Abstract
Realistic models based on the renormalizable grand unified theories have varieties of scalars, many of which are capable of mediating baryon (B) and lepton (L) number non-conserving processes. We identify all such scalar fields residing in 10, \( \overline{\mathbf{126}} \) and 120 dimensional irreducible representations of SO(10) which can induce baryon and lepton number violating interactions through the leading order d = 6 and d = 7 operators. Explicitly computing their couplings with the standard model fermions, we derive the effective operators including the possibility of mixing between the scalars stemming from a given representation. We find that such interactions at d = 6 are mediated by only three sets of scalars: T(3, 1, −1/3), \( \mathcal{T} \)(3, 1, −4/3) and \( \mathbbm{T} \)(3, 3, −1/3) and their conjugates. In the models with 10 and \( \overline{\mathbf{126}} \), only the first has appropriate couplings to mediate the proton decay. While \( \mathcal{T} \) and \( \mathbbm{T} \) can induce baryon number violating interactions when 120 is present, \( \mathcal{T} \) does not contribute to the proton decay at tree level because of its flavour antisymmetric coupling. Three additional colour triplets and their conjugates can mediate nucleon decay via d = 7 operators which violate also the B − L. We give general expressions for partial widths of proton in terms of the fundamental Yukawa couplings and use these results to explicitly compute the proton lifetime and branching ratios for the minimal non-supersymmetric SO(10) model based on 10 and \( \overline{\mathbf{126}} \) Higgs. We find that the proton preferably decays into \( \overline{\nu} \)K+ or μ+ K0 and list several distinct features of scalar mediated proton decay. If the latter dominates over the gauge mediated contributions, the proton decay spectrum provides a direct probe to the flavour structure of the underlying grand unified theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [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. Dimopoulos, L.J. Hall and S. Raby, A Predictive framework for fermion masses in supersymmetric theories, Phys. Rev. Lett. 68 (1992) 1984 [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].
T.E. Clark, T.-K. Kuo and N. Nakagawa, A SO(10) supersymmetric grand unified theory, Phys. Lett. B 115 (1982) 26 [INSPIRE].
C.S. Aulakh and R.N. Mohapatra, Implications of Supersymmetric SO(10) Grand Unification, Phys. Rev. D 28 (1983) 217 [INSPIRE].
C.S. Aulakh, B. Bajc, A. Melfo, G. Senjanović and F. Vissani, The Minimal supersymmetric grand unified theory, Phys. Lett. B 588 (2004) 196 [hep-ph/0306242] [INSPIRE].
B. Bajc, A. Melfo, G. Senjanović and F. Vissani, Yukawa sector in non-supersymmetric renormalizable SO(10), Phys. Rev. D 73 (2006) 055001 [hep-ph/0510139] [INSPIRE].
A.S. Joshipura and K.M. Patel, Fermion Masses in SO(10) Models, Phys. Rev. D 83 (2011) 095002 [arXiv:1102.5148] [INSPIRE].
M. Bordone, G. Isidori and A. Pattori, On the Standard Model predictions for RK and \( {R}_{K^{\ast }} \), Eur. Phys. J. C 76 (2016) 440 [arXiv:1605.07633] [INSPIRE].
G. Bélanger et al., Leptoquark manoeuvres in the dark: a simultaneous solution of the dark matter problem and the \( {R}_{D^{\left(\ast \right)}} \) anomalies, JHEP 02 (2022) 042 [arXiv:2111.08027] [INSPIRE].
P. Fileviez Perez, C. Murgui and A.D. Plascencia, Leptoquarks and matter unification: Flavor anomalies and the muon g-2, Phys. Rev. D 104 (2021) 035041 [arXiv:2104.11229] [INSPIRE].
S. Sahoo, S. Singirala and R. Mohanta, Dark matter and flavor anomalies in the light of vector-like fermions and scalar leptoquark, arXiv:2112.04382 [INSPIRE].
M. Bauer and M. Neubert, Minimal Leptoquark Explanation for the \( {R}_{D^{\left(\ast \right)}} \), RK, and (g − 2)μ Anomalies, Phys. Rev. Lett. 116 (2016) 141802 [arXiv:1511.01900] [INSPIRE].
C.-H. Chen, T. Nomura and H. Okada, Excesses of muon g − 2, \( {R}_{D^{\left(\ast \right)}} \), and RK in a leptoquark model, Phys. Lett. B 774 (2017) 456 [arXiv:1703.03251] [INSPIRE].
I. Doršner, S. Fajfer and O. Sumensari, Muon g − 2 and scalar leptoquark mixing, JHEP 06 (2020) 089 [arXiv:1910.03877] [INSPIRE].
I. Dorsner, S. Fajfer, J.F. Kamenik and N. Kosnik, Light colored scalars from grand unification and the forward-backward asymmetry in t t-bar production, Phys. Rev. D 81 (2010) 055009 [arXiv:0912.0972] [INSPIRE].
K.M. Patel and P. Sharma, Forward-backward asymmetry in top quark production from light colored scalars in SO(10) model, JHEP 04 (2011) 085 [arXiv:1102.4736] [INSPIRE].
I. Doršner, S. Fajfer, A. Greljo, J.F. Kamenik and N. Košnik, Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rept. 641 (2016) 1 [arXiv:1603.04993] [INSPIRE].
K.S. Babu and R.N. Mohapatra, B-L Violating Proton Decay Modes and New Baryogenesis Scenario in SO(10), Phys. Rev. Lett. 109 (2012) 091803 [arXiv:1207.5771] [INSPIRE].
K.S. Babu and R.N. Mohapatra, B-L Violating Nucleon Decay and GUT Scale Baryogenesis in SO(10), Phys. Rev. D 86 (2012) 035018 [arXiv:1203.5544] [INSPIRE].
P. Fileviez Perez, H. Iminniyaz and G. Rodrigo, Proton Stability, Dark Matter and Light Color Octet Scalars in Adjoint SU(5) Unification, Phys. Rev. D 78 (2008) 015013 [arXiv:0803.4156] [INSPIRE].
J.C. Pati and A. Salam, Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions, Phys. Rev. D 8 (1973) 1240 [INSPIRE].
S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
F. Wilczek and A. Zee, Operator Analysis of Nucleon Decay, Phys. Rev. Lett. 43 (1979) 1571 [INSPIRE].
P. Langacker, Grand Unified Theories and Proton Decay, Phys. Rept. 72 (1981) 185 [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].
K.S. Babu et al., Working Group Report: Baryon Number Violation, in Community Summer Study 2013: Snowmass on the Mississippi, 11, 2013 [arXiv:1311.5285] [INSPIRE].
S. Raby, Supersymmetric Grand Unified Theories: From Quarks to Strings via SUSY GUTs, vol. 939, Springer (2017), https://doi.org/10.1007/978-3-319-55255-2 [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].
E. Golowich, Scalar mediated proton decay, Phys. Rev. D 24 (1981) 2899 [INSPIRE].
I. Dorsner, S. Fajfer and N. Kosnik, Heavy and light scalar leptoquarks in proton decay, Phys. Rev. D 86 (2012) 015013 [arXiv:1204.0674] [INSPIRE].
I. Dorsner and P. Fileviez Perez, Could we rotate proton decay away?, Phys. Lett. B 606 (2005) 367 [hep-ph/0409190] [INSPIRE].
P. Fileviez Perez, Fermion mixings versus d = 6 proton decay, Phys. Lett. B 595 (2004) 476 [hep-ph/0403286] [INSPIRE].
I. Dorsner and P. Fileviez Perez, How long could we live?, Phys. Lett. B 625 (2005) 88 [hep-ph/0410198] [INSPIRE].
H. Kolešová and M. Malinský, Flavor structure of GUTs and uncertainties in proton lifetime estimates, Phys. Rev. D 99 (2019) 035005 [arXiv:1612.09178] [INSPIRE].
W. Buchmüller and K.M. Patel, Proton decay in flux compactifications, JHEP 05 (2019) 196 [arXiv:1904.08810] [INSPIRE].
R.N. Mohapatra and B. Sakita, SO(2n) Grand Unification in an SU(N) Basis, Phys. Rev. D 21 (1980) 1062 [INSPIRE].
P. Nath and R.M. Syed, Analysis of couplings with large tensor representations in SO(2N) and proton decay, Phys. Lett. B 506 (2001) 68 [Erratum ibid. 508 (2001) 216] [hep-ph/0103165] [INSPIRE].
R.M. Syed, Couplings in SO(10) grand unification, thesis (2005) [hep-ph/0508153] [INSPIRE].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [INSPIRE].
S. Weinberg, Varieties of Baryon and Lepton Nonconservation, Phys. Rev. D 22 (1980) 1694 [INSPIRE].
H.A. Weldon and A. Zee, Operator Analysis of New Physics, Nucl. Phys. B 173 (1980) 269 [INSPIRE].
M. Claudson, M.B. Wise and L.J. Hall, Chiral Lagrangian for Deep Mine Physics, Nucl. Phys. B 195 (1982) 297 [INSPIRE].
S. Chadha and M. Daniel, Chiral Lagrangian Calculation of Nucleon Decay Modes Induced by d = 5 Supersymmetric Operators, Nucl. Phys. B 229 (1983) 105 [INSPIRE].
JLQCD collaboration, Nucleon decay matrix elements from lattice QCD, Phys. Rev. D 62 (2000) 014506 [hep-lat/9911026] [INSPIRE].
G. Altarelli and D. Meloni, A non supersymmetric SO(10) grand unified model for all the physics below MGUT , JHEP 08 (2013) 021 [arXiv:1305.1001] [INSPIRE].
A. Dueck and W. Rodejohann, Fits to SO(10) Grand Unified Models, JHEP 09 (2013) 024 [arXiv:1306.4468] [INSPIRE].
D. Meloni, T. Ohlsson and S. Riad, Effects of intermediate scales on renormalization group running of fermion observables in an SO(10) model, JHEP 12 (2014) 052 [arXiv:1409.3730] [INSPIRE].
D. Meloni, T. Ohlsson and S. Riad, Renormalization Group Running of Fermion Observables in an Extended Non-Supersymmetric SO(10) Model, JHEP 03 (2017) 045 [arXiv:1612.07973] [INSPIRE].
K.S. Babu, B. Bajc and S. Saad, Yukawa Sector of Minimal SO(10) Unification, JHEP 02 (2017) 136 [arXiv:1612.04329] [INSPIRE].
T. Ohlsson and M. Pernow, Running of Fermion Observables in Non-Supersymmetric SO(10) Models, JHEP 11 (2018) 028 [arXiv:1804.04560] [INSPIRE].
V.S. Mummidi and K.M. Patel, Leptogenesis and fermion mass fit in a renormalizable SO(10) model, JHEP 12 (2021) 042 [arXiv:2109.04050] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
N. Cabibbo, E.C. Swallow and R. Winston, Semileptonic hyperon decays, Ann. Rev. Nucl. Part. Sci. 53 (2003) 39 [hep-ph/0307298] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
R. Alonso, H.-M. Chang, E.E. Jenkins, A.V. Manohar and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734 (2014) 302 [arXiv:1405.0486] [INSPIRE].
Super-Kamiokande collaboration, Search for proton decay via p → e+π0 and p → μ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV, Phys. Rev. D 102 (2020) 112011 [arXiv:2010.16098] [INSPIRE].
Super-Kamiokande collaboration, Search for Proton Decay via p → μ+K0 in Super-Kamiokande I, II, and III, Phys. Rev. D 86 (2012) 012006 [arXiv:1205.6538] [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].
M. Machacek, The Decay Modes of the Proton, Nucl. Phys. B 159 (1979) 37 [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: 2203.07748
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
Patel, K.M., Shukla, S.K. Anatomy of scalar mediated proton decays in SO(10) models. J. High Energ. Phys. 2022, 42 (2022). https://doi.org/10.1007/JHEP08(2022)042
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)042