Numerical simulations of two-dimensional QED

We describe the computer simulation of two-dimensional QED on a 64 × 64 Euclidean space-time lattice using the Susskind lattice fermion action. The order parameter for chiral symmetry breaking and the low-lying meson masses are calculated for both the model with two continuum flavours, which arises naturally in this formulation, and the model with one continuum flavour obtained by including a nonsymmetric mass term and setting one fermion mass equal to the cut-off. Results are compared with those obtained using the quenched approximation, and with analytic predictions.     

Instantons,fermion mass generation and supercomplementarity

We consider the possibility that hypercolor instantons can provide fermion masses in preon models of quark and leptons. After discussing the basic ideas of this mechanism in a non-supersymmetric preon model we consider a supersymmetric, QCD-like preon model. We work within the so-called complementarity picture and show the equivalence between the mass term of the elementary fermions, generated by a vacuum expectation value of a elementary scalar, and the mass term of the composite fermions, generated by the hypercolor instantons.     

Hierarchical fermion masses from grand unification

A mechanism is presented for generating fermion masses as a reflection of the superheavy fermions existing in a class of grand unified theories. By means of it we propose a way of understanding how, giving a driving mass term for the top-generation, the charm-generation mass results as a relative first-order perturbation in the unified gauge coupling g²/4π ≈ 10^?2, and the up-generation mass as a second-order perturbation. An illustrative calculation of the charm-generation mass is described in a model based on E₆.     

Fermion masses in grand unified theories: Effective Yukawa terms

It is argued that effective non-renormalizable terms of the type recently proposed by Ellis and Gaillard can give rise to large contributions to the fermion masses. The combined effect of this kind of term and the usual Yukawa couplings could explain the observed hierarchy of fermion masses. Two toy-models based on the gauge groups SU (5)×SU(2) _H and SO(10)×SU(2) _H (where SU(2) _H is a gauged “horizontal” symmetry) are shown in which one can obtain some interesting mass relations previously obtained under very different assumptions.     

Curing fermion mass gauge variance in QED

The problem of the gauge dependence of the fermion mass in the Maxwell-Chern-Simons QED is revisited. Using Proca mass term as an intermediate infrared regulator we are demonstrating gauge-invariance of the fermion mass shell in QED in all orders of the perturbation theory.     

Scales of mass generation for quarks, leptons, and majorana neutrinos

We study 2-->n inelastic fermion-(anti)fermion scattering into multiple longitudinal weak gauge bosons and derive universal upper bounds on the scales of fermion mass generation by imposing unitarity of the S matrix. We place new upper limits on the scales of fermion mass generation, independent of the electroweak symmetry breaking scale. Strikingly, we find that the strongest 2-->n limits fall in a narrow range, 3-170 TeV (with n=2-24), depending on the observed fermion masses.     

A renormalizable SO(10) GUT scenario with spontaneous CP violation

We consider fermion masses and mixings in a renormalizable SUSY SO(10) GUT with Yukawa couplings of scalar fields in the representation . We investigate a scenario defined by the following assumptions. (i) We have a single large scale in the theory, the GUT scale. (ii) The small neutrino masses are generated by the type I seesaw mechanism with negligible type II contributions. (iii) We assume a suitable form of spontaneous CP breaking that induces hermitian mass matrices for all fermion mass terms of the Dirac type. Our assumptions define an 18-parameter scenario for the fermion mass matrices for 18 experimentally known observables. Performing a numerical analysis, we find excellent fits to all observables in the case of both the normal and inverted neutrino mass spectrum.     

Results for all reactions e^+ e^- \rightarrow 4{\rm f}, 4{\rm f}\gamma with nonzero fermion masses

We accomplish our efforts to obtain predictions for all four–fermion final states of –annihilation and the corresponding bremsstrahlung reactions which are possible in the framework of the Standard Model. For this purpose we have developed a program ee4 . Our predictions are valid for fermions of arbitrary masses and we can obtain results for total cross sections without any collinear cut. Keeping exact fermion masses is of course required for top quark production. We give a detailed phenomenological analysis of fermion mass effects and real photon radiation for all channels of four–fermion production at LEP-II and next linear collider energies. Received: 2 October 2001 / Revised version: 2 January 2002 / Published online: 1 March 2002     

A Model of Fermion Masses and Flavor Mixings with Family SymmetrySU(3)\otimes U(1)

The family symmetrySU}(3)\otimes U(1) is proposed to solve flavor problems about fermion masses and flavor mixings. It is breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z₂ is introduced to generate tiny neutrino masses, which is broken by a real singlet
scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation
quark masses and the values ofθ₁₃^l and J_CP^l in neutrino physics. All of the results are promising to be tested in the future experiments.     

Mass of the Higgs boson in the standard model with four generations

We study the functional behavior of the quartic scalar coupling in the standard model with four generations. From the assumed boundedness of its ratio to theU(1) gauge coupling and the stability of the Higgs potential under radiative corrections, we derive upper and lower bounds on the Higgs-boson mass as functions of the fourth-generation fermion masses. We also obtain a solution in which the Higgs-boson mass is determined as a function of the other masses of the model.     

Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model

Ward-Takahashi identities with composite fields are utilized to inverstigate (2+1) dimensional model with SU(2) four-fermion couplings.When SU(2) chiral symmetry is both explicitly and dynamically broken,fermion mass is dynamically generated and mass spectra of the bound states are obtained The properties of vector and axial-vector currents are discussed.It turns out that the bound state π_α acquires a mass and the axial-vector current is partially conserved,and the Goldberger-Treimab relation is approximately valid in the case of small fermion current masses.     

General electroweak mixing models and extended gauge theories

General electroweak mixing schemes containing an arbitrary number of weak bosons and agreeing with the predictions of the standard model for neutrino scattering and polarized electron scattering in the low energy approximation are analyzed using the propagator matrix formalism. The mean charged boson mass is bounded while the mean neutral boson mass is unbounded and determined as a function of the mean charged one. Under a special assumption on the electroweak mixing parameters the four fermion interaction agrees with the one of extended gauge theories and the mean boson masses agree with the boson masses of the standard model.     

Physical particles of the massive Schwinger model

The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consist of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low-mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This representation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with exact calculations wherever possible, and find good agreement.     

Zeta function regularization, anomaly and complex mass term

If zeta function regularization is used and a complex mass term considered for fermions, the phase does not appear in the fermion determinant. This is not a drawback of the regularization, which can recognize the phase through source terms, as demonstrated by the anomaly equation which is explicitly derived here for a complex mass term.     

Top quark mass in exophobic Pati-Salam heterotic string model

We analyse the phenomenology of an exemplary exophobic Pati-Salam heterotic string vacuum, in which no exotic fractionally charged states exist in the massless string spectrum. Our model also contains the Higgs representations that are needed to break the gauge symmetry to that of the Standard Model and to generate fermion masses at the electroweak scale. We show that the requirement of a leading mass term for the heavy generation, which is not degenerate with the mass terms of the lighter generations, places an additional strong constraint on the viability of the models. In many models a top quark Yukawa may not exist at all, whereas in others two or more generations may obtain a mass term at leading order. In our exemplary model a mass term at leading order exist only for one family. Additionally, we demonstrate the existence of supersymmetric F- and D-flat directions that give heavy mass to all the colour triplets beyond those of the Standard Model and leave one pair of electroweak Higgs doublets light. Hence, below the Pati-Salam breaking scale, the matter states in our model that are charged under the observable gauge symmetries, consist solely of those of the Minimal Supersymmetric Standard Model.     

Explicit SO(10) supersymmetric grand unified model for the higgs and yukawa sectors

A complete set of fermion and Higgs superfields is introduced with well-defined SO(10) properties and U(1)xZ2xZ2 family charges from which the Higgs and Yukawa superpotentials are constructed. The structures derived for the four Dirac fermion and right-handed Majorana neutrino mass matrices coincide with those previously obtained from an effective operator approach. Ten mass matrix input parameters accurately yield the twenty masses and mixings of the quarks and leptons with the bimaximal atmospheric and solar neutrino vacuum solutions favored in this simplest version.     

Gravity and the frame field

The covariant derivative of a single massive fermion field on a Riemannian manifold is defined. The standard method of defining free bosonic Lagrangians from the fermion covariant derivative does not give the usual Lagrangian density for the free gravitational field. We express the fermion Lagrangian mass term as a frame field term added to the covariant derivative; this extended covariant derivative defines a gravitational Lagrangian density proportional to the usual scalar curvatureR, plus a term quadratic in the curvature components. The quadratic term is expected to be negligible at distances much greater than the fermion Compton wavelength, and is of a general form widely studied in recent years. The frame field term used to derive this gravitational Lagrangian is essentially the same as that used previously to derive the electroweak interaction boson mass matrix without using the Higgs-Kibble mechanism.     

A microscopic formula for actinide masses

A fully microscopic actinide mass formula is derived using the fermion dynamical symmetry model approximation to the spherical shell model. A rich dynamical symmetry phase structure is confirmed, and the mass formula fits the masses of 322 nuclei with an RMS deviation of 0.34 MeV.     

Grand unification at intermediate mass scales through extra dimensions

One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to the TeV scale) through the appearance of extra space-time dimensions. Such extra dimensions are a natural consequence of string theories with large-radius compactifications. We show that extra space-time dimensions naturally lead to gauge coupling unification at intermediate mass scales, and moreover may provide a natural mechanism for explaining the fermion mass hierarchy by permitting the fermion masses to evolve with a power-law dependence on the mass scale. We also show that proton-decay constraints may be satisfied in our scenario due to the higher-dimensional cancellation of proton-decay amplitudes to all orders in perturbation theory. Finally, we extend these results by considering theories without supersymmetry; experimental collider signatures; and embeddings into string theory. The latter also enables us to develop several novel methods of explaining the fermion mass hierarchy via D-branes. Our results therefore suggest a new approach towards understanding the physics of grand unification as well as the phenomenology of large-radius string compactifications.     

A technocolor model with softly broken flavor symmetry

I describe an explicit technicolor model in which the interactions that give rise to the quark and lepton masses are generated by the exchange of massive gauge bosons as in extended technocolor models but in which the gauge bosons couple the quarks and leptons not directly to the technifermions, but to heavy fermions. Quark and lepton masses arise from box diagrams. The masses of the heavy fermions in this model come both from bare fermion mass terms and from the renormalizable interactions of a set of spinless fields. The model has a softly broken flavor symmetry that realizes the GIM suppression of FCNC effects as in a CTSM model.