Abstract
The universal radiative corrections common to neutron and super-allowed nuclear beta decays (also known as ``inner'' corrections) are revisited in light of a recent dispersion relation study that found $+2.467(22)\%$, i.e.~about $2.4\sigma$ larger than the previous evaluation. For comparison, we consider several alternative computational methods. All employ an updated perturbative QCD four-loop Bjorken sum rule (BjSR) defined QCD coupling supplemented with a nucleon form factor based Born amplitude to estimate axial-vector induced hadronic contributions. In addition, we now include hadronic contributions from low $Q^2$ loop effects based on duality considerations and vector meson resonance interpolators. Our primary result, $2.426(32)\%$ corresponds to an average of a Light Front Holomorphic QCD approach and a three resonance interpolator fit. It reduces the dispersion relation discrepancy to approximately $1.1\sigma$ and thereby provides a consistency check. Consequences of our new radiative correction estimate, along with that of the dispersion relation result, for CKM unitarity are discussed. The neutron lifetime-$g_A$ connection is updated and shown to suggest a shorter neutron lifetime $< 879$ s. We also find an improved bound on exotic, non-Standard Model, neutron decays or oscillations of the type conjectured as solutions to the neutron lifetime problem, $\text{BR}(n\to \text{exotics}) < 0.16 \%$.
Highlights
Precision tests of the Standard Model (SM) require accurate calculations of electroweak radiative corrections (RCs) [1,2,3,4,5,6,7]
Unitarity of the CabibboKobayashi-Maskawa (CKM) quark mixing matrix leads to orthonormal relationships among row and column matrix elements and provides a means to search for indications of “new physics” via departures from SM expectations
LFHQCD approach, we evaluate hadronic effects using a three-resonance interpolator function fixed by boundary conditions
Summary
Precision tests of the Standard Model (SM) require accurate calculations of electroweak radiative corrections (RCs) [1,2,3,4,5,6,7]. All three terms depend on hadronic structure and/or perturbative QCD Those axial-vector induced loop contributions increase the decay rate by about 2.9α=π ∼ 6.7 × 10−3. Employing the known BjSR or equivalent GLS nonsinglet sum rule four-loop QCD corrections as input allows a precise evaluation of the perturbative QCD corrections to the γW box diagrams for loop momentum above the demarcation scale Q20 [see Eq (12) and discussion below], Q20 < Q2 < ∞, with little uncertainty. The DR uses the GLS nonsinglet sum rule data at low Q2 for guidance, while our method follows ideas developed from BjSR studies [10] Both have the same perturbative QCD corrections modulo singlet contributions ( the DR approach applies only the first three loops of the known four-loop effects [13]) and include similar estimates of the Born amplitude but differ in the low Q2 evaluation of other hadronic effects. As we later discuss, that one should probably anticipate a future reduction in the neutron lifetime to the range 878–879 s or a decrease in the value of gA
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