Chen, M. C., King, S. F., Medina, O., & Valle, J. W. F. (2024). Quark-lepton mass relations from modular flavor symmetry. J. High Energy Phys., 02(2), 160–28pp.
Abstract: The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Gamma 4 approximately equal to S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.
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de Medeiros Varzielas, I., King, S. F., Luhn, C., & Neder, T. (2017). Spontaneous CP violation in multi-Higgs potentials with triplets of Delta(3n(2)) and Delta(6n(2)). J. High Energy Phys., 11(11), 136–56pp.
Abstract: Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fi elds (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the Delta(3n(2)) and Delta(6n(2)) series, including A(4), S-4, Delta(27) and Delta(54). For each case, we give the potential and fi nd various global minima for di ff erent regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have geometrical phases.
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de Medeiros Varzielas, I., King, S. F., Luhn, C., & Neder, T. (2017). Minima of multi-Higgs potentials with triplets of Delta(3n(2)) and Delta(6n(2)). Phys. Lett. B, 775, 303–310.
Abstract: We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries A(4), S-4, Delta (27), Delta (54), as well as Delta (3n(2)) and Delta(6n2) with n > 3. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry.
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Di Bari, P., King, S. F., & Hossain Rahat, M. (2024). Gravitational waves from phase transitions and cosmic strings in neutrino mass models with multiple majorons. J. High Energy Phys., 05(5), 068–31pp.
Abstract: We explore the origin of Majorana masses within the majoron model and how this can lead to the generation of a distinguishable primordial stochastic background of gravitational waves. We first show how in the simplest majoron model only a contribution from cosmic string can be within the reach of planned experiments. We then consider extensions containing multiple complex scalars, demonstrating how in this case a spectrum comprising contributions from both a strong first order phase transition and cosmic strings can naturally emerge. We show that the interplay between multiple scalar fields can amplify the phase transition signal, potentially leading to double peaks over the wideband sloped spectrum from cosmic strings. We also underscore the possibility of observing such a gravitational wave background to provide insights into the reheating temperature of the universe. We conclude highlighting how the model can be naturally combined with scenarios addressing the origin of matter of the universe, where baryogenesis occurs via leptogenesis and a right-handed neutrino plays the role of dark matter.
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Fernandez Navarro, M., King, S. F., & Vicente, A. (2024). Tri-unification: a separate SU(5) for each fermion family. J. High Energy Phys., 05(5), 130–32pp.
Abstract: In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{U}}{\left(1\right)}_{Y}<^>{3}$$\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+pi 0 channel.
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Fernandez Navarro, M., King, S. F., & Vicente, A. (2024). Minimal complete tri-hypercharge theories of flavour. J. High Energy Phys., 07(7), 147–36pp.
Abstract: The tri-hypercharge proposal introduces a separate gauged weak hypercharge assigned to each fermion family as the origin of flavour. This is arguably one of the simplest setups for building “gauge non-universal theories of flavour” or “flavour deconstructed theories”. In this paper we propose and study two minimal but ultraviolet complete and renormalisable tri-hypercharge models. We show that both models, which differ only by the heavy messengers that complete the effective theory, are able to explain the observed patterns of fermion masses and mixings (including neutrinos) with all fundamental coefficients being of O(1). In fact, both models translate the complicated flavour structure of the Standard Model into three simple physical scales above electroweak symmetry breaking, completely correlated with each other, that carry meaningful phenomenology. In particular, the heavy messenger sector determines the origin and size of fermion mixing, which controls the size and nature of the flavour-violating currents mediated by the two heavy Z ' gauge bosons of the theory. The phenomenological implications of the two minimal models are compared. In both models the lightest Z ' remains discoverable in dilepton searches at the LHC Run 3.
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Fu, B. W., Ghoshal, A., King, S. F., & Hossain Rahat, M. (2024). Type-I two-Higgs-doublet model and gravitational waves from domain walls bounded by strings. J. High Energy Phys., 08(8), 237–25pp.
Abstract: The spontaneous breaking of a U(1) symmetry via an intermediate discrete symmetry may yield a hybrid topological defect of domain walls bounded by cosmic strings. The decay of this defect network leads to a unique gravitational wave signal spanning many orders in observable frequencies, that can be distinguished from signals generated by other sources. We investigate the production of gravitational waves from this mechanism in the context of the type-I two-Higgs-doublet model extended by a U(1)R symmetry, that simultaneously accommodates the seesaw mechanism, anomaly cancellation, and eliminates flavour-changing neutral currents. The gravitational wave spectrum produced by the string-bounded-wall network can be detected for U(1)R breaking scale from 1012 to 1015 GeV in forthcoming interferometers including LISA and Einstein Telescope, with a distinctive f3 slope and inflexion in the frequency range between microhertz and hertz.
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King, S. F., Marfatia, D., & Rahat, M. H. (2024). Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves. Phys. Rev. D, 109(3), 035014–13pp.
Abstract: We propose a new method toward distinguishing the Dirac versus Majorana nature of neutrino masses from the spectrum of gravitational waves (GWs) associated with neutrino mass genesis. Motivated by the principle of generating small neutrino masses without tiny Yukawa couplings, we assume generic seesaw mechanisms for both Majorana and Dirac neutrino masses. For Majorana neutrinos, we further assume a spontaneously broken gauged U(1)B-L symmetry, independently of the type of Majorana seesaw mechanism, which gives a cosmic string induced GW signal flat over a wide range of frequencies. For Dirac neutrinos, we assume the spontaneous breaking of a Z2 symmetry, the minimal symmetry choice associated with all Dirac seesaw mechanisms, which is softly broken, generating a peaked GW spectrum from the annihilation of the resulting domain walls. In fact, the GW spectra for all types of Dirac seesaws with such a broken Z2 symmetry are identical, subject to a mild caveat. As an illustrative example, we study the simplest respective type-I seesaw mechanisms, and show that the striking difference in the shapes of the GW spectra can help differentiate between these Dirac and Majorana seesaws, complementing results of neutrinoless double beta decay experiments. We also discuss detailed implications of the recent NANOGrav data for Majorana and Dirac seesaw models.
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King, S. F., Molina Sedgwick, S., Parke, S. J., & Prouse, N. W. (2020). Effects of matter density profiles on neutrino oscillations for T2HK and T2HKK. Phys. Rev. D, 101(7), 076019–16pp.
Abstract: This paper explores the effects of changes in matter density profiles on neutrino oscillation probabilities, and whether these could potentially be seen by the future Hyper-Kamiokande long-baseline oscillation experiment (T2HK). The analysis is extended to include the possibility of having an additional detector in Korea (T2HKK). In both cases, we find that these effects will be immeasurable, as the magnitudes of the changes in the oscillation probabilities induced in all density profile scenarios considered here remain smaller than the estimated experimental sensitivity to the oscillation probabilities of each experiment, for both appearance and disappearance channels. Therefore, we conclude that using a constant density profile is sufficient for both the T2HK and T2HKK experiments.
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King, S. F., Morisi, S., Peinado, E., & Valle, J. W. F. (2013). Quark-lepton mass relation in a realistic A(4) extension of the Standard Model. Phys. Lett. B, 724(1-3), 68–72.
Abstract: We propose a realistic A(4) extension of the Standard Model involving a particular quark-lepton mass relation, namely that the ratio of the third family mass to the geometric mean of the first and second family masses are equal for down-type quarks and charged leptons. This relation, which is approximately renormalization group invariant, is usually regarded as arising from the Georgi-Jarlskog relations, but in the present model there is no unification group or supersymmetry. In the neutrino sector we propose a simple modification of the so-called Zee-Wolfenstein mass matrix pattern which allows an acceptable reactor angle along with a deviation of the atmospheric and solar angles from their bi-maximal values. Quark masses, mixing angles and CP violation are well described by a numerical fit.
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