Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Sirlin, Large mW, mZ Behavior of the Oα Corrections to Semileptonic Processes Mediated by W, Nucl. Phys. B 196 (1982) 83 [INSPIRE].
J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [INSPIRE].
J. Bijnens and P. Talavera, Kℓ3 decays in chiral perturbation theory, Nucl. Phys. B 669 (2003) 341 [hep-ph/0303103] [INSPIRE].
V. Cirigliano, M. Giannotti and H. Neufeld, Electromagnetic effects in Kℓ3 decays, JHEP 11 (2008) 006 [arXiv:0807.4507] [INSPIRE].
FlaviaNet Working Group on Kaon Decays collaboration, An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays, Eur. Phys. J. C 69 (2010) 399 [arXiv:1005.2323] [INSPIRE].
M. Moulson, Experimental determination of Vus from kaon decays, PoS CKM2016 (2017) 033 [arXiv:1704.04104] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
M. Moulson, The status of Vus, Talk given at the workshop Current and Future Status of First-Row CKM Unitarity, Amherst Center for Fundamental Interactions, UMass Amherst, Amherst, Massachusetts, U.S.A., May 17, 2019.
V. Cirigliano and H. Neufeld, A note on isospin violation in Pℓ2(γ) decays, Phys. Lett. B 700 (2011) 7 [arXiv:1102.0563] [INSPIRE].
D. Giusti et al., First lattice calculation of the QED corrections to leptonic decay rates, Phys. Rev. Lett. 120 (2018) 072001 [arXiv:1711.06537] [INSPIRE].
E. Passemar, Extraction of Vus from experimental measurements, talk given at the International Conference on Kaon Physics 2019, University of Perugia, Perugia, Italy, September 10, 2019.
T. Kitahara, Hunt for new physics in kaon decays, talk given at the 2nd Workshop on Hadronic Contributions to New Physics Searches, Tenerife, Spain, September 27, 2019.
M. Di Carlo et al., Light-meson leptonic decay rates in lattice QCD+QED, Phys. Rev. D 100 (2019) 034514 [arXiv:1904.08731] [INSPIRE].
W.J. Marciano and A. Sirlin, Improved calculation of electroweak radiative corrections and the value of V(ud), Phys. Rev. Lett. 96 (2006) 032002 [hep-ph/0510099] [INSPIRE].
J.C. Hardy and I.S. Towner, Superallowed 0+ → 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model, Phys. Rev. B 79 (2009) 055502 [arXiv:0812.1202] [INSPIRE].
I.S. Towner and J.C. Hardy, The evaluation of Vud and its impact on the unitarity of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix, Rept. Prog. Phys. 73 (2010) 046301 [INSPIRE].
J.C. Hardy and I.S. Towner, Superallowed 0+ → 0+ nuclear β decays: 2014 critical survey, with precise results for Vud and CKM unitarity, Phys. Rev. C 91 (2015) 025501 [arXiv:1411.5987] [INSPIRE].
C.-Y. Seng, M. Gorchtein, H.H. Patel and M.J. Ramsey-Musolf, Reduced Hadronic Uncertainty in the Determination of Vud, Phys. Rev. Lett. 121 (2018) 241804 [arXiv:1807.10197] [INSPIRE].
C.Y. Seng, M. Gorchtein and M.J. Ramsey-Musolf, Dispersive evaluation of the inner radiative correction in neutron and nuclear β decay, Phys. Rev. D 100 (2019) 013001 [arXiv:1812.03352] [INSPIRE].
M. Gorchtein, γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum, Phys. Rev. Lett. 123 (2019) 042503 [arXiv:1812.04229] [INSPIRE].
A. Czarnecki, W.J. Marciano and A. Sirlin, Radiative Corrections to Neutron and Nuclear Beta Decays Revisited, Phys. Rev. D 100 (2019) 073008 [arXiv:1907.06737] [INSPIRE].
W.J. Marciano, Precise determination of |Vus| from lattice calculations of pseudoscalar decay constants, Phys. Rev. Lett. 93 (2004) 231803 [hep-ph/0402299] [INSPIRE].
V. Bernard, M. Oertel, E. Passemar and J. Stern, Tests of non-standard electroweak couplings of right-handed quarks, JHEP 01 (2008) 015 [arXiv:0707.4194] [INSPIRE].
FlaviaNet Working Group on Kaon Decays collaboration, Precision tests of the Standard Model with leptonic and semileptonic kaon decays, in 5th International Workshop on e+ e− Collisions from Phi to Psi, Frascati, Rome, Italy, 7–10 April 2008 arXiv:0801.1817 [INSPIRE].
V. Cirigliano, J. Jenkins and M. González-Alonso, Semileptonic decays of light quarks beyond the Standard Model, Nucl. Phys. B 830 (2010) 95 [arXiv:0908.1754] [INSPIRE].
V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].
T. Bhattacharya et al., Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC, Phys. Rev. D 85 (2012) 054512 [arXiv:1110.6448] [INSPIRE].
V. Cirigliano, M. González-Alonso and M.L. Graesser, Non-standard Charged Current Interactions: beta decays versus the LHC, JHEP 02 (2013) 046 [arXiv:1210.4553] [INSPIRE].
V. Cirigliano, S. Gardner and B. Holstein, Beta Decays and Non-Standard Interactions in the LHC Era, Prog. Part. Nucl. Phys. 71 (2013) 93 [arXiv:1303.6953] [INSPIRE].
O. Naviliat-Cuncic and M. González-Alonso, Prospects for precision measurements in nuclear β decay at the LHC era, Annalen Phys. 525 (2013) 600 [arXiv:1304.1759] [INSPIRE].
J.L. Rosner, S. Stone and R.S. Van de Water, Leptonic Decays of Charged Pseudoscalar Mesons — 2015, arXiv:1509.02220 [INSPIRE].
S. Alioli, V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Right-handed charged currents in the era of the Large Hadron Collider, JHEP 05 (2017) 086 [arXiv:1703.04751] [INSPIRE].
G.C. Branco and L. Lavoura, Wolfenstein Type Parametrization of the Quark Mixing Matrix, Phys. Rev. D 38 (1988) 2295 [INSPIRE].
CKMfitter Group collaboration, CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [INSPIRE].
B. Belfatto, R. Beradze and Z. Berezhiani, The CKM unitarity problem: A trace of new physics at the TeV scale?, Eur. Phys. J. C 80 (2020) 149 [arXiv:1906.02714] [INSPIRE].
W. Tan, Laboratory tests of the ordinary-mirror particle oscillations and the extended CKM matrix, arXiv:1906.10262 [INSPIRE].
M. González-Alonso and J. Martin Camalich, Global Effective-Field-Theory analysis of New-Physics effects in (semi)leptonic kaon decays, JHEP 12 (2016) 052 [arXiv:1605.07114] [INSPIRE].
L. Demortier, P values: What they are and how to use them, https://www-cdf.fnal.gov/∼luc/statistics/cdf8662.pdf (2007).
M. Wiebusch, Numerical Computation of p-values with myFitter, Comput. Phys. Commun. 184 (2013) 2438 [arXiv:1207.1446] [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
Fermilab Lattice and MILC collaborations, |Vus| from Kℓ3 decay and four-flavor lattice QCD, Phys. Rev. D 99 (2019) 114509 [arXiv:1809.02827] [INSPIRE].
J.C. Pati and A. Salam, Are There Anomalous Lepton-Hadron Interactions?, Phys. Rev. Lett. 32 (1974) 1083 [INSPIRE].
R.N. Mohapatra and J.C. Pati, A Natural Left-Right Symmetry, Phys. Rev. D 11 (1975) 2558 [INSPIRE].
R.N. Mohapatra and J.C. Pati, Left-Right Gauge Symmetry and an Isoconjugate Model of CP-violation, Phys. Rev. D 11 (1975) 566 [INSPIRE].
F.A. Wilczek, A. Zee, R.L. Kingsley and S.B. Treiman, Weak Interaction Models with New Quarks and Righthanded Currents, Phys. Rev. D 12 (1975) 2768 [INSPIRE].
G. Senjanović and R.N. Mohapatra, Exact Left-Right Symmetry and Spontaneous Violation of Parity, Phys. Rev. D 12 (1975) 1502 [INSPIRE].
G. Senjanović, Spontaneous Breakdown of Parity in a Class of Gauge Theories, Nucl. Phys. B 153 (1979) 334 [INSPIRE].
V. Bernard, M. Oertel, E. Passemar and J. Stern, \( {K}_{\mu 3}^L \) decay: A stringent test of right-handed quark currents, Phys. Lett. B 638 (2006) 480 [hep-ph/0603202] [INSPIRE].
G. Senjanović and V. Tello, Right Handed Quark Mixing in Left-Right Symmetric Theory, Phys. Rev. Lett. 114 (2015) 071801 [arXiv:1408.3835] [INSPIRE].
V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, An ϵ′ improvement from right-handed currents, Phys. Lett. B 767 (2017) 1 [arXiv:1612.03914] [INSPIRE].
B.W. Lee and R.E. Shrock, Natural Suppression of Symmetry Violation in Gauge Theories: Muon-Lepton and Electron Lepton Number Nonconservation, Phys. Rev. D 16 (1977) 1444 [INSPIRE].
D.A. Bryman and R. Shrock, Constraints on Sterile Neutrinos in the MeV to GeV Mass Range, Phys. Rev. D 100 (2019) 073011 [arXiv:1909.11198] [INSPIRE].
A.M. Coutinho, A. Crivellin and C.A. Manzari, Global Fit to Modified Neutrino Couplings and the Cabibbo-Angle Anomaly, arXiv:1912.08823 [INSPIRE].
A. Crivellin and M. Hoferichter, Beta decays as sensitive probes of lepton flavor universality, arXiv:2002.07184 [INSPIRE].
A. Pich, Precision tau physics, Prog. Part. Nucl. Phys. 75 (2014) 41 [arXiv:1310.7922] [INSPIRE].
A. Lusiani, Status and progress of the HFLAV-Tau group activities, EPJ Web Conf. 218 (2019) 05002 [arXiv:1804.08436] [INSPIRE].
A. Czarnecki, W.J. Marciano and A. Sirlin, Pion beta decay and Cabibbo-Kobayashi-Maskawa unitarity, Phys. Rev. D 101 (2020) 091301 [arXiv:1911.04685] [INSPIRE].
Open Access
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
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1911.07821
Rights and permissions
Open Access . 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.
About this article
Cite this article
Grossman, Y., Passemar, E. & Schacht, S. On the statistical treatment of the Cabibbo angle anomaly. J. High Energ. Phys. 2020, 68 (2020). https://doi.org/10.1007/JHEP07(2020)068
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)068