Abstract
The left-right symmetric model (LRSM), originally proposed to explain parity violation in low energy processes, has since emerged as an attractive framework for light neutrino masses via the seesaw mechanism. The scalar sector of the minimal LRSM consists of an SU(2) bi-doublet, as well as left- and right-handed weak isospin triplets, thus making the corresponding vacuum structure much more complicated than that of the Standard Model. In particular, the desired ground state of the Higgs potential should be a charge conserving, and preferably global, minimum with parity violation at low scales. We show that this is not a generic feature of the LRSM potential and happens only for a small fraction of the parameter space of the potential. We also analytically study the potential for some simplified cases and obtain sufficient conditions (though not necessary) to achieve successful symmetry breaking. We then carry out a detailed statistical analysis of the minima of the Higgs potential using numerical minimization and find that for a large fraction of the parameter space, the potential does not have a good vacuum. Imposing the analytically obtained conditions, we can readily find the small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [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].
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [INSPIRE].
R.N. Mohapatra and J.C. Pati, A Natural Left-Right Symmetry, Phys. Rev. D 11 (1975) 2558 [INSPIRE].
G. Senjanović and R.N. Mohapatra, Exact Left-Right Symmetry and Spontaneous Violation of Parity, Phys. Rev. D 12 (1975) 1502 [INSPIRE].
R.N. Mohapatra and R.E. Marshak, Local B − L Symmetry of Electroweak Interactions, Majorana Neutrinos and Neutron Oscillations, Phys. Rev. Lett. 44 (1980) 1316 [Erratum ibid. 44 (1980) 1643] [INSPIRE].
G.C. Branco and L. Lavoura, Natural CP Breaking in Left-right Symmetric Theories, Phys. Lett. B 165 (1985) 327 [INSPIRE].
J. Basecq, J. Liu, J. Milutinovic and L. Wolfenstein, Spontaneous CP Violation in SU(2)L × SU(2)R × U(1)B − L Models, Nucl. Phys. B 272 (1986) 145 [INSPIRE].
J.F. Gunion, J. Grifols, A. Mendez, B. Kayser and F.I. Olness, Higgs Bosons in Left-Right Symmetric Models, Phys. Rev. D 40 (1989) 1546 [INSPIRE].
N.G. Deshpande, J.F. Gunion, B. Kayser and F.I. Olness, Left-right symmetric electroweak models with triplet Higgs, Phys. Rev. D 44 (1991) 837 [INSPIRE].
P. Duka, J. Gluza and M. Zralek, Quantization and renormalization of the manifest left-right symmetric model of electroweak interactions, Annals Phys. 280 (2000) 336 [hep-ph/9910279] [INSPIRE].
G. Barenboim, M. Gorbahn, U. Nierste and M. Raidal, Higgs Sector of the Minimal Left-Right Symmetric Model, Phys. Rev. D 65 (2002) 095003 [hep-ph/0107121] [INSPIRE].
K. Kiers, M. Assis and A.A. Petrov, Higgs sector of the left-right model with explicit CP-violation, Phys. Rev. D 71 (2005) 115015 [hep-ph/0503115] [INSPIRE].
J. Chakrabortty, P. Konar and T. Mondal, Constraining a class of B − L extended models from vacuum stability and perturbativity, Phys. Rev. D 89 (2014) 056014 [arXiv:1308.1291] [INSPIRE].
J. Chakrabortty, P. Konar and T. Mondal, Copositive Criteria and Boundedness of the Scalar Potential, Phys. Rev. D 89 (2014) 095008 [arXiv:1311.5666] [INSPIRE].
R.N. Mohapatra and Y. Zhang, TeV Scale Universal Seesaw, Vacuum Stability and Heavy Higgs, JHEP 06 (2014) 072 [arXiv:1401.6701] [INSPIRE].
T. Mondal, U.K. Dey and P. Konar, Implications of unitarity and charge breaking minima in a left-right symmetric model, Phys. Rev. D 92 (2015) 096005 [arXiv:1508.04960] [INSPIRE].
P.S.B. Dev, R.N. Mohapatra and Y. Zhang, Probing the Higgs Sector of the Minimal Left-Right Symmetric Model at Future Hadron Colliders, JHEP 05 (2016) 174 [arXiv:1602.05947] [INSPIRE].
A. Maiezza, M. Nemevšek and F. Nesti, Perturbativity and mass scales in the minimal left-right symmetric model, Phys. Rev. D 94 (2016) 035008 [arXiv:1603.00360] [INSPIRE].
J. Chakrabortty, J. Gluza, T. Jelinski and T. Srivastava, Theoretical constraints on masses of heavy particles in Left-Right Symmetric Models, Phys. Lett. B 759 (2016) 361 [arXiv:1604.06987] [INSPIRE].
A. Maiezza, G. Senjanović and J.C. Vasquez, Higgs sector of the minimal left-right symmetric theory, Phys. Rev. D 95 (2017) 095004 [arXiv:1612.09146] [INSPIRE].
B. Brahmachari, M.K. Samal and U. Sarkar, Potential minimization in left-right symmetric models, hep-ph/9402323 [INSPIRE].
J. Choi and R.R. Volkas, The Effective potential at finite temperature in the left-right symmetric model, Phys. Rev. D 48 (1993) 1258 [hep-ph/9210223] [INSPIRE].
K.S. Babu and A. Patra, Higgs Boson Spectra in Supersymmetric Left-Right Models, Phys. Rev. D 93 (2016) 055030 [arXiv:1412.8714] [INSPIRE].
L. Basso, B. Fuks, M.E. Krauss and W. Porod, Doubly-charged Higgs and vacuum stability in left-right supersymmetry, JHEP 07 (2015) 147 [arXiv:1503.08211] [INSPIRE].
X.-J. Xu, Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential, Phys. Rev. D 95 (2017) 115019 [arXiv:1705.08965] [INSPIRE].
X.-J. Xu, Minima of the scalar potential in the type-II seesaw model: From local to global, Phys. Rev. D 94 (2016) 115025 [arXiv:1612.04950] [INSPIRE].
N. Chen, C. Du, Y. Wu and X.-J. Xu, Further study of the global minimum constraint on the two-Higgs-doublet models: LHC searches for heavy Higgs bosons, Phys. Rev. D 99 (2019) 035011 [arXiv:1810.04689] [INSPIRE].
Y.B. Zeldovich, I.Y. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3 [Sov. Phys. JETP 40 (1974) 1] [INSPIRE].
S.E. Larsson, S. Sarkar and P.L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55 (1997) 5129 [hep-ph/9608319] [INSPIRE].
J.E. Camargo-Molina, B. O’Leary, W. Porod and F. Staub, Vevacious: A Tool For Finding The Global Minima Of One-Loop Effective Potentials With Many Scalars, Eur. Phys. J. C 73 (2013) 2588 [arXiv:1307.1477] [INSPIRE].
G. Chauhan, P.S.B. Dev, R.N. Mohapatra and Y. Zhang, Perturbativity constraints on U(1)B − L and left-right models and implications for heavy gauge boson searches, JHEP 01 (2019)208 [arXiv:1811.08789] [INSPIRE].
V. Tello, M. Nemevšek, F. Nesti, G. Senjanović and F. Vissani, Left-Right Symmetry: from LHC to Neutrinoless Double Beta Decay, Phys. Rev. Lett. 106 (2011) 151801 [arXiv:1011.3522] [INSPIRE].
M. Nemevšek, F. Nesti, G. Senjanović and Y. Zhang, First Limits on Left-Right Symmetry Scale from LHC Data, Phys. Rev. D 83 (2011) 115014 [arXiv:1103.1627] [INSPIRE].
S.P. Das, F.F. Deppisch, O. Kittel and J.W.F. Valle, Heavy Neutrinos and Lepton Flavour Violation in Left-Right Symmetric Models at the LHC, Phys. Rev. D 86 (2012) 055006 [arXiv:1206.0256] [INSPIRE].
J. Barry and W. Rodejohann, Lepton number and flavour violation in TeV-scale left-right symmetric theories with large left-right mixing, JHEP 09 (2013) 153 [arXiv:1303.6324] [INSPIRE].
P.S.B. Dev, S. Goswami, M. Mitra and W. Rodejohann, Constraining neutrino mass from neutrinoless double beta decay, Phys. Rev. D 88 (2013) 091301 [arXiv:1305.0056] [INSPIRE].
C.-Y. Chen, P.S.B. Dev and R.N. Mohapatra, Probing Heavy-Light Neutrino Mixing in Left-Right Seesaw Models at the LHC, Phys. Rev. D 88 (2013) 033014 [arXiv:1306.2342] [INSPIRE].
O. Castillo-Felisola, C.O. Dib, J.C. Helo, S.G. Kovalenko and S.E. Ortiz, Left-Right Symmetric Models at the High-Intensity Frontier, Phys. Rev. D 92 (2015) 013001 [arXiv:1504.02489] [INSPIRE].
P.S.B. Dev, D. Kim and R.N. Mohapatra, Disambiguating Seesaw Models using Invariant Mass Variables at Hadron Colliders, JHEP 01 (2016) 118 [arXiv:1510.04328] [INSPIRE].
G. Bambhaniya, P.S.B. Dev, S. Goswami and M. Mitra, The scalar triplet contribution to lepton flavour violation and neutrinoless double beta decay in Left-Right Symmetric Model, JHEP 04 (2016) 046 [arXiv:1512.00440] [INSPIRE].
M. Lindner, F.S. Queiroz and W. Rodejohann, Dilepton bounds on left-right symmetry at the LHC run II and neutrinoless double beta decay, Phys. Lett. B 762 (2016) 190 [arXiv:1604.07419] [INSPIRE].
M. Lindner, F.S. Queiroz, W. Rodejohann and C.E. Yaguna, Left-Right Symmetry and Lepton Number Violation at the Large Hadron Electron Collider, JHEP 06 (2016) 140 [arXiv:1604.08596] [INSPIRE].
C. Bonilla, M.E. Krauss, T. Opferkuch and W. Porod, Perspectives for Detecting Lepton Flavour Violation in Left-Right Symmetric Models, JHEP 03 (2017) 027 [arXiv:1611.07025] [INSPIRE].
M. Nemevšek, F. Nesti and J.C. Vasquez, Majorana Higgses at colliders, JHEP 04 (2017) 114 [arXiv:1612.06840] [INSPIRE].
P. Fileviez Perez and C. Murgui, Lepton Flavour Violation in Left-Right Theory, Phys. Rev. D 95 (2017) 075010 [arXiv:1701.06801] [INSPIRE].
P.S.B. Dev, R.N. Mohapatra and Y. Zhang, Long Lived Light Scalars as Probe of Low Scale Seesaw Models, Nucl. Phys. B 923 (2017) 179 [arXiv:1703.02471] [INSPIRE].
S. Mandal, M. Mitra and N. Sinha, Constraining the right-handed gauge boson mass from lepton number violating meson decays in a low scale left-right model, Phys. Rev. D 96 (2017) 035023 [arXiv:1705.01932] [INSPIRE].
M. Nemevšek, F. Nesti and G. Popara, Keung-Senjanović process at the LHC: From lepton number violation to displaced vertices to invisible decays, Phys. Rev. D 97 (2018) 115018 [arXiv:1801.05813] [INSPIRE].
J. Barry, L. Dorame and W. Rodejohann, Linear collider test of a neutrinoless double beta decay mechanism in left-right symmetric theories, Eur. Phys. J. C 72 (2012) 2023 [arXiv:1203.3365] [INSPIRE].
P.S.B. Dev and Y. Zhang, Displaced vertex signatures of doubly charged scalars in the type-II seesaw and its left-right extensions, JHEP 10 (2018) 199 [arXiv:1808.00943] [INSPIRE].
G. Senjanović, Spontaneous Breakdown of Parity in a Class of Gauge Theories, Nucl. Phys. B 153 (1979) 334 [INSPIRE].
D. Chang, R.N. Mohapatra and M.K. Parida, A New Approach to Left-Right Symmetry Breaking in Unified Gauge Theories, Phys. Rev. D 30 (1984) 1052 [INSPIRE].
E.K. Akhmedov, M. Lindner, E. Schnapka and J.W.F. Valle, Dynamical left-right symmetry breaking, Phys. Rev. D 53 (1996) 2752 [hep-ph/9509255] [INSPIRE].
B. Brahmachari, E. Ma and U. Sarkar, Truly minimal left right model of quark and lepton masses, Phys. Rev. Lett. 91 (2003) 011801 [hep-ph/0301041] [INSPIRE].
M. Malinsky, J.C. Romao and J.W.F. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95 (2005) 161801 [hep-ph/0506296] [INSPIRE].
P.S.B. Dev and R.N. Mohapatra, TeV Scale Inverse Seesaw in SO(10) and Leptonic Non-Unitarity Effects, Phys. Rev. D 81 (2010) 013001 [arXiv:0910.3924] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, Radiative Symmetry Breaking of the Minimal Left-Right Symmetric Model, Phys. Rev. D 82 (2010) 055002 [arXiv:0911.0710] [INSPIRE].
J. Chakrabortty, Type I and new seesaw in left-right symmetric theories, Phys. Lett. B 690 (2010) 382 [arXiv:1005.1377] [INSPIRE].
D. Borah, S. Patra and U. Sarkar, TeV scale Left Right Symmetry with spontaneous D-parity breaking, Phys. Rev. D 83 (2011) 035007 [arXiv:1006.2245] [INSPIRE].
J. Heeck and S. Patra, Minimal Left-Right Symmetric Dark Matter, Phys. Rev. Lett. 115 (2015) 121804 [arXiv:1507.01584] [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].
V. Brdar and A.Y. Smirnov, Low Scale Left-Right Symmetry and Naturally Small Neutrino Mass, JHEP 02 (2019) 045 [arXiv:1809.09115] [INSPIRE].
C. Majumdar, S. Patra, S. Senapati and U.A. Yajnik, Neutrinoless double beta decay in a minimal left-right symmetric model with gauge coupling unification, arXiv:1809.10577 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, Phys. Rev. D 23 (1981) 165 [INSPIRE].
J. Nocedal, Numerical optimization, Springer, New York U.S.A. (2006).
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: 1811.06869
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
Dev, P.S.B., Mohapatra, R.N., Rodejohann, W. et al. Vacuum structure of the left-right symmetric model. J. High Energ. Phys. 2019, 154 (2019). https://doi.org/10.1007/JHEP02(2019)154
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2019)154