Abstract
We propose a minimal A4 flavor symmetric model, assisted by Z2 × Z3 symmetry, which can naturally takes care of the appropriate lepton mixing and neutrino masses via Type-I seesaw. It turns out that the framework, originated due to a specific flavor structure, favors the normal hierarchy of light neutrinos and simultaneously narrows down the range of Dirac CP violating phase. It predicts an interesting correlation between the atmospheric mixing angle and the Dirac CP phase too. While the flavor structure indicates an exact degeneracy of the right-handed neutrino masses, renormalization group running of the same from a high scale is shown to make it quasi-degenerate and a successful flavor leptogenesis takes place within the allowed parameter space obtained from neutrino phenomenology.
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References
Super-Kamiokande collaboration, Constraints on neutrino oscillations using 1258 days of Super-Kamiokande solar neutrino data, Phys. Rev. Lett. 86 (2001) 5656 [hep-ex/0103033] [INSPIRE].
Super-Kamiokande collaboration, Determination of solar neutrino oscillation parameters using 1496 days of Super-Kamiokande I data, Phys. Lett. B 539 (2002) 179 [hep-ex/0205075] [INSPIRE].
Super-Kamiokande collaboration, A measurement of atmospheric neutrino oscillation parameters by Super-Kamiokande I, Phys. Rev. D 71 (2005) 112005 [hep-ex/0501064] [INSPIRE].
SNO collaboration, Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89 (2002) 011301 [nucl-ex/0204008] [INSPIRE].
SNO collaboration, Measurement of day and night neutrino energy spectra at SNO and constraints on neutrino mixing parameters, Phys. Rev. Lett. 89 (2002) 011302 [nucl-ex/0204009] [INSPIRE].
KamLAND collaboration, Precision measurement of neutrino oscillation parameters with KamLAND, Phys. Rev. Lett. 100 (2008) 221803 [arXiv:0801.4589] [INSPIRE].
T2K collaboration, Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].
Double CHOOZ collaboration, Indication of reactor \( {\overline{v}}_e \) disappearance in the double CHOOZ experiment, Phys. Rev. Lett. 108 (2012) 131801 [arXiv:1112.6353] [INSPIRE].
T2K collaboration, Observation of electron neutrino appearance in a muon neutrino beam, Phys. Rev. Lett. 112 (2014) 061802 [arXiv:1311.4750] [INSPIRE].
P. Minkowski, μ → eγ at a rate of one out of 109 muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
R. N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
R. N. Mohapatra, Mechanism for understanding small neutrino mass in superstring theories, Phys. Rev. Lett. 56 (1986) 561 [INSPIRE].
M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. B 94 (1980) 61 [INSPIRE].
G. Lazarides, Q. Shafi and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B 181 (1981) 287 [INSPIRE].
J. Schechter and J. W. F. Valle, Neutrino masses in SU(2) × U(1) theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].
R. N. Mohapatra and J. W. F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34 (1986) 1642 [INSPIRE].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
Z.-Z. Xing, Flavor structures of charged fermions and massive neutrinos, Phys. Rept. 854 (2020) 1 [arXiv:1909.09610] [INSPIRE].
S. F. King, Models of neutrino mass, mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
W. Grimus and P. O. Ludl, Finite flavour groups of fermions, J. Phys. A 45 (2012) 233001 [arXiv:1110.6376] [INSPIRE].
S. F. King, Unified models of neutrinos, flavour and CP-violation, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413] [INSPIRE].
S. F. King and C. Luhn, Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models, JHEP 09 (2011) 042 [arXiv:1107.5332] [INSPIRE].
S. F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
D. Wyler, Discrete symmetries in the six quark SU(2) × U(1) model, Phys. Rev. D 19 (1979) 3369 [INSPIRE].
G. C. Branco, H. P. Nilles and V. Rittenberg, Fermion masses and hierarchy of symmetry breaking, Phys. Rev. D 21 (1980) 3417 [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].
E. Ma and G. Rajasekaran, Softly broken A4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].
E. Ma, A4 symmetry and neutrinos with very different masses, Phys. Rev. D 70 (2004) 031901 [hep-ph/0404199] [INSPIRE].
G. Altarelli and D. Meloni, A simplest A4 model for tri-bimaximal neutrino mixing, J. Phys. G 36 (2009) 085005 [arXiv:0905.0620] [INSPIRE].
P. F. Harrison, D. H. Perkins and W. G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
P. F. Harrison and W. G. Scott, Symmetries and generalizations of tri-bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [INSPIRE].
Daya Bay collaboration, Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
RENO collaboration, Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
G. C. Branco, R. Gonzalez Felipe, F. R. Joaquim and H. Serodio, Spontaneous leptonic CP-violation and nonzero θ13, Phys. Rev. D 86 (2012) 076008 [arXiv:1203.2646] [INSPIRE].
C.-C. Li, J.-N. Lu and G.-J. Ding, A4 and CP symmetry and a model with maximal CP-violation, Nucl. Phys. B 913 (2016) 110 [arXiv:1608.01860] [INSPIRE].
T. Araki, J. Mei and Z.-Z. Xing, Intrinsic deviation from the tri-bimaximal neutrino mixing in a class of A4 flavor models, Phys. Lett. B 695 (2011) 165 [arXiv:1010.3065] [INSPIRE].
N. Memenga, W. Rodejohann and H. Zhang, A4 flavor symmetry model for Dirac neutrinos and sizable Ue3, Phys. Rev. D 87 (2013) 053021 [arXiv:1301.2963] [INSPIRE].
D. Borah and B. Karmakar, A4 flavour model for Dirac neutrinos: type I and inverse seesaw, Phys. Lett. B 780 (2018) 461 [arXiv:1712.06407] [INSPIRE].
D. Borah, B. Karmakar and D. Nanda, Common origin of Dirac neutrino mass and freeze-in massive particle dark matter, JCAP 07 (2018) 039 [arXiv:1805.11115] [INSPIRE].
D. Borah and B. Karmakar, Linear seesaw for Dirac neutrinos with A4 flavour symmetry, Phys. Lett. B 789 (2019) 59 [arXiv:1806.10685] [INSPIRE].
G. C. Branco, R. Gonzalez Felipe, M. N. Rebelo and H. Serodio, Resonant leptogenesis and tribimaximal leptonic mixing with A4 symmetry, Phys. Rev. D 79 (2009) 093008 [arXiv:0904.3076] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
M. A. Luty, Baryogenesis via leptogenesis, Phys. Rev. D 45 (1992) 455 [INSPIRE].
M. Plümacher, Baryogenesis and lepton number violation, Z. Phys. C 74 (1997) 549 [hep-ph/9604229] [INSPIRE].
L. Covi, E. Roulet and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384 (1996) 169 [hep-ph/9605319] [INSPIRE].
A. Datta, R. Roshan and A. Sil, Imprint of the seesaw mechanism on feebly interacting dark matter and the baryon asymmetry, arXiv:2104.02030 [INSPIRE].
D. Borah, M. K. Das and A. Mukherjee, Common origin of nonzero θ13 and baryon asymmetry of the universe in a TeV scale seesaw model with A4 flavor symmetry, Phys. Rev. D 97 (2018) 115009 [arXiv:1711.02445] [INSPIRE].
B. Karmakar and A. Sil, Nonzero θ13 and leptogenesis in a type-I seesaw model with A4 symmetry, Phys. Rev. D 91 (2015) 013004 [arXiv:1407.5826] [INSPIRE].
B. Karmakar and A. Sil, Spontaneous CP-violation in lepton-sector: a common origin for θ13, the Dirac CP phase, and leptogenesis, Phys. Rev. D 93 (2016) 013006 [arXiv:1509.07090] [INSPIRE].
S. Bhattacharya, B. Karmakar, N. Sahu and A. Sil, Unifying the flavor origin of dark matter with leptonic nonzero θ13, Phys. Rev. D 93 (2016) 115041 [arXiv:1603.04776] [INSPIRE].
S. Bhattacharya, B. Karmakar, N. Sahu and A. Sil, Flavor origin of dark matter and its relation with leptonic nonzero θ13 and Dirac CP phase δ, JHEP 05 (2017) 068 [arXiv:1611.07419] [INSPIRE].
C. Hagedorn, E. Molinaro and S. T. Petcov, Majorana phases and leptogenesis in see-saw models with A4 symmetry, JHEP 09 (2009) 115 [arXiv:0908.0240] [INSPIRE].
E. E. Jenkins and A. V. Manohar, Tribimaximal mixing, leptogenesis, and θ13, Phys. Lett. B 668 (2008) 210 [arXiv:0807.4176] [INSPIRE].
P. Das, M. K. Das and N. Khan, Phenomenological study of neutrino mass, dark matter and baryogenesis within the framework of minimal extended seesaw, JHEP 03 (2020) 018 [arXiv:1911.07243] [INSPIRE].
A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56 (1997) 5431 [hep-ph/9707235] [INSPIRE].
B. Karmakar and A. Sil, An A4 realization of inverse seesaw: neutrino masses, θ13 and leptonic non-unitarity, Phys. Rev. D 96 (2017) 015007 [arXiv:1610.01909] [INSPIRE].
X.-G. He, Y.-Y. Keum and R. R. Volkas, A4 flavor symmetry breaking scheme for understanding quark and neutrino mixing angles, JHEP 04 (2006) 039 [hep-ph/0601001] [INSPIRE].
Y. Lin, A predictive A4 model, charged lepton hierarchy and tri-bimaximal sum rule, Nucl. Phys. B 813 (2009) 91 [arXiv:0804.2867] [INSPIRE].
W. Rodejohann and X.-J. Xu, A left-right symmetric flavor symmetry model, Eur. Phys. J. C 76 (2016) 138 [arXiv:1509.03265] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
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].
P. Langacker, S. T. Petcov, G. Steigman and S. Toshev, On the Mikheev-Smirnov-Wolfenstein (MSW) mechanism of amplification of neutrino oscillations in matter, Nucl. Phys. B 282 (1987) 589 [INSPIRE].
S. Vagnozzi et al., Unveiling ν secrets with cosmological data: neutrino masses and mass hierarchy, Phys. Rev. D 96 (2017) 123503 [arXiv:1701.08172] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
A. Ilakovac and A. Pilaftsis, Flavor violating charged lepton decays in seesaw-type models, Nucl. Phys. B 437 (1995) 491 [hep-ph/9403398] [INSPIRE].
D. Tommasini, G. Barenboim, J. Bernabeu and C. Jarlskog, Nondecoupling of heavy neutrinos and lepton flavor violation, Nucl. Phys. B 444 (1995) 451 [hep-ph/9503228] [INSPIRE].
S. Bhattacharya, R. Roshan, A. Sil and D. Vatsyayan, Symmetry origin of baryon asymmetry, dark matter and neutrino mass, arXiv:2105.06189 [INSPIRE].
S. Y. Khlebnikov and M. E. Shaposhnikov, The statistical theory of anomalous fermion number nonconservation, Nucl. Phys. B 308 (1988) 885 [INSPIRE].
P. B. Arnold and L. D. McLerran, The sphaleron strikes back, Phys. Rev. D 37 (1988) 1020 [INSPIRE].
B. Adhikary, M. Chakraborty and A. Ghosal, Flavored leptogenesis with quasidegenerate neutrinos in a broken cyclic symmetric model, Phys. Rev. D 93 (2016) 113001 [arXiv:1407.6173] [INSPIRE].
A. Pilaftsis and T. E. J. Underwood, Resonant leptogenesis, Nucl. Phys. B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
B. Dev, M. Garny, J. Klaric, P. Millington and D. Teresi, Resonant enhancement in leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842003 [arXiv:1711.02863] [INSPIRE].
J. A. Casas, J. R. Espinosa, A. Ibarra and I. Navarro, Naturalness of nearly degenerate neutrinos, Nucl. Phys. B 556 (1999) 3 [hep-ph/9904395] [INSPIRE].
R. Gonzalez Felipe, F. R. Joaquim and B. M. Nobre, Radiatively induced leptogenesis in a minimal seesaw model, Phys. Rev. D 70 (2004) 085009 [hep-ph/0311029] [INSPIRE].
P. H. Chankowski and S. Pokorski, Quantum corrections to neutrino masses and mixing angles, Int. J. Mod. Phys. A 17 (2002) 575 [hep-ph/0110249] [INSPIRE].
M. Flanz, E. A. Paschos, U. Sarkar and J. Weiss, Baryogenesis through mixing of heavy Majorana neutrinos, Phys. Lett. B 389 (1996) 693 [hep-ph/9607310] [INSPIRE].
S. Pascoli, S. T. Petcov and A. Riotto, Leptogenesis and low energy CP-violation in neutrino physics, Nucl. Phys. B 774 (2007) 1 [hep-ph/0611338] [INSPIRE].
A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada and A. Riotto, Flavor issues in leptogenesis, JCAP 04 (2006) 004 [hep-ph/0601083] [INSPIRE].
J. M. Cline, K. Kainulainen and K. A. Olive, Protecting the primordial baryon asymmetry from erasure by sphalerons, Phys. Rev. D 49 (1994) 6394 [hep-ph/9401208] [INSPIRE].
A. Abada, S. Davidson, A. Ibarra, F. X. Josse-Michaux, M. Losada and A. Riotto, Flavour matters in leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].
E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP 01 (2006) 164 [hep-ph/0601084] [INSPIRE].
E. Nardi, Y. Nir, J. Racker and E. Roulet, On Higgs and sphaleron effects during the leptogenesis era, JHEP 01 (2006) 068 [hep-ph/0512052] [INSPIRE].
T. Asaka and T. Yoshida, Resonant leptogenesis at TeV-scale and neutrinoless double beta decay, JHEP 09 (2019) 089 [arXiv:1812.11323] [INSPIRE].
M. Plümacher, Baryon asymmetry, neutrino mixing and supersymmetric SO(10) unification, Ph.D. thesis, Hamburg U., Hamburg, Germany (1998) [hep-ph/9807557] [INSPIRE].
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Datta, A., Karmakar, B. & Sil, A. Flavored leptogenesis and neutrino mass with A4 symmetry. J. High Energ. Phys. 2021, 51 (2021). https://doi.org/10.1007/JHEP12(2021)051
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DOI: https://doi.org/10.1007/JHEP12(2021)051