{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T00:24:36Z","timestamp":1772497476063,"version":"3.50.1"},"reference-count":157,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>We study Standard Model extensions with isodoublet vector-like quarks with standard charges. Their presence induces right-handed charged and neutral currents. We identify minimal sets of independent parameters characterizing these extensions, describe useful weak bases, and provide parameterizations for all quark mixing. We analyze the intricacies of CP violation in such scenarios, finding a complete set of CP-odd invariants for the single doublet case. Crucially, we uncover a connection between weak-basis invariants and effective rephasing invariants involving only standard quarks. These results allow us to explore the phenomenology of doublet vector-like quarks through a rephasing-invariant analysis, with an emphasis on CP violation, including the potential role of these fields in explaining the Cabibbo angle anomalies.<\/jats:p>","DOI":"10.1007\/jhep08(2025)061","type":"journal-article","created":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T11:45:15Z","timestamp":1754653515000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Vector-like quark doublets, weak-basis invariants and CP violation"],"prefix":"10.1007","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4993-1805","authenticated-orcid":false,"given":"F.","family":"Albergaria","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8660-3456","authenticated-orcid":false,"given":"J. F.","family":"Bastos","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6191-8494","authenticated-orcid":false,"given":"B.","family":"Belfatto","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5974-7043","authenticated-orcid":false,"given":"G. C.","family":"Branco","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8438-3341","authenticated-orcid":false,"given":"J. T.","family":"Penedo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/009wnjh50","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN, Sezione di Roma Tre"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7291-2146","authenticated-orcid":false,"given":"A.","family":"Rodr\u00edguez-S\u00e1nchez","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043nxc105","id-type":"ROR","asserted-by":"publisher"}],"name":"Universitat de Val\u00e8ncia \u2013 CSIC"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2296-7629","authenticated-orcid":false,"given":"J. I.","family":"Silva-Marcos","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]}],"member":"297","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"26920_CR1","doi-asserted-by":"crossref","unstructured":"F. Gursey, P. Ramond and P. Sikivie, A Universal Gauge Theory Model Based on E6, Phys. Lett. B 60 (1976) 177 [INSPIRE].","DOI":"10.1016\/0370-2693(76)90417-2"},{"key":"26920_CR2","doi-asserted-by":"crossref","unstructured":"Y. Achiman and B. Stech, Quark Lepton Symmetry and Mass Scales in an E6 Unified Gauge Model, Phys. Lett. B 77 (1978) 389 [INSPIRE].","DOI":"10.1016\/0370-2693(78)90584-1"},{"key":"26920_CR3","unstructured":"Z.G. Berezhiani and G.R. Dvali, Possible solution of the hierarchy problem in supersymmetrical grand unification theories, Bull. Lebedev Phys. Inst. 5 (1989) 55 [INSPIRE]."},{"key":"26920_CR4","doi-asserted-by":"crossref","unstructured":"R. Barbieri et al., Flavor in supersymmetric grand unification: A Democratic approach, Nucl. Phys. B 432 (1994) 49 [hep-ph\/9405428] [INSPIRE].","DOI":"10.1016\/0550-3213(94)90593-2"},{"key":"26920_CR5","doi-asserted-by":"crossref","unstructured":"Z. Berezhiani, SUSY SU(6) GIFT for doublet-triplet splitting and fermion masses, Phys. Lett. B 355 (1995) 481 [hep-ph\/9503366] [INSPIRE].","DOI":"10.1016\/0370-2693(95)00705-P"},{"key":"26920_CR6","doi-asserted-by":"crossref","unstructured":"L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph\/9905221] [INSPIRE].","DOI":"10.1103\/PhysRevLett.83.3370"},{"key":"26920_CR7","doi-asserted-by":"crossref","unstructured":"N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513 (2001) 232 [hep-ph\/0105239] [INSPIRE].","DOI":"10.1016\/S0370-2693(01)00741-9"},{"key":"26920_CR8","doi-asserted-by":"crossref","unstructured":"N. Arkani-Hamed, A.G. Cohen, T. Gregoire and J.G. Wacker, Phenomenology of electroweak symmetry breaking from theory space, JHEP 08 (2002) 020 [hep-ph\/0202089] [INSPIRE].","DOI":"10.1088\/1126-6708\/2002\/08\/020"},{"key":"26920_CR9","doi-asserted-by":"crossref","unstructured":"M. Perelstein, M.E. Peskin and A. Pierce, Top quarks and electroweak symmetry breaking in little Higgs models, Phys. Rev. D 69 (2004) 075002 [hep-ph\/0310039] [INSPIRE].","DOI":"10.1103\/PhysRevD.69.075002"},{"key":"26920_CR10","doi-asserted-by":"crossref","unstructured":"T. Han, H.E. Logan, B. McElrath and L.-T. Wang, Phenomenology of the little Higgs model, Phys. Rev. D 67 (2003) 095004 [hep-ph\/0301040] [INSPIRE].","DOI":"10.1103\/PhysRevD.67.095004"},{"key":"26920_CR11","doi-asserted-by":"crossref","unstructured":"S. Fajfer, A. Greljo, J.F. Kamenik and I. Mustac, Light Higgs and Vector-like Quarks without Prejudice, JHEP 07 (2013) 155 [arXiv:1304.4219] [INSPIRE].","DOI":"10.1007\/JHEP07(2013)155"},{"key":"26920_CR12","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani, The Weak Mixing Angles in Gauge Models with Horizontal Symmetry: A New Approach to Quark and Lepton Masses, Phys. Lett. B 129 (1983) 99 [INSPIRE].","DOI":"10.1016\/0370-2693(83)90737-2"},{"key":"26920_CR13","doi-asserted-by":"crossref","unstructured":"S. Dimopoulos, Natural Generation of Fermion Masses, Phys. Lett. B 129 (1983) 417 [INSPIRE].","DOI":"10.1016\/0370-2693(83)90132-6"},{"key":"26920_CR14","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani, Horizontal Symmetry and Quark-Lepton Mass Spectrum: The SU(5)SU(3)-h Model, Phys. Lett. B 150 (1985) 177 [INSPIRE].","DOI":"10.1016\/0370-2693(85)90164-9"},{"key":"26920_CR15","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani and R. Rattazzi, Universal seesaw and radiative quark mass hierarchy, Phys. Lett. B 279 (1992) 124 [INSPIRE].","DOI":"10.1016\/0370-2693(92)91851-Y"},{"key":"26920_CR16","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani and R. Rattazzi, Inverse hierarchy approach to fermion masses, Nucl. Phys. B 407 (1993) 249 [hep-ph\/9212245] [INSPIRE].","DOI":"10.1016\/0550-3213(93)90057-V"},{"key":"26920_CR17","doi-asserted-by":"crossref","unstructured":"Z. Berezhiani and A. Rossi, Predictive grand unified textures for quark and neutrino masses and mixings, Nucl. Phys. B 594 (2001) 113 [hep-ph\/0003084] [INSPIRE].","DOI":"10.1016\/S0550-3213(00)00653-2"},{"key":"26920_CR18","unstructured":"Z.G. Berezhiani and J.L. Chkareuli, Low-energy horizontal symmetry of SU(3)-H \u00d7 U(1)-H and $$ B\\overline{B} $$ oscillation (in Russian), Sov. J. Nucl. Phys. 52 (1990) 383 [INSPIRE]."},{"key":"26920_CR19","doi-asserted-by":"crossref","unstructured":"Z. Berezhiani, Unified picture of the particle and sparticle masses in SUSY GUT, Phys. Lett. B 417 (1998) 287 [hep-ph\/9609342] [INSPIRE].","DOI":"10.1016\/S0370-2693(97)01359-2"},{"key":"26920_CR20","doi-asserted-by":"crossref","unstructured":"A. Anselm and Z. Berezhiani, Weak mixing angles as dynamical degrees of freedom, Nucl. Phys. B 484 (1997) 97 [hep-ph\/9605400] [INSPIRE].","DOI":"10.1016\/S0550-3213(96)00597-4"},{"key":"26920_CR21","doi-asserted-by":"crossref","unstructured":"Z. Berezhiani and A. Rossi, Flavor structure, flavor symmetry and supersymmetry, Nucl. Phys. B Proc. Suppl. 101 (2001) 410 [hep-ph\/0107054] [INSPIRE].","DOI":"10.1016\/S0920-5632(01)01527-4"},{"key":"26920_CR22","doi-asserted-by":"crossref","unstructured":"J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].","DOI":"10.1103\/PhysRevLett.43.103"},{"key":"26920_CR23","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani and M.Y. Khlopov, Cosmology of Spontaneously Broken Gauge Family Symmetry, Z. Phys. C 49 (1991) 73 [INSPIRE].","DOI":"10.1007\/BF01570798"},{"key":"26920_CR24","doi-asserted-by":"crossref","unstructured":"A.E. Nelson, Naturally Weak CP Violation, Phys. Lett. B 136 (1984) 387 [INSPIRE].","DOI":"10.1016\/0370-2693(84)92025-2"},{"key":"26920_CR25","doi-asserted-by":"crossref","unstructured":"S.M. Barr, Solving the Strong CP Problem Without the Peccei-Quinn Symmetry, Phys. Rev. Lett. 53 (1984) 329 [INSPIRE].","DOI":"10.1103\/PhysRevLett.53.329"},{"key":"26920_CR26","doi-asserted-by":"crossref","unstructured":"K.S. Babu and R.N. Mohapatra, A solution to the Strong CP Problem Without an Axion, Phys. Rev. D 41 (1990) 1286 [INSPIRE].","DOI":"10.1103\/PhysRevD.41.1286"},{"key":"26920_CR27","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani, On the possibility of a solution to the strong CP problem without axion in a SU(3)-M family symmetry model, Mod. Phys. Lett. A 6 (1991) 2437 [INSPIRE].","DOI":"10.1142\/S0217732391002864"},{"key":"26920_CR28","doi-asserted-by":"crossref","unstructured":"Z.G. Berezhiani, R.N. Mohapatra and G. Senjanovic, Planck scale physics and solutions to the strong CP problem without axion, Phys. Rev. D 47 (1993) 5565 [hep-ph\/9212318] [INSPIRE].","DOI":"10.1103\/PhysRevD.47.5565"},{"key":"26920_CR29","doi-asserted-by":"crossref","unstructured":"L. Vecchi, Spontaneous CP violation and the strong CP problem, JHEP 04 (2017) 149 [arXiv:1412.3805] [INSPIRE].","DOI":"10.1007\/JHEP04(2017)149"},{"key":"26920_CR30","unstructured":"R. Kuchimanchi, P and CP solution of the strong CP puzzle, Phys. Rev. D 108 (2023) 095023 [arXiv:2306.03039] [INSPIRE]."},{"key":"26920_CR31","doi-asserted-by":"crossref","unstructured":"G.C. Branco and L. Lavoura, On the Addition of Vector Like Quarks to the Standard Model, Nucl. Phys. B 278 (1986) 738 [INSPIRE].","DOI":"10.1016\/0550-3213(86)90060-X"},{"key":"26920_CR32","doi-asserted-by":"crossref","unstructured":"F. del Aguila, L. Ametller, G.L. Kane and J. Vidal, Vector Like Fermion and Standard Higgs Production at Hadron Colliders, Nucl. Phys. B 334 (1990) 1 [INSPIRE].","DOI":"10.1016\/0550-3213(90)90655-W"},{"key":"26920_CR33","doi-asserted-by":"crossref","unstructured":"Y. Nir and D.J. Silverman, Z Mediated Flavor Changing Neutral Currents and Their Implications for CP Asymmetries in D0 Decays, Phys. Rev. D 42 (1990) 1477 [INSPIRE].","DOI":"10.1103\/PhysRevD.42.1477"},{"key":"26920_CR34","doi-asserted-by":"crossref","unstructured":"F. del Aguila, M. P\u00e9rez-Victoria and J. Santiago, Observable contributions of new exotic quarks to quark mixing, JHEP 09 (2000) 011 [hep-ph\/0007316] [INSPIRE].","DOI":"10.1088\/1126-6708\/2000\/09\/011"},{"key":"26920_CR35","doi-asserted-by":"crossref","unstructured":"G. Barenboim, F.J. Botella and O. Vives, Constraining Models with Vector-Like Fermions from FCNC in K and B Physics, Nucl. Phys. B 613 (2001) 285 [hep-ph\/0105306] [INSPIRE].","DOI":"10.1016\/S0550-3213(01)00390-X"},{"key":"26920_CR36","doi-asserted-by":"crossref","unstructured":"G. Cacciapaglia, A. Deandrea, D. Harada and Y. Okada, Bounds and Decays of New Heavy Vector-like Top Partners, JHEP 11 (2010) 159 [arXiv:1007.2933] [INSPIRE].","DOI":"10.1007\/JHEP11(2010)159"},{"key":"26920_CR37","doi-asserted-by":"crossref","unstructured":"F.J. Botella, G.C. Branco and M. Nebot, The Hunt for New Physics in the Flavour Sector with up vector-like quarks, JHEP 12 (2012) 040 [arXiv:1207.4440] [INSPIRE].","DOI":"10.1007\/JHEP12(2012)040"},{"key":"26920_CR38","doi-asserted-by":"crossref","unstructured":"K. Ishiwata, Z. Ligeti and M.B. Wise, New Vector-Like Fermions and Flavor Physics, JHEP 10 (2015) 027 [arXiv:1506.03484] [INSPIRE].","DOI":"10.1007\/JHEP10(2015)027"},{"key":"26920_CR39","doi-asserted-by":"crossref","unstructured":"W. Wang, Z.-H. Xiong and X.-Y. Zhao, General scan in flavor parameter space in models with vector quark doublets and an enhancement in the B \u2192 Xs\u03b3 process, Chin. Phys. C 40 (2016) 093102 [arXiv:1603.05756] [INSPIRE].","DOI":"10.1088\/1674-1137\/40\/9\/093102"},{"key":"26920_CR40","doi-asserted-by":"crossref","unstructured":"A. Biek\u00f6tter et al., Complementarity of Resonant Scalar, Vector-Like Quark and Superpartner Searches in Elucidating New Phenomena, Int. J. Mod. Phys. A 32 (2017) 1750032 [arXiv:1608.01312] [INSPIRE].","DOI":"10.1142\/S0217751X17500324"},{"key":"26920_CR41","doi-asserted-by":"crossref","unstructured":"C. Bobeth, A.J. Buras, A. Celis and M. Jung, Patterns of Flavour Violation in Models with Vector-Like Quarks, JHEP 04 (2017) 079 [arXiv:1609.04783] [INSPIRE].","DOI":"10.1007\/JHEP04(2017)079"},{"key":"26920_CR42","doi-asserted-by":"crossref","unstructured":"F.J. Botella et al., Vector-like Quarks at the Origin of Light Quark Masses and Mixing, Eur. Phys. J. C 77 (2017) 408 [arXiv:1610.03018] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-017-4933-3"},{"key":"26920_CR43","doi-asserted-by":"crossref","unstructured":"G. Cacciapaglia et al., The LHC potential of Vector-like quark doublets, JHEP 11 (2018) 055 [arXiv:1806.01024] [INSPIRE].","DOI":"10.1007\/JHEP11(2018)055"},{"key":"26920_CR44","doi-asserted-by":"crossref","unstructured":"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].","DOI":"10.1140\/epjc\/s10052-020-7691-6"},{"key":"26920_CR45","doi-asserted-by":"crossref","unstructured":"B. Belfatto and Z. Berezhiani, Are the CKM anomalies induced by vector-like quarks? Limits from flavor changing and Standard Model precision tests, JHEP 10 (2021) 079 [arXiv:2103.05549] [INSPIRE].","DOI":"10.1007\/JHEP10(2021)079"},{"key":"26920_CR46","doi-asserted-by":"crossref","unstructured":"G.C. Branco et al., Addressing the CKM unitarity problem with a vector-like up quark, JHEP 07 (2021) 099 [arXiv:2103.13409] [INSPIRE].","DOI":"10.1007\/JHEP07(2021)099"},{"key":"26920_CR47","doi-asserted-by":"crossref","unstructured":"S. Balaji, Asymmetry in flavour changing electromagnetic transitions of vector-like quarks, JHEP 05 (2022) 015 [arXiv:2110.05473] [INSPIRE].","DOI":"10.1007\/JHEP05(2022)015"},{"key":"26920_CR48","doi-asserted-by":"crossref","unstructured":"F.J. Botella et al., Decays of the heavy top and new insights on \u03f5K in a one-VLQ minimal solution to the CKM unitarity problem, Eur. Phys. J. C 82 (2022) 360 [Erratum ibid. 82 (2022) 423] [arXiv:2111.15401] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-022-10398-7"},{"key":"26920_CR49","doi-asserted-by":"crossref","unstructured":"B. Belfatto and S. Trifinopoulos, Cabibbo angle anomalies and oblique corrections: The remarkable role of the vectorlike quark doublet, Phys. Rev. D 108 (2023) 035022 [arXiv:2302.14097] [INSPIRE].","DOI":"10.1103\/PhysRevD.108.035022"},{"key":"26920_CR50","doi-asserted-by":"crossref","unstructured":"R. Cepedello, F. Esser, M. Hirsch and V. Sanz, Faking ZZZ vertices at the LHC, JHEP 12 (2024) 098 [arXiv:2409.06776] [INSPIRE].","DOI":"10.1007\/JHEP12(2024)098"},{"key":"26920_CR51","doi-asserted-by":"crossref","unstructured":"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].","DOI":"10.1007\/JHEP05(2020)117"},{"key":"26920_CR52","doi-asserted-by":"crossref","unstructured":"M. Endo and S. Mishima, Muon g \u2013 2 and CKM unitarity in extra lepton models, JHEP 08 (2020) 004 [arXiv:2005.03933] [INSPIRE].","DOI":"10.1007\/JHEP08(2020)004"},{"key":"26920_CR53","doi-asserted-by":"crossref","unstructured":"A. Crivellin, F. Kirk, C.A. Manzari and M. Montull, Global Electroweak Fit and Vector-Like Leptons in Light of the Cabibbo Angle Anomaly, JHEP 12 (2020) 166 [arXiv:2008.01113] [INSPIRE].","DOI":"10.1007\/JHEP12(2020)166"},{"key":"26920_CR54","doi-asserted-by":"crossref","unstructured":"A. Crivellin, M. Kirk, T. Kitahara and F. Mescia, Global fit of modified quark couplings to EW gauge bosons and vector-like quarks in light of the Cabibbo angle anomaly, JHEP 03 (2023) 234 [arXiv:2212.06862] [INSPIRE].","DOI":"10.1007\/JHEP03(2023)234"},{"key":"26920_CR55","doi-asserted-by":"crossref","unstructured":"R. Dcruz and K.S. Babu, Resolving W boson mass shift and CKM unitarity violation in left-right symmetric models with a universal seesaw mechanism, Phys. Rev. D 108 (2023) 095011 [arXiv:2212.09697] [INSPIRE].","DOI":"10.1103\/PhysRevD.108.095011"},{"key":"26920_CR56","doi-asserted-by":"crossref","unstructured":"J.M. Alves et al., Vector-like singlet quarks: A roadmap, Phys. Rept. 1057 (2024) 1 [arXiv:2304.10561] [INSPIRE].","DOI":"10.1016\/j.physrep.2023.12.004"},{"key":"26920_CR57","doi-asserted-by":"crossref","unstructured":"F. del Aguila, M. P\u00e9rez-Victoria and J. Santiago, Effective description of quark mixing, Phys. Lett. B 492 (2000) 98 [hep-ph\/0007160] [INSPIRE].","DOI":"10.1016\/S0370-2693(00)01071-6"},{"key":"26920_CR58","doi-asserted-by":"crossref","unstructured":"J.A. Aguilar-Saavedra, R. Benbrik, S. Heinemeyer and M. P\u00e9rez-Victoria, Handbook of vectorlike quarks: Mixing and single production, Phys. Rev. D 88 (2013) 094010 [arXiv:1306.0572] [INSPIRE].","DOI":"10.1103\/PhysRevD.88.094010"},{"key":"26920_CR59","doi-asserted-by":"crossref","unstructured":"V. Cirigliano et al., Anomalies in global SMEFT analyses. A case study of first-row CKM unitarity, JHEP 03 (2024) 033 [arXiv:2311.00021] [INSPIRE].","DOI":"10.1007\/JHEP03(2024)033"},{"key":"26920_CR60","doi-asserted-by":"crossref","unstructured":"J. Bernabeu, G.C. Branco and M. Gronau, CP Restrictions on Quark Mass Matrices, Phys. Lett. B 169 (1986) 243 [INSPIRE].","DOI":"10.1016\/0370-2693(86)90659-3"},{"key":"26920_CR61","doi-asserted-by":"crossref","unstructured":"M. Gronau, A. Kfir and R. Loewy, Basis Independent Tests of CP Violation in Fermion Mass Matrices, Phys. Rev. Lett. 56 (1986) 1538 [INSPIRE].","DOI":"10.1103\/PhysRevLett.56.1538"},{"key":"26920_CR62","doi-asserted-by":"crossref","unstructured":"M. Olechowski and S. Pokorski, Some Useful Invariants of Quark Mass Matrices, Phys. Lett. B 231 (1989) 165 [INSPIRE].","DOI":"10.1016\/0370-2693(89)90132-9"},{"key":"26920_CR63","doi-asserted-by":"crossref","unstructured":"F. del Aguila and J.A. Aguilar-Saavedra, Invariant formulation of CP violation for four quark families, Phys. Lett. B 386 (1996) 241 [hep-ph\/9605418] [INSPIRE].","DOI":"10.1016\/0370-2693(96)00939-2"},{"key":"26920_CR64","doi-asserted-by":"crossref","unstructured":"F. del Aguila, J.A. Aguilar-Saavedra and G.C. Branco, CP violation from new quarks in the chiral limit, Nucl. Phys. B 510 (1998) 39 [hep-ph\/9703410] [INSPIRE].","DOI":"10.1016\/S0550-3213(98)81003-1"},{"key":"26920_CR65","doi-asserted-by":"crossref","unstructured":"G.C. Branco and J.I. Silva-Marcos, Invariants, Alignment and the Pattern of Fermion Masses and Mixing, Phys. Lett. B 715 (2012) 315 [arXiv:1112.1631] [INSPIRE].","DOI":"10.1016\/j.physletb.2012.07.064"},{"key":"26920_CR66","doi-asserted-by":"crossref","unstructured":"F. Albergaria, G.C. Branco, J.F. Bastos and J.I. Silva-Marcos, CP-odd and CP-even weak-basis invariants in the presence of vector-like quarks, J. Phys. G 50 (2023) 055001 [arXiv:2210.14248] [INSPIRE].","DOI":"10.1088\/1361-6471\/acc349"},{"key":"26920_CR67","doi-asserted-by":"crossref","unstructured":"M.P. Bento, J.P. Silva and A. Trautner, The basis invariant flavor puzzle, JHEP 01 (2024) 024 [arXiv:2308.00019] [INSPIRE].","DOI":"10.1007\/JHEP01(2024)024"},{"key":"26920_CR68","doi-asserted-by":"crossref","unstructured":"E.L.F. de Lima and C.C. Nishi, Flavor invariants for the SM with one singlet vector-like quark, JHEP 11 (2024) 157 [arXiv:2408.10325] [INSPIRE].","DOI":"10.1007\/JHEP11(2024)157"},{"key":"26920_CR69","doi-asserted-by":"publisher","unstructured":"G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Oxford University Press (1999) [https:\/\/doi.org\/10.1093\/oso\/9780198503996.001.0001].","DOI":"10.1093\/oso\/9780198503996.001.0001"},{"key":"26920_CR70","doi-asserted-by":"crossref","unstructured":"C.-Y. Chen, S. Dawson and Y. Zhang, Higgs CP Violation from Vectorlike Quarks, Phys. Rev. D 92 (2015) 075026 [arXiv:1507.07020] [INSPIRE].","DOI":"10.1103\/PhysRevD.92.075026"},{"key":"26920_CR71","unstructured":"J.F. Bastos and J.I. Silva-Marcos, Reducing Complex Phases and other Subtleties of CP Violation, arXiv:2407.07158 [INSPIRE]."},{"key":"26920_CR72","unstructured":"J.I. Silva-Marcos, On the reduction of CP violation phases, hep-ph\/0212089 [INSPIRE]."},{"key":"26920_CR73","doi-asserted-by":"crossref","unstructured":"C. Jarlskog, Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Nonconservation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].","DOI":"10.1103\/PhysRevLett.55.1039"},{"key":"26920_CR74","doi-asserted-by":"crossref","unstructured":"C. Jarlskog, A Basis Independent Formulation of the Connection Between Quark Mass Matrices, CP Violation and Experiment, Z. Phys. C 29 (1985) 491 [INSPIRE].","DOI":"10.1007\/BF01565198"},{"key":"26920_CR75","unstructured":"ATLAS collaboration, Search for pair-produced vectorlike quarks coupling to light quarks in the lepton plus jets final state using 13 TeV pp collisions with the ATLAS detector, Phys. Rev. D 110 (2024) 052009 [arXiv:2405.19862] [INSPIRE]."},{"key":"26920_CR76","unstructured":"ATLAS collaboration, Search for pair-production of vector-like quarks in pp collision events at s=13 TeV with at least one leptonically decaying Z boson and a third-generation quark with the ATLAS detector, Phys. Lett. B 843 (2023) 138019 [arXiv:2210.15413] [INSPIRE]."},{"key":"26920_CR77","unstructured":"CMS collaboration, Search for pair production of vector-like quarks in leptonic final states in proton-proton collisions at $$ \\sqrt{s} $$ = 13 TeV, JHEP 07 (2023) 020 [arXiv:2209.07327] [INSPIRE]."},{"key":"26920_CR78","unstructured":"CMS collaboration, A search for bottom-type, vector-like quark pair production in a fully hadronic final state in proton-proton collisions at $$ \\sqrt{s} $$ = 13 TeV, Phys. Rev. D 102 (2020) 112004 [arXiv:2008.09835] [INSPIRE]."},{"key":"26920_CR79","doi-asserted-by":"crossref","unstructured":"S.L. Glashow, J. Iliopoulos and L. Maiani, Weak Interactions with Lepton-Hadron Symmetry, Phys. Rev. D 2 (1970) 1285 [INSPIRE].","DOI":"10.1103\/PhysRevD.2.1285"},{"key":"26920_CR80","doi-asserted-by":"crossref","unstructured":"S.L. Glashow and S. Weinberg, Natural Conservation Laws for Neutral Currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE].","DOI":"10.1103\/PhysRevD.15.1958"},{"key":"26920_CR81","doi-asserted-by":"crossref","unstructured":"E.A. Paschos, Diagonal Neutral Currents, Phys. Rev. D 15 (1977) 1966 [INSPIRE].","DOI":"10.1103\/PhysRevD.15.1966"},{"key":"26920_CR82","doi-asserted-by":"crossref","unstructured":"C.Y. Seng, M. Gorchtein and M.J. Ramsey-Musolf, Dispersive evaluation of the inner radiative correction in neutron and nuclear \u03b2 decay, Phys. Rev. D 100 (2019) 013001 [arXiv:1812.03352] [INSPIRE].","DOI":"10.1103\/PhysRevD.100.013001"},{"key":"26920_CR83","doi-asserted-by":"crossref","unstructured":"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].","DOI":"10.1103\/PhysRevLett.121.241804"},{"key":"26920_CR84","unstructured":"J.C. Hardy and I.S. Towner, Superallowed 0+ \u2192 0+ nuclear \u03b2 decays: 2020 critical survey, with implications for Vud and CKM unitarity, Phys. Rev. C 102 (2020) 045501 [INSPIRE]."},{"key":"26920_CR85","doi-asserted-by":"crossref","unstructured":"M. Gorchtein, \u03b3W Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum, Phys. Rev. Lett. 123 (2019) 042503 [arXiv:1812.04229] [INSPIRE].","DOI":"10.1103\/PhysRevLett.123.042503"},{"key":"26920_CR86","unstructured":"UCN\u03c4 collaboration, Improved neutron lifetime measurement with UCN\u03c4 , Phys. Rev. Lett. 127 (2021) 162501 [arXiv:2106.10375] [INSPIRE]."},{"key":"26920_CR87","doi-asserted-by":"crossref","unstructured":"V.F. Ezhov et al., Measurement of the neutron lifetime with ultra-cold neutrons stored in a magneto-gravitational trap, JETP Lett. 107 (2018) 671 [arXiv:1412.7434] [INSPIRE].","DOI":"10.1134\/S0021364018110024"},{"key":"26920_CR88","doi-asserted-by":"crossref","unstructured":"R.W. Pattie Jr. et al., Measurement of the neutron lifetime using a magneto-gravitational trap and in situ detection, Science 360 (2018) 627 [arXiv:1707.01817] [INSPIRE].","DOI":"10.1126\/science.aan8895"},{"key":"26920_CR89","unstructured":"A.P. Serebrov et al., Neutron lifetime measurements with a large gravitational trap for ultracold neutrons, Phys. Rev. C 97 (2018) 055503 [arXiv:1712.05663] [INSPIRE]."},{"key":"26920_CR90","doi-asserted-by":"crossref","unstructured":"S. Arzumanov et al., A measurement of the neutron lifetime using the method of storage of ultracold neutrons and detection of inelastically up-scattered neutrons, Phys. Lett. B 745 (2015) 79 [INSPIRE].","DOI":"10.1016\/j.physletb.2015.04.021"},{"key":"26920_CR91","doi-asserted-by":"crossref","unstructured":"A. Steyerl et al., Quasielastic scattering in the interaction of ultracold neutrons with a liquid wall and application in a reanalysis of the Mambo I neutron-lifetime experiment, Phys. Rev. C 85 (2012) 065503 [INSPIRE].","DOI":"10.1103\/PhysRevC.85.065503"},{"key":"26920_CR92","doi-asserted-by":"crossref","unstructured":"A. Pichlmaier, V. Varlamov, K. Schreckenbach and P. Geltenbort, Neutron lifetime measurement with the UCN trap-in-trap MAMBO II, Phys. Lett. B 693 (2010) 221 [INSPIRE].","DOI":"10.1016\/j.physletb.2010.08.032"},{"key":"26920_CR93","doi-asserted-by":"crossref","unstructured":"A. Serebrov et al., Measurement of the neutron lifetime using a gravitational trap and a low-temperature Fomblin coating, Phys. Lett. B 605 (2005) 72 [nucl-ex\/0408009] [INSPIRE].","DOI":"10.1016\/j.physletb.2004.11.013"},{"key":"26920_CR94","unstructured":"D. Mund et al., Determination of the Weak Axial Vector Coupling from a Measurement of the Beta-Asymmetry Parameter A in Neutron Beta Decay, Phys. Rev. Lett. 110 (2013) 172502 [arXiv:1204.0013] [INSPIRE]."},{"key":"26920_CR95","unstructured":"UCNA collaboration, New result for the neutron \u03b2-asymmetry parameter A0 from UCNA, Phys. Rev. C 97 (2018) 035505 [arXiv:1712.00884] [INSPIRE]."},{"key":"26920_CR96","doi-asserted-by":"crossref","unstructured":"B. M\u00e4rkisch et al., Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam, Phys. Rev. Lett. 122 (2019) 242501 [arXiv:1812.04666] [INSPIRE].","DOI":"10.1103\/PhysRevLett.122.242501"},{"key":"26920_CR97","doi-asserted-by":"crossref","unstructured":"Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-022-10536-1"},{"key":"26920_CR98","unstructured":"Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2024, arXiv:2411.04268 [INSPIRE]."},{"key":"26920_CR99","doi-asserted-by":"crossref","unstructured":"C.-Y. Seng, D. Galviz, W.J. Marciano and U.-G. Mei\u00dfner, Update on |Vus| and |Vus\/Vud| from semileptonic kaon and pion decays, Phys. Rev. D 105 (2022) 013005 [arXiv:2107.14708] [INSPIRE].","DOI":"10.1007\/JHEP07(2022)071"},{"key":"26920_CR100","doi-asserted-by":"crossref","unstructured":"C.-Y. Seng, D. Galviz, M. Gorchtein and U.-G. Mei\u00dfner, Complete theory of radiative corrections to K\u21133 decays and the Vus update, JHEP 07 (2022) 071 [arXiv:2203.05217] [INSPIRE].","DOI":"10.1007\/JHEP07(2022)071"},{"key":"26920_CR101","doi-asserted-by":"crossref","unstructured":"M. Moulson, Experimental determination of Vus from kaon decays, PoS CKM2016 (2017) 033 [arXiv:1704.04104] [INSPIRE].","DOI":"10.22323\/1.291.0033"},{"key":"26920_CR102","doi-asserted-by":"crossref","unstructured":"W.J. Marciano, Precise determination of |Vus| from lattice calculations of pseudoscalar decay constants, Phys. Rev. Lett. 93 (2004) 231803 [hep-ph\/0402299] [INSPIRE].","DOI":"10.1103\/PhysRevLett.93.231803"},{"key":"26920_CR103","doi-asserted-by":"crossref","unstructured":"V. Cirigliano and H. Neufeld, A note on isospin violation in Pl2(gamma) decays, Phys. Lett. B 700 (2011) 7 [arXiv:1102.0563] [INSPIRE].","DOI":"10.1016\/j.physletb.2011.04.038"},{"key":"26920_CR104","doi-asserted-by":"crossref","unstructured":"M. Di Carlo et al., Light-meson leptonic decay rates in lattice QCD+QED, Phys. Rev. D 100 (2019) 034514 [arXiv:1904.08731] [INSPIRE].","DOI":"10.1103\/PhysRevD.100.034514"},{"key":"26920_CR105","doi-asserted-by":"crossref","unstructured":"P. Boyle et al., Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses, JHEP 02 (2023) 242 [arXiv:2211.12865] [INSPIRE].","DOI":"10.1007\/JHEP02(2023)242"},{"key":"26920_CR106","doi-asserted-by":"crossref","unstructured":"Y. Grossman, E. Passemar and S. Schacht, On the Statistical Treatment of the Cabibbo Angle Anomaly, JHEP 07 (2020) 068 [arXiv:1911.07821] [INSPIRE].","DOI":"10.1007\/JHEP07(2020)068"},{"key":"26920_CR107","doi-asserted-by":"crossref","unstructured":"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].","DOI":"10.1103\/PhysRevLett.125.071802"},{"key":"26920_CR108","doi-asserted-by":"crossref","unstructured":"A. Crivellin and M. Hoferichter, \u03b2 Decays as Sensitive Probes of Lepton Flavor Universality, Phys. Rev. Lett. 125 (2020) 111801 [arXiv:2002.07184] [INSPIRE].","DOI":"10.1103\/PhysRevLett.125.111801"},{"key":"26920_CR109","doi-asserted-by":"crossref","unstructured":"B. Capdevila, A. Crivellin, C.A. Manzari and M. Montull, Explaining b \u2192 s\u2113+\u2113\u2212 and the Cabibbo angle anomaly with a vector triplet, Phys. Rev. D 103 (2021) 015032 [arXiv:2005.13542] [INSPIRE].","DOI":"10.1103\/PhysRevD.103.015032"},{"key":"26920_CR110","doi-asserted-by":"crossref","unstructured":"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].","DOI":"10.1103\/PhysRevD.103.035004"},{"key":"26920_CR111","doi-asserted-by":"crossref","unstructured":"C.A. Manzari, A.M. Coutinho and A. Crivellin, Modified lepton couplings and the Cabibbo-angle anomaly, PoS LHCP2020 (2021) 242 [arXiv:2009.03877] [INSPIRE].","DOI":"10.22323\/1.382.0242"},{"key":"26920_CR112","doi-asserted-by":"crossref","unstructured":"A.K. Alok, A. Dighe, S. Gangal and J. Kumar, The role of non-universal Z couplings in explaining the Vus anomaly, Nucl. Phys. B 971 (2021) 115538 [arXiv:2010.12009] [INSPIRE].","DOI":"10.1016\/j.nuclphysb.2021.115538"},{"key":"26920_CR113","unstructured":"A. Crivellin, C.A. Manzari, M. Alguero and J. Matias, Combined Explanation of the $$ Z\\to b\\overline{b} $$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, and \u03c4 \u2192 \u03bc\u03bd\u03bd and b \u2192 s\u2113+\u2113\u2212 Data, Phys. Rev. Lett. 127 (2021) 011801 [arXiv:2010.14504] [INSPIRE]."},{"key":"26920_CR114","doi-asserted-by":"crossref","unstructured":"A. Crivellin, F. Kirk, C.A. Manzari and L. Panizzi, Searching for lepton flavor universality violation and collider signals from a singly charged scalar singlet, Phys. Rev. D 103 (2021) 073002 [arXiv:2012.09845] [INSPIRE].","DOI":"10.1103\/PhysRevD.103.073002"},{"key":"26920_CR115","doi-asserted-by":"crossref","unstructured":"A. Crivellin, M. Hoferichter and C.A. Manzari, Fermi Constant from Muon Decay Versus Electroweak Fits and Cabibbo-Kobayashi-Maskawa Unitarity, Phys. Rev. Lett. 127 (2021) 071801 [arXiv:2102.02825] [INSPIRE].","DOI":"10.1103\/PhysRevLett.127.071801"},{"key":"26920_CR116","doi-asserted-by":"crossref","unstructured":"D. Marzocca and S. Trifinopoulos, Minimal Explanation of Flavor Anomalies: B-Meson Decays, Muon Magnetic Moment, and the Cabibbo Angle, Phys. Rev. Lett. 127 (2021) 061803 [arXiv:2104.05730] [INSPIRE].","DOI":"10.1103\/PhysRevLett.127.061803"},{"key":"26920_CR117","doi-asserted-by":"crossref","unstructured":"O. Fischer et al., Unveiling hidden physics at the LHC, Eur. Phys. J. C 82 (2022) 665 [arXiv:2109.06065] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-022-10541-4"},{"key":"26920_CR118","doi-asserted-by":"crossref","unstructured":"A. Pich and A. Rodr\u00edguez-S\u00e1nchez, SU(3) analysis of four-quark operators: K \u2192 \u03c0\u03c0 and vacuum matrix elements, JHEP 06 (2021) 005 [arXiv:2102.09308] [INSPIRE].","DOI":"10.1007\/JHEP06(2021)005"},{"key":"26920_CR119","unstructured":"T. Blum et al., Lattice determination of the K \u2192 (\u03c0\u03c0)I=2 Decay Amplitude A2, Phys. Rev. D 86 (2012) 074513 [arXiv:1206.5142] [INSPIRE]."},{"key":"26920_CR120","unstructured":"RBC and UKQCD collaborations, Standard Model Prediction for Direct CP Violation in K\u2192\u03c0\u03c0 Decay, Phys. Rev. Lett. 115 (2015) 212001 [arXiv:1505.07863] [INSPIRE]."},{"key":"26920_CR121","unstructured":"RBC and UKQCD collaborations, Direct CP violation and the \u2206I = 1\/2 rule in K \u2192 \u03c0\u03c0 decay from the standard model, Phys. Rev. D 102 (2020) 054509 [arXiv:2004.09440] [INSPIRE]."},{"key":"26920_CR122","doi-asserted-by":"crossref","unstructured":"S. Bertolini, A. Maiezza and F. Nesti, K \u2192 \u03c0\u03c0 hadronic matrix elements of left-right current-current operators, Phys. Rev. D 88 (2013) 034014 [arXiv:1305.5739] [INSPIRE].","DOI":"10.1103\/PhysRevD.88.034014"},{"key":"26920_CR123","doi-asserted-by":"crossref","unstructured":"V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, An \u03f5\u2032 improvement from right-handed currents, Phys. Lett. B 767 (2017) 1 [arXiv:1612.03914] [INSPIRE].","DOI":"10.1016\/j.physletb.2017.01.037"},{"key":"26920_CR124","doi-asserted-by":"crossref","unstructured":"P. Chen, H. Ke and X. Ji, Direct CP Violation in K-decay and Minimal Left-Right Symmetry Scale, Phys. Lett. B 677 (2009) 157 [arXiv:0810.2576] [INSPIRE].","DOI":"10.1016\/j.physletb.2009.04.016"},{"key":"26920_CR125","doi-asserted-by":"crossref","unstructured":"Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 110 (2024) 030001 [INSPIRE].","DOI":"10.1103\/PhysRevD.110.030001"},{"key":"26920_CR126","doi-asserted-by":"crossref","unstructured":"H. Gisbert and A. Pich, Direct CP violation in K0 \u2192 \u03c0\u03c0: Standard Model Status, Rept. Prog. Phys. 81 (2018) 076201 [arXiv:1712.06147] [INSPIRE].","DOI":"10.1088\/1361-6633\/aac18e"},{"key":"26920_CR127","doi-asserted-by":"crossref","unstructured":"V. Cirigliano, H. Gisbert, A. Pich and A. Rodr\u00edguez-S\u00e1nchez, Theoretical status of \u03b5\u2032\/\u03b5, J. Phys. Conf. Ser. 1526 (2020) 012011 [arXiv:1912.04736] [INSPIRE].","DOI":"10.1088\/1742-6596\/1526\/1\/012011"},{"key":"26920_CR128","doi-asserted-by":"crossref","unstructured":"V. Cirigliano, H. Gisbert, A. Pich and A. Rodr\u00edguez-S\u00e1nchez, Isospin-violating contributions to \u03f5\u2032\/\u03f5, JHEP 02 (2020) 032 [arXiv:1911.01359] [INSPIRE].","DOI":"10.1007\/JHEP02(2020)032"},{"key":"26920_CR129","unstructured":"C. Abel et al., Measurement of the Permanent Electric Dipole Moment of the Neutron, Phys. Rev. Lett. 124 (2020) 081803 [arXiv:2001.11966] [INSPIRE]."},{"key":"26920_CR130","doi-asserted-by":"crossref","unstructured":"B.K. Sahoo, Improved limits on the hadronic and semihadronic CP violating parameters and role of a dark force carrier in the electric dipole moment of 199Hg, Phys. Rev. D 95 (2017) 013002 [arXiv:1612.09371] [INSPIRE].","DOI":"10.1103\/PhysRevD.95.013002"},{"key":"26920_CR131","doi-asserted-by":"crossref","unstructured":"S. Alioli et al., Right-handed charged currents in the era of the Large Hadron Collider, JHEP 05 (2017) 086 [arXiv:1703.04751] [INSPIRE].","DOI":"10.1007\/JHEP05(2017)086"},{"key":"26920_CR132","doi-asserted-by":"crossref","unstructured":"V. Cirigliano et al., Beta-decay implications for the W-boson mass anomaly, Phys. Rev. D 106 (2022) 075001 [arXiv:2204.08440] [INSPIRE].","DOI":"10.1103\/PhysRevD.106.075001"},{"key":"26920_CR133","unstructured":"T. Inami and C.S. Lim, Effects of Superheavy Quarks and Leptons in Low-Energy Weak Processes $$ {K}_L\\to \\mu \\overline{\\mu} $$, $$ {K}^{+}\\to {\\pi}^{+}\\nu \\overline{\\nu} $$ and $$ {K}_0\\leftrightarrow {\\overline{K}}_0 $$, Prog. Theor. Phys. 65 (1981) 297 [Erratum ibid. 65 (1981) 1772] [INSPIRE]."},{"key":"26920_CR134","doi-asserted-by":"crossref","unstructured":"G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph\/9512380] [INSPIRE].","DOI":"10.1103\/RevModPhys.68.1125"},{"key":"26920_CR135","unstructured":"Z. Bai et al., KL \u2013 KS Mass Difference from Lattice QCD, Phys. Rev. Lett. 113 (2014) 112003 [arXiv:1406.0916] [INSPIRE]."},{"key":"26920_CR136","doi-asserted-by":"crossref","unstructured":"Z. Bai, N.H. Christ and C.T. Sachrajda, The KL-KS Mass Difference, EPJ Web Conf. 175 (2018) 13017 [INSPIRE].","DOI":"10.1051\/epjconf\/201817513017"},{"key":"26920_CR137","unstructured":"Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE]."},{"key":"26920_CR138","doi-asserted-by":"crossref","unstructured":"RBC\/UKQCD collaboration, Neutral Kaon Mixing Beyond the Standard Model with nf = 2 + 1 Chiral Fermions Part 1: Bare Matrix Elements and Physical Results, JHEP 11 (2016) 001 [arXiv:1609.03334] [INSPIRE].","DOI":"10.1007\/JHEP11(2016)001"},{"key":"26920_CR139","doi-asserted-by":"crossref","unstructured":"A.J. Buras, S. Jager and J. Urban, Master formulae for \u2206F = 2 NLO QCD factors in the standard model and beyond, Nucl. Phys. B 605 (2001) 600 [hep-ph\/0102316] [INSPIRE].","DOI":"10.1016\/S0550-3213(01)00207-3"},{"key":"26920_CR140","doi-asserted-by":"crossref","unstructured":"C. Bobeth, A.J. Buras, A. Celis and M. Jung, Yukawa enhancement of Z-mediated new physics in \u2206S = 2 and \u2206B = 2 processes, JHEP 07 (2017) 124 [arXiv:1703.04753] [INSPIRE].","DOI":"10.1007\/JHEP07(2017)124"},{"key":"26920_CR141","doi-asserted-by":"crossref","unstructured":"M. Bona et al., Unitarity Triangle global fits beyond the Standard Model: UTfit 2021 NP update, PoS EPS-HEP2021 (2022) 500 [INSPIRE].","DOI":"10.22323\/1.398.0500"},{"key":"26920_CR142","unstructured":"L.S. Littenberg, The CP Violating Decay $$ {K}_L^0\\to {\\pi}^0\\nu \\overline{\\nu} $$, Phys. Rev. D 39 (1989) 3322 [INSPIRE]."},{"key":"26920_CR143","unstructured":"B. Kayser, CP Violation in the K and B Systems, in the proceedings of the ICTP Summer School in High-energy Physics and Cosmology, Trieste, Italy, June 12 \u2013 July 28 (1995) [hep-ph\/9702264] [INSPIRE]."},{"key":"26920_CR144","doi-asserted-by":"crossref","unstructured":"Y. Grossman and Y. Nir, KL \u2192 \u03c00\u03bd\u03bd beyond the standard model, Phys. Lett. B 398 (1997) 163 [hep-ph\/9701313] [INSPIRE].","DOI":"10.1016\/S0370-2693(97)00210-4"},{"key":"26920_CR145","doi-asserted-by":"crossref","unstructured":"G. Buchalla and G. Isidori, The CP conserving contribution to $$ {K}_L\\to {\\pi}^0\\nu \\overline{\\nu} $$ neutrino anti-neutrino in the standard model, Phys. Lett. B 440 (1998) 170 [hep-ph\/9806501] [INSPIRE].","DOI":"10.1016\/S0370-2693(98)01088-0"},{"key":"26920_CR146","doi-asserted-by":"crossref","unstructured":"A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, $$ {K}^{+}\\to {\\pi}^{+}\\nu \\overline{\\nu} $$ and $$ {K}_L\\to {\\pi}^0\\nu \\overline{\\nu} $$ in the Standard Model: status and perspectives, JHEP 11 (2015) 033 [arXiv:1503.02693] [INSPIRE].","DOI":"10.1007\/JHEP11(2015)033"},{"key":"26920_CR147","doi-asserted-by":"publisher","unstructured":"A. Pich, Effective Field Theory with Nambu-Goldstone Modes, arXiv:1804.05664 [https:\/\/doi.org\/10.1093\/oso\/9780198855743.003.0003] [INSPIRE].","DOI":"10.1093\/oso\/9780198855743.003.0003"},{"key":"26920_CR148","doi-asserted-by":"crossref","unstructured":"A. Santamaria, Masses, mixings, Yukawa couplings and their symmetries, Phys. Lett. B 305 (1993) 90 [hep-ph\/9302301] [INSPIRE].","DOI":"10.1016\/0370-2693(93)91110-9"},{"key":"26920_CR149","doi-asserted-by":"crossref","unstructured":"J. Berger and Y. Grossman, Parameter counting in models with global symmetries, Phys. Lett. B 675 (2009) 365 [arXiv:0811.1019] [INSPIRE].","DOI":"10.1016\/j.physletb.2009.04.050"},{"key":"26920_CR150","doi-asserted-by":"crossref","unstructured":"L.-L. Chau and W.-Y. Keung, Comments on the Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 53 (1984) 1802 [INSPIRE].","DOI":"10.1103\/PhysRevLett.53.1802"},{"key":"26920_CR151","doi-asserted-by":"crossref","unstructured":"F.J. Botella and L.-L. Chau, Anticipating the Higher Generations of Quarks from Rephasing Invariance of the Mixing Matrix, Phys. Lett. B 168 (1986) 97 [INSPIRE].","DOI":"10.1016\/0370-2693(86)91468-1"},{"key":"26920_CR152","doi-asserted-by":"crossref","unstructured":"J. de Blas, J.C. Criado, M. P\u00e9rez-Victoria and J. Santiago, Effective description of general extensions of the Standard Model: the complete tree-level dictionary, JHEP 03 (2018) 109 [arXiv:1711.10391] [INSPIRE].","DOI":"10.1007\/JHEP03(2018)109"},{"key":"26920_CR153","doi-asserted-by":"crossref","unstructured":"A. Crivellin, M. Kirk, T. Kitahara and F. Mescia, Large t \u2192 cZ as a sign of vectorlike quarks in light of the W mass, Phys. Rev. D 106 (2022) L031704 [arXiv:2204.05962] [INSPIRE].","DOI":"10.1103\/PhysRevD.106.L031704"},{"key":"26920_CR154","doi-asserted-by":"crossref","unstructured":"L. Allwicher et al., Computing tools for effective field theories: SMEFT-Tools 2022 Workshop Report, 14\u201316th September 2022, Z\u00fcrich, Eur. Phys. J. C 84 (2024) 170 [arXiv:2307.08745] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-023-12323-y"},{"key":"26920_CR155","doi-asserted-by":"crossref","unstructured":"A. Carmona, A. Lazopoulos, P. Olgoso and J. Santiago, Matchmakereft: automated tree-level and one-loop matching, SciPost Phys. 12 (2022) 198 [arXiv:2112.10787] [INSPIRE].","DOI":"10.21468\/SciPostPhys.12.6.198"},{"key":"26920_CR156","doi-asserted-by":"crossref","unstructured":"J. Fuentes-Mart\u00edn et al., A proof of concept for matchete: an automated tool for matching effective theories, Eur. Phys. J. C 83 (2023) 662 [arXiv:2212.04510] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-023-11726-1"},{"key":"26920_CR157","doi-asserted-by":"crossref","unstructured":"E.E. Jenkins, A.V. Manohar and P. Stoffer, Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching, JHEP 03 (2018) 016 [Erratum ibid. 12 (2023) 043] [arXiv:1709.04486] [INSPIRE].","DOI":"10.1007\/JHEP03(2018)016"}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP08(2025)061.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP08(2025)061\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP08(2025)061.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T20:16:28Z","timestamp":1757276188000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP08(2025)061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,7]]},"references-count":157,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["26920"],"URL":"https:\/\/doi.org\/10.1007\/jhep08(2025)061","relation":{"has-preprint":[{"id-type":"arxiv","id":"2412.21201","asserted-by":"subject"}]},"ISSN":["1029-8479"],"issn-type":[{"value":"1029-8479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,7]]},"assertion":[{"value":"4 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2025 The Author(s)","order":1,"name":"copyright_statement","label":"Copyright Statement","group":{"name":"ArticleCopyright","label":"Copyright Information"}},{"value":"The Author(s)","order":2,"name":"copyright_holder","label":"Copyright Holder","group":{"name":"ArticleCopyright","label":"Copyright Information"}},{"value":"2025","order":3,"name":"copyright_year","label":"Copyright Year","group":{"name":"ArticleCopyright","label":"Copyright Information"}}],"article-number":"61"}}