Abstract
We discuss the thermal leptogenesis mechanism within the minimal gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) model to explain the observed baryon asymmetry of the Universe (BAU). In such framework, the phases of the Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix and the sum of the Standard Model neutrino masses are predictable because of a restricted neutrino mass matrix structure. Additionally, in the context of thermal leptogenesis, the BAU can be computed in terms of the three remaining free variables that parameterise the right-handed neutrino masses and their Yukawa couplings to the Higgs and lepton doublets. We identify the ranges of such parameters for which the correct BAU can be reproduced. We adopt the formalism of the density matrix equations to fully account for flavour effects and consider the decays of all the three right-handed neutrinos. Our analysis reveals that thermal leptogenesis is feasible within a wide parameter space, specifically for Yukawa couplings ranging from approximate unity to \( \mathcal{O} \)(0.03–0.05) and mass of the lightest right-handed neutrino M1 ≳ 1011−12 GeV, setting a leptogenesis scale in the considered model which is higher than that of the non-thermal scenario.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
R.J. Cooke, M. Pettini and C.C. Steidel, One Percent Determination of the Primordial Deuterium Abundance, Astrophys. J. 855 (2018) 102 [arXiv:1710.11129] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe, Phys. Lett. B 155 (1985) 36 [INSPIRE].
D. Bodeker and W. Buchmüller, Baryogenesis from the weak scale to the grand unification scale, Rev. Mod. Phys. 93 (2021) 035004 [arXiv:2009.07294] [INSPIRE].
R. Foot, New Physics From Electric Charge Quantization?, Mod. Phys. Lett. A 6 (1991) 527 [INSPIRE].
X.G. He, G.C. Joshi, H. Lew and R.R. Volkas, New Z′ phenomenology, Phys. Rev. D 43 (1991) 22 [INSPIRE].
X.-G. He, G.C. Joshi, H. Lew and R.R. Volkas, Simplest Z′ model, Phys. Rev. D 44 (1991) 2118 [INSPIRE].
R. Foot, X.G. He, H. Lew and R.R. Volkas, Model for a light Z′ boson, Phys. Rev. D 50 (1994) 4571 [hep-ph/9401250] [INSPIRE].
P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
S.L. Glashow, The Future of Elementary Particle Physics, NATO Sci. Ser. B 61 (1980) 687 [INSPIRE].
R.N. Mohapatra and G. Senjanovic, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
G.C. Branco, W. Grimus and L. Lavoura, The Seesaw Mechanism in the Presence of a Conserved Lepton Number, Nucl. Phys. B 312 (1989) 492 [INSPIRE].
S. Choubey and W. Rodejohann, A Flavor symmetry for quasi-degenerate neutrinos: Lμ − Lτ, Eur. Phys. J. C 40 (2005) 259 [hep-ph/0411190] [INSPIRE].
T. Araki, J. Heeck and J. Kubo, Vanishing Minors in the Neutrino Mass Matrix from Abelian Gauge Symmetries, JHEP 07 (2012) 083 [arXiv:1203.4951] [INSPIRE].
J. Heeck, Neutrinos and Abelian Gauge Symmetries, Ph.D. Thesis, Heidelberg U. (2014) [INSPIRE].
A. Crivellin, G. D’Ambrosio and J. Heeck, Addressing the LHC flavor anomalies with horizontal gauge symmetries, Phys. Rev. D 91 (2015) 075006 [arXiv:1503.03477] [INSPIRE].
R. Plestid, Consequences of an Abelian Z′ for neutrino oscillations and dark matter, Phys. Rev. D 93 (2016) 035011 [arXiv:1602.06651] [INSPIRE].
K. Asai, K. Hamaguchi and N. Nagata, Predictions for the neutrino parameters in the minimal gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) model, Eur. Phys. J. C 77 (2017) 763 [arXiv:1705.00419] μ τ [INSPIRE].
K. Asai et al., Minimal Gauged \( \textrm{U}{(1)}_{L_{\alpha }-{L}_{\beta }} \) Models Driven into a Corner, Phys. Rev. D 99 (2019) 055029 [arXiv:1811.07571] [INSPIRE].
K. Asai, Predictions for the neutrino parameters in the minimal model extended by linear combination of \( \textrm{U}{(1)}_{L_e-{L}_{\mu }} \), \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) and U(1)B−L gauge symmetries, Eur. Phys. J. C 80 (2020) 76 [arXiv:1907.04042] [INSPIRE].
K. Asai, K. Hamaguchi, N. Nagata and S.-Y. Tseng, Leptogenesis in the minimal gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) model and the sign of the cosmological baryon asymmetry, JCAP 11 (2020) 013 [arXiv:2005.01039] [INSPIRE].
D. Borah, A. Dasgupta and D. Mahanta, TeV scale resonant leptogenesis with Lμ − Lτ gauge symmetry in light of the muon g-2, Phys. Rev. D 104 (2021) 075006 [arXiv:2106.14410] [INSPIRE].
X.X. Qi, W. Liu and H. Sun, Leptogenesis and light scalar dark matter in a Lμ − Lτ model, arXiv:2204.01086 [INSPIRE].
S. Eijima, M. Ibe and K. Murai, Muon g − 2 and non-thermal leptogenesis in \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) model, JHEP 05 (2023) 010 [arXiv:2303.09751] [INSPIRE].
S. Blanchet and P. Di Bari, The minimal scenario of leptogenesis, New J. Phys. 14 (2012) 125012 [arXiv:1211.0512] [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, Cosmic microwave background, matter-antimatter asymmetry and neutrino masses, Nucl. Phys. B 643 (2002) 367 [Erratum ibid. 793 (2008) 362] [hep-ph/0205349] [INSPIRE].
J.R. Ellis and M. Raidal, Leptogenesis and the violation of lepton number and CP at low-energies, Nucl. Phys. B 643 (2002) 229 [hep-ph/0206174] [INSPIRE].
W. Buchmüller, P. Di Bari and M. Plümacher, The Neutrino mass window for baryogenesis, Nucl. Phys. B 665 (2003) 445 [hep-ph/0302092] [INSPIRE].
W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240] [INSPIRE].
R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].
H.B. Nielsen and Y. Takanishi, Baryogenesis via lepton number violation and family replicated gauge group, Nucl. Phys. B 636 (2002) 305 [hep-ph/0204027] [INSPIRE].
T. Endoh, T. Morozumi and Z.-H. Xiong, Primordial lepton family asymmetries in seesaw model, Prog. Theor. Phys. 111 (2004) 123 [hep-ph/0308276] [INSPIRE].
E. Nardi, Y. Nir, E. Roulet and J. Racker, The Importance of flavor in leptogenesis, JHEP 01 (2006) 164 [hep-ph/0601084] [INSPIRE].
A. Abada et al., Flavor issues in leptogenesis, JCAP 04 (2006) 004 [hep-ph/0601083] [INSPIRE].
A. Abada et al., Flavour Matters in Leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].
A. De Simone and A. Riotto, On the impact of flavour oscillations in leptogenesis, JCAP 02 (2007) 005 [hep-ph/0611357] [INSPIRE].
S. Blanchet, P. Di Bari and G.G. Raffelt, Quantum Zeno effect and the impact of flavor in leptogenesis, JCAP 03 (2007) 012 [hep-ph/0611337] [INSPIRE].
S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP 01 (2013) 041 [arXiv:1112.4528] [INSPIRE].
P.S.B. Dev et al., Flavor effects in leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842001 [arXiv:1711.02861] [INSPIRE].
K. Moffat et al., Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev. D 98 (2018) 015036 [arXiv:1804.05066] [INSPIRE].
A. Granelli, K. Moffat and S.T. Petcov, Aspects of high scale leptogenesis with low-energy leptonic CP violation, JHEP 11 (2021) 149 [arXiv:2107.02079] [INSPIRE].
A. Granelli et al., ULYSSES: Universal LeptogeneSiS Equation Solver, Comput. Phys. Commun. 262 (2021) 107813 [arXiv:2007.09150] [INSPIRE].
A. Granelli et al., ULYSSES, universal LeptogeneSiS equation solver: Version 2, Comput. Phys. Commun. 291 (2023) 108834 [arXiv:2301.05722] [INSPIRE].
H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [INSPIRE].
L. Lavoura, Zeros of the inverted neutrino mass matrix, Phys. Lett. B 609 (2005) 317 [hep-ph/0411232] [INSPIRE].
E.I. Lashin and N. Chamoun, Zero minors of the neutrino mass matrix, Phys. Rev. D 78 (2008) 073002 [arXiv:0708.2423] [INSPIRE].
B. Pontecorvo, Neutrino Experiments and the Problem of Conservation of Leptonic Charge, Zh. Eksp. Teor. Fiz. 53 (1967) 1717 [INSPIRE].
B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6 (1957) 429 [INSPIRE].
B. Pontecorvo, Inverse beta processes and nonconservation of lepton charge, Zh. Eksp. Teor. Fiz. 34 (1957) 247 [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
NuFIT collaboration, NuFIT v5.2, http://www.nu-fit.org.
I. Esteban et al., The fate of hints: updated global analysis of three-flavor neutrino oscillations, JHEP 09 (2020) 178 [arXiv:2007.14792] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
F. Capozzi et al., Global constraints on absolute neutrino masses and their ordering, Phys. Rev. D 95 (2017) 096014 [Addendum ibid. 101 (2020) 116013] [arXiv:2003.08511] [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].
S. Roy Choudhury and S. Hannestad, Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods, JCAP 07 (2020) 037 [arXiv:1907.12598] [INSPIRE].
M.M. Ivanov, M. Simonović and M. Zaldarriaga, Cosmological Parameters and Neutrino Masses from the Final Planck and Full-Shape BOSS Data, Phys. Rev. D 101 (2020) 083504 [arXiv:1912.08208] [INSPIRE].
DES collaboration, Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing, Phys. Rev. D 105 (2022) 023520 [arXiv:2105.13549] [INSPIRE].
I. Tanseri et al., Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements, JHEAp 36 (2022) 1 [arXiv:2207.01913] [INSPIRE].
KamLAND-Zen collaboration, Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen, Phys. Rev. Lett. 130 (2023) 051801 [arXiv:2203.02139] [INSPIRE].
M. Agostini, G. Benato and J. Detwiler, Discovery probability of next-generation neutrinoless double-β decay experiments, Phys. Rev. D 96 (2017) 053001 [arXiv:1705.02996] [INSPIRE].
C. Adams et al., Neutrinoless Double Beta Decay, arXiv:2212.11099 [INSPIRE].
K. Moffat, S. Pascoli, S.T. Petcov and J. Turner, Leptogenesis from Low Energy CP Violation, JHEP 03 (2019) 034 [arXiv:1809.08251] [INSPIRE].
A. Granelli, K. Moffat and S.T. Petcov, Flavoured resonant leptogenesis at sub-TeV scales, Nucl. Phys. B 973 (2021) 115597 [arXiv:2009.03166] [INSPIRE].
F. Hahn-Woernle, M. Plümacher and Y.Y.Y. Wong, Full Boltzmann equations for leptogenesis including scattering, JCAP 08 (2009) 028 [arXiv:0907.0205] [INSPIRE].
S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].
B. Garbrecht, More Viable Parameter Space for Leptogenesis, Phys. Rev. D 90 (2014) 063522 [arXiv:1401.3278] [INSPIRE].
T. Frossard, A. Kartavtsev and D. Mitrouskas, Systematic approach to ∆L = 1 processes in thermal leptogenesis, Phys. Rev. D 87 (2013) 125006 [arXiv:1304.1719] [INSPIRE].
B. Garbrecht, P. Klose and C. Tamarit, Relativistic and spectator effects in leptogenesis with heavy sterile neutrinos, JHEP 02 (2020) 117 [arXiv:1904.09956] [INSPIRE].
M. Flanz, E.A. Paschos and U. Sarkar, Baryogenesis from a lepton asymmetric universe, Phys. Lett. B 345 (1995) 248 [Erratum ibid. 382 (1996) 447] [Erratum ibid. 384 (1996) 487] [hep-ph/9411366] [INSPIRE].
L. Covi, E. Roulet and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384 (1996) 169 [hep-ph/9605319] [INSPIRE].
L. Covi and E. Roulet, Baryogenesis from mixed particle decays, Phys. Lett. B 399 (1997) 113 [hep-ph/9611425] [INSPIRE].
W. Buchmüller and M. Plümacher, CP asymmetry in Majorana neutrino decays, Phys. Lett. B 431 (1998) 354 [hep-ph/9710460] [INSPIRE].
S. Biondini et al., Status of rates and rate equations for thermal leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842004 [arXiv:1711.02864] [INSPIRE].
A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56 (1997) 5431 [hep-ph/9707235] [INSPIRE].
A. Pilaftsis, Resonant CP violation induced by particle mixing in transition amplitudes, Nucl. Phys. B 504 (1997) 61 [hep-ph/9702393] [INSPIRE].
A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys. B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
A. Pilaftsis and T.E.J. Underwood, Electroweak-scale resonant leptogenesis, Phys. Rev. D 72 (2005) 113001 [hep-ph/0506107] [INSPIRE].
T. Hambye, Leptogenesis at the TeV scale, Nucl. Phys. B 633 (2002) 171 [hep-ph/0111089] [INSPIRE].
T. Hambye, J. March-Russell and S.M. West, TeV scale resonant leptogenesis from supersymmetry breaking, JHEP 07 (2004) 070 [hep-ph/0403183] [INSPIRE].
V. Cirigliano, G. Isidori and V. Porretti, CP violation and Leptogenesis in models with Minimal Lepton Flavour Violation, Nucl. Phys. B 763 (2007) 228 [hep-ph/0607068] [INSPIRE].
Z.-Z. Xing and S. Zhou, Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis, Phys. Lett. B 653 (2007) 278 [hep-ph/0607302] [INSPIRE].
G.C. Branco et al., Another look at minimal lepton flavour violation, li → ljγ, leptogenesis, and the ratio Mν/ΛLFV, JHEP 09 (2007) 004 [hep-ph/0609067] [INSPIRE].
E.J. Chun and K. Turzynski, Quasi-degenerate neutrinos and leptogenesis from Lμ − Lτ, Phys. Rev. D 76 (2007) 053008 [hep-ph/0703070] [INSPIRE].
T. Kitabayashi, Remark on the minimal seesaw model and leptogenesis with tri/bi-maximal mixing, Phys. Rev. D 76 (2007) 033002 [hep-ph/0703303] [INSPIRE].
F.F. Deppisch, P.S. Bhupal Dev and A. Pilaftsis, Neutrinos and Collider Physics, New J. Phys. 17 (2015) 075019 [arXiv:1502.06541] [INSPIRE].
I. Brivio et al., Leptogenesis in the Neutrino Option, JHEP 10 (2019) 059 [Erratum ibid. 02 (2020) 148] [arXiv:1905.12642] [INSPIRE].
B. Dev et al., Resonant enhancement in leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842003 [arXiv:1711.02863] [INSPIRE].
M. Garny, A. Kartavtsev and A. Hohenegger, Leptogenesis from first principles in the resonant regime, Annals Phys. 328 (2013) 26 [arXiv:1112.6428] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Flavour effects in Resonant Leptogenesis from semi-classical and Kadanoff-Baym approaches, J. Phys. Conf. Ser. 631 (2015) 012087 [arXiv:1502.07987] [INSPIRE].
P.C. da Silva, D. Karamitros, T. McKelvey and A. Pilaftsis, Tri-Resonant Leptogenesis, arXiv:2303.15227 [INSPIRE].
T2K collaboration, The T2K Experiment, Nucl. Instrum. Meth. A 659 (2011) 106 [arXiv:1106.1238] [INSPIRE].
NOvA collaboration, Improved measurement of neutrino oscillation parameters by the NOvA experiment, Phys. Rev. D 106 (2022) 032004 [arXiv:2108.08219] [INSPIRE].
DUNE collaboration, Deep Underground Neutrino Experiment (DUNE) Near Detector Conceptual Design Report, Instruments 5 (2021) 31 [arXiv:2103.13910] [INSPIRE].
Hyper-Kamiokande collaboration, Hyper-Kamiokande Experiment: A Snowmass White Paper, in the proceedings of the Snowmass 2021, (2022) [arXiv:2203.02029] [INSPIRE].
P. Huber et al., Snowmass Neutrino Frontier Report, in the proceedings of the Snowmass 2021, (2022) [arXiv:2211.08641] [INSPIRE].
Acknowledgments
A.G. wishes to thank the Kavli IPMU and the Department of Physics of the University of Tokyo at Hongo Campus for the kind hospitality offered during the first part of this project. A.G. acknowledges the use of computational resources from the parallel computing cluster of the Open Physics Hub (https://site.unibo.it/openphysicshub/en) at the Physics and Astronomy Department in Bologna. The work of A.G. has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Staff Exchange grant agreement No. 101086085 — ASYMMETRY. The work of K.H., N.N., and M.R.Q. was supported in part by the Grant-in-Aid for Innovative Areas (No. 19H05810 [K.H.], No. 19H05802 [K.H.], No. 18H05542 [N.N.]), Scientific Research B (No. 20H01897 [K.H., N.N., and M.R.Q.]), and Young Scientists (No. 21K13916 [N.N.]). The work of J.W. is supported by the JSPS KAKENHI Grant (No. 22J21260).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2305.18100
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Granelli, A., Hamaguchi, K., Nagata, N. et al. Thermal leptogenesis in the minimal gauged \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) model. J. High Energ. Phys. 2023, 79 (2023). https://doi.org/10.1007/JHEP09(2023)079
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2023)079