Abstract
We investigate the Higgs-Yukawa system with Majorana masses of a fermion within asymptotically safe quantum gravity. Using the functional renormalization group method we derive the beta functions of the Majorana masses and the Yukawa coupling constant and discuss the possibility of a non-trivial fixed point for the Yukawa coupling constant. In the gravitational sector we take into account higher derivative terms such as R2 and RμνRμν in addition to the Einstein-Hilbert term for our truncation. For a certain value of the gravitational coupling constants and the Majorana masses, the Yukawa coupling constant has a non-trivial fixed point value and becomes an irrelevant parameter being thus a prediction of the theory. We also discuss consequences due to the Majorana mass terms to the running of the quartic coupling constant in the scalar sector.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: An Einstein Centenary Survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979), chapter 16.
M. Niedermaier and M. Reuter, The Asymptotic Safety Scenario in Quantum Gravity, Living Rev. Rel.9 (2006) 5 [INSPIRE].
M. Niedermaier, The Asymptotic safety scenario in quantum gravity: An Introduction, Class. Quant. Grav.24 (2007) R171 [gr-qc/0610018] [INSPIRE].
R. Percacci, Asymptotic Safety, arXiv:0709.3851 [INSPIRE].
M. Reuter and F. Saueressig, Quantum Einstein Gravity, New J. Phys.14 (2012) 055022 [arXiv:1202.2274] [INSPIRE].
S. Nagy, Lectures on renormalization and asymptotic safety, Annals Phys.350 (2014) 310 [arXiv:1211.4151] [INSPIRE].
A. Codello, R. Percacci and C. Rahmede, Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation, Annals Phys.324 (2009) 414 [arXiv:0805.2909] [INSPIRE].
R. Percacci, 100 Years of General Relativity. Vol. 3: An Introduction to Covariant Quantum Gravity and Asymptotic Safety, World Scientific, New York U.S.A. (2017).
A. Eichhorn, An asymptotically safe guide to quantum gravity and matter, Front. Astron. Space Sci.5 (2019) 47 [arXiv:1810.07615] [INSPIRE].
M. Reuter and F. Saueressig, Quantum Gravity and the Functional Renormalization Group, Cambridge University Press, Cambridge U.K. (2019).
C. Wetterich, Quantum scale symmetry, arXiv:1901.04741 [INSPIRE].
H. Kawai and M. Ninomiya, Renormalization Group and Quantum Gravity, Nucl. Phys.B 336 (1990) 115 [INSPIRE].
J. Ambjørn, A. Görlich, J. Jurkiewicz and R. Loll, Nonperturbative Quantum Gravity, Phys. Rept.519 (2012) 127 [arXiv:1203.3591] [INSPIRE].
J. Laiho, S. Bassler, D. Coumbe, D. Du and J.T. Neelakanta, Lattice Quantum Gravity and Asymptotic Safety, Phys. Rev.D 96 (2017) 064015 [arXiv:1604.02745] [INSPIRE].
T.R. Morris, Elements of the continuous renormalization group, Prog. Theor. Phys. Suppl.131 (1998) 395 [hep-th/9802039] [INSPIRE].
J. Berges, N. Tetradis and C. Wetterich, Nonperturbative renormalization flow in quantum field theory and statistical physics, Phys. Rept.363 (2002) 223 [hep-ph/0005122] [INSPIRE].
K. Aoki, Introduction to the nonperturbative renormalization group and its recent applications, Int. J. Mod. Phys.B 14 (2000) 1249 [INSPIRE].
C. Bagnuls and C. Bervillier, Exact renormalization group equations. An Introductory review, Phys. Rept.348 (2001) 91 [hep-th/0002034] [INSPIRE].
J. Polonyi, Lectures on the functional renormalization group method, Central Eur. J. Phys.1 (2003) 1 [hep-th/0110026] [INSPIRE].
J.M. Pawlowski, Aspects of the functional renormalisation group, Annals Phys.322 (2007) 2831 [hep-th/0512261] [INSPIRE].
H. Gies, Introduction to the functional RG and applications to gauge theories, Lect. Notes Phys.852 (2012) 287 [hep-ph/0611146] [INSPIRE].
B. Delamotte, An Introduction to the nonperturbative renormalization group, Lect. Notes Phys.852 (2012) 49 [cond-mat/0702365] [INSPIRE].
O.J. Rosten, Fundamentals of the Exact Renormalization Group, Phys. Rept.511 (2012) 177 [arXiv:1003.1366] [INSPIRE].
J. Braun, Fermion Interactions and Universal Behavior in Strongly Interacting Theories, J. Phys.G 39 (2012) 033001 [arXiv:1108.4449] [INSPIRE].
M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev.D 57 (1998) 971 [hep-th/9605030] [INSPIRE].
W. Souma, Nontrivial ultraviolet fixed point in quantum gravity, Prog. Theor. Phys.102 (1999) 181 [hep-th/9907027] [INSPIRE].
M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation, Phys. Rev.D 65 (2002) 065016 [hep-th/0110054] [INSPIRE].
D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett.92 (2004) 201301 [hep-th/0312114] [INSPIRE].
A. Codello and R. Percacci, Fixed points of higher derivative gravity, Phys. Rev. Lett.97 (2006) 221301 [hep-th/0607128] [INSPIRE].
D. Benedetti, P.F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity, Mod. Phys. Lett.A 24 (2009) 2233 [arXiv:0901.2984] [INSPIRE].
D. Benedetti, P.F. Machado and F. Saueressig, Taming perturbative divergences in asymptotically safe gravity, Nucl. Phys.B 824 (2010) 168 [arXiv:0902.4630] [INSPIRE].
E. Manrique, M. Reuter and F. Saueressig, Bimetric Renormalization Group Flows in Quantum Einstein Gravity, Annals Phys.326 (2011) 463 [arXiv:1006.0099] [INSPIRE].
E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically Safe Lorentzian Gravity, Phys. Rev. Lett.106 (2011) 251302 [arXiv:1102.5012] [INSPIRE].
N. Christiansen, D.F. Litim, J.M. Pawlowski and A. Rodigast, Fixed points and infrared completion of quantum gravity, Phys. Lett.B 728 (2014) 114 [arXiv:1209.4038] [INSPIRE].
K. Falls, D.F. Litim, K. Nikolakopoulos and C. Rahmede, A bootstrap towards asymptotic safety, arXiv:1301.4191 [INSPIRE].
D. Benedetti, On the number of relevant operators in asymptotically safe gravity, EPL102 (2013) 20007 [arXiv:1301.4422] [INSPIRE].
A. Codello, G. D’Odorico and C. Pagani, Consistent closure of renormalization group flow equations in quantum gravity, Phys. Rev.D 89 (2014) 081701 [arXiv:1304.4777] [INSPIRE].
K. Falls, D.F. Litim, K. Nikolakopoulos and C. Rahmede, Further evidence for asymptotic safety of quantum gravity, Phys. Rev.D 93 (2016) 104022 [arXiv:1410.4815] [INSPIRE].
N. Christiansen, B. Knorr, J.M. Pawlowski and A. Rodigast, Global Flows in Quantum Gravity, Phys. Rev.D 93 (2016) 044036 [arXiv:1403.1232] [INSPIRE].
N. Christiansen, B. Knorr, J. Meibohm, J.M. Pawlowski and M. Reichert, Local Quantum Gravity, Phys. Rev.D 92 (2015) 121501 [arXiv:1506.07016] [INSPIRE].
H. Gies, B. Knorr and S. Lippoldt, Generalized Parametrization Dependence in Quantum Gravity, Phys. Rev.D 92 (2015) 084020 [arXiv:1507.08859] [INSPIRE].
H. Gies, B. Knorr, S. Lippoldt and F. Saueressig, Gravitational Two-Loop Counterterm Is Asymptotically Safe, Phys. Rev. Lett.116 (2016) 211302 [arXiv:1601.01800] [INSPIRE].
J. Biemans, A. Platania and F. Saueressig, Quantum gravity on foliated spacetimes: Asymptotically safe and sound, Phys. Rev.D 95 (2017) 086013 [arXiv:1609.04813] [INSPIRE].
N. Christiansen, Four-Derivative Quantum Gravity Beyond Perturbation Theory, arXiv:1612.06223 [INSPIRE].
T. Denz, J.M. Pawlowski and M. Reichert, Towards apparent convergence in asymptotically safe quantum gravity, Eur. Phys. J.C 78 (2018) 336 [arXiv:1612.07315] [INSPIRE].
B. Knorr and S. Lippoldt, Correlation functions on a curved background, Phys. Rev.D 96 (2017) 065020 [arXiv:1707.01397] [INSPIRE].
B. Knorr, Infinite order quantum-gravitational correlations, Class. Quant. Grav.35 (2018) 115005 [arXiv:1710.07055] [INSPIRE].
N. Christiansen, K. Falls, J.M. Pawlowski and M. Reichert, Curvature dependence of quantum gravity, Phys. Rev.D 97 (2018) 046007 [arXiv:1711.09259] [INSPIRE].
K. Falls, C.R. King, D.F. Litim, K. Nikolakopoulos and C. Rahmede, Asymptotic safety of quantum gravity beyond Ricci scalars, Phys. Rev.D 97 (2018) 086006 [arXiv:1801.00162] [INSPIRE].
K.G. Falls, D.F. Litim and J. Schröder, Aspects of asymptotic safety for quantum gravity, Phys. Rev.D 99 (2019) 126015 [arXiv:1810.08550] [INSPIRE].
R. Percacci and D. Perini, Constraints on matter from asymptotic safety, Phys. Rev.D 67 (2003) 081503 [hep-th/0207033] [INSPIRE].
R. Percacci and D. Perini, Asymptotic safety of gravity coupled to matter, Phys. Rev.D 68 (2003) 044018 [hep-th/0304222] [INSPIRE].
G. Narain and R. Percacci, Renormalization Group Flow in Scalar-Tensor Theories. I, Class. Quant. Grav.27 (2010) 075001 [arXiv:0911.0386] [INSPIRE].
O. Zanusso, L. Zambelli, G.P. Vacca and R. Percacci, Gravitational corrections to Yukawa systems, Phys. Lett.B 689 (2010) 90 [arXiv:0904.0938] [INSPIRE].
A. Eichhorn and H. Gies, Light fermions in quantum gravity, New J. Phys.13 (2011) 125012 [arXiv:1104.5366] [INSPIRE].
A. Eichhorn, Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario, Phys. Rev.D 86 (2012) 105021 [arXiv:1204.0965] [INSPIRE].
P. Donà, A. Eichhorn and R. Percacci, Matter matters in asymptotically safe quantum gravity, Phys. Rev.D 89 (2014) 084035 [arXiv:1311.2898] [INSPIRE].
P. Donà, A. Eichhorn and R. Percacci, Consistency of matter models with asymptotically safe quantum gravity, Can. J. Phys.93 (2015) 988 [arXiv:1410.4411] [INSPIRE].
P. Labus, R. Percacci and G.P. Vacca, Asymptotic safety in O(N) scalar models coupled to gravity, Phys. Lett.B 753 (2016) 274 [arXiv:1505.05393] [INSPIRE].
K.-y. Oda and M. Yamada, Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity, Class. Quant. Grav.33 (2016) 125011 [arXiv:1510.03734] [INSPIRE].
J. Meibohm, J.M. Pawlowski and M. Reichert, Asymptotic safety of gravity-matter systems, Phys. Rev.D 93 (2016) 084035 [arXiv:1510.07018] [INSPIRE].
P. Donà, A. Eichhorn, P. Labus and R. Percacci, Asymptotic safety in an interacting system of gravity and scalar matter, Phys. Rev.D 93 (2016) 044049 [Erratum ibid.D 93 (2016) 129904][arXiv:1512.01589] [INSPIRE].
J. Meibohm and J.M. Pawlowski, Chiral fermions in asymptotically safe quantum gravity, Eur. Phys. J.C 76 (2016) 285 [arXiv:1601.04597] [INSPIRE].
A. Eichhorn, A. Held and J.M. Pawlowski, Quantum-gravity effects on a Higgs-Yukawa model, Phys. Rev.D 94 (2016) 104027 [arXiv:1604.02041] [INSPIRE].
A. Eichhorn and S. Lippoldt, Quantum gravity and Standard-Model-like fermions, Phys. Lett.B 767 (2017) 142 [arXiv:1611.05878] [INSPIRE].
J. Biemans, A. Platania and F. Saueressig, Renormalization group fixed points of foliated gravity-matter systems, JHEP05 (2017) 093 [arXiv:1702.06539] [INSPIRE].
Y. Hamada and M. Yamada, Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system, JHEP08 (2017) 070 [arXiv:1703.09033] [INSPIRE].
N. Christiansen, A. Eichhorn and A. Held, Is scale-invariance in gauge-Yukawa systems compatible with the graviton?, Phys. Rev.D 96 (2017) 084021 [arXiv:1705.01858] [INSPIRE].
A. Eichhorn and A. Held, Viability of quantum-gravity induced ultraviolet completions for matter, Phys. Rev.D 96 (2017) 086025 [arXiv:1705.02342] [INSPIRE].
A. Eichhorn, The asymptotic safety paradigm for quantum spacetime and matter, in Black Holes, Gravitational Waves and Spacetime Singularities, Rome Italy (2017).
A. Eichhorn, S. Lippoldt and V. Skrinjar, Nonminimal hints for asymptotic safety, Phys. Rev.D 97 (2018) 026002 [arXiv:1710.03005] [INSPIRE].
N. Christiansen, D.F. Litim, J.M. Pawlowski and M. Reichert, Asymptotic safety of gravity with matter, Phys. Rev.D 97 (2018) 106012 [arXiv:1710.04669] [INSPIRE].
A. Eichhorn, Y. Hamada, J. Lumma and M. Yamada, Quantum gravity fluctuations flatten the Planck-scale Higgs potential, Phys. Rev.D 97 (2018) 086004 [arXiv:1712.00319] [INSPIRE].
N. Alkofer and F. Saueressig, Asymptotically safe f (R)-gravity coupled to matter I: the polynomial case, Annals Phys.396 (2018) 173 [arXiv:1802.00498] [INSPIRE].
A. Eichhorn, P. Labus, J.M. Pawlowski and M. Reichert, Effective universality in quantum gravity, SciPost Phys.5 (2018) 031 [arXiv:1804.00012] [INSPIRE].
A. Eichhorn, S. Lippoldt, J.M. Pawlowski, M. Reichert and M. Schiffer, How perturbative is quantum gravity?, Phys. Lett.B 792 (2019) 310 [arXiv:1810.02828] [INSPIRE].
A. Eichhorn, S. Lippoldt and M. Schiffer, Zooming in on fermions and quantum gravity, Phys. Rev.D 99 (2019) 086002 [arXiv:1812.08782] [INSPIRE].
J.M. Pawlowski, M. Reichert, C. Wetterich and M. Yamada, Higgs scalar potential in asymptotically safe quantum gravity, Phys. Rev.D 99 (2019) 086010 [arXiv:1811.11706] [INSPIRE].
A. Codello, R. Percacci and C. Rahmede, Ultraviolet properties of f(R)-gravity, Int. J. Mod. Phys.A 23 (2008) 143 [arXiv:0705.1769] [INSPIRE].
P.F. Machado and F. Saueressig, On the renormalization group flow of f(R)-gravity, Phys. Rev.D 77 (2008) 124045 [arXiv:0712.0445] [INSPIRE].
G.P. De Brito, N. Ohta, A.D. Pereira, A.A. Tomaz and M. Yamada, Asymptotic safety and field parametrization dependence in the f (R) truncation, Phys. Rev.D 98 (2018) 026027 [arXiv:1805.09656] [INSPIRE].
U. Harst and M. Reuter, QED coupled to QEG, JHEP05 (2011) 119 [arXiv:1101.6007] [INSPIRE].
N. Christiansen and A. Eichhorn, An asymptotically safe solution to the U(1) triviality problem, Phys. Lett.B 770 (2017) 154 [arXiv:1702.07724] [INSPIRE].
A. Eichhorn and F. Versteegen, Upper bound on the Abelian gauge coupling from asymptotic safety, JHEP01 (2018) 030 [arXiv:1709.07252] [INSPIRE].
M. Shaposhnikov and C. Wetterich, Asymptotic safety of gravity and the Higgs boson mass, Phys. Lett.B 683 (2010) 196 [arXiv:0912.0208] [INSPIRE].
A. Eichhorn, A. Held and C. Wetterich, Quantum-gravity predictions for the fine-structure constant, Phys. Lett.B 782 (2018) 198 [arXiv:1711.02949] [INSPIRE].
A. Eichhorn and A. Held, Mass difference for charged quarks from asymptotically safe quantum gravity, Phys. Rev. Lett.121 (2018) 151302 [arXiv:1803.04027] [INSPIRE].
C. Wetterich and M. Yamada, Gauge hierarchy problem in asymptotically safe gravity — the resurgence mechanism, Phys. Lett.B 770 (2017) 268 [arXiv:1612.03069] [INSPIRE].
C. Wetterich, Graviton fluctuations erase the cosmological constant, Phys. Lett.B 773 (2017) 6 [arXiv:1704.08040] [INSPIRE].
P. Minkowski, μ → eγ at a Rate of One Out of 109Muon Decays?, Phys. Lett.67B (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].
T. Yanagida, Horizontal Symmetry and Masses of Neutrinos, Prog. Theor. Phys.64 (1980) 1103 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett.44 (1980) 912 [INSPIRE].
K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev.D 16 (1977) 953 [INSPIRE].
B. Holdom and J. Ren, Quadratic gravity: from weak to strong, Int. J. Mod. Phys.D 25 (2016) 1643004 [arXiv:1605.05006] [INSPIRE].
J.F. Donoghue, Quartic propagators, negative norms and the physical spectrum, Phys. Rev.D 96 (2017) 044007 [arXiv:1704.01533] [INSPIRE].
D. Anselmi and M. Piva, The Ultraviolet Behavior of Quantum Gravity, JHEP05 (2018) 027 [arXiv:1803.07777] [INSPIRE].
D. Becker, C. Ripken and F. Saueressig, On avoiding Ostrogradski instabilities within Asymptotic Safety, JHEP12 (2017) 121 [arXiv:1709.09098] [INSPIRE].
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett.B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].
A. Nink, Field Parametrization Dependence in Asymptotically Safe Quantum Gravity, Phys. Rev.D 91 (2015) 044030 [arXiv:1410.7816] [INSPIRE].
N. Ohta, R. Percacci and A.D. Pereira, Gauges and functional measures in quantum gravity I: Einstein theory, JHEP06 (2016) 115 [arXiv:1605.00454] [INSPIRE].
N. Ohta, R. Percacci and A.D. Pereira, Gauges and functional measures in quantum gravity II: Higher derivative gravity, Eur. Phys. J.C 77 (2017) 611 [arXiv:1610.07991] [INSPIRE].
N. Ohta, R. Percacci and A.D. Pereira, f (R, \( {R}_{\mu \nu}^2 \)) at one loop, Phys. Rev.D 97 (2018) 104039 [arXiv:1804.01608] [INSPIRE].
G.P. De Brito, A. Eichhorn and A.D. Pereira, A link that matters: Towards phenomenological tests of unimodular asymptotic safety, arXiv:1907.11173 [INSPIRE].
J.W. York, Jr., Conformatlly invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial value problem of general relativity, J. Math. Phys.14 (1973) 456 [INSPIRE].
D.F. Litim, Optimized renormalization group flows, Phys. Rev.D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].
P. Donà and R. Percacci, Functional renormalization with fermions and tetrads, Phys. Rev.D 87 (2013) 045002 [arXiv:1209.3649] [INSPIRE].
A. Eichhorn and A. Held, Top mass from asymptotic safety, Phys. Lett.B 777 (2018) 217 [arXiv:1707.01107] [INSPIRE].
I.L. Shapiro, Asymptotic Behavior of Effective Yukawa Coupling Constants in Quantum R 2Gravity With Matter, Class. Quant. Grav.6 (1989) 1197 [INSPIRE].
I.L. Buchbinder, O.K. Kalashnikov, I.L. Shapiro, V.B. Vologodsky and J.J. Wolfengaut, The Stability of Asymptotic Freedom in Grand Unified Models Coupled to R 2Gravity, Phys. Lett.B 216 (1989) 127 [INSPIRE].
I. Buchbinder, S. Odintsov and I. Shapiro, Effective Action in Quantum Gravity, CRC Press, Boca Raton U.S.A. (1992).
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett.B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett.B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
G.P. Vacca and O. Zanusso, Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter, Phys. Rev. Lett.105 (2010) 231601 [arXiv:1009.1735] [INSPIRE].
L. Bosma, B. Knorr and F. Saueressig, Resolving Spacetime Singularities within Asymptotic Safety, arXiv:1904.04845 [INSPIRE].
B. Knorr, C. Ripken and F. Saueressig, Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox, arXiv:1907.02903 [INSPIRE].
F. Bezrukov, M. Yu. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs Boson Mass and New Physics, JHEP10 (2012) 140 [arXiv:1205.2893] [INSPIRE].
F. Finster, Local U(2, 2) symmetry in relativistic quantum mechanics, J. Math. Phys.39 (1998) 6276 [hep-th/9703083] [INSPIRE].
H.A. Weldon, Fermions without vierbeins in curved space-time, Phys. Rev.D 63 (2001) 104010 [gr-qc/0009086][INSPIRE].
H. Gies and S. Lippoldt, Fermions in gravity with local spin-base invariance, Phys. Rev.D 89 (2014) 064040 [arXiv:1310.2509] [INSPIRE].
S. Lippoldt, Spin-base invariance of Fermions in arbitrary dimensions, Phys. Rev.D 91 (2015) 104006 [arXiv:1502.05607] [INSPIRE].
D. Becker and M. Reuter, En route to Background Independence: Broken split-symmetry and how to restore it with bi-metric average actions, Annals Phys.350 (2014) 225 [arXiv:1404.4537] [INSPIRE].
P. Labus, T.R. Morris and Z.H. Slade, Background independence in a background dependent renormalization group, Phys. Rev.D 94 (2016) 024007 [arXiv:1603.04772] [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1905.11114
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
de Brito, G.P., Hamada, Y., Pereira, A.D. et al. On the impact of Majorana masses in gravity-matter systems. J. High Energ. Phys. 2019, 142 (2019). https://doi.org/10.1007/JHEP08(2019)142
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)142