{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T01:59:10Z","timestamp":1772330350351,"version":"3.50.1"},"reference-count":113,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,5,26]],"date-time":"2015-05-26T00:00:00Z","timestamp":1432598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["1130599"],"award-info":[{"award-number":["1130599"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["1130617"],"award-info":[{"award-number":["1130617"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Mecesup","award":["FSM1204"],"award-info":[{"award-number":["FSM1204"]}]},{"name":"NRF-MEST","award":["2011-0017430"],"award-info":[{"award-number":["2011-0017430"]}]},{"name":"NRF-MEST","award":["2011-0020333"],"award-info":[{"award-number":["2011-0020333"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles. There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as \u03c0\u00b1,K\u00b1 and B\u00b1, in scenarios where extra neutrinos are heavy and can be on their mass shell. We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model (\u03bdMSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.<\/jats:p>","DOI":"10.3390\/sym7020726","type":"journal-article","created":{"date-parts":[[2015,5,26]],"date-time":"2015-05-26T11:07:05Z","timestamp":1432638425000},"page":"726-773","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":60,"title":["Probing Majorana Neutrinos and their CP Violation in Decays of Charged Scalar Mesons \u03c0, K, D, Ds, B, Bc"],"prefix":"10.3390","volume":"7","author":[{"given":"Gorazd","family":"Cveti\u010d","sequence":"first","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda (UTFSM), Casilla 110-V,Valpara\u00edso, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudio","family":"Dib","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda (UTFSM), Casilla 110-V,Valpara\u00edso, Chile"},{"name":"Centro Cient\u00edfico Tecnol\u00f3gico de Valpara\u00edso, UTFSM, Casilla 110-V, Valpara\u00edso, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Choong","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Physics and IPAP, Yonsei University, Seoul 120-749, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jilberto","family":"Zamora-Sa\u00e1","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda (UTFSM), Casilla 110-V,Valpara\u00edso, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1007\/BF02961321","article-title":"On the symmetry of particle and antiparticle","volume":"14","author":"Racah","year":"1937","journal-title":"Nuovo Cim"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1103\/PhysRev.56.1184","article-title":"On transition probabilities in double beta-disintegration","volume":"56","author":"Furry","year":"1939","journal-title":"Phys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1088\/0034-4885\/22\/1\/305","article-title":"Double beta decay","volume":"22","author":"Primakoff","year":"1959","journal-title":"Rep. Prog. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1103\/PhysRev.184.1925","article-title":"Nuclear double-beta decay and a new limit on lepton nonconservation","volume":"184","author":"Primakoff","year":"1969","journal-title":"Phys. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1146\/annurev.ns.31.120181.001045","article-title":"Baryon number and lepton number conservation laws","volume":"31","author":"Primakoff","year":"1981","journal-title":"Ann. Rev. Nucl. Part. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2951","DOI":"10.1103\/PhysRevD.25.2951","article-title":"Neutrinoless double beta decay in SU(2)\u00d7U(1) theories","volume":"25","author":"Schechter","year":"1982","journal-title":"Phys. Rev. D"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1143\/PTPS.83.1","article-title":"Double beta decay and Majorana neutrino","volume":"83","author":"Doi","year":"1985","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"R183","DOI":"10.1088\/0954-3899\/30\/9\/R01","article-title":"Double beta decay","volume":"30","author":"Elliott","year":"2004","journal-title":"J. Phys. G"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.nuclphysa.2005.12.004","article-title":"Assessment of uncertainties in QRPA 0v\u03b2\u03b2-decay nuclear matrix elements","volume":"766","author":"Rodin","year":"2006","journal-title":"Nucl. Phys. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.nuclphysa.2007.06.014","article-title":"Erratum to: \u201cAssessment of uncertainties in QRPA 0\u03bd\u03b2\u03b2-decay nuclear matrix elements\u201d [Nucl. Phys. A 766 (2006) 107]","volume":"793","author":"Rodin","year":"2007","journal-title":"Nucl. Phys. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1103\/PhysRevLett.50.1427","article-title":"Majorana neutrinos and the production of the right-handed charged gauge boson","volume":"50","author":"Keung","year":"1983","journal-title":"Phys. Rev. Lett"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Tello, V., Nemev\u0161ek, M., Nesti, F., Senjanovi\u0107, G., and Vissani, F. (2011). Left-right symmetry: From LHC to neutrinoless double beta decay. Phys. Rev. Lett, 106.","DOI":"10.1103\/PhysRevLett.106.151801"},{"key":"ref_13","unstructured":"Nemev\u0161ek, M., Nesti, F., Senjanovi\u0107, G., and Tello, V. Available online: http:\/\/arxiv.org\/abs\/1112.3061."},{"key":"ref_14","first-page":"1","article-title":"Neutrino mass: From LHC to grand unification","volume":"34","year":"2011","journal-title":"Riv. Nuovo Cim."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0550-3213(91)80024-G","article-title":"Heavy Majorana neutrinos in electron-positron and electron-proton collisions","volume":"363","author":"Greub","year":"1991","journal-title":"Nucl. Phys. B"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Helo, J., Hirsch, M., and Kovalenko, S. (2014). Heavy neutrino searches at the LHC with displaced vertices. Phys. Rev. D, 89.","DOI":"10.1103\/PhysRevD.89.073005"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1016\/j.physletb.2012.12.048","article-title":"Lepton number violation at the LHC with leptoquark and diquark","volume":"718","author":"Kohda","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Chen, C.Y., and Bhupal Dev, P.S. (2012). Multi-lepton collider signatures of heavy Dirac and Majorana neutrinos. Phys. Rev. D, 85.","DOI":"10.1103\/PhysRevD.85.093018"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chen, C.Y., Bhupal Dev, P.S., and Mohapatra, R.N. (2013). Probing heavy-light neutrino mixing in Left-Right Seesaw models at the LHC. Phys. Rev. D, 88.","DOI":"10.1103\/PhysRevD.88.033014"},{"key":"ref_20","first-page":"081801:1","article-title":"New production mechanism for heavy neutrinos at the LHC","volume":"112","author":"Pilaftsis","year":"2014","journal-title":"Phys. Rev. Lett"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.physletb.2014.06.058","article-title":"Direct bounds on electroweak scale pseudo-Dirac neutrinos from s=8 TeV LHC data","volume":"735","author":"Das","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1103\/PhysRevLett.68.443","article-title":"Upper bounds on lepton number violating meson decays","volume":"68","author":"Littenberg","year":"1992","journal-title":"Phys. Rev. Lett"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/S0370-2693(00)01041-8","article-title":"Implications of improved upper bounds on |\u0394L| = 2 processes","volume":"491","author":"Littenberg","year":"2000","journal-title":"Phys. Lett. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/S0370-2693(00)01134-5","article-title":"K meson neutrinoless double muon decay as a probe of neutrino masses and mixings","volume":"493","author":"Dib","year":"2000","journal-title":"Phys. Lett. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s100520100702","article-title":"Majorana neutrinos and same sign dilepton production at LHC and in rare meson decays","volume":"21","author":"Ali","year":"2001","journal-title":"Eur. Phys. J. C"},{"key":"ref_26","unstructured":"Cveti\u010d, G., Dib, C., Kang, S.K., and Kim, C.S. (2010). Probing Majorana neutrinos in rare K and D, Ds, B, Bc meson decays. Phys. Rev. D, 82."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ivanov, M.A., and Kovalenko, S.G. (2005). Hadronic structure aspects of K+\u2192\u03c0\u2212+\u21131++\u21132+ decays. Phys. Rev. D, 71.","DOI":"10.1103\/PhysRevD.71.053004"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"De Gouvea, A., and Jenkins, J. (2008). A Survey of lepton number violation via effective operators. Phys. Rev. D, 77.","DOI":"10.1103\/PhysRevD.77.013008"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Atre, A., Han, T., Pascoli, S., and Zhang, B. (2009). The Search for heavy Majorana neutrinos. JHEP, 0905, and references therein.","DOI":"10.1088\/1126-6708\/2009\/05\/030"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.nuclphysb.2011.07.020","article-title":"Sterile neutrinos in lepton number and lepton flavor violating decays","volume":"853","author":"Helo","year":"2011","journal-title":"Nucl. Phys. B"},{"key":"ref_31","unstructured":"Quintero, N., L\u00f3pez Castro, G., and Delepine, D. (2011). Lepton number violation in top quark and neutral B meson decays. Phys. Rev. D, 84."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Quintero, N., L\u00f3pez Castro, G., and Delepine, D. (2012). Erratum: Lepton number violation in top quark and neutral B meson decays [Phys. Rev. D 84, 096011 (2011)]. Phys. Rev. D, 86.","DOI":"10.1103\/PhysRevD.86.079904"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"L\u00f3pez Castro, G., and Quintero, N. (2013). Bounding resonant Majorana neutrinos from four-body B and D decays. Phys. Rev. D, 87.","DOI":"10.1103\/PhysRevD.87.077901"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"091","DOI":"10.1007\/JHEP02(2014)091","article-title":"Sterile neutrinos in leptonic and semileptonic decays","volume":"1402","author":"Abada","year":"2014","journal-title":"JHEP"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.physletb.2014.08.006","article-title":"Study Majorana neutrino contribution to B-meson semi-leptonic rare decays","volume":"736","author":"Wang","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Boyanovsky, D. (2014). Nearly degenerate heavy sterile neutrinos in cascade decay: Mixing and oscillations. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.105024"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Cveti\u010d, G., Dib, C., and Kim, C.S. (2012). Probing Majorana neutrinos in rare \u03c0+\u2192e+e+\u03bc\u2212v decays. JHEP, 1206.","DOI":"10.1007\/JHEP06(2012)149"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Cveti\u010d, G., Kim, C.S., and Zamora-Sa\u00e1, J. (2014). CP violations in \u03c0\u00b1 meson decay. J. Phys. G, 41.","DOI":"10.1088\/0954-3899\/41\/7\/075004"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Cveti\u010d, G., Kim, C.S., and Zamora-Sa\u00e1, J. (D2014). CP violation in lepton number violating semileptonic decays of K, D, Ds,B, Bc. Phys. Rev., 89.","DOI":"10.1103\/PhysRevD.89.093012"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Dib, CO., Campos, M., and Kim, C.S. (2015). CP Violation with Majorana neutrinos in K meson decays. JHEP, 1502.","DOI":"10.1007\/JHEP02(2015)108"},{"key":"ref_41","unstructured":"(1998). Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett, 81, 1562\u20131567."},{"key":"ref_42","unstructured":"(2002). Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory. Phys. Rev. Lett, 89."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Lipari, P. (2001). CP violation effects and high-energy neutrinos. Phys. Rev. D, 64.","DOI":"10.1103\/PhysRevD.64.033002"},{"key":"ref_44","unstructured":"Rahman, Z., Dasgupta, A., and Adhikari, R. Available online: http:\/\/arxiv.org\/abs\/1210.2603."},{"key":"ref_45","unstructured":"Rahman, Z., Dasgupta, A., and Adhikari, R. Available online: http:\/\/arxiv.org\/abs\/1210.4801."},{"key":"ref_46","unstructured":"(2003). First results from KamLAND: Evidence for reactor anti-neutrino disappearance. Phys. Rev. Lett., 90."},{"key":"ref_47","unstructured":"(2014). Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys., 571, A16:1\u2013A16:66."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/0370-2693(77)90435-X","article-title":"\u03bc\u2192e\u03b3 at a rate of one out of 1-billion muon decays?","volume":"67","author":"Minkowski","year":"1977","journal-title":"Phys. Lett. B"},{"key":"ref_49","unstructured":"van Nieuwenhuizen, P., and Freedman, D.Z. (1979). Supergravity, North-Holland."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1143\/PTP.64.1103","article-title":"Horizontal symmetry and masses of neutrinos","volume":"64","author":"Yanagida","year":"1980","journal-title":"Prog. Theor. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"L\u00e9vy, M., Basdevant, J.-L., Speiser, D., Weyers, J., Gastmans, R., and Jacob, M. (1980). Quarks and Leptons, Cargese, Plenum.","DOI":"10.1007\/978-1-4684-7197-7"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1103\/PhysRevLett.44.912","article-title":"Neutrino mass and spontaneous parity violation","volume":"44","author":"Mohapatra","year":"1980","journal-title":"Phys. Rev. Lett"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0550-3213(83)90482-0","article-title":"Massless neutrinos in left-right symmetric models","volume":"218","author":"Wyler","year":"1983","journal-title":"Nucl. Phys. B"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0550-3213(85)90603-0","article-title":"Symmetry breaking patterns in superstring models","volume":"258","author":"Witten","year":"1985","journal-title":"Nucl. Phys. B"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1103\/PhysRevD.34.1642","article-title":"Neutrino mass and baryon number nonconservation in superstring models","volume":"34","author":"Mohapatra","year":"1986","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"161801:1","DOI":"10.1103\/PhysRevLett.95.161801","article-title":"Novel supersymmetric SO(10) seesaw mechanism","volume":"95","author":"Malinsky","year":"2005","journal-title":"Phys. Rev. Lett"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Dev, P.S.B., and Mohapatra, R.N. (2010). TeV Scale Inverse Seesaw in SO(10) and Leptonic Non-Unitarity Effects. Phys. Rev. D, 81.","DOI":"10.1103\/PhysRevD.81.013001"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Dev, P.S.B., and Pilaftsis, A. (2012). Minimal Radiative Neutrino Mass Mechanism for Inverse Seesaw Models. Phys. Rev. D, 86.","DOI":"10.1103\/PhysRevD.86.113001"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Lee, C.H., Dev, P.S.B., and Mohapatra, R.N. (2013). Natural TeV-scale left-right seesaw mechanism for neutrinos and experimental tests. Phys. Rev. D, 88.","DOI":"10.1103\/PhysRevD.88.093010"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.physletb.2005.09.070","article-title":"The \u03bdMSM, dark matter and neutrino masses","volume":"631","author":"Asaka","year":"2005","journal-title":"Phys. Lett. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.physletb.2005.06.020","article-title":"The \u03bdMSM, dark matter and baryon asymmetry of the universe","volume":"620","author":"Asaka","year":"2005","journal-title":"Phys. Lett. B"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"He, X.G., Oh, S., Tandean, S.J., and Wen, C.C. (2009). Large mixing of light and heavy neutrinos in seesaw models and the LHC. Phys. Rev. D, 80.","DOI":"10.1103\/PhysRevD.80.073012"},{"key":"ref_63","first-page":"3339","article-title":"Looking for signals beyond the neutrino Standard Model","volume":"38","author":"Zralek","year":"2007","journal-title":"Acta Phys. Polon. B"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Kersten, J., and Smirnov, A.Y. (2007). Right-handed neutrinos at CERN LHC and the mechanism of neutrino mass generation. Phys. Rev. D, 76.","DOI":"10.1103\/PhysRevD.76.073005"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/JHEP09(2010)108","article-title":"TeV scale see-saw mechanisms of neutrino mass generation, the Majorana nature of the heavy singlet neutrinos and (\u03b2\u03b2)0\u03bd-Decay","volume":"1009","author":"Ibarra","year":"2010","journal-title":"JHEP"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0370-2693(78)90132-6","article-title":"Time reversal violation in neutrino oscillation","volume":"72","author":"Cabibbo","year":"1978","journal-title":"Phys. Lett. B"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Gorbunov, D., and Shaposhnikov, M. (2007). How to find neutral leptons of the \u03bdMSM?. JHEP, 0710.","DOI":"10.1088\/1126-6708\/2007\/10\/015"},{"key":"ref_68","unstructured":"Shaposhnikov, M. Available online: http:\/\/arxiv.org\/abs\/0708.3550."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1146\/annurev.nucl.010909.083654","article-title":"The role of sterile neutrinos in cosmology and astrophysics","volume":"59","author":"Boyarsky","year":"2009","journal-title":"Ann. Rev. Nucl. Part. Sci."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Shaposhnikov, M. (2013). Neutrino physics within and beyond the three flavour oscillation. J. Phys. Conf. Ser., 408.","DOI":"10.1088\/1742-6596\/408\/1\/012015"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Canetti, L., Drewes, M., and Shaposhnikov, M. (2013). Sterile neutrinos as the origin of dark and baryonic matter. Phys. Rev. Lett, 110.","DOI":"10.1103\/PhysRevLett.110.061801"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Canetti, L., Drewes, M., Frossard, T, and Shaposhnikov, M. (2013). Dark matter, baryogenesis and neutrino oscillations from right handed neutrinos. Phys. Rev. D, 87.","DOI":"10.1103\/PhysRevD.87.093006"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Canetti, L., Drewes, M., and Garbrecht, B. (2014). Probing leptogenesis with GeV-scale sterile neutrinos at LHCb and Belle II. Phys. Rev. D, 90.","DOI":"10.1103\/PhysRevD.90.125005"},{"key":"ref_74","unstructured":"Drewes, M., and Garbrecht, B. Available online: http:\/\/arxiv.org\/abs\/1502.00477."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"5431","DOI":"10.1103\/PhysRevD.56.5431","article-title":"CP violation and baryogenesis due to heavy Majorana neutrinos","volume":"56","author":"Pilaftsis","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.nuclphysb.2007.07.002","article-title":"Resonant CP violation due to heavy neutrinos at the LHC","volume":"786","author":"Bray","year":"2007","journal-title":"Nucl. Phys. B"},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Akhmedov, E., Kartavtsev, A., Lindner, M., Michaels, L., and Smirnov, J. (2013). Improving Electro-Weak Fits with TeV-scale Sterile Neutrinos. JHEP, 1305.","DOI":"10.1007\/JHEP05(2013)081"},{"key":"ref_78","unstructured":"Qian, X., Zhang, C, Diwan, M., and Vogel, P. Available online: http:\/\/arxiv.org\/abs\/1308.5700."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Basso, L., Fischer, O., and van der Bij, JJ. (2014). Precision tests of unitarity in leptonic mixing. Europhys. Lett., 105.","DOI":"10.1209\/0295-5075\/105\/11001"},{"key":"ref_80","unstructured":"Bonivento, W., Boyarsky, A., Dijkstra, H., Egede, U., Ferro-Luzzi, M., Goddard, B., Golutvin, A., Gorbunov, D., Jacobsson, R., and Panman, J. Available online: http:\/\/arxiv.org\/abs\/1310.1762."},{"key":"ref_81","unstructured":"Jacobson, R. Available online: https:\/\/indico.cern.ch\/event\/252857\/contribution\/215."},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Dib, CO., and Kim, C.S. (D2014). Remarks on the lifetime of sterile neutrinos and the effect on detection of rare meson decays M+ \u2192 M\u2032 \u2212 \u2113+\u2113+. Phys. Rev., 89.","DOI":"10.1103\/PhysRevD.89.077301"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Bene\u0161, P., Faessler, A., \u0160imkovi\u0107, F., and Kovalenko, S. (2005). Sterile neutrinos in neutrinoless double beta decay. Phys. Rev. D, 71.","DOI":"10.1103\/PhysRevD.71.077901"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"6292","DOI":"10.1103\/PhysRevD.53.6292","article-title":"Inverse neutrinoless double beta decay revisited","volume":"53","author":"Boudjema","year":"1996","journal-title":"Phys. Rev. D"},{"key":"ref_85","unstructured":"London, D. Available online: http:\/\/arxiv.org\/abs\/hep-ph\/9907419."},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Kusenko, A., Pascoli, S., and Semikoz, D. (2005). New bounds on MeV sterile neutrinos based on the accelerator and Super-Kamiokande results. JHEP, 0511.","DOI":"10.1088\/1126-6708\/2005\/11\/028"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"(1985). Search for heavy neutrino decays in the BEBC beam dump experiment. Phys. Lett. B, 160, 207\u2013211.","DOI":"10.1016\/0370-2693(85)91493-5"},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"(1986). Mass and lifetime limits on new longlived particles in 300GeV\/c \u03c0\u2212 interactions. Z. Phys. C, 31, 21\u201332.","DOI":"10.1007\/BF01559588"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/0370-2693(88)90563-1","article-title":"Further limits on heavy neutrino couplings","volume":"203","author":"Bernardi","year":"1988","journal-title":"Phys. Lett. B"},{"key":"ref_90","unstructured":"(1995). Search for neutral weakly interacting massive particles in the Fermilab Tevatron wide band neutrino beam. Phys. Rev. D, 52."},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"(1999). Search for neutral heavy leptons in a high-energy neutrino beam. Phys. Rev. Lett, 83, 4943\u20134946.","DOI":"10.1103\/PhysRevLett.83.4943"},{"key":"ref_92","unstructured":"(1992). Search for isosinglet neutral heavy leptons in Z0 decays. Phys. Lett. B, 295, 371\u2013382."},{"key":"ref_93","unstructured":"(1995). Search for heavy isosinglet neutrinos. Phys. Lett. B, 343, 453\u2013458. Phys. Lett. B 1995, 351, 387\u2013392."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s002880050370","article-title":"Search for neutral heavy leptons produced in Z decays. Z","volume":"74","author":"DELPHI","year":"1997","journal-title":"Phys. C"},{"key":"ref_95","unstructured":"(2001). Search for heavy neutrinos mixing with tau neutrinos. Phys. Lett. B, 506, 27\u201338."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/S0370-2693(02)02769-7","article-title":"Limits on the mixing of tau neutrino to heavy neutrinos","volume":"550","author":"Orloff","year":"2002","journal-title":"Phys. Lett. B"},{"key":"ref_97","unstructured":"(2014). Review of Particle Physics. Chin. Phys. C, 38."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.physletb.2004.06.092","article-title":"Decay constants of heavy meson of 0-state in relativistic Salpeter method","volume":"596","author":"Kim","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_99","unstructured":"PIENU, Collaboration. (2011). Search for massive neutrinos in the decay \u03c0 \u2192 e\u03bd. Phys. Rev. D, 84."},{"key":"ref_100","first-page":"262","article-title":"Search for Heavy Neutrinos in Kaon Decay","volume":"840719","author":"Yamazaki","year":"1984","journal-title":"Conf. Proc. C"},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Hayano, R.S., Taniguchi, T., Yamanaka, T., Tanimori, T., Enomoto, R., Ishibashi, A., Ishikawa, T., Sato, S., Fujii, T., and Yamazaki, T. (1982). Heavy neutrino search using K\u03bc2 decay. Phys. Rev. Lett, 49.","DOI":"10.1103\/PhysRevLett.49.1305"},{"key":"ref_102","doi-asserted-by":"crossref","unstructured":"Kusenko, A., Pascoli, S., and Semikoz, D. (2005). New bounds on MeV sterile neutrinos based on the accelerator and Super-Kamiokande results. JHEP, 0511.","DOI":"10.1088\/1126-6708\/2005\/11\/028"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/S0370-2693(02)02769-7","article-title":"Limits on the mixing of tau neutrino to heavy neutrinos","volume":"550","author":"Orloff","year":"2002","journal-title":"Phys. Lett. B"},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Ruchayskiy, O., and Ivashko, A. (2012). Experimental bounds on sterile neutrino mixing angles. JHEP, 1206.","DOI":"10.1007\/JHEP06(2012)100"},{"key":"ref_105","unstructured":"Deppisch, F.F., Dev, P.S.B., and Pilaftsis, A. Available online: http:\/\/arxiv.org\/abs\/1502.06541."},{"key":"ref_106","unstructured":"Available online: http:\/\/www.fnal.gov\/projectx\/pdfs\/ProjectXwhitepaperJan.v2.pdf."},{"key":"ref_107","unstructured":"Geer, S. (2012). Private communication, Fermilab."},{"key":"ref_108","first-page":"172","article-title":"Inverse beta processes and nonconservation of lepton charge","volume":"7","author":"Pontecorvo","year":"1958","journal-title":"Sov. Phys. JETP"},{"key":"ref_109","unstructured":"(1968). Neutrino experiments and the problem of conservation of leptonic charge. Sov. Phys. JETP, 26, 984\u2013988. Zh. Eksp. Teor. Fiz. 1967, 53, 1717."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1143\/PTP.28.870","article-title":"Remarks on the unified model of elementary particles","volume":"28","author":"Maki","year":"1962","journal-title":"Prog. Theor. Phys."},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Bilenky, S. (2010). Introduction to the Physics of Massive and Mixed Neutrinos, Springer Verlag.","DOI":"10.1007\/978-3-642-14043-3"},{"key":"ref_112","doi-asserted-by":"crossref","unstructured":"Gamiz, E., Prades, J., and Scimemi, I. (2003). Charged kaon K \u2192 3\u03c0 CP violating asymmetries at NLO in CHPT. JHEP, 0310.","DOI":"10.1088\/1126-6708\/2003\/10\/042"},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0550-3213(01)00169-9","article-title":"Sterile neutrinos in tau lepton decays","volume":"607","author":"Gribanov","year":"2001","journal-title":"Nucl. Phys. 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