Abstract
In this work, we have proposed a modular A4 symmetric model of neutrino mass which, simultaneously, explains observed baryon asymmetry of the Universe (BAU). In minimal extension of the standard model (SM) with two right-handed neutrinos we work in a supersymmetric framework. At Type-I seesaw level, the model predicts scaling in the neutrino mass matrix. In order to have correct low energy phenomenology, we propose two possible scenarios of scale-breaking in the neutrino mass matrix emanating from Type-I seesaw. Scenario-1 is based on the dimension-5 Weinberg operator whereas scenario-2 implements Type-II seesaw via scalar triplet Higgs superfields (∆, \( \overline{\Delta } \)). Interestingly, the breaking patterns in both, otherwise dynamically different scenarios, are similar which can be attributed to the same charge assignments of superfields (∆, \( \overline{\Delta } \)) and the Higgs superfield Hu under modular A4 symmetry. The breaking is found to be proportional to the Yukawa coupling of modular weight 10 (\( {Y}_{1,1\prime}^{10} \)). We, further, investigates the predictions of the model under scenario-2 (Type-I+II) for neutrino mass, mixings and matter-antimatter asymmetry of the Universe. The model predicts normal hierarchical neutrino masses and provide a robust range (0.05 − 0.08)eV for sum of neutrino masses (Σmi). Lepton number violating 0νββ decay amplitude (Mee) is obtained to lie in the range (0.04 − 0.06)eV. Future 0νββ decay experiments such as NEXT and nEXO shall pose crucial test for the model. Both CP conserving and CP violating solutions are allowed in the model. Interesting correlations are obtained, specially, between Yukawa couplings of modular weight 2 and complex modulus τ. Contrary to \( {Y}_2^2 \) and \( {Y}_3^2 \), the Yukawa coupling \( {Y}_1^2 \) is found to be insensitive to τ and thus to CP violation because complex modulus τ is the only source of CP violation in the model. We, also, investigate the prediction of the model for BAU. The model exhibit consistent explanation of BAU for right-handed Majorana neutrino mass scale in the range ((1 − 5) × 1013) GeV.
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References
S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
A.Y. Smirnov, Neutrino mass, mixing and discrete symmetries, J. Phys. Conf. Ser. 447 (2013) 012004 [arXiv:1305.4827] [INSPIRE].
Y. Cai, J. Herrero-García, M.A. Schmidt, A. Vicente and R.R. Volkas, From the trees to the forest: a review of radiative neutrino mass models, Front. Phys. 5 (2017) 63.
J. Herrero-García and M.A. Schmidt, Neutrino mass models: New classification and model-independent upper limits on their scale, Eur. Phys. J. C 79 (2019) 938 [arXiv:1903.10552] [INSPIRE].
F. Riva, Low-Scale Leptogenesis and the Domain Wall Problem in Models with Discrete Flavor Symmetries, Phys. Lett. B 690 (2010) 443 [arXiv:1004.1177] [INSPIRE].
S. Antusch and D. Nolde, Matter inflation with A4 flavour symmetry breaking, JCAP 10 (2013) 028 [arXiv:1306.3501] [INSPIRE].
S.F. King and Y.-L. Zhou, Spontaneous breaking of SO(3) to finite family symmetries with supersymmetry — an A4 model, JHEP 11 (2018) 173 [arXiv:1809.10292] [INSPIRE].
J. Berger and Y. Grossman, Model of leptons from SO(3) → A4, JHEP 02 (2010) 071 [arXiv:0910.4392] [INSPIRE].
J. Lauer, J. Mas and H.P. Nilles, Duality and the Role of Nonperturbative Effects on the World Sheet, Phys. Lett. B 226 (1989) 251 [INSPIRE].
J. Lauer, J. Mas and H.P. Nilles, Twisted sector representations of discrete background symmetries for two-dimensional orbifolds, Nucl. Phys. B 351 (1991) 353 [INSPIRE].
W. Lerche, D. Lüst and N.P. Warner, Duality Symmetries in N = 2 Landau-Ginzburg Models, Phys. Lett. B 231 (1989) 417 [INSPIRE].
D. Cremades, L.E. Ibáñez and F. Marchesano, Computing Yukawa couplings from magnetized extra dimensions, JHEP 05 (2004) 079 [hep-th/0404229] [INSPIRE].
T. Kobayashi and S. Nagamoto, Zero-modes on orbifolds: magnetized orbifold models by modular transformation, Phys. Rev. D 96 (2017) 096011 [arXiv:1709.09784] [INSPIRE].
X. Wang, Lepton flavor mixing and CP violation in the minimal type-(I+II) seesaw model with a modular A4 symmetry, Nucl. Phys. B 957 (2020) 115105.
T. Kobayashi, T. Nomura and T. Shimomura, Type II seesaw models with modular A4 symmetry, Phys. Rev. D 102 (2020) 035019 [arXiv:1912.00637] [INSPIRE].
T. Nomura, H. Okada and S. Patra, An inverse seesaw model with A4-modular symmetry, Nucl. Phys. B 967 (2021) 115395 [arXiv:1912.00379] [INSPIRE].
T. Nomura and H. Okada, Modular A4 symmetric inverse seesaw model with SU(2)L multiplet fields, arXiv:2007.15459 [INSPIRE].
T. Nomura and H. Okada, A linear seesaw model with A4-modular flavor and local U(1)B−L symmetries, arXiv:2007.04801 [INSPIRE].
M.K. Behera, S. Mishra, S. Singirala and R. Mohanta, Implications of A4 modular symmetry on Neutrino mass, Mixing and Leptogenesis with Linear Seesaw, arXiv:2007.00545 [INSPIRE].
T. Nomura, H. Okada and O. Popov, A modular A4 symmetric scotogenic model, Phys. Lett. B 803 (2020) 135294.
H. Okada and Y. Orikasa, Modular S3 symmetric radiative seesaw model, Phys. Rev. D 100 (2019) 115037 [arXiv:1907.04716] [INSPIRE].
M.K. Behera, S. Singirala, S. Mishra and R. Mohanta, A modular A4 symmetric Scotogenic model for Neutrino mass and Dark Matter, arXiv:2009.01806 [INSPIRE].
P.H. Frampton, S.L. Glashow and D. Marfatia, Zeroes of the neutrino mass matrix, Phys. Lett. B 536 (2002) 79 [hep-ph/0201008] [INSPIRE].
B.R. Desai, D.P. Roy and A.R. Vaucher, Three neutrino mass matrices with two texture zeros, Mod. Phys. Lett. A 18 (2003) 1355 [hep-ph/0209035] [INSPIRE].
Z.-z. Xing, Texture zeros and Majorana phases of the neutrino mass matrix, Phys. Lett. B 530 (2002) 159 [hep-ph/0201151] [INSPIRE].
S. Verma and M. Kashav, Ramifications of texture one-zero neutrino mass model in coherence with the latest neutrino data, Mod. Phys. Lett. A 35 (2020) 2050165 [INSPIRE].
S. Kaneko, H. Sawanaka and M. Tanimoto, Hybrid textures of neutrinos, JHEP 08 (2005) 073 [hep-ph/0504074] [INSPIRE].
S. Dev, S. Verma and S. Gupta, Phenomenological Analysis of Hybrid Textures of Neutrinos, Phys. Lett. B 687 (2010) 53 [arXiv:0909.3182] [INSPIRE].
S. Goswami, S. Khan and A. Watanabe, Hybrid textures in minimal seesaw mass matrices, Phys. Lett. B 693 (2010) 249 [arXiv:0811.4744] [INSPIRE].
R.N. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett. B 644 (2007) 59 [hep-ph/0608111] [INSPIRE].
W. Grimus and L. Lavoura, Softly broken lepton number Le – Lμ – Lτ with non-maximal solar neutrino mixing, J. Phys. G 31 (2005) 683 [hep-ph/0410279] [INSPIRE].
A.S. Joshipura and W. Rodejohann, Scaling in the Neutrino Mass Matrix, μ-τ Symmetry and the See-Saw Mechanism, Phys. Lett. B 678 (2009) 276 [arXiv:0905.2126] [INSPIRE].
C.S. Lam, Magic neutrino mass matrix and the Bjorken-Harrison-Scott parameterization, Phys. Lett. B 640 (2006) 260 [hep-ph/0606220] [INSPIRE].
K.S. Channey and S. Kumar, Two simple textures of the magic neutrino mass matrix, J. Phys. G 46 (2019) 015001 [arXiv:1812.10268] [INSPIRE].
S. Verma and M. Kashav, Magic neutrino mass model with broken μ − τ symmetry and leptogenesis, J. Phys. G 47 (2020) 085003 [arXiv:1910.04467] [INSPIRE].
J.-N. Lu, X.-G. Liu and G.-J. Ding, Modular symmetry origin of texture zeros and quark lepton unification, Phys. Rev. D 101 (2020) 115020 [arXiv:1912.07573] [INSPIRE].
D. Zhang, A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix, Nucl. Phys. B 952 (2020) 114935 [arXiv:1910.07869] [INSPIRE].
S.J.D. King and S.F. King, Fermion mass hierarchies from modular symmetry, JHEP 09 (2020) 043 [arXiv:2002.00969] [INSPIRE].
A. Blum, R.N. Mohapatra and W. Rodejohann, Inverted mass hierarchy from scaling in the neutrino mass matrix: Low and high energy phenomenology, Phys. Rev. D 76 (2007) 053003 [arXiv:0706.3801] [INSPIRE].
T. Kobayashi, K. Tanaka and T.H. Tatsuishi, Neutrino mixing from finite modular groups, Phys. Rev. D 98 (2018) 016004 [arXiv:1803.10391] [INSPIRE].
T. Nomura and H. Okada, A modular A4 symmetric model of dark matter and neutrino, Phys. Lett. B 797 (2019) 134799 [arXiv:1904.03937] [INSPIRE].
J.T. Penedo and S.T. Petcov, Lepton Masses and Mixing from Modular S4 Symmetry, Nucl. Phys. B 939 (2019) 292 [arXiv:1806.11040] [INSPIRE].
S.F. King and Y.-L. Zhou, Trimaximal TM1 mixing with two modular S4 groups, Phys. Rev. D 101 (2020) 015001 [arXiv:1908.02770] [INSPIRE].
T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto and T.H. Tatsuishi, New A4 lepton flavor model from S4 modular symmetry, JHEP 02 (2020) 097 [arXiv:1907.09141] [INSPIRE].
P.P. Novichkov, J.T. Penedo, S.T. Petcov and A.V. Titov, Modular A5 symmetry for flavour model building, JHEP 04 (2019) 174 [arXiv:1812.02158] [INSPIRE].
G.-J. Ding, S.F. King and X.-G. Liu, Neutrino mass and mixing with A5 modular symmetry, Phys. Rev. D 100 (2019) 115005 [arXiv:1903.12588] [INSPIRE].
F. Feruglio, Are neutrino masses modular forms?, arXiv:1706.08749 [INSPIRE].
T. Asaka, Y. Heo, T.H. Tatsuishi and T. Yoshida, Modular A4 invariance and leptogenesis, JHEP 01 (2020) 144 [arXiv:1909.06520] [INSPIRE].
A.S. Barabash, SeperNEMO double beta decay experiment, J. Phys. Conf. Ser. 375 (2012) 042012 [arXiv:1112.1784] [INSPIRE].
KamLAND-Zen collaboration, Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [Addendum ibid. 117 (2016) 109903] [arXiv:1605.02889] [INSPIRE].
NEXT collaboration, NEXT, a HPGXe TPC for neutrinoless double beta decay searches, arXiv:0907.4054 [INSPIRE].
NEXT collaboration, Present status and future perspectives of the NEXT experiment, Adv. High Energy Phys. 2014 (2014) 907067 [arXiv:1307.3914] [INSPIRE].
nEXO collaboration, The Sensitivity of the nEXO Experiment to Majorana Neutrinos, J. Phys. Conf. Ser. 888 (2017) 012237 [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].
H. Okada and M. Tanimoto, Towards unification of quark and lepton flavors in A4 modular invariance, Eur. Phys. J. C 81 (2021) 52 [arXiv:1905.13421] [INSPIRE].
S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, JHEP 11 (2013) 115 [arXiv:1306.6879] [INSPIRE].
F. Björkeroth, F.J. de Anda, I. de Medeiros Varzielas and S.F. King, Towards a complete A4 × SU(5) SUSY GUT, JHEP 06 (2015) 141 [arXiv:1503.03306] [INSPIRE].
M. Borah, D. Borah, M.K. Das and S. Patra, Perturbations to μ − τ Symmetry, Leptogenesis and Lepton Flavour Violation with Type II Seesaw, Phys. Rev. D 90 (2014) 095020 [arXiv:1408.3191] [INSPIRE].
E. Giusarma, M. Gerbino, O. Mena, S. Vagnozzi, S. Ho and K. Freese, Improvement of cosmological neutrino mass bounds, Phys. Rev. D 94 (2016) 083522 [arXiv:1605.04320] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
A.D. Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Sov. Phys. Usp. 34 (1991) 392 [INSPIRE].
V. Domcke, K. Kamada, K. Mukaida, K. Schmitz and M. Yamada, Wash-In Leptogenesis, Phys. Rev. Lett. 126 (2021) 201802 [arXiv:2011.09347] [INSPIRE].
S. Antusch and S.F. King, Type II Leptogenesis and the neutrino mass scale, Phys. Lett. B 597 (2004) 199 [hep-ph/0405093] [INSPIRE].
T. Hambye and G. Senjanović, Consequences of triplet seesaw for leptogenesis, Phys. Lett. B 582 (2004) 73 [hep-ph/0307237] [INSPIRE].
W. Buchmuller, P. Di Bari and M. Plumacher, Some aspects of thermal leptogenesis, New J. Phys. 6 (2004) 105.
P.S.B. Dev, P. Di Bari, B. Garbrecht, S. Lavignac, P. Millington and D. Teresi, Flavor effects in leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842001 [arXiv:1711.02861] [INSPIRE].
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Kashav, M., Verma, S. Broken scaling neutrino mass matrix and leptogenesis based on A4 modular invariance. J. High Energ. Phys. 2021, 100 (2021). https://doi.org/10.1007/JHEP09(2021)100
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DOI: https://doi.org/10.1007/JHEP09(2021)100