{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:41Z","timestamp":1760242541889,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,10,25]],"date-time":"2017-10-25T00:00:00Z","timestamp":1508889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portugal)","award":["UID\/FIS\/00099\/2013"],"award-info":[{"award-number":["UID\/FIS\/00099\/2013"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia  (Portugal)","award":["SFRH\/BPD\/101403\/2014","POPH\/FSE"],"award-info":[{"award-number":["SFRH\/BPD\/101403\/2014","POPH\/FSE"]}]},{"name":"New College of Florida","award":["summer faculty development funds"],"award-info":[{"award-number":["summer faculty development funds"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Violation of CPT and Lorentz symmetry in the photon sector is described within the minimal Standard-Model Extension by a dimension-3 Chern\u2013Simons-like operator parametrized by a four-vector parameter     k  A F      that has been very tightly bounded by astrophysical observations. On the other hand, in the context of the     S U ( 2 ) \u00d7 U ( 1 )     electroweak gauge sector of the Standard-Model Extension, CPT and Lorentz violation is described similarly, by dimension-3 operators parametrized by four-vector parameters     k 1     and     k 2    . In this work, we investigate in detail the effects of the resulting CPT and Lorentz violation in the photon and Z-boson sectors upon electroweak-symmetry breaking. In particular, we show that, for the photon sector, the relevant Lorentz-violating effects are described at the lowest order by the     k  A F      term, but that there are higher-order momentum-dependent effects due to photon-Z boson mixing. As bounds on CPT and Lorentz violation in the Z sector are relatively weak, these effects could be important phenomenologically. We investigate these effects in detail in this work.<\/jats:p>","DOI":"10.3390\/sym9110248","type":"journal-article","created":{"date-parts":[[2017,10,25]],"date-time":"2017-10-25T11:13:27Z","timestamp":1508930007000},"page":"248","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["CPT and Lorentz Violation in the Photon and Z-Boson Sector"],"prefix":"10.3390","volume":"9","author":[{"given":"Donald","family":"Colladay","sequence":"first","affiliation":[{"name":"New College of Florida, Sarasota, FL 34243, USA"}]},{"given":"Jacob","family":"Noordmans","sequence":"additional","affiliation":[{"name":"CENTRA, Departamento de F\u00edsica, Universidade do Algarve, 8005-139 Faro, Portugal"}]},{"given":"Robertus","family":"Potting","sequence":"additional","affiliation":[{"name":"CENTRA, Departamento de F\u00edsica, Universidade do Algarve, 8005-139 Faro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1103\/PhysRevD.39.683","article-title":"Spontaneous breaking of Lorentz symmetry in string theory","volume":"39","author":"Samuel","year":"1989","journal-title":"Phys. Rev. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1886","DOI":"10.1103\/PhysRevD.40.1886","article-title":"Gravitational phenomenology in higher-dimensional theories and strings","volume":"40","author":"Samuel","year":"1989","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/0550-3213(91)90071-5","article-title":"CPT and strings","volume":"359","author":"Potting","year":"1991","journal-title":"Nucl. Phys. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1023\/A:1026720723556","article-title":"Search for quantum gravity","volume":"31","author":"Ellis","year":"1999","journal-title":"Gen. Rel. Grav."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"124021","DOI":"10.1103\/PhysRevD.59.124021","article-title":"Nonstandard optics from quantum space-time","volume":"59","author":"Gambini","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"043","DOI":"10.1088\/1126-6708\/2002\/03\/043","article-title":"Loop-generated bounds on changes to the graviton dispersion relation","volume":"0203","author":"Burgess","year":"2002","journal-title":"JHEP"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6760","DOI":"10.1103\/PhysRevD.55.6760","article-title":"CPT violation and the standard model","volume":"55","author":"Colladay","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"116002","DOI":"10.1103\/PhysRevD.58.116002","article-title":"Lorentz-violating extension of the standard model","volume":"58","author":"Colladay","year":"1998","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"231602","DOI":"10.1103\/PhysRevLett.89.231602","article-title":"CPT violation implies violation of Lorentz invariance","volume":"89","author":"Greenberg","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"025025","DOI":"10.1103\/PhysRevD.95.025025","article-title":"Covariant quantization of CPT-violating photons","volume":"95","author":"Colladay","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"035034","DOI":"10.1103\/PhysRevD.96.035034","article-title":"Cosmic-ray fermion decay by emission of on-shell W bosons with CPT violation","volume":"96","author":"Colladay","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1103\/PhysRevD.41.1231","article-title":"Limits on a Lorentz- and parity-violating modification of electrodynamics","volume":"41","author":"Carroll","year":"1990","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1103\/RevModPhys.83.11","article-title":"Data tables for Lorentz and CPT violation","volume":"83","author":"Kostelecky","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"015020","DOI":"10.1103\/PhysRevD.80.015020","article-title":"Electrodynamics with Lorentz-violating operators of arbitrary dimension","volume":"80","author":"Kostelecky","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.physletb.2017.07.027","article-title":"Extended hamiltonian formalism and Lorentz-violating lagrangians","volume":"772","author":"Colladay","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_16","first-page":"716","article-title":"Bipartite Riemann-Finsler geometry and Lorentz violation","volume":"470","author":"Kostelecky","year":"2012","journal-title":"Phys. Lett. B"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/11\/248\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:48:24Z","timestamp":1760208504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/11\/248"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,25]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["sym9110248"],"URL":"https:\/\/doi.org\/10.3390\/sym9110248","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,10,25]]}}}