Generations Of Standard Model Fermions Research Articles

Semisimple extensions of the Standard Model gauge algebra

We show how one may classify all semisimple algebras containing the $\mathfrak{su}(3)\oplus \mathfrak{su}(2) \oplus \mathfrak{u}(1)$ symmetry of the Standard Model and acting on some given matter sector, enabling theories beyond the Standard Model with unification (partial or total) of symmetries (gauge or global) to be catalogued. With just a single generation of Standard Model fermions plus a singlet neutrino, the only {gauge} symmetries correspond to the well-known algebras $\mathfrak{su}(5),\mathfrak{so}(10),$ and $\mathfrak{su}(4)\oplus \mathfrak{su}(2) \oplus \mathfrak{su}(2)$, but with two or more generations a limited number of exotic symmetries mixing flavour, colour, and electroweak degrees of freedom become possible. We provide a complete catalogue in the case of 3 generations or fewer and outline how our method generalizes to cases with additional matter.

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.

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.

Braided fermions from Hurwitz algebras

Some curious structural similarities between a recent braid - and Hurwitz algebraic description of the unbroken internal symmetries for a single generations of Standard Model fermions were recently identified. The non-trivial braid groups that can be represented using the four normed division algebras are B2 and , exactly those required to represent a single generation of fermions in terms of simple three strand ribbon braids. These braided fermion states can be identified with the basis states of the minimal left ideals of the Clifford algebra Cℓ(6), generated from the nested left actions of the complex octonions on itself. That is, the ribbon spectrum can be related to octonion algebras. Some speculative ideas relating to ongoing research that attempts to construct a unified theory based on braid groups and Hurwitz algebras are discussed.

SU(5) heterotic Standard Model bundles

We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and give three generations of Standard Model fermions after symmetry breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard Model gauge group. Among the solutions we find some which can be perturbed to solutions of the Strominger system. Thus these solutions provide a step toward the construction of phenomenologically realistic heterotic flux compactifications via non-Kahler deformations of Calabi-Yau geometries with bundles. This particular class of solutions involves a rank two hidden sector bundle and does not require background fivebranes for anomaly cancellation.

Natural four-generation mass textures in MSSM brane worlds

A fourth generation of standard model fermions is usually considered unlikely due to constraints from direct searches, electroweak precision measurements, and perturbative unitarity. We show that fermion mass textures consistent with all constraints may be obtained naturally in a model with four generations constructed from intersecting $D6$-branes on a ${T}^{6}/({\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2})$ orientifold. The Yukawa matrices of the model are rank 2, so that only the third- and fourth-generation fermions obtain masses at the trilinear level. The first two generations obtain masses via higher-order couplings and are therefore naturally lighter. In addition, we find that the third and fourth generations automatically split in mass, but do not mix at leading order. Furthermore, the standard model gauge couplings automatically unify at the string scale, and all the hidden-sector gauge groups become confining in the range ${10}^{13}--{10}^{16}\text{ }\text{ }\mathrm{GeV}$, so that the model becomes effectively a four-generation minimal supersymmetric standard model at low energies.

Casimir energy and brane stability

We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S 1 / Z 2 orbifold, which includes the Randall–Sundrum two brane model (RS1). We employ a ζ -function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produces a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of fine tuning needed for stabilization of the brane separation. Finally, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.

Electroweak precision constraints on the Lee-Wick standard model

We perform an analysis of the electroweak precision observables in the Lee-Wick Standard Model. The most stringent restrictions come from the S and T parameters that receive important tree level and one loop contributions. In general the model predicts a large positive S and a negative T. To reproduce the electroweak data, if all the Lee-Wick masses are of the same order, the Lee-Wick scale is of order 5 TeV. We show that it is possible to find some regions in the parameter space with a fermionic state as light as 2.4-3.5 TeV, at the price of rising all the other masses to be larger than 5-8 TeV. To obtain a light Higgs with such heavy resonances a fine-tuning of order a few per cent, at least, is needed. We also propose a simple extension of the model including a fourth generation of Standard Model fermions with their Lee-Wick partners. We show that in this case it is possible to pass the electroweak constraints with Lee-Wick fermionic masses of order 0.4-1.5 TeV and Lee-Wick gauge masses of order 3 TeV.

Electroweak symmetry breaking from a holographic fourth generation

We consider a model with four generations of standard model fermions propagating in an extra dimension with an AdS background metric. We show that if the zero modes of the fourth generation are highly localized towards the infrared brane, it is possible to break the electroweak symmetry via their condensation, partly driven by their interactions with the Kaluza-Klein excitations of the gauge bosons, as well as by the presence of bulk higher-dimensional operators. This dynamical mechanism results in a composite Higgs, which is highly localized and generally heavy. The localization of fermions in the five-dimensional bulk naturally leads to the standard model Yukawa couplings via the action of the bulk higher-dimensional operators, which are suppressed by the Planck scale. We obtain the spectrum of the model and explore some of its phenomenological consequences, both for electroweak precision constraints as well as at the Large Hadron Collider.