Fermionic Sector Research Articles

The metric nature of matter

We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric structure is an infinite-dimensional Bott-Dirac operator and the fermionic sector of the emerging quantum field theory is generated by the infinite-dimensional Clifford algebra required to construct this operator. The Bott-Dirac operator interacts with the HD(M) algebra, which is a non-commutative algebra generated by holonomy-diffeomorphisms on the underlying manifold, i.e. parallel-transforms along flows of vector fields. This algebra combined with the Bott-Dirac operator encode the canonical commutation and anti-commutation relations of the quantised bosonic and fermionic fields. The square of the Bott-Dirac operator produces both the Yang-Mills Hamilton operator and the Dirac Hamilton operator as well as a topological Yang-Mills term alongside higher-derivative terms and a metric invariant.

Cosmological constant, axial anomalies and photon mass dynamos from chiral fermionic torsion

Motivated by Palle’s investigation on the handness of chirality of vorticity in Einstein–Cartan cosmology [Entropy 5 (2014)], several aspects of chiral torsional handness in magnetogenesis and cosmology are presented. In the first one, we obtain torsion bounds from massive photons and axial anomalies. In the second, we deal with magnetogenesis from photon mass and in the third, we discuss chiral torsion degrees of freedom to obtain a torsion cosmological constant dependent solution. The torsion solution decays fast and implies a strong suppression of torsion at present universe. Our result contains the Poplawski [Phys. Lett. B (2010)] results in the case axial torsion vector associated to Einstein–Cartan fermionic sector matter and conformal anomalies of quarks. In the third example, a magnetic field bound from chiral torsionic dynamos is obtained as [Formula: see text]. In the non-minimal cosmological models, chiral dynamos are sourced by massive photons, London currents and chiral magnetic effect (CME). Chiral chemical potential is found to be mimic by torsion. Cosmological constant bound [Formula: see text] is found. At the early universe, the cosmological constant [Formula: see text] is obtained. Torsion used in the present universe is [Formula: see text]. In the last and fourth example, chiral anisotropic currents are obtained and magnetic helicity is shown to depend upon torsion when the chiral chemical potential is non-constant.

$SU(5)_{L} \times U(1)_{Y}$ electroweak unification

Abstract We propose here—for the first time in the literature, to our best knowledge—an electroweak unification based on the $SU(5)_{L}\times U(1)_{Y}$ gauge group. The spontaneous symmetry breaking takes place in the manner $SU(5)_{L}\times U(1)_{Y} \rightarrow U(1)_{em}$, due to a particular Higgs sector consisting of five scalar quintuplets. Each scalar quintuplet acquires its own vacuum expectation value, by means of a proper parametrization which is worked out once an overall vacuum expectation value in the model is established. The decoupling of the low-energy regime (corresponding to the Standard Model) from the high scale (required by our model here) is straightforwardly achieved in order to preserve the consistency with the present experimental data. Finally, a promising phenomenological outcome is derived by simply tuning a single free parameter. Our results also include, besides a viable one-parameter mass spectrum, the prediction of precisely three generations in the fermion sector and the electric charge quantization.

Custodial symmetry violation in the SMEFT

We investigate precision observables sensitive to custodial symmetric/violating UV physics beyond the Standard Model. We use the SMEFT framework which in general includes non-oblique corrections that requires a generalization of the Peskin-Takeuchi $T$ parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparameterization-invariant replacement, that we call $\mathscr{T}$, valid at least for tree-level custodial violating contributions. We utilize a new custodial basis of $\nu$SMEFT (SMEFT augmented by right-handed neutrinos) which explicitly identifies the global $SU(2)_R$ symmetries of the Higgs and fermion sectors, that in turn permits easy identification of higher-dimensional operators that are custodial preserving or violating. We carefully consider equation-of-motion redundancies that cause custodial symmetric operators in one basis to be equivalent to a set of custodial symmetric and/or violating operators in another basis. Utilizing known results about tree/loop operator generation, we demonstrate that the basis-dependent appearance of custodial-violating operators does not invalidate our $\mathscr{T}$ parameter at tree-level. We illustrate our results with several UV theory examples, demonstrating that $\mathscr{T}$ faithfully identifies custodial symmetry violation, while $T$ can fail.

Non‐perturbative Quantum Field Theory and the Geometry of Functional Spaces

AbstractIn this paper we construct a non‐commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non‐perturbative quantum gauge theory coupled to a fermionic field on a curved background. The non‐commutative geometry is given by an infinite‐dimensional Bott‐Dirac type operator, whose square gives the Hamilton operator, and which interacts with an algebra generated by holonomy‐diffeomorphisms. The Bott‐Dirac operator and the associated Hilbert space relies on a metric on the configuration space of connections, which effectively works as a covariant ultra‐violet regulator. We show that the construction coincides with perturbative quantum field theory in a local limit. Questions concerning Lorentz invariance and the fermionic sector as well as the issue of existence are left open.

Fermion–charged-boson stars

Fermion-boson stars are starlike systems composed of the ordinary nuclear matter of a neutron star and bosonic dark matter. The bosonic dark matter has typically been taken to be a complex scalar field. A natural extension is for the complex scalar field to be charged. We make the simplest extension and gauge the scalar field under U(1). We therefore study fermion-charged-boson stars. We make a detailed study of the stability of this system by computing critical curves over the whole of parameter space. We then study how the fermion and boson sectors contribute to the total mass of the star. Finally, we present mass-radius diagrams, showing that an increase in charge can lead to more massive and more compact stars.

A model of muon anomalies

The Standard Model (SM) is augmented with a U(1)B−3Lμ gauge symmetry spontaneously broken above the TeV scale when an SM-singlet scalar condenses. Scalar leptoquarks S1(3)=(3‾,1(3),13) charged under U(1)B−3Lμ mediate the intriguing effects observed in muon (g−2), RK(⁎), and b→sμ+μ− angular distributions, while generically evading all other phenomenological constraints. The fermionic sector is minimally extended with three right-handed neutrinos, and a successful type-I seesaw mechanism is realized. Charged lepton flavor violation is effectively suppressed, and proton decay—a common prediction of leptoquarks—is postponed to the dimension-6 effective Lagrangian. Unavoidable radiative corrections in the Higgs mass and muon Yukawa favor leptoquark masses interesting for collider searches. The parameters of the model are radiatively stable and can be evolved by the renormalization group to the Planck scale without inconsistencies. Alternative lepton-flavored gauge extensions of the SM, under which leptoquarks become muoquarks, are proposed for comparison.

One-dimensional long-range Falikov-Kimball model: Thermal phase transition and disorder-free localization

Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model extension at higher orders in Lorentz violation

We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operators $\hat{b}_{\mu}$ and $\hat{H}_{\mu\nu}$ as perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This paper closes one of the last gaps in understanding classical-particle propagation in the presence of Lorentz violation. Lagrangians of the kind presented will turn out to be valuable for describing particle propagation in curved backgrounds with diffeomorphism invariance and/or local Lorentz symmetry explicitly violated.

Automated one-loop computations in the standard model effective field theory

We present the automation of one-loop computations in the standard-model effective field theory at dimension six. Our general implementation, dubbed SMEFT@NLO, covers all types of operators: bosonic, two- and four-fermion ones. Included ultraviolet and rational counterterms presently allow for fully differential predictions, possibly matched to parton shower, up to the one-loop level in the strong coupling or in four-quark operator coefficients. Exact flavor symmetries are imposed among light quark generations and an initial focus is set on top-quark interactions in the fermionic sector. We illustrate the potential of this implementation with novel loop-induced and next-to-leading-order computations relevant for top-quark, electroweak, and Higgs-boson phenomenology at the LHC and future colliders.

The Variational Field Equations of Cosmological Topologically Massive Supergravity

AbstractWe discuss the formulation of cosmological topologically massive (simple) supergravity theory in three‐dimensional Riemann‐Cartan space‐times. We use the language of exterior differential forms and the properties of Majorana spinors on 3‐dimensional space‐times to explicitly demonstrate the local supersymmetry of the action density involved. Exact coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion‐constraint imposed by the method of Lagrange multipliers. Cotton and Cottino 2‐forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated.

In medium properties of an axion within a 2+1 flavor Polyakov loop enhanced Nambu–Jona-Lasinio model

We estimate the axion properties i.e. its mass, topological susceptibility and the self-coupling within the framework of Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical potential. PNJL model, where quarks couple simultaneously to the chiral condensate and to a background temporal quantum chromodynamics (QCD) gauge field, includes two important features of QCD phase transition, i.e. deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model plays an important role near the critical temperature. We have shown significant difference in the axion properties calculated in PNJL model compared to the same obtained using Nambu-Jona-Lasinio (NJL) model. We find that both the mass of the axion and its self-coupling are correlated with the chiral transition as well as the confinement-deconfinement transition. We have also estimated the axion properties at finite chemical potential. Across the QCD transition temperature and/or quark chemical potential axion mass and its self-coupling also changes significantly. Since the PNJL model includes both the fermionic sector and the gauge fields, it can give reliable estimates of the axion properties, i.e. it's mass and the self-coupling in a hot and dense QCD medium. We also compare our results with the lattice QCD results whenever available.

Structure of flavor changing Goldstone boson interactions

General flavor changing Goldstone boson (GB) interactions with fermions from a spontaneous global U(1)G symmetry breaking are discussed. This GB may be the Axion, solving the strong QCD CP problem, if there is a QCD anomaly for the assignments of quarks U(1)G charge. Or it may be the Majoron, producing seesaw Majorana neutrino masses by lepton number violation, if the symmetry breaking scale is much higher than the electroweak scale. It may also, in principle, play the roles of Axion and Majoron simultaneously as far as providing solution for the strong CP problem and generating a small Majorana neutrino masses are concerned. Great attentions have been focused on flavor conserving GB interactions. Recently flavor changing Axion and Majoron models have been studied in the hope to find new physics from rare decays in the intensity frontier. In this work, we will provide a systematic model building aspect study for flavor changing neutral current (FCNC) GB interactions in the fermion sectors, or separately in the quark, charged lepton and neutrino sectors and will identify in detail the sources of FCNC interactions in a class of beyond standard model with a spontaneous global U(1)G symmetry breaking. We also provide a general proof of the equivalence of using physical GB components and GB broken generators for calculating GB couplings to two gluons and two photons, and discuss some issues related to spontaneous CP violation models. Besides, we will also provide some details for obtaining FCNC GB interactions in several popular models, such as the Type-I, -II, -III seesaw and Left-Right symmetric models, and point out some special features in these models.

Twin modular S4 with SU(5) GUT

We discuss the SU(5) grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular S4 groups, one acting in the charged fermion sector, associated with a modulus field value τT with residual {Z}_3^T symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value τSU with residual {Z}_2^{SU} symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM1 lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.

Sum rules in the standard model effective field theory from helicity amplitudes

The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.

Thermal aspects of interacting quantum gases in Lorentz-violating scenarios

In this work, we study the interaction of quantum gases in Lorentz-violating scenarios considering both boson and fermion sectors. In the latter case, we investigate the consequences of a system governed by scalar, vector, pseudovector and tensor operators. Besides, we examine the implications of $\left( \hat{k}_{a}\right) ^{\kappa }$ and $\left( \hat{k}_{c}\right) ^{\kappa \xi }$ operators for the boson case as well. For doing so, we regard the grand canonical ensemble seeking the so-called partition function, which suffices to provide analytically the calculations of interest, i.e., mean particle number, entropy, mean total energy and pressure. Furthermore, in low temperature regime, such quantities converge until reaching a similar behavior being in contrast with what is shown in high temperature regime, which brings out the differentiation of their effects. In addition, particle number, entropy and energy exhibit an extensive characteristic even in the presence of Lorentz violation. Finally, for peseudovector and tensor operators, we notice a remarkable feature due to the breaking process of spin degeneracy: the system turns out to have greater energy and particle number for the spin-down particles in comparison with spin-up ones.

Adjoint SU(5) GUT model with modular S4 symmetry

We study the textures of SM fermion mass matrices and their mixings in a supersymmetric adjoint SU(5) Grand Unified Theory with modular S4 being the horizontal symmetry. The Yukawa entries of both quarks and leptons are expressed by modular forms with lower weights. Neutrino sector has an adjoint SU(5) representation 24 as matter superfield, which is a triplet of S4. The effective light neutrino masses is generated through Type-III and Type-I seesaw mechanism. The only common complex parameter in both charged fermion and neutrino sectors is modulus τ . Down-type quarks and charged leptons have the same joint effective operators with adjoint scalar in them, and their mass discrepancy in the same generation depends on Clebsch-Gordan factor. Especially for the first two generations the respective Clebsch-Gordan factors made the double Yukawa ratio \U0001d4b4d\U0001d4b4μ/\U0001d4b4e\U0001d4b4s = 12, in excellent agreement with the experimental result. We reproduce proper CKM mixing parameters and all nine Yukawa eigenvalues of quarks and charged leptons. Neutrino masses and MNS parameters are also produced properly with normal ordering is preferred.

A note on gauge anomaly cancellation in effective field theories

The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

No radiative corrections to the Carroll–Field–Jackiw term beyond one-loop order

We demonstrate explicitly the absence of the quantum corrections to the Carroll–Field–Jackiw (CFJ) term beyond one-loop within the Lorentz-breaking CPT-odd extension of QED. The proof holds within two prescriptions of quantum calculations, with the axial vector in the fermion sector treated either as a perturbation or as a contribution in the exact propagator of the fermion field.

Alpha -attractors from supersymmetry breaking

We construct new models of inflation and spontaneous supersymmetry breaking in de Sitter vacuum, with a single chiral superfield, where inflaton is the superpartner of the goldstino. Our approach is based on hyperbolic Kähler geometry, and a gauged (non-axionic) U(1)_R symmetry rotating the chiral scalar field by a phase. The U(1)_R gauge field combines with the angular component of the chiral scalar to form a massive vector, and single-field inflation is driven by the radial part of the scalar. We find that in a certain parameter range they can be approximated by simplest Starobinsky-like (E-model) alpha -attractors, thus predicting n_s and r within 1sigma CMB constraints. Supersymmetry (and R-symmetry) is broken at a high scale with the gravitino mass m_{3/2} > rsim 10^{14} GeV, and the fermionic sector also includes a heavy spin-1/2 field. In all the considered cases the inflaton is the lightest field of the model.