Abstract
We revisit mixing sum rule relations in the lepton and quark sectors under the assumption that the 1-3 elements of the flavour mixing matrices (\( {V}_L^u \), \( {V}_L^d \), \( {V}_L^e \), \( {V}_L^{\nu } \)) are zero in the flavour basis. We consider the exact relations resulting from the validity of this “zero 1-3 flavour mixing hypothesis” and analyse their implications based on the current experimental data, including effects from RG running. In particular, we analyse how the existing precise measurement of \( {\theta}_{13}^{\mathrm{PMNS}} \) allows to derive predictions for \( {\theta}_{23}^{\mathrm{PMNS}} \) in models with constrained \( {\theta}_{12}^{\mathrm{e}} \). As examples, we calculate the predictions for \( {\theta}_{23}^{\mathrm{PMNS}} \) which arise in 12 classes of Pati-Salam models and SU(5) GUTs that relate \( {\theta}_{12}^{\mathrm{e}} \) to \( {\theta}_{12}^{\mathrm{d}} \). We also derive a novel “lepton phase sum rule”, valid under the additional assumption of small charged lepton mixing contributions. We furthermore point out that, in the context of GUT flavour models, the quark and lepton CP violating phases δCKM and δPMNS can both be predicted from a single imaginary element in the mass matrices.
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References
S.F. King, Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification, JHEP 08 (2005) 105 [hep-ph/0506297] [INSPIRE].
I. Masina, A maximal atmospheric mixing from a maximal CP-violating phase, Phys. Lett. B 633 (2006) 134 [hep-ph/0508031] [INSPIRE].
S. Antusch and S.F. King, Charged lepton corrections to neutrino mixing angles and CP phases revisited, Phys. Lett. B 631 (2005) 42 [hep-ph/0508044] [INSPIRE].
S. Antusch, P. Huber, S.F. King and T. Schwetz, Neutrino mixing sum rules and oscillation experiments, JHEP 04 (2007) 060 [hep-ph/0702286] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, \( {\theta}_{13}^{PMNS} \) = θC/\( \sqrt{2} \) from GUTs, Nucl. Phys. B 866 (2013) 255 [arXiv:1205.1051] [INSPIRE].
S. Antusch, S.F. King, M. Malinsky and M. Spinrath, Quark mixing sum rules and the right unitarity triangle, Phys. Rev. D 81 (2010) 033008 [arXiv:0910.5127] [INSPIRE].
Ckmfitter group webpage, http://ckmfitter.in2p3.fr (2022).
P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt, Testing solar lepton mixing sum rules in neutrino oscillation experiments, JHEP 12 (2014) 122 [arXiv:1410.7573] [INSPIRE].
D. Marzocca, S.T. Petcov, A. Romanino and M.C. Sevilla, Nonzero |Ue3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle, JHEP 05 (2013) 073 [arXiv:1302.0423] [INSPIRE].
S.T. Petcov, Predicting the values of the leptonic CP-violation phases in theories with discrete flavour symmetries, Nucl. Phys. B 892 (2015) 400 [arXiv:1405.6006] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
S.F. King, Constructing the large mixing angle MNS matrix in seesaw models with right-handed neutrino dominance, JHEP 09 (2002) 011 [hep-ph/0204360] [INSPIRE].
S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].
S. Antusch and S.F. King, Sequential dominance, New J. Phys. 6 (2004) 110 [hep-ph/0405272] [INSPIRE].
S. Antusch, S. Boudjemaa and S.F. King, Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO, JHEP 09 (2010) 096 [arXiv:1003.5498] [INSPIRE].
Nufit webpage, http://www.nu-fit.org (october 2021).
I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, T. Schwetz and A. Zhou, The fate of hints: updated global analysis of three-flavor neutrino oscillations, JHEP 09 (2020) 178 [arXiv:2007.14792] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner and M. Ratz, Running neutrino masses, mixings and CP phases: Analytical results and phenomenological consequences, Nucl. Phys. B 674 (2003) 401 [hep-ph/0305273] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, JHEP 11 (2013) 115 [arXiv:1306.6879] [INSPIRE].
J.C. Pati and A. Salam, Is Baryon Number Conserved?, Phys. Rev. Lett. 31 (1973) 661 [INSPIRE].
J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. 11 (1975) 703] [INSPIRE].
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
H. Georgi, H.R. Quinn and S. Weinberg, Hierarchy of Interactions in Unified Gauge Theories, Phys. Rev. Lett. 33 (1974) 451 [INSPIRE].
H. Georgi, The state of the Art — Gauge Theories, AIP Conf. Proc. 23 (1975) 575 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
S. Antusch and V. Maurer, Large neutrino mixing angle \( {\theta}_{13}^{\mathrm{MNS}} \) and quark-lepton mass ratios in unified flavour models, Phys. Rev. D 84 (2011) 117301 [arXiv:1107.3728] [INSPIRE].
S. Antusch, C. Hohl and V. Susič, Yukawa ratio predictions in non-renormalizable SO(10) GUT models, JHEP 02 (2020) 086 [arXiv:1911.12807] [INSPIRE].
S. Antusch and M. Spinrath, New GUT predictions for quark and lepton mass ratios confronted with phenomenology, Phys. Rev. D 79 (2009) 095004 [arXiv:0902.4644] [INSPIRE].
S. Antusch, S.F. King and M. Spinrath, GUT predictions for quark-lepton Yukawa coupling ratios with messenger masses from non-singlets, Phys. Rev. D 89 (2014) 055027 [arXiv:1311.0877] [INSPIRE].
S. Antusch, C. Hohl, C.K. Khosa and V. Susic, Predicting δPMNS, \( {\theta}_{23}^{PMNS} \) and fermion mass ratios from flavour GUTs with CSD2, JHEP 12 (2018) 025 [arXiv:1808.09364] [INSPIRE].
J.M. Alves, F.J. Botella, G.C. Branco, F. Cornet-Gomez and M. Nebot, The framework for a common origin of δCKM and δPMNS, Eur. Phys. J. C 81 (2021) 727 [arXiv:2105.14054] [INSPIRE].
S. Antusch, S.F. King, C. Luhn and M. Spinrath, Right Unitarity Triangles and Tri-Bimaximal Mixing from Discrete Symmetries and Unification, Nucl. Phys. B 850 (2011) 477 [arXiv:1103.5930] [INSPIRE].
S. Antusch, M. Holthausen, M.A. Schmidt and M. Spinrath, Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle, Nucl. Phys. B 877 (2013) 752 [arXiv:1307.0710] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, A flavour GUT model with \( {\theta}_{13}^{PMNS} \) ≃ θC/\( \sqrt{2} \), Nucl. Phys. B 877 (2013) 772 [arXiv:1305.6612] [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, Inverse neutrino mass hierarchy in a flavour GUT model, Nucl. Phys. B 879 (2014) 19 [arXiv:1306.3984] [INSPIRE].
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Antusch, S., Hinze, K. & Saad, S. Implications of the zero 1-3 flavour mixing hypothesis: predictions for \( {\theta}_{23}^{\mathrm{PMNS}} \) and δPMNS. J. High Energ. Phys. 2022, 45 (2022). https://doi.org/10.1007/JHEP08(2022)045
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DOI: https://doi.org/10.1007/JHEP08(2022)045