{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T03:20:52Z","timestamp":1771903252177,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["CFTP-FCT Unit 777 (UIDB\/00777\/2020)"],"award-info":[{"award-number":["CFTP-FCT Unit 777 (UIDB\/00777\/2020)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["CFTP-FCT Unit 777 (UIDP\/0077)"],"award-info":[{"award-number":["CFTP-FCT Unit 777 (UIDP\/0077)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Eur. Phys. J. C"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We put forward the conjecture that the small numbers in the <jats:inline-formula><jats:alternatives><jats:tex-math>$$V_\\text {CKM}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mtext>CKM<\/mml:mtext>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> matrix, are generated by physics beyond the Standard Model. We identify as small numbers <jats:inline-formula><jats:alternatives><jats:tex-math>$$V_{ub}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mi>ub<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and the strength of CP violation, measured by <jats:inline-formula><jats:alternatives><jats:tex-math>$$|\\text {Im}Q|$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mtext>Im<\/mml:mtext>\n                    <mml:mi>Q<\/mml:mi>\n                    <mml:mo>|<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where <jats:italic>Q<\/jats:italic> stands for a rephasing invariant quartet of <jats:inline-formula><jats:alternatives><jats:tex-math>$$V_\\text {CKM}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mtext>CKM<\/mml:mtext>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We illustrate how the conjecture can be realised in the context of an extension of the Standard Model where an up-type vector-like quark is introduced leading to a realistic spectrum of quark masses and an effective <jats:inline-formula><jats:alternatives><jats:tex-math>$$V_\\text {CKM}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mtext>CKM<\/mml:mtext>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in agreement with experiment.<\/jats:p>","DOI":"10.1140\/epjc\/s10052-023-11279-3","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T10:05:17Z","timestamp":1676282717000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Do the small numbers in the quark mixing arise from new physics?"],"prefix":"10.1140","volume":"83","author":[{"given":"G. C.","family":"Branco","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8660-3456","authenticated-orcid":false,"given":"Jos\u00e9 Filipe","family":"Bastos","sequence":"additional","affiliation":[]},{"given":"J. I.","family":"Silva-Marcos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"11279_CR1","first-page":"1","volume":"103","author":"GC Branco","year":"1999","unstructured":"G.C. Branco, L. Lavoura, J.P. Silva, C.P. Violation, Int. Ser. Monogr. Phys. 103, 1\u2013536 (1999)","journal-title":"Int. Ser. Monogr. Phys."},{"key":"11279_CR2","unstructured":"Particle Data Group collaboration, R.L. Workman et\u00a0al., Rev. Particle Physics, PTEP 2022, 083C01 (2022)"},{"key":"11279_CR3","doi-asserted-by":"publisher","unstructured":"Particle Data Group Collaboration, P.\u00a0Zyla et\u00a0al., Rev. Particle Phys., PTEP 2020, 083C01 (2020). https:\/\/doi.org\/10.1093\/ptep\/ptaa104","DOI":"10.1093\/ptep\/ptaa104"},{"key":"11279_CR4","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/JHEP01(2021)143","volume":"01","author":"Y Grossman","year":"2021","unstructured":"Y. Grossman, J.T. Ruderman, CKM substructure. JHEP 01, 143 (2021). https:\/\/doi.org\/10.1007\/JHEP01(2021)143. arXiv:2007.12695 [hep-ph]","journal-title":"JHEP"},{"key":"11279_CR5","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1140\/epjc\/s10052-020-7691-6","volume":"80","author":"B Belfatto","year":"2020","unstructured":"B. Belfatto, R. Beradze, Z. Berezhiani, The CKM unitarity problem: a trace of new physics at the TeV scale? Eur. Phys. J. C 80, 149 (2020). https:\/\/doi.org\/10.1140\/epjc\/s10052-020-7691-6. arXiv:1906.02714","journal-title":"Eur. Phys. J. C"},{"key":"11279_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.013001","volume":"100","author":"CY Seng","year":"2019","unstructured":"C.Y. Seng, M. Gorchtein, M.J. Ramsey-Musolf, Dispersive evaluation of the inner radiative correction in neutron and nuclear $$\\beta $$ decay. Phys. Rev. D 100, 013001 (2019). https:\/\/doi.org\/10.1103\/PhysRevD.100.013001. arXiv:1812.03352","journal-title":"Phys. Rev. D"},{"key":"11279_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.073008","volume":"100","author":"A Czarnecki","year":"2019","unstructured":"A. Czarnecki, W.J. Marciano, A. Sirlin, Radiative corrections to neutron and nuclear beta decays revisited. Phys. Rev. D 100, 073008 (2019). https:\/\/doi.org\/10.1103\/PhysRevD.100.073008. arXiv:1907.06737","journal-title":"Phys. Rev. D"},{"key":"11279_CR8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.111301","volume":"101","author":"C-Y Seng","year":"2020","unstructured":"C.-Y. Seng, X. Feng, M. Gorchtein, L.-C. Jin, Joint lattice QCD-dispersion theory analysis confirms the quark-mixing top-row unitarity deficit. Phys. Rev. D 101, 111301 (2020). https:\/\/doi.org\/10.1103\/PhysRevD.101.111301. arXiv:2003.11264","journal-title":"Phys. Rev. D"},{"key":"11279_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.113001","volume":"103","author":"L Hayen","year":"2021","unstructured":"L. Hayen, Standard model $$\\cal{O} (\\alpha )$$ renormalization of $$g_A$$ and its impact on new physics searches. Phys. Rev. D 103, 113001 (2021). https:\/\/doi.org\/10.1103\/PhysRevD.103.113001. arXiv:2010.07262","journal-title":"Phys. Rev. D"},{"key":"11279_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.104.033003","volume":"104","author":"K Shiells","year":"2021","unstructured":"K. Shiells, P.G. Blunden, W. Melnitchouk, Electroweak axial structure functions and improved extraction of the $$V_{ud}$$ CKM matrix element. Phys. Rev. D 104, 033003 (2021). https:\/\/doi.org\/10.1103\/PhysRevD.104.033003. arXiv:2012.01580","journal-title":"Phys. Rev. D"},{"key":"11279_CR11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.70.093006","volume":"70","author":"A Czarnecki","year":"2004","unstructured":"A. Czarnecki, W.J. Marciano, A. Sirlin, Precision measurements and CKM unitarity. Phys. Rev. D 70, 093006 (2004). https:\/\/doi.org\/10.1103\/PhysRevD.70.093006. arXiv:hep-ph\/0406324","journal-title":"Phys. Rev. D"},{"key":"11279_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.071802","volume":"125","author":"AM Coutinho","year":"2020","unstructured":"A.M. Coutinho, A. Crivellin, Global fit to modified neutrino couplings. Phys. Rev. Lett. 125, 071802 (2020). https:\/\/doi.org\/10.1103\/PhysRevLett.125.071802. arXiv:1912.08823","journal-title":"Phys. Rev. Lett."},{"key":"11279_CR13","unstructured":"Y. Aoki et al., FLAG Review (2021). arXiv:2111.09849"},{"key":"11279_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.241804","volume":"121","author":"C-Y Seng","year":"2018","unstructured":"C.-Y. Seng, M. Gorchtein, H.H. Patel, M.J. Ramsey-Musolf, Reduced hadronic uncertainty in the determination of $$V_{ud}$$. Phys. Rev. Lett. 121, 241804 (2018). https:\/\/doi.org\/10.1103\/PhysRevLett.121.241804. arXiv:1807.10197","journal-title":"Phys. Rev. Lett."},{"key":"11279_CR15","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/JHEP09(2010)106","volume":"09","author":"AJ Buras","year":"2010","unstructured":"A.J. Buras, B. Duling, T. Feldmann, T. Heidsieck, C. Promberger, S. Recksiegel, Patterns of flavour violation in the presence of a fourth generation of quarks and leptons. JHEP 09, 106 (2010). https:\/\/doi.org\/10.1007\/JHEP09(2010)106. arXiv:1002.2126","journal-title":"JHEP"},{"key":"11279_CR16","doi-asserted-by":"publisher","unstructured":"J.A.\u00a0Aguilar-Saavedra, Effects of mixing with quark singlets. Phys. Rev. D 67, 035003 (2003) [Erratum: Phys. Rev. D 69 (2004), 099901]. https:\/\/doi.org\/10.1103\/PhysRevD.69.099901. arXiv:hep-ph\/0210112","DOI":"10.1103\/PhysRevD.69.099901"},{"key":"11279_CR17","doi-asserted-by":"publisher","first-page":"070","DOI":"10.1007\/JHEP03(2012)070","volume":"03","author":"G Cacciapaglia","year":"2012","unstructured":"G. Cacciapaglia, A. Deandrea, L. Panizzi, N. Gaur, D. Harada, Y. Okada, Heavy vector-like top partners at the LHC and flavour constraints. JHEP 03, 070 (2012). https:\/\/doi.org\/10.1007\/JHEP03(2012)070. arXiv:1108.6329","journal-title":"JHEP"},{"key":"11279_CR18","doi-asserted-by":"publisher","unstructured":"F.J. Botella, G.C.\u00a0Branco, M. Nebot, M.N.\u00a0Rebelo, J.I.\u00a0Silva-Marcos., Vector-like quarks at the origin of light quark masses and mixing. Eur. Phys. J. C 77, 408. (2017). https:\/\/doi.org\/10.1140\/epjc\/s10052-017-4933-3. arXiv:1610.03018","DOI":"10.1140\/epjc\/s10052-017-4933-3"},{"key":"11279_CR19","unstructured":"F.J. Botella, G.C. Branco, M. Nebot, Singlet heavy fermions as the origin of B anomalies in flavour changing neutral currents. arXiv:1712.04470"},{"key":"11279_CR20","doi-asserted-by":"publisher","unstructured":"E. Nardi, Top-charm flavor changing contributions to the effective bsZ vertex. Phys. Lett. B 365, 327 (1996). https:\/\/doi.org\/10.1016\/0370-2693(95)01308-3. arXiv:hep-ph\/9509233","DOI":"10.1016\/0370-2693(95)01308-3"},{"key":"11279_CR21","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/S0370-2693(98)00695-9","volume":"433","author":"G Barenboim","year":"1998","unstructured":"G. Barenboim, F.J. Botella, Delta F=2 effective Lagrangian in theories with vector-like fermions. Phys. Lett. B 433, 385 (1998). https:\/\/doi.org\/10.1016\/S0370-2693(98)00695-9. arXiv:hep-ph\/9708209","journal-title":"Phys. Lett. B"},{"key":"11279_CR22","doi-asserted-by":"publisher","first-page":"015","DOI":"10.1007\/JHEP05(2022)015","volume":"05","author":"S Balaji","year":"2022","unstructured":"S. Balaji, Asymmetry in flavour changing electromagnetic transitions of vector-like quarks. JHEP 05, 015 (2022). https:\/\/doi.org\/10.1007\/JHEP05(2022)015. arXiv:hep-ph\/2110.05473","journal-title":"JHEP"},{"key":"11279_CR23","doi-asserted-by":"publisher","unstructured":"G.C.\u00a0Branco, P.A.\u00a0Parada, M.N.\u00a0Rebelo, D0- anti-D0 mixing in the presence of isosinglet quarks. Phys. Rev. D 52, 4217\u20134222 (1995). https:\/\/doi.org\/10.1103\/PhysRevD.52.4217. arXiv:hep-ph\/9501347","DOI":"10.1103\/PhysRevD.52.4217"},{"key":"11279_CR24","doi-asserted-by":"publisher","unstructured":"F.J. Botella, G.C. Branco, M.N. Rebelo, J.I. Silva-Marcos, J.\u00a0Filipe Bastos, Decays of the heavy top and new insights on $$\\varepsilon _K$$ in a one-VLQ minimal solution to the CKM unitarity problem. Eur. Phys. J. C 82(4), 360 (2022). https:\/\/doi.org\/10.1140\/epjc\/s10052-022-10299-9. arXiv:2111.15401","DOI":"10.1140\/epjc\/s10052-022-10299-9"},{"key":"11279_CR25","doi-asserted-by":"publisher","unstructured":"G.C. Branco, J.T. Penedo, P.M.F. Pereira, M.N. Rebelo, J.I. Silva-Marcos, Addressing the CKM unitarity problem with a vector-like up quark. JHEP 07, 099 (2021). https:\/\/doi.org\/10.1007\/JHEP07(2021)099. arXiv:2103.13409","DOI":"10.1007\/JHEP07(2021)099"},{"key":"11279_CR26","doi-asserted-by":"publisher","first-page":"079","DOI":"10.1007\/JHEP10(2021)079","volume":"10","author":"B Belfatto","year":"2021","unstructured":"B. Belfatto, Z. Berezhiani, Are the CKM anomalies induced by vector-like quarks? Limits from flavor changing and Standard Model precision tests. JHEP 10, 079 (2021). https:\/\/doi.org\/10.1007\/JHEP10(2021)079. arXiv:2103.13409","journal-title":"JHEP"},{"key":"11279_CR27","doi-asserted-by":"publisher","unstructured":"Y.S. Amhis et al. [HFLAV], Averages of b-hadron, c-hadron, and $$\\tau $$-lepton properties as of 2018. Eur. Phys. J. C. 81(3), 226 (2021). https:\/\/doi.org\/10.1140\/epjc\/s10052-020-8156-7. arXiv:1909.12524","DOI":"10.1140\/epjc\/s10052-020-8156-7"},{"key":"11279_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.79.114030","volume":"79","author":"E Golowich","year":"2009","unstructured":"E. Golowich, J. Hewett, S. Pakvasa, A.A. Petrov, Relating D0-anti-D0 mixing and D0 \u2013$${>}$$ l+ l$$-$$ with new physics. Phys. Rev. D 79, 114030 (2009). https:\/\/doi.org\/10.1103\/PhysRevD.79.114030. arXiv:0903.2830","journal-title":"Phys. Rev. D"},{"key":"11279_CR29","doi-asserted-by":"publisher","unstructured":"A.M. Sirunyan et al. [CMS], Search for vectorlike light-flavor quark partners in proton-proton collisions at $$\\sqrt{s}$$ =8 TeV. Phys. Rev. D 97, 072008 (2018). https:\/\/doi.org\/10.1103\/PhysRevD.97.072008. arXiv:1708.02510","DOI":"10.1103\/PhysRevD.97.072008"},{"key":"11279_CR30","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0370-2693(86)91468-1","volume":"168","author":"F Botella","year":"1986","unstructured":"F. Botella, L.-L. Chau, Anticipating the higher generations of quarks from rephasing invariance of the mixing matrix. Phys. Lett. B 168, 97 (1986). https:\/\/doi.org\/10.1016\/0370-2693(86)91468-1","journal-title":"Phys. Lett. B"},{"key":"11279_CR31","doi-asserted-by":"publisher","unstructured":"J.\u00a0Brod, M.\u00a0Gorbahn, E.\u00a0Stamou, Standard-model prediction of $$\\varepsilon _K$$ with manifest quark-mixing unitarity. Phys. Rev. Lett. 125(17), 171803 (2020). https:\/\/doi.org\/10.1103\/PhysRevLett.125.171803. arXiv:1911.06822","DOI":"10.1103\/PhysRevLett.125.171803"},{"key":"11279_CR32","doi-asserted-by":"publisher","unstructured":"T. Inami, C.S. Lim, Effects of superheavy quarks and leptons in low-energy weak processes k(L) \u2014$${>}$$ mu anti-mu, K+ \u2014$${>}$$ pi+ neutrino anti-neutrino and K0 $${<}$$\u2014$${>}$$ anti-K0. Prog. Theor. Phys. 65, 297 (1981). https:\/\/doi.org\/10.1143\/PTP.65.297 [Erratum: Prog. Theor. Phys. 65, 1772 (1981)]","DOI":"10.1143\/PTP.65.297"}],"container-title":["The European Physical Journal C"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1140\/epjc\/s10052-023-11279-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1140\/epjc\/s10052-023-11279-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1140\/epjc\/s10052-023-11279-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T15:18:11Z","timestamp":1679930291000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1140\/epjc\/s10052-023-11279-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,13]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["11279"],"URL":"https:\/\/doi.org\/10.1140\/epjc\/s10052-023-11279-3","relation":{},"ISSN":["1434-6052"],"issn-type":[{"value":"1434-6052","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,13]]},"assertion":[{"value":"17 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"141"}}