Fermion Families Research Articles

Effective interactions for the SM fermion mass hierarchy and their possible UV realization.

Abstract We built an extended 2HDM theory with a spontaneously broken U(1)X global symmetry, where the tree level Universal Seesaw Mechanism generates the mass hierarchy of the Standard Model charged fermions and the Zee-Babu mechanism produces tiny active neutrino masses. The third family of SM charged fermions gets tree level masses from Yukawa interactions involving the Higgs doublets H1 (for the top quark) and H2 (for the bottom quark and tau lepton). The model under consideration is consistent with SM fermion masses and mixings, with the muon and electron g − 2 anomalies and successfully accommodates the constraints arising from charged lepton flavor violation and meson oscillations. The proposed model predicts rates for charged lepton flavor violating decays within the reach of forthcoming experiments.

Minimal complete tri-hypercharge theories of flavour

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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(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.

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.

Higher category theory and n-groups as gauge symmetries for quantum gravity

Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n-group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a topological action called nBF action, living on a corresponding n-principal bundle over a spacetime manifold. Similarly as for the Plebanski action, one can deform the topological nBF action by adding appropriate simplicity constraints, in order to describe the correct dynamics of both gravity and matter fields. Specifically, one can describe the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter. In addition, the properties of the gauge n-group structure open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, in a similar way to the ordinary gauge group that prescribes the spectrum of gauge vector bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

Flavor-dependent U(1) extension inspired by lepton, baryon and color numbers

There is no reason why the gauge symmetry extension is family universal as in the standard model and the most well-motivated models, e.g. left-right symmetry and grand unification. Hence, we propose a simplest extension of the standard model – a flavor-dependent U(1) gauge symmetry – and find the new physics insight. For this aim, the U(1) charge, called X, is expressed as X=xB+yL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X=x B+y L$$\\end{document} in which x and y are free parameters as functions of flavor index, e.g. for a flavor i they take xi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_i$$\\end{document} and yi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y_i$$\\end{document} respectively, where B and L denote normal baryon and lepton numbers. Imposing a relation involved by the color number 3, i.e. -x1,2,…,n=xn+1,n+2,…,n+m=3y1,2,…,n+m≡3z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-x_{1,2,\\ldots ,n}=x_{n+1,n+2,\\ldots ,n+m}=3y_{1,2,\\ldots ,n+m}\\equiv 3z$$\\end{document}, for arbitrarily nonzero z, we achieve a novel U(1) theory with implied X-charge. This theory not only explains the origin of the number of observed fermion families but also offers a possible solution for both neutrino mass and dark matter, which differs from B-L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B-L$$\\end{document} extension. Two typical models based on this idea are examined, yielding interesting results for flavor-changing neutral currents and particle colliders, besides those of neutrino mass and dark matter.

Tri-hypercharge: a separate gauged weak hypercharge for each fermion family as the origin of flavour

We propose a tri-hypercharge (TH) extension of the Standard Model (SM) in which a separate gauged weak hypercharge is associated with each fermion family. In this way, every quark and lepton multiplet carries unique gauge quantum numbers under the extended gauge group, providing the starting point for a theory of flavour. If the Higgs doublets only carry third family hypercharge, then only third family renormalisable Yukawa couplings are allowed. However, non-renormalisable Yukawa couplings may be induced by the high scale Higgs fields (hyperons) which break the three hypercharges down to the SM hypercharge, providing an explanation for fermion mass hierarchies and the smallness of CKM quark mixing. Following a similar methodology, we study the origin of neutrino masses and mixing in this model. Due to the TH gauge symmetry, the implementation of a seesaw mechanism naturally leads to a low scale seesaw, where the right-handed neutrinos in the model may be as light as the TeV scale. We present simple examples of hyperon fields which can reproduce all quark and lepton (including neutrino) masses and mixing. After a preliminary phenomenological study, we conclude that one of the massive Z′ bosons can be as light as a few TeV, with implications for flavour-violating observables, LHC physics and electroweak precision observables.

Charge Asymmetry of New Stable Families in Baryon Asymmetrical Universe

The new stable fermion family, with Standard Model electroweak (EW) charges, should take part in sphaleron transitions in the early Universe before breaking of the EW symmetry. The conditions of balance between the excess of new fermions (additional generation of new superheavy U, D quarks and new E, N leptons) and baryon asymmetry, were considered at temperatures above, and below, the phase transition, using a system of equations for chemical potentials.

Vacuum stability in the Standard Model with vectorlike fermions

The discovery of Standard-Model like Higgs at 125 GeV may raise more questions than the answers it provides. In particular, the hierarchy problem remains unsolved, and the Standard Model Higgs quartic self-coupling becomes negative below the Planck scale, necessitating new physics beyond the Standard Model. In this work we investigate a popular scenario, extensions of the Standard Model with vector-like fermion fields, such as the ones present in models with extra dimensions or in Higgs composite models, using a model independent approach. Since fermions decrease the Higgs quartic coupling at high energies, only exacerbating the self-coupling problem, we introduce first an additional scalar, which by itself is enough to overcome the vacuum stability limit, and then explore the effects of vector-like fermions in singlet, doublet and triplet representations. For each model, we identify the allowed fermion masses and mixing angles with the third family fermions required to satisfy the vacuum stability condition, and compare different representations. Allowed fermion masses emerge at around 1 TeV, raising hope that these will be found at the LHC. We also examine corrections to oblique parameters S and T from additional scalar and vector-like quarks which also impose constraints on mixing and mass splitting of both sectors., but these restrictions are relatively weak compared to the vacuum stability.

B-anomalies in a twin Pati-Salam theory of flavour including the 2022 LHCb {R}_{K^{left(ast right)}} analysis

We perform a comprehensive phenomenological analysis of the twin Pati-Salam theory of flavour, focussing on the parameter space relevant for interpreting the B-anomalies via vector leptoquark U1 exchange. This model provides a very predictive framework in which the U1 couplings and the Yukawa couplings find a common origin via mixing of chiral quarks and leptons with vector-like fermions, providing a direct link between the B-anomalies and the fermion masses and mixing. We propose and study a simplified model with three vector-like fermion families, in the massless first family approximation, and show that the second and third family charged fermion masses and mixings and the B-anomalies can be simultaneously explained and related. The model has the proper flavour structure to be compatible with all low-energy observables, and leads to predictions in promising observables such as τ → 3μ, τ → μγ and Bto {K}^{left(ast right)}nu overline{nu} at Belle II and LHCb. The model also predicts a rich spectrum of TeV scale gauge bosons and vector-like fermions, all accessible to the LHC. In this updated version we have included an extended analysis considering the new 2022 LHCb data on {R}_{K^{left(ast right)}} , which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the {R}_{D^{left(ast right)}} anomalies at 1σ in a narrow window, however we expect small deviations from the SM on the {R}_{K^{left(ast right)}} ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict RD = {R}_{D^{ast }} , with future measurements shifting the world averages to slightly smaller central values.

INFLATION AND AXION DARK MATTER IN THE 3-3-1 MODEL

We consider a renormalizable theory, which successfully explains the number of Standard Model(SM) fermion families and whose non-SM scalar sector includes an axion dark matter as well asa field responsible for cosmological inflation. In such theory, the axion gets its mass via radiativecorrections at one-loop level mediated by virtual top quark, right handed Majorana neutrinos andSM gauge bosons. Its mass is obtained in the range 4 keV÷ 40 keV, consistent with the onepredicted by XENON1T experiment, when the right handed Majorana neutrino mass is varied from100 GeV up to 350 GeV, thus implying that the light active neutrino masses are generated from a lowscale type I seesaw mechanism. Furthermore, the theory under consideration can also successfullyaccommodates the XENON1T excess provided that the PQ symmetry is spontaneously broken atthe 1010 GeV scale.PACS numbers: 11.30.Fs, 12.15.Ff, 12.60.-i

Viable quark-lepton Yukawa ratios and nucleon decay predictions in SU(5) GUTs with type-II seesaw

We investigate the viability of predictive schemes for quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) Grand Unified Theories (GUTs) where neutrino masses are generated by a type II seesaw mechanism. The scalar sector of the considered scenario contains 5-, 24- and 45-dimensional representations plus a 15-dimensional representation for realizing the type II seesaw. Predictions for the ratios of the quark and lepton Yukawa couplings emerge when the relevant entries of the Yukawa matrices are generated from single joint GUT operators (i.e. under the condition of single operator dominance). Focusing on the 2nd and 3rd family and hierarchical Yukawa matrices, we show that only two sets of predictions, yτyb=32, yμys=92 and yτyb=2, yμys=6 are viable. To further investigate both options, we extend the minimal scenarios to two “toy models”, including the 1st family of charged fermions, and calculate the models' predictions, e.g. for the nucleon decay rates and for the masses of the light relics that are potentially within reach of colliders.

Improving methods and predictions at high-energy e+e− colliders within collinear factorisation

We illustrate how electron Parton Distribution Functions (PDFs) with next-to-leading collinear logarithmic accuracy must be employed in the context of perturbative predictions for high-energy e+e−-collision processes. In particular, we discuss how the renormalisation group equation evolution of such PDFs is affected by the presence of multiple fermion families and their respective mass thresholds, and by the dependences on the choices of the factorisation and renormalisation schemes. We study the impact of the uncertainties associated with the PDFs on physical cross sections, in order to arrive at realistic precision estimates for observables computed with collinear-factorisation formulae. We do so by presenting results for the production of a heavy neutral object as well as for toverline{t} and W+W− pairs, including next-to-leading-order effects of electroweak origin.

Electroweak flavour unification

We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6)L× Sp(6)R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, ΨL ∼ (4,6,1) and ΨR ∼ (4,1,6), thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via ‘flavour-deconstructed’ gauge groups; for instance, we propose a pattern Sp(6)L→ {prod}_{i=1}^3mathrm{SU}{(2)}_{L,i}to mathrm{SU}{(2)}_L for the left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values.

Speed of sound in cosmological phase transitions and effect on gravitational waves

The energy budget for gravitational waves of a cosmological first order phase transitions depends on the speed of sound in the thermal plasma in both phases around the bubble wall. Working in the real-singlet augmented Standard Model, which admits a strong two-step electroweak phase transition, we compute higher order corrections to the pressure and sound speed. We compare our result to lower-order approximations to the sound speed and the energy budget and investigate the impact on the gravitational wave signal. We find that deviations in the speed of sound from {c}_s^2 = 1/3 are enhanced up to mathcal{O} (5%) in our higher-order computation. This results in a suppression in the energy budget of up to mathcal{O} (50%) compared to approximations assuming {c}_s^2 = 1/3. The effect is most significant for hybrid and detonation solutions. We generalise our discussion to the case of multiple inert scalars and the case of a reduced number of fermion families in order to mimic hypothetical dark sector phase transitions. In this sector with modified field content, the sound speed can receive significant suppression, with potential order-of-magnitude impact on the gravitational wave amplitude.

Configuration entropy for N-Dirac fermions with dissipation and external field: An effective-mass phase transition

Dirac fermions in solid state are defined through a homogeneous dispersion relation of degree one. Consequently, the group velocity, having a superior bound, becomes invariant under spatial scaling. This fact allows considering the dynamics of a family or set of Dirac fermions at different spatial dimensions and subjected to an external field and dissipation. From the degeneration of the stationary states, the non-Hermitian dynamics allows defining the configuration entropy. With the applied external field being the control parameter, an inflection point becomes associated with entropy. Consequently, an effective-mass phase transition is conjectured including the usual Dirac fermions in a graphene sheet. The critical field and the critical angle are analytically calculated.

Evolving Heterotic Gauge Backgrounds: Genetic Algorithms versus Reinforcement Learning

AbstractThe immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisation and search can, however, significantly improve the prospects of constructing the standard model in string theory. In this paper we scrutinise a corner of the heterotic string landscape consisting of compactifications on Calabi‐Yau three‐folds with monad bundles and show that genetic algorithms can be successfully used to generate anomaly‐free supersymmetric GUTs with three families of fermions that have the right ingredients to accommodate the standard model. We compare this method with reinforcement learning and find that the two methods have similar efficacy but somewhat complementary characteristics.

Anomalous magnetic moment and Higgs coupling of the muon in a sequential U(1) gauge model with dark matter

We study an Abelian gauge extension of the standard model with fermion families having non-universal gauge charges. The gauge charges and scalar content are chosen in such an anomaly-free way that only the third generation fermions receive Dirac masses via renormalisable couplings with the Higgs boson. Incorporating additional vector like fermions and scalars with appropriate $U(1)$ charges can lead to radiative Dirac masses of first two generations with neutral fermions going in the loop being dark matter candidates. Focusing on radiative muon mass, we constrain the model from the requirement of satisfying muon mass, recently measured muon anomalous magnetic moment by the E989 experiment at Fermilab along with other experimental bounds including the large hadron collider (LHC) limits. The anomalous Higgs coupling to muon is constrained from the LHC measurements of Higgs to dimuon decay. The singlet fermion dark matter phenomenology is discussed showing the importance of both annihilation and coannihilation effects. Incorporating all bounds lead to a constrained parameter space which can be probed at different experiments.

Two-to-Two Processes at an Electron-Muon Collider

Based on a recent proposal to build an electron-muon collider, we study two-to-two production processes e − μ + ⟶ f f ¯ , γ γ that originate from dimension 6 and 8 operators. We compare the sensitivity to those effective couplings obtained at the collider with that of low energy measurements of μ ⟶ e γ , μ ⟶ e e ¯ e , and μ ⟶ e conversion that have recently been reported in the literature. Whereas for the production of first family fermions, the sensitivity of the collider processes is much weaker; for the second and third family fermions, it is similar or stronger than that of low-energy processes. In the case of e − μ + ⟶ γ γ , the sensitivity to a dimension 8 contact operator turns out to be the strongest in comparison.

Universal inverse seesaw mechanism as a source of the SM fermion mass hierarchy

We build a renormalizable theory where the inverse seesaw mechanism explains the pattern of SM fermion masses. To the best of our knowledge, our model corresponds to the first implementation of the inverse seesaw mechanism for the charged fermion sector. In our theory, the inverse seesaw mechanism is implemented at the tree and one-loop levels in order to generate the masses for the second and first families of the SM charged fermions, respectively. The third family of SM charged fermions obtain tree-level masses from the Higgs doublets phi _{1} (for the top quark) and phi _{2} (for the bottom quark and tau lepton). The masses of the active light neutrinos are generated from a two-loop level inverse seesaw mechanism. Our model successfully explains the observed SM fermion mass hierarchy, the tiny masses of the active light neutrinos, contains the necessary means for efficient leptogenesis and is in accordance with the constraints resulting from meson oscillations, as well as with the measured values of the observed dark matter relic density and of the muon and electron anomalous magnetic moments.

Evaporating black holes: Constraints on anomalous emission mechanisms

Hawking radiation of astrophysical black holes is minute and thought to be unobservable. However, different mechanisms could contribute to an anomalously high emission rate: extra dimensions, new "dark" families of bosons or fermions, or a lower fundamental Planck scale. Do black holes flood the Universe with gravitational waves via mass loss? Here, we show that the formation of black hole binaries and the absence of a stochastic background of gravitational waves can limit the emission rate to $|\dot{M}|\lesssim 10^{-15}M_{\odot}/{\rm yr}$, seven orders of magnitude more stringent than bounds from resolvable inspiralling binaries.