On the statistical treatment of the Cabibbo angle anomaly

Yuval Grossman, Emilie Passemar, Stefan Schacht

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We point out that testing the equality of the Cabibbo angle as extracted from Γ(K → πlν), the ratio Γ(K → lν)/Γ(π → lν) and nuclear β decays is not identical to a test of first row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The reason is that a CKM unitarity test involves only two parameters, while the degrees of freedom for the assessment of the goodness-of-fit of the universality of the Cabibbo angle entailed by the Standard Model (SM) is equal to the number of measurements minus one. Beyond the SM all different processes could in principle give different Cabibbo angles. Consequently, the difference between the two tests becomes relevant starting from three observables giving results for the Cabibbo angle that are in tension with each other. With current data, depending on the treatment of the nuclear β decays, we find that New Physics is favored over the SM at 5.1 σ or 3.6 σ while CKM unitarity is rejected at 4.8σ or 3.0σ, respectively. We argue that the best method to test the SM is to test the equality of the Cabibbo angle, because CKM unitarity is only one aspect of the SM.

Original languageEnglish
Article number68
JournalJournal of High Energy Physics
Issue number7
StatePublished - 1 Jul 2020
Externally publishedYes

Bibliographical note

Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Publisher Copyright:
© 2020, The Author(s).


  • Beyond Standard Model
  • Kaon Physics
  • Quark Masses and SM Parameters


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