Abstract
The SUSY SO(10) GUT is in severe tension with the experimental bounds on proton partial lifetimes because proton decay mediated by colored Higgsinos (dimension-five proton decay) is too rapid. In this paper, we pursue the possibility that a texture of the Yukawa coupling matrices in a renormalizable SUSY SO(10) GUT model suppresses dimension-five proton decay. We focus on a general renormalizable SUSY SO(10) GUT model which contains 10 + 126 + \( \overline{\textbf{126}} \) + 120 representation fields and where the Yukawa coupling matrices of the 16 matter fields with the 10, \( \overline{\textbf{126}} \), 120 fields, Y10, Y126, Y120, provide the quark and lepton Yukawa couplings and Majorana mass of the singlet neutrinos. We find that if components in certain flavor bases, \( {\left({Y}_{10}\right)}_{u_R{d}_R} \), \( {\left({Y}_{126}\right)}_{u_R{d}_R} \), \( {\left({Y}_{10}\right)}_{u_R{s}_R} \), \( {\left({Y}_{126}\right)}_{u_R{s}_R} \), \( {\left({Y}_{10}\right)}_{u_L{d}_L} \), \( {\left({Y}_{126}\right)}_{u_L{d}_L} \), \( {\left({Y}_{10}\right)}_{u_L{s}_L} \), \( {\left({Y}_{126}\right)}_{u_L{s}_L} \), \( {\left({Y}_{10}\right)}_{u_L{u}_L} \), \( {\left({Y}_{126}\right)}_{u_L{u}_L} \), are all on the order of the up quark Yukawa coupling, dimension-five proton decay can be suppressed while the Yukawa coupling matrices still reproduce the realistic quark and lepton masses and flavor mixings. We numerically obtain specific Yukawa coupling matrices satisfying the above conditions, calculate proton partial lifetimes from them and evaluate how dimension-five proton decay is suppressed when these conditions are met.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Georgi, The state of the art — gauge theories, AIP Conf. Proc. 23 (1975) 575 [INSPIRE].
H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Annals Phys. 93 (1975) 193 [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 gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].
T. Yanagida, Horizontal symmetry and mass of the top quark, Phys. Rev. D 20 (1979) 2986 [INSPIRE].
R.N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
S. Weinberg, Supersymmetry at ordinary energies. 1. Masses and conservation laws, Phys. Rev. D 26 (1982) 287 [INSPIRE].
N. Sakai and T. Yanagida, Proton decay in a class of supersymmetric grand unified models, Nucl. Phys. B 197 (1982) 533 [INSPIRE].
T. Goto and T. Nihei, Effect of RRRR dimension five operator on the proton decay in the minimal SU(5) SUGRA GUT model, Phys. Rev. D 59 (1999) 115009 [hep-ph/9808255] [INSPIRE].
Super-Kamiokande collaboration, Search for proton decay via p → νK+ using 260 kiloton·year data of Super-Kamiokande, Phys. Rev. D 90 (2014) 072005 [arXiv:1408.1195] [INSPIRE].
K. Matsuda, Y. Koide and T. Fukuyama, Can the SO(10) model with two Higgs doublets reproduce the observed fermion masses?, Phys. Rev. D 64 (2001) 053015 [hep-ph/0010026] [INSPIRE].
K. Matsuda, Y. Koide, T. Fukuyama and H. Nishiura, How far can the SO(10) two Higgs model describe the observed neutrino masses and mixings?, Phys. Rev. D 65 (2002) 033008 [Erratum ibid. 65 (2002) 079904] [hep-ph/0108202] [INSPIRE].
T. Fukuyama and N. Okada, Neutrino oscillation data versus minimal supersymmetric SO(10) model, JHEP 11 (2002) 011 [hep-ph/0205066] [INSPIRE].
B. Bajc, G. Senjanovic and F. Vissani, b-τ unification and large atmospheric mixing: a case for noncanonical seesaw, Phys. Rev. Lett. 90 (2003) 051802 [hep-ph/0210207] [INSPIRE].
H.S. Goh, R.N. Mohapatra and S.-P. Ng, Minimal SUSY SO(10), b τ unification and large neutrino mixings, Phys. Lett. B 570 (2003) 215 [hep-ph/0303055] [INSPIRE].
C.S. Aulakh, B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, The minimal supersymmetric grand unified theory, Phys. Lett. B 588 (2004) 196 [hep-ph/0306242] [INSPIRE].
H.S. Goh, R.N. Mohapatra and S.-P. Ng, Minimal SUSY SO(10) model and predictions for neutrino mixings and leptonic CP violation, Phys. Rev. D 68 (2003) 115008 [hep-ph/0308197] [INSPIRE].
B. Dutta, Y. Mimura and R.N. Mohapatra, CKM CP violation in a minimal SO(10) model for neutrinos and its implications, Phys. Rev. D 69 (2004) 115014 [hep-ph/0402113] [INSPIRE].
B. Bajc, G. Senjanovic and F. Vissani, Probing the nature of the seesaw in renormalizable SO(10), Phys. Rev. D 70 (2004) 093002 [hep-ph/0402140] [INSPIRE].
S. Bertolini, M. Frigerio and M. Malinsky, Fermion masses in SUSY SO(10) with type II seesaw: a non-minimal predictive scenario, Phys. Rev. D 70 (2004) 095002 [hep-ph/0406117] [INSPIRE].
W.-M. Yang and Z.-G. Wang, Fermion masses and flavor mixing in a supersymmetric SO(10) model, Nucl. Phys. B 707 (2005) 87 [hep-ph/0406221] [INSPIRE].
B. Dutta, Y. Mimura and R.N. Mohapatra, Neutrino masses and mixings in a predictive SO(10) model with CKM CP violation, Phys. Lett. B 603 (2004) 35 [hep-ph/0406262] [INSPIRE].
B. Dutta, Y. Mimura and R.N. Mohapatra, Suppressing proton decay in the minimal SO(10) model, Phys. Rev. Lett. 94 (2005) 091804 [hep-ph/0412105] [INSPIRE].
K.S. Babu and C. Macesanu, Neutrino masses and mixings in a minimal SO(10) model, Phys. Rev. D 72 (2005) 115003 [hep-ph/0505200] [INSPIRE].
B. Dutta, Y. Mimura and R.N. Mohapatra, Neutrino mixing predictions of a minimal SO(10) model with suppressed proton decay, Phys. Rev. D 72 (2005) 075009 [hep-ph/0507319] [INSPIRE].
S. Bertolini, T. Schwetz and M. Malinsky, Fermion masses and mixings in SO(10) models and the neutrino challenge to SUSY GUTs, Phys. Rev. D 73 (2006) 115012 [hep-ph/0605006] [INSPIRE].
A.S. Joshipura and K.M. Patel, Fermion masses in SO(10) models, Phys. Rev. D 83 (2011) 095002 [arXiv:1102.5148] [INSPIRE].
A. Dueck and W. Rodejohann, Fits to SO(10) grand unified models, JHEP 09 (2013) 024 [arXiv:1306.4468] [INSPIRE].
T. Fukuyama, K. Ichikawa and Y. Mimura, Revisiting fermion mass and mixing fits in the minimal SUSY SO(10) GUT, Phys. Rev. D 94 (2016) 075018 [arXiv:1508.07078] [INSPIRE].
T. Fukuyama, K. Ichikawa and Y. Mimura, Relation between proton decay and PMNS phase in the minimal SUSY SO(10) GUT, Phys. Lett. B 764 (2017) 114 [arXiv:1609.08640] [INSPIRE].
T. Fukuyama, N. Okada and H.M. Tran, Sparticle spectroscopy of the minimal SO(10) model, Phys. Lett. B 767 (2017) 295 [arXiv:1611.08341] [INSPIRE].
K.S. Babu, B. Bajc and S. Saad, Yukawa sector of minimal SO(10) unification, JHEP 02 (2017) 136 [arXiv:1612.04329] [INSPIRE].
K.S. Babu, B. Bajc and S. Saad, Resurrecting minimal Yukawa sector of SUSY SO(10), JHEP 10 (2018) 135 [arXiv:1805.10631] [INSPIRE].
T. Deppisch, S. Schacht and M. Spinrath, Confronting SUSY SO(10) with updated lattice and neutrino data, JHEP 01 (2019) 005 [arXiv:1811.02895] [INSPIRE].
T. Fukuyama, N. Okada and H.M. Tran, Alternative renormalizable SO(10) GUTs and data fitting, Nucl. Phys. B 954 (2020) 114992 [arXiv:1907.02948] [INSPIRE].
N. Haba, Y. Mimura and T. Yamada, Enhanced \( \Gamma \left(p\to {K}^0{\mu}^{+}\right)/\Gamma \left(p\to {K}^{+}{\overline{\nu}}_{\mu}\right) \) as a signature of minimal renormalizable SUSY SO(10) GUT, PTEP 2020 (2020) 093B01 [arXiv:2002.11413] [INSPIRE].
N. Haba, Y. Mimura and T. Yamada, Renormalizable SO(10) grand unified theory with suppressed dimension-5 proton decays, PTEP 2021 (2021) 023B01 [arXiv:2008.05362] [INSPIRE].
H.S. Goh, R.N. Mohapatra and S. Nasri, SO(10) symmetry breaking and type II seesaw, Phys. Rev. D 70 (2004) 075022 [hep-ph/0408139] [INSPIRE].
P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [INSPIRE].
T. Fukuyama, A. Ilakovac, T. Kikuchi, S. Meljanac and N. Okada, General formulation for proton decay rate in minimal supersymmetric SO(10) GUT, Eur. Phys. J. C 42 (2005) 191 [hep-ph/0401213] [INSPIRE].
C.S. Aulakh and A. Girdhar, SO(10) MSGUT: spectra, couplings and threshold effects, Nucl. Phys. B 711 (2005) 275 [hep-ph/0405074] [INSPIRE].
T. Fukuyama, A. Ilakovac, T. Kikuchi, S. Meljanac and N. Okada, SO(10) group theory for the unified model building, J. Math. Phys. 46 (2005) 033505 [hep-ph/0405300] [INSPIRE].
T. Fukuyama, A. Ilakovac, T. Kikuchi, S. Meljanac and N. Okada, Higgs masses in the minimal SUSY SO(10) GUT, Phys. Rev. D 72 (2005) 051701 [hep-ph/0412348] [INSPIRE].
B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, The minimal supersymmetric grand unified theory. 1. Symmetry breaking and the particle spectrum, Phys. Rev. D 70 (2004) 035007 [hep-ph/0402122] [INSPIRE].
B. Bajc, A. Melfo, G. Senjanovic and F. Vissani, Fermion mass relations in a supersymmetric SO(10) theory, Phys. Lett. B 634 (2006) 272 [hep-ph/0511352] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2022 (2022) 083C01 [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
Fermilab Lattice, MILC and TUMQCD collaborations, Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, Phys. Rev. D 98 (2018) 054517 [arXiv:1802.04248] [INSPIRE].
D. Giusti et al., Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with twisted-mass fermions, Phys. Rev. D 95 (2017) 114504 [arXiv:1704.06561] [INSPIRE].
European Twisted Mass collaboration, Up, down, strange and charm quark masses with Nf = 2 + 1 + 1 twisted mass lattice QCD, Nucl. Phys. B 887 (2014) 19 [arXiv:1403.4504] [INSPIRE].
HPQCD collaboration, Determination of quark masses from nf = 4 lattice QCD and the RI-SMOM intermediate scheme, Phys. Rev. D 98 (2018) 014513 [arXiv:1805.06225] [INSPIRE].
B. Chakraborty et al., High-precision quark masses and QCD coupling from nf = 4 lattice QCD, Phys. Rev. D 91 (2015) 054508 [arXiv:1408.4169] [INSPIRE].
C. Alexandrou, V. Drach, K. Jansen, C. Kallidonis and G. Koutsou, Baryon spectrum with Nf = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 90 (2014) 074501 [arXiv:1406.4310] [INSPIRE].
HPQCD collaboration, Charmonium properties from lattice QCD+QED: hyperfine splitting, J/ψ leptonic width, charm quark mass, and \( {a}_{\mu}^c \), Phys. Rev. D 102 (2020) 054511 [arXiv:2005.01845] [INSPIRE].
D. Hatton, C.T.H. Davies, J. Koponen, G.P. Lepage and A.T. Lytle, Determination of \( {\overline{m}}_b/{\overline{m}}_c \) and \( {\overline{m}}_b \) from nf = 4 lattice QCD+QED, Phys. Rev. D 103 (2021) 114508 [arXiv:2102.09609] [INSPIRE].
B. Colquhoun, R.J. Dowdall, C.T.H. Davies, K. Hornbostel and G.P. Lepage, Υ and Υ′ leptonic widths, \( {a}_{\mu}^b \) and mb from full lattice QCD, Phys. Rev. D 91 (2015) 074514 [arXiv:1408.5768] [INSPIRE].
ETM collaboration, Mass of the b quark and B-meson decay constants from Nf = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D 93 (2016) 114505 [arXiv:1603.04306] [INSPIRE].
P. Gambino, A. Melis and S. Simula, Extraction of heavy-quark-expansion parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses, Phys. Rev. D 96 (2017) 014511 [arXiv:1704.06105] [INSPIRE].
CMS collaboration, Measurement of \( t\overline{t} \) normalised multi-differential cross sections in pp collisions at \( \sqrt{s} \) = 13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions, Eur. Phys. J. C 80 (2020) 658 [arXiv:1904.05237] [INSPIRE].
CKMfitter Group collaboration, CP violation and the CKM matrix: assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [INSPIRE].
B.A. Kniehl, A.F. Pikelner and O.L. Veretin, mr: a C++ library for the matching and running of the standard model parameters, Comput. Phys. Commun. 206 (2016) 84 [arXiv:1601.08143] [INSPIRE].
F. Jegerlehner, M.Y. Kalmykov and O. Veretin, MS versus pole masses of gauge bosons: electroweak bosonic two loop corrections, Nucl. Phys. B 641 (2002) 285 [hep-ph/0105304] [INSPIRE].
F. Jegerlehner, M.Y. Kalmykov and O. Veretin, MS-bar versus pole masses of gauge bosons. 2. Two loop electroweak fermion corrections, Nucl. Phys. B 658 (2003) 49 [hep-ph/0212319] [INSPIRE].
F. Jegerlehner and M.Y. Kalmykov, O(ααs) correction to the pole mass of the t quark within the standard model, Nucl. Phys. B 676 (2004) 365 [hep-ph/0308216] [INSPIRE].
F. Jegerlehner and M.Y. Kalmykov, O(ααs) relation between pole- and MS-bar mass of the t quark, Acta Phys. Polon. B 34 (2003) 5335 [hep-ph/0310361] [INSPIRE].
F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs boson mass and new physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark mass relations to four-loop order in perturbative QCD, Phys. Rev. Lett. 114 (2015) 142002 [arXiv:1502.01030] [INSPIRE].
B.A. Kniehl, A.F. Pikelner and O.L. Veretin, Two-loop electroweak threshold corrections in the standard model, Nucl. Phys. B 896 (2015) 19 [arXiv:1503.02138] [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, Nucl. Phys. B 249 (1985) 70 [INSPIRE].
T. Blazek, S. Raby and S. Pokorski, Finite supersymmetric threshold corrections to CKM matrix elements in the large tan β regime, Phys. Rev. D 52 (1995) 4151 [hep-ph/9504364] [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].
NuFIT webpage, version 5.1, http://www.nu-fit.org/ (2021).
S. Borsanyi et al., SU(2) chiral perturbation theory low-energy constants from 2 + 1 flavor staggered lattice simulations, Phys. Rev. D 88 (2013) 014513 [arXiv:1205.0788] [INSPIRE].
Y. Aoki, T. Izubuchi, E. Shintani and A. Soni, Improved lattice computation of proton decay matrix elements, Phys. Rev. D 96 (2017) 014506 [arXiv:1705.01338] [INSPIRE].
J. Hisano, H. Murayama and T. Yanagida, Nucleon decay in the minimal supersymmetric SU(5) grand unification, Nucl. Phys. B 402 (1993) 46 [hep-ph/9207279] [INSPIRE].
Super-Kamiokande collaboration, Search for proton decay via p → μ+K0 in 0.37 megaton-years exposure of Super-Kamiokande, Phys. Rev. D 106 (2022) 072003 [arXiv:2208.13188] [INSPIRE].
Super-Kamiokande collaboration, Search for nucleon decay via modes favored by supersymmetric grand unification models in Super-Kamiokande-I, Phys. Rev. D 72 (2005) 052007 [hep-ex/0502026] [INSPIRE].
Hyper-Kamiokande collaboration, Hyper-Kamiokande design report, arXiv:1805.04163 [INSPIRE].
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: 2211.10091
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
Haba, N., Yamada, T. Conditions for suppressing dimension-five proton decay in renormalizable SUSY SO(10) GUT. J. High Energ. Phys. 2023, 148 (2023). https://doi.org/10.1007/JHEP02(2023)148
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2023)148