Generations Of Fermions Research Articles

Exceptional Jordan matrix models, octonionic strings/branes and star product deformations

A brief review of the essentials behind the construction of a Chern-Simons-like brane action from the Large N limit of Exceptional Jordan Matrix Models paves the way to the construction of actions for membranes and p-branes moving in octonionic-spacetime backgrounds endowed with octonionic-valued metrics. It is found that the action of a membrane moving in spacetime backgrounds endowed with an octonionic-valued metric is not invariant under the usual diffeomorphisms of its world volume coordinates σa→σ′a(σb), but instead, it is invariant under the rigid E6(−26) transformations which preserve the volume (cubic) form. An extensive study of the bosonic octonionic string moving in flat backgrounds, and its quantization, follows. One of the most significant findings (without invoking supersymmetry) is that the number of degrees of freedom of three (massless) fermion generations is the same as the number of transverse dimensions of an octonionic string moving in D=26 octonionic dimensions. The star-product deformations of octonionic p-branes follow. In particular, we focus on the octonionic membrane along with the phase space quantization methods developed by [30] within the context of Nonassociative Quantum Mechanics. We finalize with an analysis of two octonionic gravitational actions and with some concluding remarks on Double and Exceptional Field theories, Nonassociative Gravity and A∞,L∞ algebras.

(g \u2212 2)\u03bc versus K \u2192 \u03c0 + Emiss induced by the (B \u2212 L)23 boson

To address the long-standing (g − 2)μ anomaly via a light boson, in ref. [1] we proposed to extend the standard model (SM) by the local (B − L)23, under which only the second and third generations of fermions are charged. It predicts an invisible Z′ with mass mathcal{O}(100) MeV, and moreover it has flavor-changing neutral current (FCNC) couplings to the up-type quarks at tree level. Such a Z′, via KL→ π0 + Z′(→ voverline{v} ) at loop level, may be a natural candidate to account for the recent KOTO anomaly. In this article, we investigate this possibility, to find that Z′ can readily do this job if it is no longer responsible for the (g − 2)μ anomaly. We further find that both anomalies can be explained with moderate tuning of the CP violation, but may contradict the B meson decays.

Signals of the QCD axion with mass of 17 MeV/c2 : Nuclear transitions and light meson decays

The QCD axion remains experimentally viable in the mass range of O(10 MeV) if (i) it couples predominantly to the first generation of SM fermions; (ii) it decays to $e^+ e^-$ with a short lifetime $\tau_a\lesssim 10^{-13}\,$s; and (iii) it has suppressed isovector couplings, i.e., if it is piophobic. Remarkably, these are precisely the properties required to explain recently observed anomalies in nuclear de-excitations, to wit: the $e^+e^-$ emission spectra of isoscalar magnetic transitions of $^{8\!}$Be and $^{4\!}$He nuclei showed a "bump-like" feature peaked at $m_{e^+e^-}\sim 17$ MeV. In this article, we argue that on-shell emission of the QCD axion (with the aforementioned properties) provides an extremely well-motivated, compatible explanation for the observed excesses in these nuclear de-excitations. The absence of anomalous features in other measured transitions is also naturally explained: piophobic axion emission is strongly suppressed in isovector magnetic transitions, and forbidden in electric transitions. This QCD axion hypothesis is further corroborated by an independent observation: a $2-3\,\sigma$ deviation in the measurement of $\Gamma(\pi^0\to e^+e^-)$ from the Standard Model theoretical expectation. This article also includes detailed estimations of various axionic signatures in rare light meson decays, which take into account contributions from low-lying QCD resonance exchange, and, in the case of rare Kaon decays, the possible effective implementations of $\Delta S=1$ octet enhancement in chiral perturbation theory. These inherent uncertainties of the effective description of the strong interactions at low energies result in large variations in the predictions for hadronic signals of the QCD axion; in spite of this, the estimated ranges for rare meson decay rates obtained here can be probed in the near future in $\eta/\eta^\prime$ and Kaon factories.

Linear Canonical Transformations in relativistic quantum physics

Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the canonical commutation relations characterizing the coordinates and momenta operators. In this work, the possibility of considering LCTs to be the elements of a symmetry group for relativistic quantum physics is studied using the principle of covariance. It is established that Lorentz transformations and multidimensional Fourier transforms are particular cases of LCTs and some of the main symmetry groups currently considered in relativistic theories can be obtained from the contractions of LCTs groups. It is also shown that a link can be established between a spinorial representation of LCTs and some properties of elementary fermions. This link leads to a classification which suggests the existence of sterile neutrinos and the possibility of describing a generation of fermions with a single field. Some possible applications of the obtained results are discussed. These results may, in particular, help in the establishment of a unified theory of fundamental interactions. Intuitively, LCTs correspond to linear combinations of energy-momentum and spacetime compatible with the principle of covariance.

Fermion and meson mass generation in non-Hermitian Nambu–Jona-Lasinio models

We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model. Two possible bilinear modifications give rise to $\mathcal{PT}$ symmetric theories; this happens when the standard NJL model is extended either by a pseudovector background field $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ or by an antisymmetric-tensor background field $g \bar\psi F_{\mu\nu}\gamma^\mu \gamma^\nu \psi$. The three remaining bilinears are {\it anti}-$\mathcal{PT}$-symmetric in nature, $ig \bar\psi B_\mu \gamma^\mu \psi, ig\bar\psi \gamma_5 \psi$ and $ig\bar\psi {1}\psi$, so that the Hamiltonian then has no overall symmetry. The pseudovector $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ and the vector $ig \bar\psi B_\mu \gamma^\mu \psi$ combinations, are, in addition, chirally symmetric. Thus, within this framework we are able to examine the effects that the various combinations of non-Hermiticity, $\mathcal{PT}$ symmetry, chiral symmetry and the two-body interactions of the NJL model have on the existence and dynamical generation of a real effective fermion mass (a feature which is absent in the corresponding modified massless free Dirac models) as well as on the masses of the composite particles, the pseudoscalar and scalar mesonic modes ($\pi$ and $\sigma$ mesons). Our findings demonstrate that $\mathcal{PT}$ symmetry is not necessary for real fermion mass solutions to exist, rather the two-body interactions of the NJL model supersede the non-Hermitian bilinear effects. The effects of chiral symmetry are evident most clearly in the meson modes, the pseudoscalar of which will always be Goldstone in nature if the system is chirally symmetric. Second solutions of the mesonic equations are also discussed.

Techni-Pati-Salam composite Higgs model

Composite Higgs models can be extended to the Planck scale by means of the partially unified partial compositeness (PUPC) framework. We present in detail the Techni-Pati-Salam model, based on a renormalizable gauge theory $SU(8)_{PS}\times SU(2)_L\times SU(2)_R$. We demonstrate that masses and mixings for all generations of standard model fermions can be obtained via partial compositeness at low energy, with four-fermion operators mediated by either heavy gauge bosons or scalars. The strong dynamics is predicted to be that of a confining $Sp(4)_{\rm HC}$ gauge group, with hyper-fermions in the fundamental and two-index anti-symmetric representations, with fixed multiplicities. This motivates for Lattice studies of the Infra-Red near-conformal walking phase, with results that may validate or rule out the model. This is the first complete and realistic attempt at providing an Ultra-Violet completion for composite Higgs models with top partial compositeness. In the baryon-number conserving vacuum, the theory also predicts a Dark Matter candidate, with mass in the few TeV range, protected by semi-integer baryon number.

Probing new U(1) gauge symmetries via exotic Z \u2192 Z\u2032\u03b3 decays

New U(1) gauge theories involving Standard Model (SM) fermions typically require additional electroweak fermions for anomaly cancellation. We study the non-decoupling properties of these new fermions, called anomalons, in the Z − Z′ − γ vertex function, reviewing the connection between the full model and the effective Wess-Zumino operator. We calculate the exotic Z → Z′γ decay width in U(1)B−L and U(1)B models, where B and L denote the SM baryon and lepton number symmetries. For U(1)B−L gauge symmetry, each generation of SM fermions is anomaly free and the exotic Z → {Z}_{BL}^{prime}gamma decay width is entirely induced by intragenerational mass splittings. In contrast, for U(1)B gauge symmetry, the existence of two distinct sources of chiral symmetry breaking enables a heavy, anomaly-free set of fermions to have an irreducible contribution to the Z → {Z}_B^{prime}gamma decay width. We show that the current LEP limits on the exotic Z → {Z}_B^{prime}gamma decay are weaker than previously estimated, and low-mass {Z}_B^{prime } dijet resonance searches are currently more constraining. We present a summary of the current collider bounds on U(1)B and a projection for a TeraZ factory on the Z → {Z}_B^{prime}gamma exotic decay, and emphasize how the Z → Z′γ decay is emblematic of new anomalous U(1) gauge symmetries.

Composite Higgs meets Planck scale: Partial compositeness from partial unification

Providing an Ultra-Violet completion valid up to the Planck scale is of paramount importance to validate the composite Higgs paradigm, on a par with supersymmetry. We propose the first complete framework, based on partial unification of a confining hypercolor gauge group with the Standard Model color group, where couplings of the standard model fermions are mediated by both gauge and scalar bosons. We demonstrate our approach by providing an explicit model based on a Techni-Pati-Salam (TPS) unification, SU(8)PS×SU(2)L×SU(2)R, able to generate masses for all fermion generations, including neutrinos, via partial compositeness. The TPS scenario features an Sp(4) hypercolor group, and lattice studies will be crucial to validate the model.

Scrutinizing vacuum stability in IDM with Type-III inverse seesaw

We consider the extension of the Standard Model (SM) with an inert Higgs doublet that also contains two or three sets of SU(2)L triplet fermions with hypercharge zero and analyze the stability of electroweak vacuum for the scenarios. The model represents a Type-III inverse seesaw mechanism for neutrino mass generation with a Dark matter candidate. An effective potential approach calculation with two-loop beta function have been carried out in deciding the fate of the electroweak vacuum. Weak gauge coupling g2 shows a different behaviour as compared to the Standard Model. The modified running of g2, along with the Higgs quartic coupling and Type-III Yukawa couplings become crucial in determining the stability of electroweak vacuum. The interplay between two and three generations of such triplet fermions reveals that extensions with two generations is favoured if we aspire for Planck scale stability. Bounds on the Higgs quartic couplings, Type-III Yukawa and number of triplet fermion generations are drawn for different mass scale of Type-III fermions. The phenomenologies of inert doublet and Type-III fermions at the LHC and other experiments are commented upon.

Evidence for Higgs boson decay to a pair of muons

Evidence for Higgs boson decay to a pair of muons is presented. This result combines searches in four exclusive categories targeting the production of the Higgs boson via gluon fusion, via vector boson fusion, in association with a vector boson, and in association with a top quark-antiquark pair. The analysis is performed using proton-proton collision data at sqrt{s} = 13 TeV, corresponding to an integrated luminosity of 137 fb−1, recorded by the CMS experiment at the CERN LHC. An excess of events over the back- ground expectation is observed in data with a significance of 3.0 standard deviations, where the expectation for the standard model (SM) Higgs boson with mass of 125.38 GeV is 2.5. The combination of this result with that from data recorded at sqrt{s} = 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7 fb−1, respectively, increases both the expected and observed significances by 1%. The measured signal strength, relative to the SM prediction, is {1.19}_{-0.39}^{+0.40}{left(mathrm{stat}right)}_{-0.14}^{+0.15}left(mathrm{syst}right) . This result constitutes the first evidence for the decay of the Higgs boson to second generation fermions and is the most precise measurement of the Higgs boson coupling to muons reported to date.

Phenomenology of vector-like leptons with Deep Learning at the Large Hadron Collider

In this paper, a model inspired by Grand Unification principles featuring three generations of vector-like fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the state-of-the-art Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vector-like leptons (VLLs) and their possible signatures at CERN’s Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vector-boson fusion and VLL pair production topologies, both involving a final state containing a pair of charged leptons of different flavor and two sterile neutrinos that provide a missing energy. We also consider the case of VLL single production where, in addition to a pair of sterile neutrinos, the final state contains only one charged lepton. We propose a novel method to identify missing transverse energy vectors by comparing the detector response with Monte-Carlo simulated data. All calculated observables are provided as data sets for Deep Learning analysis, where a neural network is constructed, based on results obtained via an evolutive algorithm, whose objective is to maximise either the accuracy metric or the Asimov significance for different masses of the VLL. Taking into account the effect of the three analysed topologies, we have found that the combined significance for the observation of new VLLs at the high-luminosity LHC can range from 5.7σ, for a mass of 1.25 TeV, all the way up to 28σ if the VLL mass is 200 GeV. We have also shown that by the end of the LHC Run-III a 200 GeV VLL can be excluded with a confidence of 8.8 standard deviations. The results obtained show that our model can be probed well before the end of the LHC operations and, in particular, providing important phenomenological information to constrain the energy scale at which new gauge symmetries emergent from the considered Grand Unification picture can be manifest.

Mass distribution and generation of elementary fermions

In this paper, we study the mass distribution of elementary fermions and find a set of empirical relations to describe the mass distribution of elementary fermions. This inspires us to investigate in depth the origin of elementary fermion mass hierarchies and generations. We present a theoretical model to explain why the elementary fermions have three generations and discuss the origin of the fundamental fermion mass hierarchies and spin.

Bilinear expansions of lattices of KP τ -functions in BKP τ -functions: A fermionic approach

We derive a bilinear expansion expressing elements of a lattice of Kadomtsev-Petviashvili (KP) τ-functions, labeled by partitions, as a sum over products of pairs of elements of an associated lattice of BKP τ-functions, labeled by strict partitions. This generalizes earlier results relating determinants and Pfaffians of minors of skew symmetric matrices, with applications to Schur functions and Schur Q-functions. It is deduced using the representations of KP and BKP τ-functions as vacuum expectation values (VEVs) of products of fermionic operators of charged and neutral type, respectively. The lattice is generated by the insertion of products of pairs of charged creation and annihilation operators. The result follows from expanding the product as a sum of monomials in the neutral fermionic generators and applying a factorization theorem for VEVs of products of operators in the mutually commuting subalgebras. Applications include the case of inhomogeneous polynomial τ-functions of KP and BKP type.

A Family-nonuniversal [formula omitted] Model for Excited Beryllium Decays

Excited beryllium has been observed to decay into electron-positron pairs with a 6.8σ anomaly. The process is properly explained by a 17 MeV proto-phobic vector boson. In present work, we consider a family-nonuniversal U(1)′ that is populated by a U(1)′ gauge boson Z′ and a scalar field S, charged under U(1)′ and singlet under the Standard Model (SM) gauge symmetry. The SM chiral fermion and scalar fields are charged under U(1)′ and we provide them to satisfy the anomaly-free conditions. The Cabibbo-Kobayashi-Maskawa (CKM) matrix is reproduced correctly by higher-dimension Yukawa interactions facilitated by S. The vector and axial-vector current couplings of the Z′ boson to the first generation of fermions do satisfy all the bounds from the various experimental data. The Z′ boson can have kinetic mixing with the hypercharge gauge boson and S can directly couple to the SM-like Higgs field. The kinetic mixing of Z′ with the hypercharge gauge boson, as we show by a detailed analysis, generates the observed beryllium anomaly. We find that beryllium anomaly can be properly explained by a MeV-scale sector with a minimal new field content. The minimal model we construct forms a framework in which various anomalous SM decays can be discussed.

Trace dynamics and division algebras: towards quantum gravity and unification

Abstract We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper, we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group G 2, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal sub-groups of G 2, the other one being SU(3), the element preserver group of octonions. This latter group, coupled with U(1) em , describes the electrocolour symmetry, as shown earlier by Furey. We predict a new massless spin one boson (the ‘Lorentz’ boson) which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group G 2, embedded in the exceptional Lie group F 4. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Although at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson, we argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in 11 dimensions.

Parity and CP operations for Majorana neutrinos

The parity transformation law of the fermion field $\psi(x)$ is usually defined by the "$\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x}) = \gamma^{0}\psi(t,-\vec{x})$ with eigenvalues $\pm 1$, while the "$i\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x})=i\gamma^{0}\psi(t,-\vec{x})$ is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majorana neutrinos constructed from chiral neutrinos in an extension of the Standard Model, the Majorana neutrinos can be characterized by CP symmetry although C and P are separately broken. It is then shown that either choice of the parity operation, $\gamma^{0}$ or $i\gamma^{0}$, in the level of the starting fermions gives rise to the consistent and physically equivalent descriptions of emergent Majorana neutrinos both for Weinberg's model of neutrinos and for a general class of seesaw models. The mechanism of this equivalence is that the Majorana neutrino constructed from a chiral neutrino, which satisfies the classical Majorana condition $\psi(x)=C\overline{\psi(x)}^{T}$, allows the phase freedom $\psi(x)=e^{i\alpha}\nu_{L}(x) + e^{-i\alpha}C\overline{\nu_{L}(x)}^{T}$ with $\alpha=0\ {\rm or}\ \pi/4$ that accounts for the phase coming from the different definitions of parity for $\nu_{L}(x)$ and ensures the consistent definitions of CP symmetry $({\cal CP})\psi(x)({\cal CP})^{\dagger}= \pm i\gamma^{0}\psi(t,-\vec{x})$.

LHC constraints on W^prime ,~Z^prime that couple mainly to third generation fermions

We use the results of CMS and ATLAS searches for resonances that decay to tau nu or tb and tau ^+tau ^- or t{bar{t}} final states to constrain the parameters of non-universal W^prime and Z^prime gauge bosons that couple preferentially to the third generation. For the former we consider production from cbar{b} annihilation and find very weak constraints on the strength of the interaction and only for the mass range between 800 and 1100 GeV from the pp rightarrow tau _h p_T^{mathrm{miss}} channel. The constraints on the latter are much stronger and arise from both t{bar{t}} and tau ^+tau ^- production. Treated separately, we find that the weak constraints on the W^prime still permit an explanation of the R(D^{(star )}) anomalies with a light sterile neutrino whereas the stronger constraints on the Z^prime exclude significant light sterile neutrino contributions to the K rightarrow pi nu bar{nu } rates. Within specific models the masses of W^prime and Z^prime are of course related and we briefly discuss the consequences.

Mass splitting in an 331-TC coupled scenario

The root of most of the technicolor (TC) problems lies in the way the ordinary fermions acquire their masses, where an ordinary fermion [Formula: see text] couples to a technifermion [Formula: see text] mediated by an extended technicolor (ETC) boson leading to fermion masses that vary with the ETC mass scale [Formula: see text] as [Formula: see text]. Recently, we discussed a new approach consisting of models where TC and QCD are coupled through a larger theory, in this case the solutions of these equations are modified compared to those of the isolated equations, and TC and QCD self-energies are of the irregular form, which allows us to build models where ETC boson masses can be pushed to very high energies. In this work we extend these results for 331-TC models, in particular considering a coupled system of Schwinger–Dyson equations, we show that all technifermions of the model exhibit the same asymptotic behavior for TC self-energies. As an application we discuss how the mass splitting of the order [Formula: see text](100) GeV could be generated between the second and third generation of fermions.

A global analysis strategy to resolve neutrino NSI degeneracies with scattering and oscillation data

Neutrino non-standard interactions (NSI) with the first generation of standard model fermions can span a parameter space of large dimension and exhibit degeneracies that cannot be broken by a single class of experiment. Oscillation experiments, together with neutrino scattering experiments, can merge their observations into a highly informational dataset to combat this problem. We consider combining neutrino-electron and neutrino-nucleus scattering data from the Borexino and COHERENT experiments, including a projection for the upcoming coherent neutrino scattering measurement at the CENNS-10 liquid argon detector. We extend the reach of these data sets over the NSI parameter space with projections for neutrino scattering at a future multi-ton scale dark matter detector and future oscillation measurements from atmospheric neutrinos at the Deep Underground Neutrino Experiment (DUNE). In order to perform this global anal- ysis, we adopt a novel approach using the copula method, utilized to combine posterior information from different experiments with a large, generalized set of NSI parameters. We find that the contributions from DUNE and a dark matter detector to the Borexino and COHERENT fits can improve constraints on the electron and quark NSI parameters by up to a factor of 2 to 3, even when relatively many NSI parameters are left free to vary in the analysis.

Dynamical symmetry breaking and fermion mass hierarchy in the scale-invariant 3-3-1 model

We propose an extension of the Standard Model (SM) based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ (3-3-1) gauge symmetry and scale invariance. Maintaining the main features of the so-called 3-3-1 models, such as the cancellation of gauge anomalies related to the number of chiral fermion generations, this model exhibits a very compact scalar sector. Only two scalar triplets and one singlet are necessary and sufficient to break the symmetries dynamically via the Coleman-Weinberg mechanism. With the introduction of an Abelian discrete symmetry and assuming a natural hierarchy among the vacuum expectation values of the neutral scalar fields, we show that all particles in the model can get phenomenologically consistent masses. In particular, most of the standard fermion masses are generated via a seesaw mechanism involving some extra heavy fermions introduced for consistency. This mechanism provides a partial solution for the fermion mass hierarchy problem in the SM. Furthermore, the simplicity of the scalar sector allows us to analytically find the conditions for the potential stability up to one-loop level and show how they can be easily satisfied. Some of the new particles, such as the scalars $H$, $H^\pm$ and all the non-SM vector bosons, are predicted to get masses around the TeV scale and, therefore, could be produced at the high-luminosity LHC. Finally, we show that the model features a residual symmetry which leads to the stability of a heavy neutral particle; the latter is expected to show up in experiments as missing energy.