Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson

We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.     

Nonperturbative inconsistency of stochastic quantization in odd dimensions

It is shown that a stochastically-quantized theory of interacting fermion and gauge fields in odd spacetime dimensions can be renormalized, preserving both gauge-and parity-invariance. Thus, the pertinent parity-violating anomalies are not reproduced by the stochastic quantization. Moreover, this theory does not possess a nonperturbative equilibrium limit unless one introduces an appropriate parity-violating counterterm. We conclude that an odd-dimensional gauge theory with fermions cannot be consistently quantized in the stochastic scheme unless the parity-violating anomalies cancel.     

Nonperturbative inconsistency of stochastic quantization in odd dimensions

It is shown that a stochastically-quantized theory of interacting fermion and gauge fields in odd spacetime dimensions can be renormalized, preserving both gauge- and parity-invariance. Thus, the pertinent parity-violating anomalies are not reproduced by the stochastic quantization. Moreover, this theory does not possess a nonperturbative equilibrium limit unless one introduces an appropriate parity-violating counterterm. We conclude that an odd-dimensional gauge theory with fermions cannot be inconsistently quantized in the stochastic scheme unless the parity-violating anomales cancel.     

Perturbative gauge invariance: electroweak theory II

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z ₂ scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.     

Goldstone fermion couplings and supersymmetry breaking in superstring models

We re-examine supersymmetry breaking in the observable sectors of superstring-inspired supergravity models by computing Goldstone fermion couplings at the one-loop level. We find that a single global U (1) phase invariance is sufficient to forbid masses for gauge non-singlet chiral scalar bosons, and that Heisenberg symmetry is not necessary.     

A novel string-derived $Z^\prime$ with stable proton,light neutrinos and R-parity violation

The standard model indicates the realization of grand unified structures in nature, and it can only be viewed as an effective theory below a higher energy cutoff. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many extensions of the standard model introduce such dimension 4, 5 and 6 operators. Furthermore, quantum gravity effects are expected to induce proton instability, indicating that the higher energy cutoff scale must be above 10¹⁶ GeV. Quasi-realistic heterotic string models provide the arena to explore how perturbative quantum gravity affects the particle physics phenomenology. An appealing explanation for the proton longevity is provided by the existence of an Abelian gauge symmetry that suppresses the proton decay mediating operators. Additionally, such a low scale U(1) symmetry should feature the following: it should allow for the suppression of the left-handed neutrino masses by a seesaw mechanism; allow for fermion Yukawa couplings to the electroweak Higgs doublets; be anomaly free; and finally be family universal. These requirements render the existence of such U(1) symmetries in quasi-realistic heterotic string models highly non-trivial. We demonstrate the existence of a U(1) symmetry that satisfies all of the above requirements in a class of left–right symmetric heterotic string models in the free fermionic formulation. The existence of the extra in the energy range accessible to future experiments is motivated by the requirement of adequate suppression of proton decay mediation. We further show that, while the extra U(1) forbids dimension 4 baryon number violating operators, it allows dimension 4 lepton number violating operators and R-parity violation.     

Invariance of fermion determinant under large gauge transformations

We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.     

Perturbative gauge invariance: the electroweak theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.     

Adjoint QCD1 + 1 in light-cone gauge, quantized at equal time

SU (2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with “twisted” boundary conditions, periodic for one color component (the diagonal 3-component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.     

A Three Higgs Doublet Model for Fermion Masses

In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken U_X(1) gauge symmetry. All the fermion Yukawa couplings except that of the top quark are of O(10^-2) in our model. Constraints on the parameter space of the model from low energy processes are studied. Besides, the lightest one of the neutral fermion fields, which is introduced to cancel the anomalies of the U(1)_X gauge symmetry can be the cold dark matter candidate. We investigate its signature in the dark matter direct detection.     

Superheavy fermions and horizontal symmetries

The mechanism which was formerly used to obtain neutrino masses is generalized to all light fermions. Correspondingly, several sets of superheavy fermions are introduced. Assignments under a horizontal symmetry group are arranged such that the heaviest among the light fermions acquire their masses, not from the ordinary Higgs-Yukawa couplings, but from couplings to the heavy fermions. Masses of the other light fermions are then obtained through horizontal gauge interactions. Accordingly, the resulting light fermion masses exhibit a hierarchical generation structure. Because of the construction, light Higgs fields do not induce dangerous flavor-changing neutral-current interactions.     

Composite Higgs scalars

We construct models in which the Higgs doublet whose vacuum expectation breaks SU(2) × U(10 is a bound state of massive strongly interacting fermions. The couplings of the composite Higgs to ordinary fermions are induced by heavy gauge boson exchange in the manner of extended technicolor. Other heavy gauge bosons generate a negative mass term for the Higgs.     

Induced quantum curvature and three-dimensional gauge theories

The effects of quantum holonomy in three-dimensional gauge theories with massless fermions is examined and different definitions of the fermion determinant are discussed. The source of a global gauge and parity anomaly is identified in Schrödinger picture quantization as an induced holonomy that arises from the fermionic sector of the theory. In certain fermion representations this holonomy leads to a global obstruction to imposing either gauge or parity invariance through the implementation of Gauss' law constraint. However, such obstructions can be removed by exploiting renormalization ambiguities inherent in the definition of composite operators.     

Gauge anomaly cancellation in chiral gauge theories

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.     

Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gausian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge invariant by the compact gauge transporters considered, and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the observables studied (propagators and masses).     

I. The isotopic Foldy-Wouthuysen representation and chiral symmetry

The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix γ⁵, these equations possess chiral invariance irrespective of whether fermions have mass or are massless. The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions. In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P — symmetry). This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.     

Fermion condensate model of electroweak interactions

A new dynamical symmetry breaking model of electroweak interactions is proposed based on interacting fermions. Two fermions of different SU_L(2) representations form a symmetry breaking condensate and generate the lepton and quark masses. The weak gauge bosons obtain their usual standard model masses from a gauge-invariant Lagrangian of a doublet scalar field composed of the new fermion fields. The new fermion fields become massive by condensation. It is shown that the new charged fermions are produced at the next linear colliders in large number. The model is a low-energy one, which cannot be renormalized perturbatively. For the parameters of the model, unitarity constraints are presented.     

Renormalization group constraints on unified gauge theories

Renormalization group constraints on the behavior of Yukawa and scalar quartic couplings in unified gauge theories are examined. Yukawa couplings are generally asymptotically free whenever the gauge couplings are, but scalar quartic couplings can be asymptotically free only for simple scalar multiplets in large groups with large fermion content. The infrared behavior of Yukawa and scalar quartic couplings implied by the renormalization group equations has interesting and phenomenologically useful consequences: infrared fixed points (or quasifixed points) lead to bounds on masses of fermions and scalars, while scalar quartic couplings can be driven out of the domain of positivity of the classical potential, with possible implications for patterns of symmetry breaking.