Unification Scale Research Articles

Flavor in SU(5)$SU(5)$ Finite Grand Unified Models

AbstractFour supersymmetric models which exhibit and/or symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all‐loop finite model based on an flavor symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two‐loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two‐loop models shows an enhanced symmetry, leading to an all‐loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings.

Leptogenesis in the minimal flipped SU(5) unification

We study the prospects of thermal leptogenesis in the framework of the minimal flipped SU(5) unified model in which the right-handed (RH) neutrino mass scale emerges as a two-loop effect. Despite its strong suppression with respect to the unification scale that tends to disfavor leptogenesis in the standard Davidson-Ibarra regime (and a notoriously large washout of the N1-generated asymmetry owing to a toplike Yukawa entry in the Dirac neutrino mass matrix) the desired ηB∼6×10−10 can still be attained in several parts of the parameter space exhibiting interesting baryon and lepton number violation phenomenology. Remarkably enough, in all these regions the mass of the lightest left-handed (LH) neutrino is so low that it yields mβ≲0.03 eV for the effective neutrino mass measured in beta decay, i.e., an order of magnitude below the design sensitivity limit of the KATRIN experiment. This makes the model potentially testable in the near future. Published by the American Physical Society 2024

Leptoquark-mediated two-loop neutrino mass in unified theory

Scalar leptoquarks naturally arise within unified theories, offering a promising avenue for addressing one of the most significant challenges of the Standard Model–the existence of non-zero neutrino masses. In this work, we present a unified theory based on the SU(5) gauge group, where neutrino mass appears at the two-loop level via the propagation of scalar leptoquarks. Due to the unified framework, the charged fermion and neutrino masses and mixings are entangled and determined by a common set of Yukawa couplings. These exotic particles not only shed light on the neutrino mass generation mechanism but also help to achieve the unification of gauge couplings and are expected to lead to substantial lepton flavor violating rates, offering tangible opportunities for experimental verification. Reproducing the observed neutrino mass scale necessitates that a set of leptoquarks reside a few orders of magnitude below the unification scale–a specific feature of the proposed scenario. Moreover, maximizing the unification scale implies TeV scale new physics states, making them accessible at colliders. The diverse roles that leptoquarks play highlight the elegance and predictive ability of the proposed unified model.

Minimal SU(5) theory on the edge: The importance of being effective

It is well known that the minimal renormalizable SU(5) grand unified theory is ruled out: it predicts the same masses of down quarks and charged leptons, the gauge couplings do not unify, and neutrinos are massless. We show here that all this can be cured simultaneously by the addition of higher-dimensional effective operators. However, the theory lives on the edge since the unification scale turns out as low as roughly 1014 GeV, threatening proton longevity. If the lower bound on the proton lifetime was to be increased by an order of magnitude, the usual desert in energies between the weak and unification scales would be populated. We also revisit two minimal extensions of this theory that offer a dynamical seesaw origin of neutrino mass and discuss the resulting consequences. Published by the American Physical Society 2024

Tri-unification: a separate SU(5) for each fermion family

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}$${\ ext{U}}{\\left(1\\right)}_{Y}^{3}$$\\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+π0 channel.

Tension between neutrino masses and gauge coupling unification in natural grand unified theories

The natural grand unified theories (GUT) solve various problems of the supersymmetric GUT and give realistic quark and lepton mass matrices under the natural assumption that all terms allowed by the symmetry are introduced with O(1) coefficients. However, because of the natural assumption, it is difficult to achieve the gauge coupling unification without tuning, while keeping neutrino masses at realistic values. In this paper, we try to avoid this tension between the neutrino masses and the gauge coupling unification, by introducing suppression factors for several terms. These suppression factors can be understood by approximate symmetries in some of the solutions. We show that one of the most important results in the natural GUT scenario, that the nucleon decay mediated by superheavy gauge fields is enhanced due to a smaller unification scale while the nucleon decay mediated by superheavy colored Higgs is suppressed, may change in those models proposed in this paper. Published by the American Physical Society 2024

Finite naturalness and quark-lepton unification

We study the implications of finite naturalness in Pati-Salam models where SU(3)C is embedded in SU(4). For the minimal realization at low scale of quark-lepton unification, which employs the inverse seesaw for neutrino masses, we find that radiative corrections to the Higgs boson mass are at least δmh2/mh2∼O(104). The one-loop contributions to the Higgs mass are suppressed by four powers of the hypercharge gauge coupling. We find that for the vector leptoquarks the naively leading part of the two-loop corrections cancel. We assume the Dirac Yukawa couplings for neutrinos are equal to the up-type quark Yukawa couplings as predicted in the minimal theory for quark-lepton unification. Despite these findings, the two-loop corrections still dominate the finite naturalness bound. We mention a way to relax the lower bound on the vector leptoquark mass and have δmh2/mh2∼O(102). Published by the American Physical Society 2024

From Dirac to Majorana: The cosmic neutrino background capture rate in the minimally extended Standard Model

We investigate the capture rate of the cosmic neutrino background on tritium within the Standard Model, extended to incorporate three right-handed singlet neutrinos with explicit lepton-number violation. We consider a scenario where the 6×6 neutrino mixing matrix factorizes into three independent 2×2 pairs and analyze the states produced from weak interactions just before neutrino decoupling. Taking into account the unrestricted Majorana mass scale associated with lepton number violation, spanning from the grand unification scale to Planck-suppressed values, we observe a gradual transition in the capture rate from a purely Majorana neutrino to a purely (pseudo) Dirac neutrino. We demonstrate that the capture rate is modified if the lightest active neutrino is relativistic, and this can be used to constrain the tiniest value of mass-squared difference ∼10−35 eV2, between the active-sterile pair, probed so far. Consequently, the cosmic neutrino capture rate could become a promising probe for discerning the underlying mechanism responsible for generating neutrino masses. Published by the American Physical Society 2024

Renormalisation group analysis of scalar Leptoquark couplings addressing flavour anomalies: emergence of lepton-flavour universality

Leptoquarks with masses between 2 TeV and 50 TeV are commonly invoked to explain deviations between data and Standard-Model (SM) predictions of several observables in the decays b→cτν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\ o c\ au \\overline{\ u} $$\\end{document} and b → sℓ+ℓ− with ℓ = e, μ. While Leptoquarks appear in theories unifying quarks and leptons, the corresponding unification scale MQLU is typically many orders of magnitude above this mass range. We study the case that the mass gap between the electroweak scale and MQLU is only populated by scalar Leptoquarks and SM particles, restricting ourselves to scenarios addressing the mentioned flavour anomalies, and determine the renormalisation-group evolution of Leptoquark couplings to fermions below MQLU. In the most general case, we consider three SU(2) triplet Leptoquarks S3ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_3^{\\ell } $$\\end{document}, ℓ = e, μ, τ, which couple quark doublets to the lepton doublet (νℓ, ℓ−) to address the b → sℓ+ℓ− anomalies. In this case, we find a scenario in which the Leptoquark couplings to electrons and muons are driven to the same infrared fixed point, so that lepton flavour universality emerges dynamically. However, the corresponding fixed point for the couplings to taus is necessarily opposite in sign, leading to a unique signature in b → sτ+τ−. For b→cτν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\ o c\ au \\overline{\ u} $$\\end{document} we complement these with either an SU(2) singlet S1τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_1^{\ au } $$\\end{document} or doublet R2τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_2^{\ au } $$\\end{document} and study further the cases that also these Leptoquarks come in three replicas. The fixed point solutions for the S3ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_3^{\\ell } $$\\end{document} couplings explain the b → sℓ+ℓ− data for S3e,μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_3^{e,\\mu } $$\\end{document} masses between 14 and 15 TeV, according to the scenario. b→cτν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\ o c\ au \\overline{\ u} $$\\end{document} data can only be fully explained by couplings exceeding their fixed-point values and evolving into Landau poles at high energies, so that one can place an upper bound on MQLU between 108 and 1011 GeV.

Higher Flavor Symmetries in the Standard Model

AbstractA study of the generalized global flavor symmetries of the Standard Model is initiated. The presence of nonzero triangle diagrams between the U(3)5 flavor currents and the hypercharge current intertwines them in the form of a higher‐group which mixes the zero‐form flavor symmetries with the one‐form magnetic hypercharge symmetry. This higher symmetry structure greatly restricts the possible flavor symmetries that may remain unbroken in any ultraviolet completion that includes magnetic monopoles. In the context of unification, this implies tight constraints on the combinations of fermion species which may be joined into multiplets. Three of four elementary possibilities are reflected in the classic unification models of Georgi–Glashow, , and Pati–Salam. The final pattern is realized non‐trivially in trinification, which exhibits the sense in which Standard Model Yukawa couplings which violate these flavor symmetries may be thought of as spurions of the higher‐group. Such modifications of the ultraviolet flavor symmetries are possible only if new vector‐like matter is introduced with masses suppressed from the unification scale by the Yukawa couplings.

PBH-infused seesaw origin of matter and unique gravitational waves

The Standard Model, extended with three right-handed (RH) neutrinos, is the simplest model that can explain light neutrino masses, the baryon asymmetry of the Universe, and dark matter (DM). Models in which RH neutrinos are light are generally easier to test in experiments. In this work, we show that, even if the RH neutrinos are super-heavy (Mi=1,2,3> 109 GeV)—close to the Grand Unification scale—the model can be tested thanks to its distinct features on the stochastic Gravitational Wave (GW) background. We consider an early Universe filled with ultralight primordial black holes (PBH) that produce a super-heavy RH neutrino DM via Hawking radiation. The other pair of RH neutrinos generates the baryon asymmetry via thermal leptogenesis, much before the PBHs evaporate. GW interferometers can test this novel spectrum of masses thanks to the GWs induced by the PBH density fluctuations. In a more refined version, wherein a U(1) gauge symmetry breaking dynamically generates the seesaw scale, the PBHs also cause observable spectral distortions on the GWs from the U(1)-breaking cosmic strings. Thence, a low-frequency GW feature related to DM genesis and detectable with a pulsar-timing array must correspond to a mid- or high-frequency GW signature related to baryogenesis at interferometer scales.

Minimal Nambu-Goldstone-Higgs model in supersymmetric SU(5) revisited

We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY) SU(5) grand unified model and study its phenomenological implications. The Higgs sector of the model possesses a global SU(6) symmetry, which is spontaneously broken and results in the Higgs doublets of the minimal SUSY Standard Model (MSSM) as NG chiral superfields. Therefore, the model naturally leads to light Higgs doublets and solves the doublet-triplet splitting problem. Because of the SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus the model is more predictive than the minimal SUSY SU(5). We determine all the grand-unified-theory parameters via the matching conditions of the gauge coupling constants at the unification scale and calculate proton lifetime, confronting this with current experimental bounds. We discuss that this model is incompatible with the constrained MSSM, whilst it has a large viable parameter space in the high-scale SUSY scenario. The perturbativity condition on the trilinear coupling of the adjoint Higgs field imposes an upper (lower) limit on the wino (gluino) mass, implying a hierarchical mass pattern for these gauginos. Future proton-decay searches can probe a large part of the parameter space, especially if the SUSY-breaking scale is $\lesssim 100$~TeV.

Dark Grand Unification in the axiverse: decaying axion dark matter and spontaneous baryogenesis

The quantum chromodynamics axion with a decay constant near the Grand Unification (GUT) scale has an ultralight mass near a neV. We show, however, that axion-like particles with masses near the keV–PeV range with GUT-scale decay constants are also well motivated in that they naturally arise from axiverse theories with dark c gauge groups. We demonstrate that the correct dark matter abundance may be achieved by the heavy axions in these models through the misalignment mechanism in combination with a period of early matter domination from the long-lived dark glueballs of the same gauge group. Heavy axion dark matter may decay to two photons, yielding mono-energetic electromagnetic signatures that may be detectable by current or next-generation space-based telescopes. We project the sensitivity of next-generation telescopes including Athena, AMEGO, and e-ASTROGAM to such decaying axion dark matter. If the dark sector contains multiple confining gauge groups, then the observed primordial baryon asymmetry may also be achieved in this scenario through spontaneous baryogenesis. We present explicit orbifold constructions where the dark gauge groups unify with the SM at the GUT scale and axions emerge as the fifth components of dark gauge fields with bulk Chern-Simons terms.

A predictive SO(10) model

We discuss some testable predictions of a non-supersymmetric SO(10) model supplemented by a Peccei-Quinn symmetry. We utilize a symmetry breaking pattern of SO(10) that yields unification of the Standard Model gauge couplings, with the unification scale also linked to inflation driven by an SO(10) singlet scalar field with a Coleman-Weinberg potential. Proton decay mediated by the superheavy gauge bosons may be observable at the proposed Hyper-Kamiokande experiment. Due to an unbroken Z 2 gauge symmetry from SO(10), the model predicts the presence of a stable intermediate mass fermion which, together with the axion, provides the desired relic abundance of dark matter. The model also predicts the presence of intermediate scale topologically stable monopoles and strings that survive inflation. The monopoles may be present in the Universe at an observable level. We estimate the stochastic gravitational wave background emitted by the strings and show that it should be testable in a number of planned and proposed space and land based experiments. Finally, we show how the observed baryon asymmetry in the Universe is realized via non-thermal leptogenesis.

Confronting the Galactic 511 keV emission with B−L gauge boson dark matter

The $B-L$ gauge symmetry motivated from the successful generation of the seesaw mechanism and leptogenesis. We show that if the $B-L$ gauge boson constitutes a small fraction of the dark matter (DM) it can explain the Galactic $511$ keV emission via the decay into an electron-positron pair. We find the model parameter space that is consistent with the seesaw mechanism, cosmologically viable, and accounting for the amplitude of the Galactic positron line. From this parameter space we derive an upper bound of the gauge boson mass and then an bound of the positron injection energy $\lesssim3$ MeV. This derived energy bound is consistent with the observational upper limit of the injection energy. The resultant model predicts the $B-L$ breaking scale to be in a relatively narrow range, i.e., $V_{B\textrm{--}L}\sim10^{15} \textrm{--} 10^{16} $GeV, which is consistent with a Grand Unification (GUT) scale seesaw mechanism. The model is consistent in several phenomenologies, suggesting their common origin from the B-L symmetry breaking.

Post-inflationary dark matter bremsstrahlung

Dark matter may only interact with the visible sector efficiently at energy scales above the inflaton mass, such as the Planck scale or the grand unification scale. In such a scenario, the dark matter is mainly produced out of equilibrium during the period of reheating, often referred to as UV freeze-in. We evaluate the abundance of the dark matter generated from bremsstrahlung off the inflaton decay products assuming no direct coupling between the inflaton and the dark matter. This process generally dominates the production of dark matter for low reheating temperatures where the production through the annihilations of particle in the thermal plasma becomes inefficient. We find that the bremsstrahlung process dominates for reheating temperatures T RH ≲ 1010 GeV, and produces the requisite density of dark matter for a UV scale ≃ 1016 GeV. As examples, we calculate numerically the yield of the dark matter bremsstrahlung through gravitation and dimension-6 vector portal effective interactions.

Gauge coupling unification in simplified grand gauge-Higgs unification

Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced. Taking the power-law running contributions from the bulk fields into account, perturbative gauge coupling unification is shown to be realized at around $10^{14}$ GeV, which is a few order smaller than the unification scale of four dimensional grand unified theories.

Tracking down the route to the SM with inflation and gravitational waves

We explore supersymmetric SO(10) models predicting observable proton decay and various topological defects which produce different shapes and strengths of gravitational wave backgrounds depending on the scales of intermediate symmetry breaking and inflation as well. We compare these to their non-supersymmetric counterparts. By identifying the scales at which gravitational wave signals appear, we would be able to track down a particular breaking chain and discern if it has a supersymmetric origin or not. It would also be useful to observe gravitational waves from more than one source among all possible topological defects and first order phase transitions for a realistic breaking chain. For these purposes, we work out specific examples in which the grand unification and relevant intermediate scales are calculable explicitly. It turns out that examples with gravitational waves from different sources are quite difficult to obtain, and the predicted gravitational wave profiles from domain walls and first order phase transitions obtained in some examples will require detectors in the kHz to MHz region.

Upper limit on the proton lifetime in minimal supersymetric SU(5)

In minimal supersymmetric SU(5) models, the proton can decay through dimension 5 operators. Since this decay depends directly on the supersymmetric soft masses, it will be constrained by other observables which depend on the soft masses, such as the Higgs mass and the dark matter relic density. In this work, we will examine the upper limit on the proton lifetime in minimal supersymmetric SU(5) with constrained minimal supersymmetric (CMSSM) boundary conditions set at the grand unification scale. We perform a random scan over the variables of the (CMSSM), with of order 106 points, and find that the proton lifetime is within reach of JUNO and Hyper-Kamiokande's experiment.

On symmetry breaking in the B − L extended spectral standard model

We apply Connes–Chamseddine spectral action to the U(1) B−L —extension of the standard model. We show that in order for the scalar potential to reach its minimum for a non-zero value of the new complex scalar field, thus triggering the breaking of B − L symmetry, a constraint on the quartic coupling constants must be satisfied at unification scale. We then explore the renormalization flow of this model in two opposite scenarios for the neutrino sector, and show that this constraint is not compatible with the pole masses of the top quark and SM Higgs boson. We also show that the model suffers from a mass-splitting problem similar to the doublet-triplet splitting problem of grand unified theories. We discuss potential implications for the noncommutative geometry program.