{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T03:30:59Z","timestamp":1774409459993,"version":"3.50.1"},"reference-count":93,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T00:00:00Z","timestamp":1757635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T00:00:00Z","timestamp":1757635200000},"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 explore the phenomenology of Weinberg\u2019s <jats:italic>\u2124<\/jats:italic>\n            <jats:sub>2<\/jats:sub> \u00d7 <jats:italic>\u2124<\/jats:italic>\n            <jats:sub>2<\/jats:sub> symmetric three-Higgs-doublet potential, allowing for spontaneous violation of CP due to complex vacuum expectation values. An overview of all possible ways of satisfying the stationary-point conditions is given, with one, two or three non-vanishing vacuum expectation values, together with conditions for CP conservation in terms of basis invariants. All possible ways of satisfying the conditions for CP conservation are given. Scans of allowed parameter regions are given, together with measures of CP violation, in terms of the invariants. The light states identified in an earlier paper are further explored in terms of their CP-violating couplings. Loop-induced CP violation in <jats:italic>WWZ<\/jats:italic> couplings, as well as charge-asymmetric scattering are also commented on.<\/jats:p>","DOI":"10.1007\/jhep09(2025)111","type":"journal-article","created":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T02:26:00Z","timestamp":1757730360000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["CP-violation in the Weinberg 3HDM potential"],"prefix":"10.1007","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8155-4176","authenticated-orcid":false,"given":"O. M.","family":"Ogreid","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05phns765","id-type":"ROR","asserted-by":"publisher"}],"name":"Western Norway University of Applied Sciences"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6727-5311","authenticated-orcid":false,"given":"P.","family":"Osland","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03zga2b32","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Bergen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8744-5146","authenticated-orcid":false,"given":"M. N.","family":"Rebelo","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":[[2025,9,12]]},"reference":[{"key":"27191_CR1","doi-asserted-by":"crossref","unstructured":"S. Weinberg, Gauge Theory of CP Violation, Phys. Rev. Lett. 37 (1976) 657 [INSPIRE].","DOI":"10.1103\/PhysRevLett.37.657"},{"key":"27191_CR2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.075029","volume":"108","author":"R Plantey","year":"2023","unstructured":"R. Plantey et al., Weinberg\u2019s 3HDM potential with spontaneous CP violation, Phys. Rev. D 108 (2023) 075029 [arXiv:2208.13594] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR3","doi-asserted-by":"crossref","unstructured":"R. Plantey et al., Light scalars in the Weinberg 3HDM potential with spontaneous CP violation, PoS DISCRETE2020-2021 (2022) 064 [arXiv:2209.06499] [INSPIRE].","DOI":"10.22323\/1.405.0064"},{"key":"27191_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.91.015001","volume":"91","author":"T Chupp","year":"2019","unstructured":"T. Chupp, P. Fierlinger, M. Ramsey-Musolf and J. Singh, Electric dipole moments of atoms, molecules, nuclei, and particles, Rev. Mod. Phys. 91 (2019) 015001 [arXiv:1710.02504] [INSPIRE].","journal-title":"Rev. Mod. Phys."},{"key":"27191_CR5","doi-asserted-by":"publisher","first-page":"021","DOI":"10.1007\/JHEP01(2015)021","volume":"01","author":"IP Ivanov","year":"2015","unstructured":"I.P. Ivanov and C.C. Nishi, Symmetry breaking patterns in 3HDM, JHEP 01 (2015) 021 [arXiv:1410.6139] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR6","doi-asserted-by":"crossref","unstructured":"G.C. Branco, Spontaneous CP Nonconservation and Natural Flavor Conservation: A Minimal Model, Phys. Rev. D 22 (1980) 2901 [INSPIRE].","DOI":"10.1103\/PhysRevD.22.2901"},{"key":"27191_CR7","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/45\/21\/215201","volume":"45","author":"IP Ivanov","year":"2012","unstructured":"I.P. Ivanov, V. Keus and E. Vdovin, Abelian symmetries in multi-Higgs-doublet models, J. Phys. A 45 (2012) 215201 [arXiv:1112.1660] [INSPIRE].","journal-title":"J. Phys. A"},{"key":"27191_CR8","doi-asserted-by":"crossref","unstructured":"I. de Medeiros Varzielas and I.P. Ivanov, Recognizing symmetries in a 3HDM in a basis-independent way, Phys. Rev. D 100 (2019) 015008 [arXiv:1903.11110] [INSPIRE].","DOI":"10.1103\/PhysRevD.100.015008"},{"key":"27191_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.095008","volume":"101","author":"N Darvishi","year":"2020","unstructured":"N. Darvishi and A. Pilaftsis, Classifying Accidental Symmetries in Multi-Higgs Doublet Models, Phys. Rev. D 101 (2020) 095008 [arXiv:1912.00887] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR10","doi-asserted-by":"crossref","unstructured":"G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Int. Ser. Monogr. Phys. 103 (1999) 1 [INSPIRE].","DOI":"10.1093\/oso\/9780198503996.001.0001"},{"key":"27191_CR11","doi-asserted-by":"crossref","unstructured":"A. Mendez and A. Pomarol, Signals of CP violation in the Higgs sector, Phys. Lett. B 272 (1991) 313 [INSPIRE].","DOI":"10.1016\/0370-2693(91)91836-K"},{"key":"27191_CR12","doi-asserted-by":"crossref","unstructured":"L. Lavoura and J.P. Silva, Fundamental CP violating quantities in a SU(2) \u00d7 U(1) model with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph\/9404276] [INSPIRE].","DOI":"10.1103\/PhysRevD.50.4619"},{"key":"27191_CR13","doi-asserted-by":"crossref","unstructured":"F.J. Botella and J.P. Silva, Jarlskog-like invariants for theories with scalars and fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph\/9411288] [INSPIRE].","DOI":"10.1103\/PhysRevD.51.3870"},{"key":"27191_CR14","doi-asserted-by":"crossref","unstructured":"G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos, CP-odd invariants in models with several Higgs doublets, Phys. Lett. B 614 (2005) 187 [hep-ph\/0502118] [INSPIRE].","DOI":"10.1016\/j.physletb.2005.03.075"},{"key":"27191_CR15","doi-asserted-by":"crossref","unstructured":"J.F. Gunion and H.E. Haber, Conditions for CP-violation in the general two-Higgs-doublet model, Phys. Rev. D 72 (2005) 095002 [hep-ph\/0506227] [INSPIRE].","DOI":"10.1103\/PhysRevD.72.095002"},{"key":"27191_CR16","doi-asserted-by":"crossref","unstructured":"S. Davidson and H.E. Haber, Basis-independent methods for the two-Higgs-doublet model, Phys. Rev. D 72 (2005) 035004 [Erratum ibid. 72 (2005) 099902] [hep-ph\/0504050] [INSPIRE].","DOI":"10.1103\/PhysRevD.72.099902"},{"key":"27191_CR17","doi-asserted-by":"crossref","unstructured":"H.E. Haber and D. O\u2019Neil, Basis-independent methods for the two-Higgs-doublet model. II. The Significance of tan\u03b2, Phys. Rev. D 74 (2006) 015018 [Erratum ibid. 74 (2006) 059905] [hep-ph\/0602242] [INSPIRE].","DOI":"10.1103\/PhysRevD.74.059905"},{"key":"27191_CR18","doi-asserted-by":"publisher","first-page":"084","DOI":"10.1007\/JHEP11(2014)084","volume":"11","author":"B Grzadkowski","year":"2014","unstructured":"B. Grzadkowski, O.M. Ogreid and P. Osland, Measuring CP violation in Two-Higgs-Doublet models in light of the LHC Higgs data, JHEP 11 (2014) 084 [arXiv:1409.7265] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.94.115002","volume":"94","author":"B Grzadkowski","year":"2016","unstructured":"B. Grzadkowski, O.M. Ogreid and P. Osland, Spontaneous CP violation in the 2HDM: physical conditions and the alignment limit, Phys. Rev. D 94 (2016) 115002 [arXiv:1609.04764] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR20","unstructured":"Wolfram Inc., Mathematica, https:\/\/www.wolfram.com\/mathematica\/."},{"key":"27191_CR21","doi-asserted-by":"publisher","first-page":"1750145","DOI":"10.1142\/S0217751X17501457","volume":"32","author":"AG Akeroyd","year":"2017","unstructured":"A.G. Akeroyd, S. Moretti, K. Yagyu and E. Yildirim, Light charged Higgs boson scenario in 3-Higgs doublet models, Int. J. Mod. Phys. A 32 (2017) 1750145 [arXiv:1605.05881] [INSPIRE].","journal-title":"Int. J. Mod. Phys. A"},{"key":"27191_CR22","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/JHEP07(2021)158","volume":"07","author":"HE Logan","year":"2021","unstructured":"H.E. Logan, S. Moretti, D. Rojas-Ciofalo and M. Song, CP violation from charged Higgs bosons in the three Higgs doublet model, JHEP 07 (2021) 158 [arXiv:2012.08846] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.104.095006","volume":"104","author":"R Boto","year":"2021","unstructured":"R. Boto, J.C. Rom\u00e3o and J.P. Silva, Current bounds on the type-Z Z3 three-Higgs-doublet model, Phys. Rev. D 104 (2021) 095006 [arXiv:2106.11977] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR24","doi-asserted-by":"publisher","first-page":"045","DOI":"10.1007\/JHEP03(2023)045","volume":"03","author":"J Hernandez-Sanchez","year":"2023","unstructured":"J. Hernandez-Sanchez, V. Keus, S. Moretti and D. Sokolowska, Complementary collider and astrophysical probes of multi-component Dark Matter, JHEP 03 (2023) 045 [arXiv:2202.10514] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR25","unstructured":"J. Hernandez-Sanchez et al., Complementary Probes of Two-component Dark Matter, arXiv:2012.11621 [INSPIRE]."},{"key":"27191_CR26","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/JHEP11(2024)108","volume":"11","author":"R Boto","year":"2024","unstructured":"R. Boto, P.N. Figueiredo, J.C. Rom\u00e3o and J.P. Silva, Novel two component dark matter features in the Z2 \u00d7 Z2 3HDM, JHEP 11 (2024) 108 [arXiv:2407.15933] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR27","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":"27191_CR28","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":"27191_CR29","unstructured":"F. Borzumati and C. Greub, 2HDMs predictions for $$ \\overline{B}\\to {X}_s\\gamma $$ in NLO QCD, Phys. Rev. D 58 (1998) 074004 [hep-ph\/9802391] [INSPIRE]."},{"key":"27191_CR30","doi-asserted-by":"crossref","unstructured":"M. Ciuchini, G. Degrassi, P. Gambino and G.F. Giudice, Next-to-leading QCD corrections to B \u2192 Xs\u03b3: Standard model and two Higgs doublet model, Nucl. Phys. B 527 (1998) 21 [hep-ph\/9710335] [INSPIRE].","DOI":"10.1016\/S0550-3213(98)00244-2"},{"key":"27191_CR31","doi-asserted-by":"crossref","unstructured":"T. Hermann, M. Misiak and M. Steinhauser, $$ \\overline{B}\\to {X}_s\\gamma $$ in the Two Higgs Doublet Model up to Next-to-Next-to-Leading Order in QCD, JHEP 11 (2012) 036 [arXiv:1208.2788] [INSPIRE].","DOI":"10.1007\/JHEP11(2012)036"},{"key":"27191_CR32","unstructured":"Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE]."},{"key":"27191_CR33","unstructured":"CMS collaboration, Analysis of the CP structure of the Yukawa coupling between the Higgs boson and \u03c4 leptons in proton-proton collisions at $$ \\sqrt{s} $$ = 13 TeV, JHEP 06 (2022) 012 [arXiv:2110.04836] [INSPIRE]."},{"key":"27191_CR34","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.ppnp.2013.03.003","volume":"71","author":"J Engel","year":"2013","unstructured":"J. Engel, M.J. Ramsey-Musolf and U. van Kolck, Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond, Prog. Part. Nucl. Phys. 71 (2013) 21 [arXiv:1303.2371] [INSPIRE].","journal-title":"Prog. Part. Nucl. Phys."},{"key":"27191_CR35","doi-asserted-by":"crossref","unstructured":"M.E. Peskin and T. Takeuchi, A New constraint on a strongly interacting Higgs sector, Phys. Rev. Lett. 65 (1990) 964 [INSPIRE].","DOI":"10.1103\/PhysRevLett.65.964"},{"key":"27191_CR36","doi-asserted-by":"crossref","unstructured":"M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [INSPIRE].","DOI":"10.1103\/PhysRevD.46.381"},{"key":"27191_CR37","doi-asserted-by":"crossref","unstructured":"I. Maksymyk, C.P. Burgess and D. London, Beyond S, T and U, Phys. Rev. D 50 (1994) 529 [hep-ph\/9306267] [INSPIRE].","DOI":"10.1103\/PhysRevD.50.529"},{"key":"27191_CR38","doi-asserted-by":"publisher","DOI":"10.1088\/0954-3899\/35\/7\/075001","volume":"35","author":"W Grimus","year":"2008","unstructured":"W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, A Precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [arXiv:0711.4022] [INSPIRE].","journal-title":"J. Phys. G"},{"key":"27191_CR39","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.nuclphysb.2008.04.019","volume":"801","author":"W Grimus","year":"2008","unstructured":"W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, The Oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B 801 (2008) 81 [arXiv:0802.4353] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"27191_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.055026","volume":"108","author":"P Asadi","year":"2023","unstructured":"P. Asadi et al., Oblique lessons from the W-mass measurement at CDF II, Phys. Rev. D 108 (2023) 055026 [arXiv:2204.05283] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR41","doi-asserted-by":"crossref","unstructured":"J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, A Phenomenological Profile of the Higgs Boson, Nucl. Phys. B 106 (1976) 292 [INSPIRE].","DOI":"10.1016\/0550-3213(76)90382-5"},{"key":"27191_CR42","unstructured":"M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-Energy Theorems for Higgs Boson Couplings to Photons, Sov. J. Nucl. Phys. 30 (1979) 711 [INSPIRE]."},{"key":"27191_CR43","unstructured":"J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunter\u2019s Guide, Front. Phys. 80 (2000) 1 [INSPIRE]."},{"key":"27191_CR44","doi-asserted-by":"crossref","unstructured":"A. Djouadi, The Anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rept. 459 (2008) 1 [hep-ph\/0503173] [INSPIRE].","DOI":"10.1016\/j.physrep.2007.10.005"},{"key":"27191_CR45","doi-asserted-by":"crossref","unstructured":"B. Grinstein and M.B. Wise, Weak Radiative B Meson Decay as a Probe of the Higgs Sector, Phys. Lett. B 201 (1988) 274 [INSPIRE].","DOI":"10.1016\/0370-2693(88)90227-4"},{"key":"27191_CR46","doi-asserted-by":"crossref","unstructured":"W.-S. Hou and R.S. Willey, Effects of Extended Higgs Sector on Loop Induced B Decays, Nucl. Phys. B 326 (1989) 54 [INSPIRE].","DOI":"10.1016\/0550-3213(89)90434-3"},{"key":"27191_CR47","doi-asserted-by":"crossref","unstructured":"B. Grinstein, R.P. Springer and M.B. Wise, Strong Interaction Effects in Weak Radiative $$ \\overline{B} $$ Meson Decay, Nucl. Phys. B 339 (1990) 269 [INSPIRE].","DOI":"10.1016\/0550-3213(90)90350-M"},{"key":"27191_CR48","doi-asserted-by":"crossref","unstructured":"A.J. Buras, M. Misiak, M. Munz and S. Pokorski, Theoretical uncertainties and phenomenological aspects of B \u2192 Xs\u03b3 decay, Nucl. Phys. B 424 (1994) 374 [hep-ph\/9311345] [INSPIRE].","DOI":"10.1016\/0550-3213(94)90299-2"},{"key":"27191_CR49","doi-asserted-by":"crossref","unstructured":"P. Ciafaloni, A. Romanino and A. Strumia, Two loop QCD corrections to charged Higgs mediated b \u2192 s\u03b3 decay, Nucl. Phys. B 524 (1998) 361 [hep-ph\/9710312] [INSPIRE].","DOI":"10.1016\/S0550-3213(98)00190-4"},{"key":"27191_CR50","doi-asserted-by":"crossref","unstructured":"C. Bobeth, M. Misiak and J. Urban, Matching conditions for b \u2192 s\u03b3 and b \u2192 sgluon in extensions of the standard model, Nucl. Phys. B 567 (2000) 153 [hep-ph\/9904413] [INSPIRE].","DOI":"10.1016\/S0550-3213(99)00688-4"},{"key":"27191_CR51","doi-asserted-by":"crossref","unstructured":"C. Bobeth, M. Misiak and J. Urban, Photonic penguins at two loops and mt dependence of BR[B \u2192 Xsl+l\u2212], Nucl. Phys. B 574 (2000) 291 [hep-ph\/9910220] [INSPIRE].","DOI":"10.1016\/S0550-3213(00)00007-9"},{"key":"27191_CR52","doi-asserted-by":"crossref","unstructured":"P. Gambino and M. Misiak, Quark mass effects in $$ \\overline{B}\\to {X}_s\\gamma $$, Nucl. Phys. B 611 (2001) 338 [hep-ph\/0104034] [INSPIRE].","DOI":"10.1016\/S0550-3213(01)00347-9"},{"key":"27191_CR53","doi-asserted-by":"crossref","unstructured":"K. Cheung and O.C.W. Kong, Can the two Higgs doublet model survive the constraint from the muon anomalous magnetic moment as suggested?, Phys. Rev. D 68 (2003) 053003 [hep-ph\/0302111] [INSPIRE].","DOI":"10.1103\/PhysRevD.68.053003"},{"key":"27191_CR54","doi-asserted-by":"crossref","unstructured":"M. Misiak and M. Steinhauser, Three loop matching of the dipole operators for b \u2192 s\u03b3 and b \u2192 sg, Nucl. Phys. B 683 (2004) 277 [hep-ph\/0401041] [INSPIRE].","DOI":"10.1016\/j.nuclphysb.2004.02.006"},{"key":"27191_CR55","doi-asserted-by":"crossref","unstructured":"M. Czakon, U. Haisch and M. Misiak, Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays, JHEP 03 (2007) 008 [hep-ph\/0612329] [INSPIRE].","DOI":"10.1088\/1126-6708\/2007\/03\/008"},{"key":"27191_CR56","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.221801","volume":"114","author":"M Misiak","year":"2015","unstructured":"M. Misiak et al., Updated NNLO QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"27191_CR57","doi-asserted-by":"crossref","unstructured":"M. Misiak and M. Steinhauser, Weak radiative decays of the B meson and bounds on $$ {M}_{H^{\\pm }} $$ in the Two-Higgs-Doublet Model, Eur. Phys. J. C 77 (2017) 201 [arXiv:1702.04571] [INSPIRE].","DOI":"10.1140\/epjc\/s10052-017-4776-y"},{"key":"27191_CR58","doi-asserted-by":"crossref","unstructured":"M. Misiak, A. Rehman and M. Steinhauser, Towards $$ \\overline{B}\\to {X}_s\\gamma $$ at the NNLO in QCD without interpolation in mc, JHEP 06 (2020) 175 [arXiv:2002.01548] [INSPIRE].","DOI":"10.1007\/JHEP06(2020)175"},{"key":"27191_CR59","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":"27191_CR60","doi-asserted-by":"crossref","unstructured":"M. Misiak and M. Steinhauser, NNLO QCD corrections to the $$ \\overline{B}\\to {X}_s\\gamma $$ matrix elements using interpolation in m(c), Nucl. Phys. B 764 (2007) 62 [hep-ph\/0609241] [INSPIRE].","DOI":"10.1016\/j.nuclphysb.2006.11.027"},{"key":"27191_CR61","doi-asserted-by":"crossref","unstructured":"S.M. Barr and A. Zee, Electric Dipole Moment of the Electron and of the Neutron, Phys. Rev. Lett. 65 (1990) 21 [Erratum ibid. 65 (1990) 2920] [INSPIRE].","DOI":"10.1103\/PhysRevLett.65.21"},{"key":"27191_CR62","doi-asserted-by":"crossref","unstructured":"A. Pilaftsis, Higgs mediated electric dipole moments in the MSSM: An application to baryogenesis and Higgs searches, Nucl. Phys. B 644 (2002) 263 [hep-ph\/0207277] [INSPIRE].","DOI":"10.1016\/S0550-3213(02)00826-X"},{"key":"27191_CR63","doi-asserted-by":"crossref","unstructured":"ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature 562 (2018) 355 [INSPIRE].","DOI":"10.1038\/s41586-018-0599-8"},{"key":"27191_CR64","doi-asserted-by":"crossref","unstructured":"T.S. Roussy et al., An improved bound on the electron\u2019s electric dipole moment, Science 381 (2023) adg4084 [arXiv:2212.11841] [INSPIRE].","DOI":"10.1126\/science.adg4084"},{"key":"27191_CR65","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.095038","volume":"106","author":"HE Haber","year":"2022","unstructured":"H.E. Haber, V. Keus and R. Santos, P-even, CP-violating signals in scalar-mediated processes, Phys. Rev. D 106 (2022) 095038 [arXiv:2206.09643] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR66","doi-asserted-by":"crossref","unstructured":"K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, Probing the Weak Boson Sector in e+e\u2212 \u2192 W +W\u2212, Nucl. Phys. B 282 (1987) 253 [INSPIRE].","DOI":"10.1016\/0550-3213(87)90685-7"},{"key":"27191_CR67","unstructured":"ATLAS collaboration, Measurement of WW\/WZ \u2192 \u2113\u03bdqq\u2032 production with the hadronically decaying boson reconstructed as one or two jets in pp collisions at $$ \\sqrt{s} $$ = 8 TeV with ATLAS, and constraints on anomalous gauge couplings, Eur. Phys. J. C 77 (2017) 563 [arXiv:1706.01702] [INSPIRE]."},{"key":"27191_CR68","unstructured":"CMS collaboration, Search for anomalous triple gauge couplings in WW and WZ production in lepton + jet events in proton-proton collisions at $$ \\sqrt{s} $$ = 13 TeV, JHEP 12 (2019) 062 [arXiv:1907.08354] [INSPIRE]."},{"key":"27191_CR69","unstructured":"CMS collaboration, Measurements of pp \u2192 ZZ production cross sections and constraints on anomalous triple gauge couplings at $$ \\sqrt{s} $$ = 13 TeV, Eur. Phys. J. C 81 (2021) 200 [arXiv:2009.01186] [INSPIRE]."},{"key":"27191_CR70","doi-asserted-by":"crossref","unstructured":"B. Grzadkowski, O.M. Ogreid and P. Osland, CP-Violation in the ZZZ and ZWW vertices at e+e\u2212 colliders in Two-Higgs-Doublet Models, JHEP 05 (2016) 025 [Erratum ibid. 11 (2017) 002] [arXiv:1603.01388] [INSPIRE].","DOI":"10.1007\/JHEP05(2016)025"},{"key":"27191_CR71","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.035001","volume":"97","author":"JL Feng","year":"2018","unstructured":"J.L. Feng, I. Galon, F. Kling and S. Trojanowski, ForwArd Search ExpeRiment at the LHC, Phys. Rev. D 97 (2018) 035001 [arXiv:1708.09389] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR72","doi-asserted-by":"publisher","first-page":"922","DOI":"10.1140\/epjc\/s10052-020-08438-1","volume":"80","author":"P Drechsel","year":"2020","unstructured":"P. Drechsel, G. Moortgat-Pick and G. Weiglein, Prospects for direct searches for light Higgs bosons at the ILC with 250 GeV, Eur. Phys. J. C 80 (2020) 922 [arXiv:1801.09662] [INSPIRE].","journal-title":"Eur. Phys. J. C"},{"key":"27191_CR73","doi-asserted-by":"publisher","first-page":"001","DOI":"10.1007\/JHEP08(2023)001","volume":"08","author":"F Kling","year":"2023","unstructured":"F. Kling et al., Light Scalars at FASER, JHEP 08 (2023) 001 [arXiv:2212.06186] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR74","doi-asserted-by":"crossref","unstructured":"T. Robens, A short overview on low mass scalars at future lepton colliders, in the proceedings of the International Workshop on Future Linear Colliders, Menlo Park, U.S.A. (2023) [arXiv:2307.15962] [INSPIRE].","DOI":"10.1051\/epjconf\/202431501025"},{"key":"27191_CR75","unstructured":"CMS collaboration, Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at $$ \\sqrt{s} $$ = 8 and 13 TeV, Phys. Lett. B 793 (2019) 320 [arXiv:1811.08459] [INSPIRE]."},{"key":"27191_CR76","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1140\/epjc\/s10052-019-7561-2","volume":"80","author":"T Biek\u00f6tter","year":"2020","unstructured":"T. Biek\u00f6tter, M. Chakraborti and S. Heinemeyer, A 96 GeV Higgs boson in the N2HDM, Eur. Phys. J. C 80 (2020) 2 [arXiv:1903.11661] [INSPIRE].","journal-title":"Eur. Phys. J. C"},{"key":"27191_CR77","unstructured":"S. Heinemeyer et al., A 96 GeV Higgs Boson in the 2HDMS: e+e\u2212 collider prospects, in the proceedings of the International Workshop on Future Linear Colliders, Online conference, Switzerland (2021) [arXiv:2105.11189] [INSPIRE]."},{"key":"27191_CR78","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.075003","volume":"106","author":"S Heinemeyer","year":"2022","unstructured":"S. Heinemeyer et al., Phenomenology of a 96 GeV Higgs boson in the 2HDM with an additional singlet, Phys. Rev. D 106 (2022) 075003 [arXiv:2112.11958] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR79","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/JHEP08(2022)201","volume":"08","author":"T Biek\u00f6tter","year":"2022","unstructured":"T. Biek\u00f6tter, S. Heinemeyer and G. Weiglein, Mounting evidence for a 95 GeV Higgs boson, JHEP 08 (2022) 201 [arXiv:2203.13180] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR80","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1140\/epjc\/s10052-023-11635-3","volume":"83","author":"T Biek\u00f6tter","year":"2023","unstructured":"T. Biek\u00f6tter, S. Heinemeyer and G. Weiglein, Excesses in the low-mass Higgs-boson search and the W-boson mass measurement, Eur. Phys. J. C 83 (2023) 450 [arXiv:2204.05975] [INSPIRE].","journal-title":"Eur. Phys. J. C"},{"key":"27191_CR81","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2023.138217","volume":"846","author":"T Biek\u00f6tter","year":"2023","unstructured":"T. Biek\u00f6tter, S. Heinemeyer and G. Weiglein, The CMS di-photon excess at 95 GeV in view of the LHC Run 2 results, Phys. Lett. B 846 (2023) 138217 [arXiv:2303.12018] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"27191_CR82","doi-asserted-by":"crossref","unstructured":"T. Biek\u00f6tter, S. Heinemeyer and G. Weiglein, 95.4 GeV diphoton excess at ATLAS and CMS, Phys. Rev. D 109 (2024) 035005 [arXiv:2306.03889] [INSPIRE].","DOI":"10.1103\/PhysRevD.109.035005"},{"key":"27191_CR83","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.055008","volume":"101","author":"J Cao","year":"2020","unstructured":"J. Cao et al., 96 GeV diphoton excess in seesaw extensions of the natural NMSSM, Phys. Rev. D 101 (2020) 055008 [arXiv:1908.07206] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"27191_CR84","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2022.137245","volume":"832","author":"R Benbrik","year":"2022","unstructured":"R. Benbrik, M. Boukidi, S. Moretti and S. Semlali, Explaining the 96 GeV Di-photon anomaly in a generic 2HDM Type-III, Phys. Lett. B 832 (2022) 137245 [arXiv:2204.07470] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"27191_CR85","doi-asserted-by":"publisher","first-page":"017","DOI":"10.1007\/JHEP11(2023)017","volume":"11","author":"D Azevedo","year":"2023","unstructured":"D. Azevedo, T. Biek\u00f6tter and P.M. Ferreira, 2HDM interpretations of the CMS diphoton excess at 95 GeV, JHEP 11 (2023) 017 [arXiv:2305.19716] [INSPIRE].","journal-title":"JHEP"},{"key":"27191_CR86","unstructured":"LEP Higgs Working Group for Higgs boson searches et al. collaborations, Search for the standard model Higgs boson at LEP, in the proceedings of the 2001 Europhysics Conference on High Energy Physics, Budapest, Hungary (2001) [hep-ex\/0107029] [INSPIRE]."},{"key":"27191_CR87","doi-asserted-by":"crossref","unstructured":"P.A. McNamara and S.L. Wu, The Higgs particle in the standard model: Experimental results from LEP, Rept. Prog. Phys. 65 (2002) 465 [INSPIRE].","DOI":"10.1088\/0034-4885\/65\/4\/201"},{"key":"27191_CR88","unstructured":"CMS collaboration, Searches for additional Higgs bosons and for vector leptoquarks in \u03c4\u03c4 final states in proton-proton collisions at $$ \\sqrt{s} $$ = 13 TeV, JHEP 07 (2023) 073 [arXiv:2208.02717] [INSPIRE]."},{"key":"27191_CR89","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1140\/epjc\/s10052-022-11028-y","volume":"82","author":"S Iguro","year":"2022","unstructured":"S. Iguro, T. Kitahara and Y. Omura, Scrutinizing the 95\u2013100 GeV di-tau excess in the top associated process, Eur. Phys. J. C 82 (2022) 1053 [arXiv:2205.03187] [INSPIRE].","journal-title":"Eur. Phys. J. C"},{"key":"27191_CR90","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1038\/s42254-024-00703-6","volume":"6","author":"A Crivellin","year":"2024","unstructured":"A. Crivellin and B. Mellado, Anomalies in particle physics and their implications for physics beyond the standard model, Nature Rev. Phys. 6 (2024) 294 [arXiv:2309.03870] [INSPIRE].","journal-title":"Nature Rev. Phys."},{"key":"27191_CR91","unstructured":"ATLAS collaboration, Search for diphoton resonances in the 66 to 110 GeV mass range using 140 fb\u22121 of 13 TeV pp collisions collected with the ATLAS detector, ATLAS-CONF-2023-035, CERN, Geneva (2023)."},{"key":"27191_CR92","unstructured":"ATLAS collaboration, ATLAS searches for additional scalars and exotic Higgs boson decays with the LHC Run 2 dataset, Phys. Rept. 1116 (2025) 184 [arXiv:2405.04914] [INSPIRE]."},{"key":"27191_CR93","unstructured":"T. Hahn, Routines for the diagonalization of complex matrices, physics\/0607103 [INSPIRE]."}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP09(2025)111.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP09(2025)111\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP09(2025)111.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T19:58:45Z","timestamp":1759867125000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP09(2025)111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,12]]},"references-count":93,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["27191"],"URL":"https:\/\/doi.org\/10.1007\/jhep09(2025)111","relation":{"has-preprint":[{"id-type":"arxiv","id":"2411.05480","asserted-by":"subject"}]},"ISSN":["1029-8479"],"issn-type":[{"value":"1029-8479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,12]]},"assertion":[{"value":"12 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 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":"111"}}