Back to CINP FunSym

Unitarity of the Cabibbo-Kobayashi-Maskawa matrix

Location: TRIUMF
Participating Canadian institutions: Guelph, Queens, Simon Fraser, Toronto, British Columbia International partners: UK, USA
External link

Precision measurements of the \(ft\) values for superallowed \(0^{+} \rightarrow 0^{+}\) Fermi \(\beta\) decays between nuclear isobaric analogue states provide demanding tests of the electroweak Standard Model. Such measurements have, for example, confirmed the conserved vector current (CVC) hypothesis at the level of \(1.2 \times 10^{-4}\), set the most stringent limit on a fundamental weak scalar current coupling to left-handed neutrinos at \((0.09 \pm 0.11)\)% of the vector strength, and, together with the Fermi coupling constant \(G_{F}\) from muon decay, provide the most precise determination of the \(V_{ud} = G_{V}/G_{F}\) element of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix 1. To determine \(G_{V}\) from the superallowed data, the experimental \(ft\) values must be combined with theoretical calculations of transition-dependent “outer” radiative corrections \((\delta_R)\), a transition-independent “inner” radiative correction (\(\Delta^V_{R}\)), and nuclear structure dependent isospin-symmetry-breaking corrections \((\delta_C)\).

Figure 1:  Corrected Ft values for the 15 precisely measured superallowed Fermi \beta decays as of June 2020. These data confirm the conserved vector current hypothesis at the level of 1.2 \times 10^{-4} and provide the most precise determination of the V_{ud} element of the CKM quark mixing matrix.

New calculations of radiative corrections to \(V_{ud}\) 2 3 4 indicate a violation of CKM unitarity of about \(1\times 10^{-3}\) at 2 to 3 \(\sigma\) significance. As a violation of CKM unitarity would require new physics beyond the current electroweak Standard Model, all inputs must be carefully scrutinized. Figure 1 shows corrected \(Ft\) values for the 15 most precisely measured decays.

The TRIUMF-ISAC facility produces high-quality beams of many of the superallowed emitters with world-record intensities and hosts a suite of state-of-the-art spectrometers capable of precision measurements of all of the experimental quantities of interest in superallowed decays. These include high-precision half-life measurements through both counting with the 4pi gas proportional counter at the ISAC-I GPS facility and gamma-ray counting with GRIFFIN, high-precision branching-ratio measurements with GRIFFIN and its auxiliary detectors, high-precision Q-value measurements with the TITAN mass spectrometer, and charge-radii measurements through collinear laser spectroscopy required as input to the isospin-symmetry-breaking calculations. In superallowed half-life and branching ratio measurements, the ISAC gamma-ray group has made significant progress recently: The half-life of the superallowed emitter \(^{18}\)Ne was determined twice as precisely, demonstrating the capabilities of the new thick tape system for precision measurements of noble gas isotopes 5 and was also used to improve the world-average half-life for the superallowed emitter \(^{22}\)Mg by more than a factor of 3 6. Finally, a first superallowed half-life measurement to better than \(10^{-4}\) was achieved with \(^{10}\)C, with the added benefit that as the lightest such emitter, it has greatest sensitity to possible scalar current contributions 7

The factor of \(300-500\) gain in \(\gamma - \gamma\) coincidence detection efficiency provided by GRIFFIN compared to the previous \(8\pi\) spectrometer at ISAC-I has also allowed major advances in the control of the so-called “Pandemonium" problem that has plagued previous attempts at high-precision branching-ratio measurements for the heavy \((A \geq 62)\) superallowed decays, as demonstrated in our recent measurement of the \(^{62}\)Ga superallowed branching ratio to \(\pm 0.0026\)8, a factor of 4 improvement over the previous world-average.

This highly successful, long-term, program of high-precision superallowed \(\beta\) decay half-life and branching ratio measurements will continue to be developed at ISAC throughout the 2022–2026 period, and beyond as new beams become available. These measurements will focus on the decays that differentiate between leading models of the isospin-symmetry-breaking corrections, namely the \(N = Z - 2\) superallowed emitters \(^{14}\)O, \(^{22}\)Mg, \(^{34}\)Ar, and \(^{38}\)Ca, and the heavy \(A \geq 62\) emitters between \(^{62}\)Ga and \(^{74}\)Rb.


  1. J.C. Hardy and I.S. Towner, arXiv:1807.01146[nucl-ex] (2018).↩︎

  2. C.Y Seng et al., Phys. Rev. D 100, 013001 (2019).↩︎

  3. A. Czarnecki et al., Phys. Rev. D 100, 073008 (2019).↩︎

  4. K. Shiells, Ph.D. thesis, University of Manitoba, 2020.↩︎

  5. A.T. Laffoley et al., Phys. Rev. C 92, 025502 (2015).↩︎

  6. M.R. Dunlop et al., Phys. Rev. C 96, 045502 (2017).↩︎

  7. M.R. Dunlop et al., Phys. Rev. Lett. 116, 172501 (2016).↩︎

  8. A.D. MacLean et al., Phys. Rev. C 102, 054325 (2020).↩︎