Abstract
Within the framework of residual symmetry, two ℤ2 type associate μτ inter- change symmetries robustly constrain the Dirac CP phase δ in a model independent way. Both of them predict simultaneous maximality of δ and the atmospheric mixing angle θ23. We show how these well known correlations will be changed if we generalize the μτ in- terchange symmetry to a μτ mixing symmetry. In particular, we show that the stringent condition of simultaneous maximality could be relaxed even with a very small departure from the exact μτ interchange. In addition, the present neutrino data on δ and θ23 can be explained better by the mixing symmetry. After discussing the impact of the μτ mix- ing in some realistic neutrino mass models, we show how the proposed mixing could be realized with two simultaneous CP transformations which also lead to novel and testable correlations between δ and the mixing angles θij . Next we discuss in particular, the ‘three flavour regime’ of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended μτ interchange symmetry, a resonant leptogenesis is possible due the generalization of μτ interchange to the μτ mixing and the resulting baryon asymmetry always requires a nonmaximal θ23 owing to the fact that the baryon to photon ratio ηB vanishes in the exact limit of θ23 = π/4. This is one of the robust predictions of this frame- work. The CP extended μτ mixing is also a novel example of a low energy effective model that provides an important insight to the off-diagonal terms of the flavour coupling matrix which have usually been neglected in literature to compute the final baryon asymmetry, in particular in the models with flavour symmetries.
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H. Georgi and S.L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett.32 (1974) 438 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Annals Phys.93 (1975) 193 [INSPIRE].
K.S. Babu and R.N. Mohapatra, Predictive neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. Lett.70 (1993) 2845 [hep-ph/9209215] [INSPIRE].
K.S. Babu and S. Khan, Minimal nonsupersymmetric SO(10) model: gauge coupling unification, proton decay and fermion masses, Phys. Rev.D 92 (2015) 075018 [arXiv:1507.06712] [INSPIRE].
K.S. Babu, B. Bajc and S. Saad, Yukawa sector of minimal SO(10) unification, JHEP02 (2017) 136 [arXiv:1612.04329] [INSPIRE].
A. Dueck and W. Rodejohann, Fits to SO(10) grand unified models, JHEP09 (2013) 024 [arXiv:1306.4468] [INSPIRE].
A.S. Joshipura and K.M. Patel, Viability of the exact tri-bimaximal mixing at MGUT in SO(10), JHEP09 (2011) 137 [arXiv:1105.5943] [INSPIRE].
P. Di Bari and L. Marzola, SO(10)-inspired solution to the problem of the initial conditions in leptogenesis, Nucl. Phys.B 877 (2013) 719 [arXiv:1308.1107] [INSPIRE].
M.K. Parida, B.P. Nayak, R. Satpathy and R.L. Awasthi, Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter and proton lifetime predictions, JHEP04 (2017) 075 [arXiv:1608.03956] [INSPIRE].
B. Sahoo, M. Chakraborty and M.K. Parida, Neutrino mass, coupling unification, verifiable proton decay, vacuum stability and WIMP dark matter in SU(5), Adv. High Energy Phys.2018 (2018) 4078657 [arXiv:1804.01803] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett.B 174 (1986) 45 [INSPIRE].
A. Riotto and M. Trodden, Recent progress in baryogenesis, Ann. Rev. Nucl. Part. Sci.49 (1999) 35 [hep-ph/9901362] [INSPIRE].
S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept.466 (2008) 105 [arXiv:0802.2962] [INSPIRE].
S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett.B 535 (2002) 25 [hep-ph/0202239] [INSPIRE].
W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys.315 (2005) 305 [hep-ph/0401240] [INSPIRE].
K. Moffat, S. Pascoli, S.T. Petcov and J. Turner, Leptogenesis from low energy CP violation, JHEP03 (2019) 034 [arXiv:1809.08251] [INSPIRE].
M.J. Dolan, T.P. Dutka and R.R. Volkas, Dirac-phase thermal leptogenesis in the extended type-I seesaw model, JCAP06 (2018) 012 [arXiv:1802.08373] [INSPIRE].
T2K collaboration, Updated T2K measurements of muon neutrino and antineutrino disappearance using 1.5 × 1021protons on target, Phys. Rev.D 96 (2017) 011102 [arXiv:1704.06409] [INSPIRE].
T2K collaboration, Combined analysis of neutrino and antineutrino oscillations at T2K, Phys. Rev. Lett.118 (2017) 151801 [arXiv:1701.00432] [INSPIRE].
NOvA collaboration, Measurement of the neutrino mixing angle θ23in NOvA, Phys. Rev. Lett.118 (2017) 151802 [arXiv:1701.05891] [INSPIRE].
NOvA collaboration, Constraints on oscillation parameters from νe appearance and νμ disappearance in NOvA, Phys. Rev. Lett.118 (2017) 231801 [arXiv:1703.03328] [INSPIRE].
A. Himmel, New neutrino oscillation results from NOvA, https://indico.cern.ch/event/696410/, (2018).
MINOS collaboration, Measurement of neutrino and antineutrino oscillations using beam and atmospheric data in MINOS, Phys. Rev. Lett.110 (2013) 251801 [arXiv:1304.6335] [INSPIRE].
MINOS collaboration, Electron neutrino and antineutrino appearance in the full MINOS data sample, Phys. Rev. Lett.110 (2013) 171801 [arXiv:1301.4581] [INSPIRE].
RENO collaboration, New results from RENO using 1500 days of data, in 15thInternational Conference on Topics in Astroparticle and Underground Physics (TAUP 2017), Sudbury, ON, Canada, 24–28 July 2017 [arXiv:1710.08204] [INSPIRE].
I. Esteban, M.C. Gonzalez-Garcia, A. Hernandez-Cabezudo, M. Maltoni and T. Schwetz, Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of θ23, δCPand the mass ordering, JHEP01 (2019) 106 [arXiv:1811.05487] [INSPIRE].
I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and T. Schwetz, Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP01 (2017) 087 [arXiv:1611.01514] [INSPIRE].
P.F. Harrison and W.G. Scott, μ − τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett.B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].
W. Grimus and L. Lavoura, A nonstandard CP transformation leading to maximal atmospheric neutrino mixing, Phys. Lett.B 579 (2004) 113 [hep-ph/0305309] [INSPIRE].
R.N. Mohapatra and C.C. Nishi, Implications of μ-τ flavored CP symmetry of leptons, JHEP08 (2015) 092 [arXiv:1506.06788] [INSPIRE].
E. Ma, Neutrino mixing: A4 variations, Phys. Lett.B 752 (2016) 198 [arXiv:1510.02501] [INSPIRE].
R. Samanta, P. Roy and A. Ghosal, Consequences of minimal seesaw with complex μ-τ antisymmetry of neutrinos, JHEP06 (2018) 085 [arXiv:1712.06555] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys.82 (2010) 2701 [arXiv:1002.0211] [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].
S.T. Petcov, Discrete flavour symmetries, neutrino mixing and leptonic CP-violation, Eur. Phys. J.C 78 (2018) 709 [arXiv:1711.10806] [INSPIRE].
I. Girardi, S.T. Petcov and A.V. Titov, Predictions for the leptonic Dirac CP-violation phase: a systematic phenomenological analysis, Eur. Phys. J.C 75 (2015) 345 [arXiv:1504.00658] [INSPIRE].
I. Girardi, S.T. Petcov, A.J. Stuart and A.V. Titov, Leptonic Dirac CP-violation predictions from residual discrete symmetries, Nucl. Phys.B 902 (2016) 1 [arXiv:1509.02502] [INSPIRE].
C.S. Lam, Symmetry of lepton mixing, Phys. Lett.B 656 (2007) 193 [arXiv:0708.3665] [INSPIRE].
C.S. Lam, Determining horizontal symmetry from neutrino mixing, Phys. Rev. Lett.101 (2008) 121602 [arXiv:0804.2622] [INSPIRE].
S.-F. Ge, D.A. Dicus and W.W. Repko, Z2 symmetry prediction for the leptonic Dirac CP phase, Phys. Lett.B 702 (2011) 220 [arXiv:1104.0602] [INSPIRE].
S.-F. Ge, D.A. Dicus and W.W. Repko, Residual symmetries for neutrino mixing with a large θ13 and nearly maximal δD , Phys. Rev. Lett.108 (2012) 041801 [arXiv:1108.0964] [INSPIRE].
S.-F. Ge, H.-J. He and F.-R. Yin, Common origin of soft μ-τ and CP breaking in neutrino seesaw and the origin of matter, JCAP05 (2010) 017 [arXiv:1001.0940] [INSPIRE].
H.-J. He and F.-R. Yin, Common origin of μ-τ and CP breaking in neutrino seesaw, baryon asymmetry and hidden flavor symmetry, Phys. Rev.D 84 (2011) 033009 [arXiv:1104.2654] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Chin. PhysC 38 (2014) 090001 [INSPIRE].
R.N. Mohapatra and S. Nussinov, Bimaximal neutrino mixing and neutrino mass matrix, Phys. Rev.D 60 (1999) 013002 [hep-ph/9809415] [INSPIRE].
T. Fukuyama and H. Nishiura, Mass matrix of Majorana neutrinos, hep-ph/9702253 [INSPIRE].
Daya Bay collaboration, New measurement of antineutrino oscillation with the full detector configuration at Daya Bay, Phys. Rev. Lett.115 (2015) 111802 [arXiv:1505.03456] [INSPIRE].
W. Grimus, A.S. Joshipura, S. Kaneko, L. Lavoura and M. Tanimoto, Lepton mixing angle θ13 = 0 with a horizontal symmetry D4, JHEP07 (2004) 078 [hep-ph/0407112] [INSPIRE].
W. Grimus, A.S. Joshipura, S. Kaneko, L. Lavoura, H. Sawanaka and M. Tanimoto, Non-vanishing Ue3and cos 2θ23from a broken Z2 symmetry, Nucl. Phys.B 713 (2005) 151 [hep-ph/0408123] [INSPIRE].
R.N. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett.B 644 (2007) 59 [hep-ph/0608111] [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].
R. Samanta, P. Roy and A. Ghosal, Extended scaling and residual flavor symmetry in the neutrino Majorana mass matrix, Eur. Phys. J.C 76 (2016) 662 [arXiv:1604.06731] [INSPIRE].
R. Samanta, P. Roy and A. Ghosal, Complex scaling in neutrino mass matrix, Acta Phys. Polon. Supp.9 (2016) 807 [arXiv:1604.01206] [INSPIRE].
R. Samanta, M. Chakraborty, P. Roy and A. Ghosal, Baryon asymmetry via leptogenesis in a neutrino mass model with complex scaling, JCAP03 (2017) 025 [arXiv:1610.10081] [INSPIRE].
R. Sinha, R. Samanta and A. Ghosal, Generalized Z2 × Z2 in scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis, JHEP12 (2017) 030 [arXiv:1706.00946] [INSPIRE].
A. Ghosal and R. Samanta, Probing texture zeros with scaling ansatz in inverse seesaw, JHEP05 (2015) 077 [arXiv:1501.00916] [INSPIRE].
R. Samanta, M. Chakraborty and A. Ghosal, Evaluation of the Majorana phases of a general Majorana neutrino mass matrix: testability of hierarchical flavour models, Nucl. Phys.B 904 (2016) 86 [arXiv:1502.06508] [INSPIRE].
G.C. Branco, D. Emmanuel-Costa, M.N. Rebelo and P. Roy, Four zero neutrino Yukawa textures in the minimal seesaw framework, Phys. Rev.D 77 (2008) 053011 [arXiv:0712.0774] [INSPIRE].
J. Liao, D. Marfatia and K. Whisnant, Seesaw mechanism with four texture zeros in the neutrino Yukawa matrix, Phys. Rev.D 87 (2013) 073013 [arXiv:1302.2372] [INSPIRE].
G. Ecker, W. Grimus and H. Neufeld, A standard form for generalized CP transformations, J. Phys.A 20 (1987) L807 [INSPIRE].
H. Neufeld, W. Grimus and G. Ecker, Generalized CP invariance, neutral flavor conservation and the structure of the mixing matrix, Int. J. Mod. Phys.A 3 (1988) 603 [INSPIRE].
W. Grimus and M.N. Rebelo, Automorphisms in gauge theories and the definition of CP and P, Phys. Rept.281 (1997) 239 [hep-ph/9506272] [INSPIRE].
R.N. Mohapatra and C.C. Nishi, S4 flavored CP symmetry for neutrinos, Phys. Rev.D 86 (2012) 073007 [arXiv:1208.2875] [INSPIRE].
S. Gupta, A.S. Joshipura and K.M. Patel, Minimal extension of tri-bimaximal mixing and generalized Z2 × Z2 symmetries, Phys. Rev.D 85 (2012) 031903 [arXiv:1112.6113] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, Lepton mixing parameters from discrete and CP symmetries, JHEP07 (2013) 027 [arXiv:1211.5560] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, CP and discrete flavour symmetries, JHEP04 (2013) 122 [arXiv:1211.6953] [INSPIRE].
M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP violation from finite groups, Nucl. Phys.B 883 (2014) 267 [arXiv:1402.0507] [INSPIRE].
G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S4 models of leptons, JHEP05 (2013) 084 [arXiv:1303.6180] [INSPIRE].
G.-J. Ding, S.F. King and A.J. Stuart, Generalised CP and A4 family symmetry, JHEP12 (2013) 006 [arXiv:1307.4212] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, A realistic pattern of lepton mixing and masses from S4 and CP, Eur. Phys. J.C 74 (2014) 2753 [arXiv:1303.7178] [INSPIRE].
P. Chen, C.-Y. Yao and G.-J. Ding, Neutrino mixing from CP symmetry, Phys. Rev.D 92 (2015) 073002 [arXiv:1507.03419] [INSPIRE].
C.C. Nishi, New and trivial CP symmetry for extended A4 flavor, Phys. Rev.D 93 (2016) 093009 [arXiv:1601.00977] [INSPIRE].
C.C. Nishi and B.L. Sánchez-Vega, μ-τ reflection symmetry with a texture-zero, JHEP01 (2017) 068 [arXiv:1611.08282] [INSPIRE].
W. Rodejohann and X.-J. Xu, Trimaximal μ-τ reflection symmetry, Phys. Rev.D 96 (2017) 055039 [arXiv:1705.02027] [INSPIRE].
R. Samanta and A. Ghosal, Probing maximal zero textures with broken cyclic symmetry in inverse seesaw, Nucl. Phys.B 911 (2016) 846 [arXiv:1507.02582] [INSPIRE].
J.T. Penedo, S.T. Petcov and A.V. Titov, Neutrino mixing and leptonic CP-violation from S4 flavour and generalised CP symmetries, JHEP12 (2017) 022 [arXiv:1705.00309] [INSPIRE].
S.F. King, Unified models of neutrinos, flavour and CP-violation, Prog. Part. Nucl. Phys.94 (2017) 217 [arXiv:1701.04413] [INSPIRE].
A. Abada, S. Davidson, A. Ibarra, F.-X. Josse-Michaux, M. Losada and A. Riotto, Flavour matters in leptogenesis, JHEP09 (2006) 010 [hep-ph/0605281] [INSPIRE].
S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP03 (2007) 018 [hep-ph/0607330] [INSPIRE].
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].
A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys.B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP01 (2006) 164 [hep-ph/0601084] [INSPIRE].
R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys.B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].
S. Antusch, P. Di Bari, D.A. Jones and S.F. King, A fuller flavour treatment of N2 -dominated leptogenesis, Nucl. Phys.B 856 (2012) 180 [arXiv:1003.5132] [INSPIRE].
P. Di Bari and S.F. King, Successful N2 leptogenesis with flavour coupling effects in realistic unified models, JCAP10 (2015) 008 [arXiv:1507.06431] [INSPIRE].
M. Hirsch, S. Morisi, E. Peinado and J.W.F. Valle, Discrete dark matter, Phys. Rev.D 82 (2010) 116003 [arXiv:1007.0871] [INSPIRE].
Y. Hamada, T. Kobayashi, A. Ogasahara, Y. Omura, F. Takayama and D. Yasuhara, Revisiting discrete dark matter model: θ13 ≠ 0 and νR dark matter, JHEP10 (2014) 183 [arXiv:1405.3592] [INSPIRE].
W. Grimus and L. Lavoura, Softly broken lepton number Le − Lμ − Lτwith non-maximal solar neutrino mixing, J. Phys.G 31 (2005) 683 [hep-ph/0410279] [INSPIRE].
P.H. Frampton and R.N. Mohapatra, Possible gauge theoretic origin for quark-lepton complementarity, JHEP01 (2005) 025 [hep-ph/0407139] [INSPIRE].
K.S. Babu and R.N. Mohapatra, Predictive schemes for bimaximal neutrino mixings, Phys. Lett.B 532 (2002) 77 [hep-ph/0201176] [INSPIRE].
M.S. Berger and M. Dawid, A Froggatt-Nielsen flavor model for neutrino physics, Int. J. Mod. Phys.A 34 (2019) 1950102 [arXiv:1901.10504] [INSPIRE].
P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Generalized μ-τ reflection symmetry and leptonic CP-violation, Phys. Lett.B 753 (2016) 644 [arXiv:1512.01551] [INSPIRE].
R. Sinha, P. Roy and A. Ghosal, CP transformed mixed μ-τ antisymmetry for neutrinos and its consequences, Phys. Rev.D 99 (2019) 033009 [arXiv:1809.06615] [INSPIRE].
P. Chen, G.-J. Ding and S.F. King, Leptogenesis and residual CP symmetry, JHEP03 (2016) 206 [arXiv:1602.03873] [INSPIRE].
E.W. Kolb and M.S. Turner, The early universe, Front. Phys.69 (1990) 1 [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].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP01 (2013) 041 [arXiv:1112.4528] [INSPIRE].
K. Moffat, S. Pascoli, S.T. Petcov, H. Schulz and J. Turner, Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev.D 98 (2018) 015036 [arXiv:1804.05066] [INSPIRE].
G. Engelhard, Y. Grossman, E. Nardi and Y. Nir, The importance of N2leptogenesis, Phys. Rev. Lett.99 (2007) 081802 [hep-ph/0612187] [INSPIRE].
D.M. Barreiros, R.G. Felipe and F.R. Joaquim, Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw, JHEP01 (2019) 223 [arXiv:1810.05454] [INSPIRE].
R. Samanta and M. Chakraborty, A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios, JCAP02 (2019) 003 [arXiv:1802.04751] [INSPIRE].
P.S. Bhupal Dev, R. Franceschini and R.N. Mohapatra, Bounds on TeV seesaw models from LHC Higgs data, Phys. Rev.D 86 (2012) 093010 [arXiv:1207.2756] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Flavour covariant transport equations: an application to resonant leptogenesis, Nucl. Phys. B 886 (2014) 569 [arXiv:1404.1003] [INSPIRE].
M. Drewes, B. Garbrecht, D. Gueter and J. Klaric, Testing the low scale seesaw and leptogenesis, JHEP08 (2017) 018 [arXiv:1609.09069] [INSPIRE].
B. Garbrecht, Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis, arXiv:1812.02651 [INSPIRE].
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Samanta, R., Sinha, R. & Ghosal, A. Importance of generalized μτ symmetry and its CP extension on neutrino mixing and leptogenesis. J. High Energ. Phys. 2019, 57 (2019). https://doi.org/10.1007/JHEP10(2019)057
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DOI: https://doi.org/10.1007/JHEP10(2019)057