Abstract
The measurements of Vus in leptonic (Kμ2) and semileptonic (Kl3) kaon decays exhibit a 3σ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the Ke3 decay rates that achieves an unprecedented level of precision of 10−4, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the “list of culprits” responsible for the Kμ2–Kl3 discrepancy.
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References
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].
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [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].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01.
W.J. Marciano, Precise determination of |V(us)| from lattice calculations of pseudoscalar decay constants, Phys. Rev. Lett. 93 (2004) 231803 [hep-ph/0402299] [INSPIRE].
V. Cirigliano and H. Neufeld, A note on isospin violation in Pl2(γ) decays, Phys. Lett. B 700 (2011) 7 [arXiv:1102.0563] [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].
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].
Y. Grossman, E. Passemar and S. Schacht, On the Statistical Treatment of the Cabibbo Angle Anomaly, JHEP 07 (2020) 068 [arXiv:1911.07821] [INSPIRE].
A.M. Coutinho, A. Crivellin and C.A. Manzari, Global Fit to Modified Neutrino Couplings and the Cabibbo-Angle Anomaly, Phys. Rev. Lett. 125 (2020) 071802 [arXiv:1912.08823] [INSPIRE].
K. Cheung, W.-Y. Keung, C.-T. Lu and P.-Y. Tseng, Vector-like Quark Interpretation for the CKM Unitarity Violation, Excess in Higgs Signal Strength, and Bottom Quark Forward-Backward Asymmetry, JHEP 05 (2020) 117 [arXiv:2001.02853] [INSPIRE].
A. Crivellin and M. Hoferichter, β Decays as Sensitive Probes of Lepton Flavor Universality, Phys. Rev. Lett. 125 (2020) 111801 [arXiv:2002.07184] [INSPIRE].
M. Endo and S. Mishima, Muon g − 2 and CKM unitarity in extra lepton models, JHEP 08 (2020) 004 [arXiv:2005.03933] [INSPIRE].
B. Capdevila, A. Crivellin, C.A. Manzari and M. Montull, Explaining b → sℓ+ ℓ− and the Cabibbo angle anomaly with a vector triplet, Phys. Rev. D 103 (2021) 015032 [arXiv:2005.13542] [INSPIRE].
M. Kirk, Cabibbo anomaly versus electroweak precision tests: An exploration of extensions of the Standard Model, Phys. Rev. D 103 (2021) 035004 [arXiv:2008.03261] [INSPIRE].
A. Crivellin, C.A. Manzari, M. Alguero and J. Matias, Combined Explanation of the Z → bb− Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, and τ → μνν and b → sℓ+ ℓ− Data, Phys. Rev. Lett. 127 (2021) 011801 [arXiv:2010.14504] [INSPIRE].
E.S. Ginsberg, Radiative Corrections to \( {K}_{e3}^{\pm } \) Decays, Phys. Rev. 142 (1966) 1035 [INSPIRE].
E.S. Ginsberg, Radiative corrections to \( {k}_{e3}^{\pm } \) decays and the ∆i = 1/2 rule, Phys. Rev. 171 (1968) 1675 [Erratum ibid. 174 (1968) 2169] [INSPIRE].
E.S. Ginsberg, Radiative corrections to the \( {K}_{e3}^{\pm } \) Dalitz plot, Phys. Rev. 162 (1967) 1570 [Erratum ibid. 187 (1969) 2280] [INSPIRE].
E.S. Ginsberg, Radiative corrections to kμ3 decays, Phys. Rev. D 1 (1970) 229 [INSPIRE].
T. Becherrawy, Radiative Correction to Kl3 Decay, Phys. Rev. D 1 (1970) 1452 [INSPIRE].
V. Bytev, E. Kuraev, A. Baratt and J. Thompson, Radiative corrections to the \( {K}_{e3}^{\pm } \) decay revised, Eur. Phys. J. C 27 (2003) 57 [Erratum ibid. 34 (2004) 523] [hep-ph/0210049] [INSPIRE].
T.C. Andre, Radiative corrections in \( {K}_{l3}^0 \) decays, Annals Phys. 322 (2007) 2518 [hep-ph/0406006] [INSPIRE].
A. Garcia and M. Maya, Model independent radiative corrections to \( {K}_{l3}^{\pm } \) decays, Phys. Rev. D 23 (1981) 2603 [INSPIRE].
C. Juarez-Leon, A. Martinez, M. Neri, J.J. Torres and R. Flores-Mendieta, Radiative corrections to the Dalitz plot of \( {K}_{l3}^{\pm } \) decays, Phys. Rev. D 83 (2011) 054004 [Erratum ibid. 86 (2012) 059901] [arXiv:1010.5547] [INSPIRE].
J.J. Torres, A. Martinez, M. Neri, C. Juarez-Leon and R. Flores-Mendieta, Radiative corrections to the Dalitz plot of \( {K}_{l3}^{\pm } \) decays: Contribution of the four-body region, Phys. Rev. D 86 (2012) 077501 [arXiv:1209.5759] [INSPIRE].
M. Neri, A. Martínez, C. Juárez-León, J.J. Torres and R. Flores-Mendieta, Radiative corrections to the Dalitz plot of \( {K}_{l3}^0 \) decays, Phys. Rev. D 92 (2015) 074022 [arXiv:1510.00401] [INSPIRE].
V. Cirigliano, M. Knecht, H. Neufeld, H. Rupertsberger and P. Talavera, Radiative corrections to Kl3 decays, Eur. Phys. J. C 23 (2002) 121 [hep-ph/0110153] [INSPIRE].
V. Cirigliano, H. Neufeld and H. Pichl, Ke3 decays and CKM unitarity, Eur. Phys. J. C 35 (2004) 53 [hep-ph/0401173] [INSPIRE].
V. Cirigliano, M. Giannotti and H. Neufeld, Electromagnetic effects in Kl3 decays, JHEP 11 (2008) 006 [arXiv:0807.4507] [INSPIRE].
R. Urech, Virtual photons in chiral perturbation theory, Nucl. Phys. B 433 (1995) 234 [hep-ph/9405341] [INSPIRE].
M. Knecht, H. Neufeld, H. Rupertsberger and P. Talavera, Chiral perturbation theory with virtual photons and leptons, Eur. Phys. J. C 12 (2000) 469 [hep-ph/9909284] [INSPIRE].
B. Ananthanarayan and B. Moussallam, Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians, JHEP 06 (2004) 047 [hep-ph/0405206] [INSPIRE].
S. Descotes-Genon and B. Moussallam, Radiative corrections in weak semi-leptonic processes at low energy: A Two-step matching determination, Eur. Phys. J. C 42 (2005) 403 [hep-ph/0505077] [INSPIRE].
A. Sirlin, Current Algebra Formulation of Radiative Corrections in Gauge Theories and the Universality of the Weak Interactions, Rev. Mod. Phys. 50 (1978) 573 [Erratum ibid. 50 (1978) 905] [INSPIRE].
C.-Y. Seng, Radiative Corrections to Semileptonic Beta Decays: Progress and Challenges, Particles 4 (2021) 397 [arXiv:2108.03279] [INSPIRE].
C.-Y. Seng, D. Galviz and U.-G. Meißner, A New Theory Framework for the Electroweak Radiative Corrections in Kl3 Decays, JHEP 02 (2020) 069 [arXiv:1910.13208] [INSPIRE].
X. Feng, M. Gorchtein, L.-C. Jin, P.-X. Ma and C.-Y. Seng, First-principles calculation of electroweak box diagrams from lattice QCD, Phys. Rev. Lett. 124 (2020) 192002 [arXiv:2003.09798] [INSPIRE].
C.-Y. Seng, X. Feng, M. Gorchtein and L.-C. Jin, Joint lattice QCD-dispersion theory analysis confirms the quark-mixing top-row unitarity deficit, Phys. Rev. D 101 (2020) 111301 [arXiv:2003.11264] [INSPIRE].
C.-Y. Seng, X. Feng, M. Gorchtein, L.-C. Jin and U.-G. Meißner, New method for calculating electromagnetic effects in semileptonic beta-decays of mesons, JHEP 10 (2020) 179 [arXiv:2009.00459] [INSPIRE].
P.-X. Ma, X. Feng, M. Gorchtein, L.-C. Jin and C.-Y. Seng, Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays, Phys. Rev. D 103 (2021) 114503 [arXiv:2102.12048] [INSPIRE].
C.-Y. Seng, D. Galviz, M. Gorchtein and U.G. Meißner, High-precision determination of the Ke3 radiative corrections, Phys. Lett. B 820 (2021) 136522 [arXiv:2103.00975] [INSPIRE].
MuLan collaboration, Detailed Report of the MuLan Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant, Phys. Rev. D 87 (2013) 052003 [arXiv:1211.0960] [INSPIRE].
NA48/2 collaboration, Measurement of the form factors of charged kaon semileptonic decays, JHEP 10 (2018) 150 [arXiv:1808.09041] [INSPIRE].
J. Erler, Electroweak radiative corrections to semileptonic tau decays, Rev. Mex. Fis. 50 (2004) 200 [hep-ph/0211345] [INSPIRE].
W.N. Cottingham, The neutron proton mass difference and electron scattering experiments, Annals Phys. 25 (1963) 424 [INSPIRE].
J. Gasser and H. Leutwyler, Implications of Scaling for the Proton-Neutron Mass Difference, Nucl. Phys. B 94 (1975) 269 [INSPIRE].
W.A. Bardeen, J. Bijnens and J.M. Gerard, Hadronic Matrix Elements and the pi+ pi0 Mass Difference, Phys. Rev. Lett. 62 (1989) 1343 [INSPIRE].
A. Walker-Loud, C.E. Carlson and G.A. Miller, The Electromagnetic Self-Energy Contribution to Mp − Mn and the Isovector Nucleon MagneticPolarizability, Phys. Rev. Lett. 108 (2012) 232301 [arXiv:1203.0254] [INSPIRE].
J. Gasser, M. Hoferichter, H. Leutwyler and A. Rusetsky, Cottingham formula and nucleon polarisabilities, Eur. Phys. J. C 75 (2015) 375 [Erratum ibid. 80 (2020) 353] [arXiv:1506.06747] [INSPIRE].
J. Gasser, H. Leutwyler and A. Rusetsky, On the mass difference between proton and neutron, Phys. Lett. B 814 (2021) 136087 [arXiv:2003.13612] [INSPIRE].
M. Gorchtein and C.-Y. Seng, Dispersion relation analysis of the radiative corrections to gA in the neutron β-decay, JHEP 10 (2021) 053 [arXiv:2106.09185] [INSPIRE].
Y.-J. Shi, C.-Y. Seng, F.-K. Guo, B. Kubis, U.-G. Meißner and W. Wang, Two-Meson Form Factors in Unitarized Chiral Perturbation Theory, JHEP 04 (2021) 086 [arXiv:2011.00921] [INSPIRE].
N. Meister and D.R. Yennie, Radiative Corrections to High-Energy Scattering Processes, Phys. Rev. 130 (1963) 1210 [INSPIRE].
A. Sirlin, General Properties of the Electromagnetic Corrections to the Beta Decay of a Physical Nucleon, Phys. Rev. 164 (1967) 1767 [INSPIRE].
D.H. Wilkinson and B.E.F. Macefield, The numerical evaluation of radiative corrections of order α to allowed nuclear β-decay, Nucl. Phys. A 158 (1970) 110 [INSPIRE].
H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
H.H. Patel, Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 218 (2017) 66 [arXiv:1612.00009] [INSPIRE].
NA7 collaboration, A Measurement of the Space-Like Pion Electromagnetic Form-Factor, Nucl. Phys. B 277 (1986) 168 [INSPIRE].
B. Ananthanarayan, I. Caprini and D. Das, Electromagnetic charge radius of the pion at high precision, Phys. Rev. Lett. 119 (2017) 132002 [arXiv:1706.04020] [INSPIRE].
G. Colangelo, M. Hoferichter and P. Stoffer, Two-pion contribution to hadronic vacuum polarization, JHEP 02 (2019) 006 [arXiv:1810.00007] [INSPIRE].
S.R. Amendolia et al., A Measurement of the Kaon Charge Radius, Phys. Lett. B 178 (1986) 435 [INSPIRE].
B. Moussallam, A Sum rule approach to the violation of Dashen’s theorem, Nucl. Phys. B 504 (1997) 381 [hep-ph/9701400] [INSPIRE].
J. Bijnens and G. Ecker, Mesonic low-energy constants, Ann. Rev. Nucl. Part. Sci. 64 (2014) 149 [arXiv:1405.6488] [INSPIRE].
V. Cirigliano, Ke3 and πe3 decays: Radiative corrections and CKM unitarity, in 38th Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs France(2003) [hep-ph/0305154] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order \( {\alpha}_s^4 \) in a General Gauge Theory, Phys. Rev. Lett. 104 (2010) 132004 [arXiv:1001.3606] [INSPIRE].
W.J. Marciano and A. Sirlin, Radiative corrections to pi(lepton 2) decays, Phys. Rev. Lett. 71 (1993) 3629 [INSPIRE].
A. Sirlin, Large m(W), m(Z) Behavior of the O(alpha) Corrections to Semileptonic Processes Mediated by W, Nucl. Phys. B 196 (1982) 83 [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].
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].
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].
A. Bazavov et al., Kaon semileptonic vector form factor and determination of |Vus| using staggered fermions, Phys. Rev. D 87 (2013) 073012 [arXiv:1212.4993] [INSPIRE].
RBC/UKQCD collaboration, The kaon semileptonic form factor in Nf = 2 + 1 domain wall lattice QCD with physical light quark masses, JHEP 06 (2015) 164 [arXiv:1504.01692] [INSPIRE].
A. Bazavov et al., Determination of |Vus| from a Lattice-QCD Calculation of the K → πℓν Semileptonic Form Factor with Physical Quark Masses, Phys. Rev. Lett. 112 (2014) 112001 [arXiv:1312.1228] [INSPIRE].
N. Carrasco, P. Lami, V. Lubicz, L. Riggio, S. Simula and C. Tarantino, K → π semileptonic form factors with Nf = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 93 (2016) 114512 [arXiv:1602.04113] [INSPIRE].
Fermilab Lattice, MILC collaboration, |Vus| from Kℓ3 decay and four-flavor lattice QCD, Phys. Rev. D 99 (2019) 114509 [arXiv:1809.02827] [INSPIRE].
PACS collaboration, Kl3 form factors at the physical point on a (10.9f m)3 volume, Phys. Rev. D 101 (2020) 094504 [arXiv:1912.13127] [INSPIRE].
M. Antonelli et al., Flavor Physics in the Quark Sector, Phys. Rept. 494 (2010) 197 [arXiv:0907.5386] [INSPIRE].
KTeV collaboration, Dispersive analysis of KLμ3 and KLe3 scalar and vector form factors using KTeV data, Phys. Rev. D 81 (2010) 052001 [arXiv:0912.1291] [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].
V. Bernard and E. Passemar, Matching chiral perturbation theory and the dispersive representation of the scalar K π form-factor, Phys. Lett. B 661 (2008) 95 [arXiv:0711.3450] [INSPIRE].
V. Bernard, M. Oertel, E. Passemar and J. Stern, Dispersive representation and shape of the Kl3 form factors: Robustness, Phys. Rev. D 80 (2009) 034034 [arXiv:0903.1654] [INSPIRE].
R.J. Hill, Constraints on the form factors for K → πlν and implications for |Vus|, Phys. Rev. D 74 (2006) 096006 [hep-ph/0607108] [INSPIRE].
J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [INSPIRE].
G. Colangelo, S. Lanz, H. Leutwyler and E. Passemar, Dispersive analysis of η → 3π, Eur. Phys. J. C 78 (2018) 947 [arXiv:1807.11937] [INSPIRE].
C.-Y. Seng, D. Galviz, W.J. Marciano and U.-G. Meißner, An update on |Vus| and |Vus/Vud| from semileptonic kaon and pion decays, arXiv:2107.14708 [INSPIRE].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Chiral Lagrangians for Massive Spin 1 Fields, Phys. Lett. B 223 (1989) 425 [INSPIRE].
V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich and J. Portoles, Towards a consistent estimate of the chiral low-energy constants, Nucl. Phys. B 753 (2006) 139 [hep-ph/0603205] [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
R. Gastmans and R. Meuldermans, Dimensional regularization of the infrared problem, Nucl. Phys. B 63 (1973) 277 [INSPIRE].
W.J. Marciano and A. Sirlin, Dimensional Regularization of Infrared Divergences, Nucl. Phys. B 88 (1975) 86 [INSPIRE].
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Seng, CY., Galviz, D., Gorchtein, M. et al. Improved Ke3 radiative corrections sharpen the Kμ2–Kl3 discrepancy. J. High Energ. Phys. 2021, 172 (2021). https://doi.org/10.1007/JHEP11(2021)172
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DOI: https://doi.org/10.1007/JHEP11(2021)172