Fermion Mass Research Articles

Phase diagram near the quantum critical point in Schwinger model at θ = π: analogy with quantum Ising chain

Abstract The Schwinger model, 1D quantum electrodynamics, has CP symmetry at θ = π due to the topological nature of the θ term. At zero temperature, it is known that as the fermion mass increases, the system undergoes a second-order phase transition to the CP broken phase, which belongs to the same universality class as the quantum Ising chain. In this paper, we obtain the phase diagram near the quantum critical point (QCP) in the temperature and fermion mass plane using first-principle Monte Carlo simulations, while avoiding the sign problem by using the lattice formulation of the bosonized Schwinger model. Specifically, we perform a detailed investigation of the correlation function of the electric field near the QCP and find that its asymptotic behavior can be described by the universal scaling function of the quantum Ising chain. This finding indicates the existence of three regions near the QCP, each characterized by a specific asymptotic form of the correlation length, and demonstrates that the CP symmetry is restored at any nonzero temperature, entirely analogous to the quantum Ising chain. The range of the scaling behavior is also examined and found to be particularly wide.

Collective modes of a massive fermion in a magnetized medium with finite anomalous magnetic moment

Collective modes of a massive fermion in a magnetized medium with finite anomalous magnetic moment

Monte Carlo study of Schwinger model without the sign problem

Monte Carlo study of the Schwinger model (quantum electrodynamics in one spatial dimension) with a topological θ term is very difficult due to the sign problem in the conventional lattice formulation. In this paper, we point out that this problem can be circumvented by utilizing the lattice formulation of the bosonized Schwinger model, initially invented by Bender et al. in 1985. After conducting a detailed review of their lattice formulation, we explicitly validate its correctness through detailed comparisons with analytical and previous numerical results at θ = 0. We also obtain the θ dependence of the chiral condensate and successfully reproduce the mass perturbation result for small fermion masses m/g ≲ 0.125. As an application, we perform a precise calculation of the string tension and quantitatively reveal the confining properties in the Schwigner model at finite temperature and θ region for the first time. In particular, we find that the string tension is negative for noninteger probe charges around θ = π at low temperatures.

One loop reduced QED for massive fermions within an innovative formalism

One loop reduced QED for massive fermions within an innovative formalism

Baryogenesis in a parity solution to the strong CP problem

Space-time parity can solve the strong CP problem and introduces a spontaneously broken SU(2)R gauge symmetry. We investigate the possibility of baryogenesis from a first-order SU(2)R phase transition similar to electroweak baryogenesis. We consider a model with the minimal Higgs content, for which the strong CP problem is indeed solved without introducing extra symmetry beyond parity. Although the parity symmetry seems to forbid the SU(2)R anomaly of the B − L symmetry, the structure of the fermion masses can allow for the SU(2)R sphaleron process to produce non-zero B − L asymmetry of Standard Model particles so that the wash out by the SU(2)L sphaleron process is avoided. The setup predicts a new hyper-charged fermion whose mass is correlated with the SU(2)R symmetry breaking scale and hence with the SU(2)R gauge boson mass, and depending on the origin of CP violation, with an electron electric dipole moment. In a setup where CP violation and the first-order phase transition are assisted by a singlet scalar field, the singlet can be searched for at future colliders.

Low-lying baryon masses using twisted mass fermions ensembles at the physical pion mass

Low-lying baryon masses using twisted mass fermions ensembles at the physical pion mass

Fermion mass hierarchy and mixing 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 are introduced. Compared to the previous model, the number of bulk fermions is reduced, which reproduces the generation mixing of SM fermions and SM fermion mass hierarchy by mildly tuning the bulk masses and parameters of the localized gauge kinetic terms.

Modular binary octahedral symmetry for flavor structure of Standard Model

We have investigated the modular binary octahedral group 2O as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion mass models based on the modular binary octahedral group 2O. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton mass models in good agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus τ. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.

The minimal flavor structure of quarks and leptons

A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a common flat structure for up-type quarks, down-type quarks, charged leptons, and Dirac neutrinos. A flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated Cabibbo–Kobayashi–Maskawa (CKM) mixing for quarks and Pontecorvo–Maki–Nakagawa–Sakata mixing for leptons. It results that the minimal flavor structure successfully addresses flavor mixings of quarks and leptons even in the mass hierarchy limit, which means that mass hierarchy and flavor mixing are two independent questions. As a prediction, a sum rule on the mixing angles and CP violation phase (CPV) is suggested, which explains the smallness of s 13 as a natural result of the mass hierarchy. Generalizing the flat structure to quarks and leptons, a unified Yukawa interaction is also achieved for all fermions with only a single coupling.

Constraining BSM discrete flavor symmetries with heavy scalar searches at colliders

Discrete Flavor Symmetries are often employed in BSM constructions to successfully recreate fermion masses and mixing patterns through several known mechanisms. Obvious constraints on these types of scenarios are the non-observation of Flavour Changing Neutral Currents which set stringent limits. In this talk I will discuss the strategy of using the scalar sector phenomenology predicted by such BSM models, and its correlation with the dark matter sector, to further strengthen the constraints by exploiting the large data available from heavy scalar searches in colliders including recent likelihood profiles provided by ATLAS and CMS.

Exploring freeze-out and freeze-in dark matter via effective Froggatt-Nielsen theory

Motivated by the dynamical reasons for the hierarchical structure of the Yukawa sector of the Standard Model (SM), we consider an extension of the SM with a complex scalar field, known as `flavon', based on the Froggatt-Nielsen mechanism. In an effective theory approach, the SM fermion masses and mixing patterns are generated in orders of the parameter related to the vacuum expectation value of the flavon field and the cut-off of the effective theory. By introducing right-handed neutrinos, we study the viability of the lightest right-handed neutrino as a dark matter candidate, where the same flavon field acts as a mediator between the dark and the SM sectors. We find that dark matter genesis is achieved both through freeze-out and freeze-in mechanisms encompassing the 𝒪(GeV) – 𝒪(TeV) mass range of the mediator and the dark matter particle. In addition to tree-level spin-dependent cross section, the model gives rise to tree- and loop-level contributions to spin-independent scattering cross section at the direct detection experiments such as XENON and LUX-ZEPLIN which can be probed in their future upgrades. By choosing suitable Froggatt-Nielsen charges for the fermions, we also generate the mass spectrum of the SM neutrinos via the Type-I seesaw mechanism. Flavor-changing neutral current processes, such as radiative lepton decay, meson mixing, and top-quark decay remain the most constraining channels and provide testability for this minimal setup that addresses several major shortcomings of the SM.

Emergent one-dimensional helical channel in higher-order topological insulators with step edges

We study theoretically the electronic structure of three-dimensional (3D) higher-order topological insulators in the presence of step edges. We numerically find that a 1D conducting state with a helical spin structure, which also has a linear dispersion near the zero energy, emerges at a step edge and on the opposite surface of the step edge. We also find that the 1D helical conducting state on the opposite surface of a step edge emerges when the electron hopping in the direction perpendicular to the step is weak. In other words, the existence of the 1D helical conducting state on the opposite surface of a step edge can be understood by considering an addition of two different-sized independent blocks of 3D higher-order topological insulators. On the other hand, when the electron hopping in the direction perpendicular to the step is strong, the location of the emergent 1D helical conducting state moves from the opposite surface of a step edge to the dip (270° edge) just below the step edge. In this case, the existence at the dip below the step edge can be understood by assigning each surface with a sign (+ or −) of the mass of the surface Dirac fermions. These two physical pictures are connected continuously without the bulk bandgap closing. Our finding paves the way for on-demand creation of 1D helical conducting states from 3D higher-order topological insulators employing experimental processes commonly used in thin-film devices, which could lead to, e.g., a realization of high-density Majorana qubits.

On hypersymmetry in three dimensions

In this work we presented a number of explicit examples for the cubic vertices describing an interaction of massless spin- frac{5}{2} field with massive boson and fermion including all hypertransformations necessary for the vertices to be gauge invariant. Here we restrict ourselves with the massive bosons with spins s = 2, 1, 0 and massive fermions with spins s = frac{3}{3} , frac{1}{2} . Our general analysis predicted that the vertex must exist for any boson and fermion with the spin difference frac{3}{2} or frac{1}{2} . And indeed it appeared that the vertex exists for all six possible pairs (2, 1, 0) ⊗ ( frac{3}{2} , frac{1}{2} ). As in the case of massive supermultiplets, our construction is based on the gauge invariant description for the massive fields with spins s ≥ 1. Moreover, we have explicitly checked that all the vertices are invariant also under the gauge symmetries of these massive fields.

Gauged SU(3)F and loop induced quark and lepton masses

We investigate a local SU(3)F flavour symmetry for its viability in generating the masses for the quarks and charged leptons of the first two families through radiative corrections. Only the third-generation fermions get tree-level masses due to specific choice of the field content and their gauge charges. Unprotected by symmetry, the remaining fermions acquire non-vanishing masses through the quantum corrections induced by the gauge bosons of broken SU(3)F. We show that inter-generational hierarchy between the masses of the first two families arises if the flavour symmetry is broken with an intermediate SU(2) leading to a specific ordering in the masses of the gauge bosons. Based on this scheme, we construct an explicit and predictive model and show its viability in reproducing the realistic charged fermion masses and quark mixing parameters in terms of not-so-hierarchical fundamental couplings. The model leads to the strange quark mass, ms ≈ 16 MeV at MZ, which is ~2.4σ away from its current central value. Large flavour violations are a generic prediction of the scheme which pushes the masses of the new gauge bosons to 103 TeV or higher.

Observation of anomalous Hall resonance of massive Dirac fermions in topological kagome-lattice magnet

The kagome-lattice materials promise emergence of Dirac fermions thanks to the special lattice geometry, which potentially realizes intriguing quantum topological states through various many-body interactions. The low-energy electromagnetic phenomena arising from such the Dirac fermions are expected to show the remarkable enhancement and, in certain conditions, to approach the universal responses, which, however, have remained elusive experimentally. Here, we show the resonantly enhanced magneto-optical response of massive Dirac fermions in kagome-lattice magnet TbMn6Sn6. The infrared magneto-optical spectroscopy reveals that the interband transition on massive Dirac bands significantly contributes to the observed resonance in the optical Hall conductivity. The analytical model expressed by a few band parameters reproduces the spectral characteristics of the resonance, which robustly produces almost 20 % of the quantized Hall conductance per one kagome layer even at room temperature. Our findings establish the general optical response of massive Dirac fermions, which is closely related to the universal electrodynamics in quantum anomalous Hall state.

Superlattice engineering of topology in massive Dirac fermions

Superlattice engineering of topology in massive Dirac fermions

Mass and Size Characterization of FRACEP Composite Elementary Fermions

Mass and Size Characterization of FRACEP Composite Elementary Fermions

Electrical, thermal and thermoelectric transport in open long-range Kitaev chain

We study electrical, thermal and thermoelectric transport in a hybrid device consisting of a long-range Kitaev (LRK) chain coupled to two metallic leads at two ends. Electrical and thermal currents are calculated in this device under both voltage and thermal bias conditions. We find that the transport characteristics of the LRK chain are distinguishably different from its short-range counterpart, which is well known for hosting zero energy Majorana edge modes under some specific range of values of the model parameters. The emergence of massive Dirac fermions, the absence of gap closing at the topological phase transition point and some special features of the energy spectrum which are unique to the LRK chain, significantly alter electrical/thermal current vs. voltage/temperature bias characteristics in comparison with that of the short-range Kitaev chain. These novel transport characteristics of the LRK model can be helpful in understanding nontrivial topological phases of the LRK chain.

A Novel Quasi-Planar Two-dimensional Carbon Sulfide with Negative Poisson's ratio and Dirac fermions.

In the present study, a novel and unconventional two-dimensional (2D) material with Dirac electronic features hasbeen designed using sulflower with the help of density functional theory methods and first principles calculations.This 2D material comprises of hetero atoms (C, S) and belongs to the tetragonal lattice with P4/nmm space group. Scrutiny of the results show that the 2D sheet exhibits a nanoporous wave-like geometrical structure. Quantummolecular dynamics simulations and phonon mode analysis emphasize the dynamical and thermal stability. Thenovel 2D sheet is an auxetic material with an anisotropy in the in-plane mechanical properties. Both compositionand geometrical features are completely different from the necessary conditions for the formation of Dirac conesin graphene. However, the presence of semi-metallic nature, linear band dispersion relation, massive fermions andmassless Dirac fermions are observed in the novel 2D sheet. The massless Dirac fermions exhibit highly isotropicFermi velocities (vf = 0.71 × 106 m/s) along all crystallographic directions. The zero-band gap semi metallic featuresof the novel 2D sheet are perturbative to the electric field and external strain.

On massive higher spin supermultiplets in d = 3

In this paper, using a frame-like gauge invariant formulation of the massive higher spin bosons and fermions, we develop a direct construction of the completely off-shell cubic vertices describing an interaction of the massless gravitino with the massive higher spin supermultiplets. To achieve the invariance under the local supersymmetry we introduce all necessary supertransformations (both for the physical as well as for the auxiliary fields) and thus all the supercurrents constructed are conserved on-shell. As an illustration of the technique used we present some lower superspin examples and then we consider the arbitrary superspin. We also check that the whole construction is completely consistent with all bosonic and fermionic gauge symmetries of the fields entering the supermultiplets.