving the precision of this fundamental parameter.

The inclusion of these corrections reduces the residual dependence of the decay rate on the renormalization scale to a negligible level, minimizing theoretical uncertainties. Measurements confirm that missing ultrasoft perturbative corrections are now a subdominant source of error, particularly for heavier systems like Vanadium-46 and Cobalt-54. Researchers calculated corrections to these decay rates by systematically accounting for interactions between low-energy photons and atomic nuclei using a heavy-particle effective field theory. Results demonstrate that these newly calculated “ultrasoft” corrections induce a relative change in decay rates ranging from 0. 001% to 0. 002%, depending on the specific nucleus undergoing decay.

Importantly, incorporating these corrections substantially reduces the theoretical uncertainty associated with the calculated decay rates. While the calculations currently focus on specific nuclei, the methods developed are broadly applicable to other phenomenological investigations.