A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

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.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

AN SU(6) GRAND UNIFIED MODEL

A model of grand unified theory based on SU(6) gauge group is proposed. It can accommodate two generations of ordinary fermions with V－A weak coupling and two generations of anomalous fermions with V+A weak coupling. In this model a new discrete symmetry is introduced which insures existence of fermions with lower masses when SU(6) gauge symmetry is spontaneously broken. We choose simple Higgs fields with appropriate vacuum expectation values so that the masses of anomalous fermions are heavier than those of ordinary fermions. This model also gives the same value of Weinberg angle, sin²θw=3/8, as in the usual SU(5) grand unified model at the grand unified scale.     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Is the peak value of σ xx at the quantum Hall transition universal?

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σ _xx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σ _xx is reduced by a factor (1 + g/2π)^?1, at least for small g. This provides some theoretical evidence for the non-universality of σ _xx , as observed in a number of experiments.     

Relation between the Lee-Wick and Nambu-Jona-Lasinio models of chiral symmetry breaking

The connection between the sigma model of Lee and Wick and the Nambu-Jona-Lasinio (NJL) model is discussed. It is shown that the sigma field potential of the linear Lee-Wick model is identical in form with the variation of the vacuum energy of the NJL system with the baryonic scalar densityn _s. The sigma field is proportional ton _s. Furthermore, the coupling constant and mass of thisσ field are fully determined by the NJL model version of the Goldberger-Treiman relation. It is shown further that the restoration of chiral symmetry with increasing baryonic density always occurs via a second order transition in the NJL model, while it is necessarily of first order in the associated linear Lee-Wick model.     

Higher orders in N−1 in the Gross-Neveu model

We study higher-order terms in the N expansion of the two-dimensional model field theory of Gross and Neveu. The quantity $\text{M}{}_{\mathrm{\sigma }}\text{2M}{}_{\mathrm{<mtext>F</mtext><mtext>?1</mtext>}}$ (M_F is the fermion mass, M_σ is the scalar bound-state mass), is conjectured to deviate from zero in O(N^?4). Order N^?1 corrections are found to leave unchanged both the symmetry-breaking, and the absence of zeros of the Callan-Symanzik function β for real non-zero coupling constant. Behavior of β for complex coupling constant is altered considerably by the corrections; consequences are discussed.We obtain the following additional results: proof that the model is renormalizable without the necessity of additional interactions; construction of a perturbation theory in the asymmetric vacuum; proof of a lemma on fermion-antifermion thresholds in two-dimensional space-time; derivation of closed formulae for arbitrary one-loop integrals in two-dimensional space-time.     

Z 2 monopoles in the standardSU (2) lattice gauge theory model

The standardSU(2) lattice gauge theory model without fermions may be considered as aZ ₂ model with monopoles and fluctuating coupling constants. At low temperatures β^?1 (=small bare coupling constant) the monopoles are confined.     

Phases of renormalized lattice gauge theories with fermions

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U(1) and SU(2) case. We determine the renormalized trajectories and the phases of the theory.     

On non-perturbative effects in the jet physics

We consider quark scattering off nonperturbative gluonic fields in the vacuum and its impact on the hadronic final state in thee ⁺ e ^?—annihilation. A conservative estimate gives a nonperturbativep _⊥?1GeV. The modification of the final state survives even at an arbitrary high energy, where the corrections to the total cross-section die away. We also argue that the coupling constant extracted from the perturbative treatment of the jet phenomenology can well be different from that governing the correction toσ _tot.     

Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear σ model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band centre (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.     

On the radiative corrections to the electroweak parameters and precision tests of the electroweak theory

The radiative corrections to the electroweak parameters are reconsidered with an emphasis on analysing prospects for future tests of the as yet untested parts of the electroweak theory, in particular the “new physics” of vector-boson self-interactions and the Higgs scalar. The vacuum polarization due to the light fermions is treated in the leading-long approximation, while the top-quark is taken into account exactly. A detailed analysis of the errors involved in our approximations and a comparison with the results of complete one-loop calculations shows that vacuum polarization due to bosons is negligible, ifm _H =100 GeV, while it may become visible in precision tests ine ⁺ e ^? annihilation, ifm _H ?1 TeV. We also give detailed results (as a function of the top-quark mass) on the radiatively correceted parameters used in model-independent fits to neutrino-scattering and in the interpretation of atomic-parity violation experiments. Technically, we diagonalize the γ-Z propagator for anyq ², and we show, when treating the top-quark vacuum polarization exactly, that the intuitively appealing notion of running coupling constants can be used beyond the leading-log approximation.     

Generations in the rishon model

We present a model for fermions composed of rishons in which colour plays a determinant role providing for only three generations. The couplings with the gauge bosons of the SU(2)_L × SU(2)_R × U(1)_B?L theory as well as with Higgs bosons are determined by the colour substructures. Two appealing possibilities emerge: the Cabibbo mixing angles could be small due to their dependence on the colour coupling constant and the fermionic mass hierarchy could be related to the fact that the products of higher representations have a richer decomposition allowing for the coupling with more Higgs fields.     

Leading large N modification of QCD2 on a cylinder by dynamical fermions

We consider two-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a 1/Nexpansion. We find that coupling to fermions nontrivially modifies the large N saddle point of the gauge theory due to the phenomenon of “decompactification” of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation value of the Wilson loop operator both of which show a nontrivial dependence on the number of quarks flavours at the leading order in 1/N.     

Topological superfluid in one-dimensional ultracold atomic system with spin-orbit coupling

We propose a one-dimensional Hamiltonian H _1D which supports Majorana fermions when d _{x² ? y²}-wave superfluid appears in the ultracold atomic system and obtain the phase diagrams both for the time-reversal-invariant (TRI) case and time-reversal-symmetry-breaking (TRSB) case. From the phase diagrams, we find that the Majorana doublets and the single Majorana fermions exist in the topological superfluid (TSF) regions for the TRI case and the TRSB case, respectively, and we can reach these regions by tuning the chemical potential μ and spin-orbit coupling α _R . Importantly, the spin-orbit coupling has been realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by H _1D is a promising platform to find the mysterious Majorana fermions.     

Mass shift of σ-meson in nuclear matter

The propagation of σ-meson in nuclear matter is studied in the Walecka model, by assuming that the sigma couples to a pair of nucleon–antinucleon states and to particle–hole states. The in-medium effect of σ–ω mixing is also studied. For completeness, the coupling of sigma to two virtual pions was also considered. It is found that the σ-meson mass decreases with respect to its value in vacuum and that the contribution of the σ–ω mixing effect on the mass shift is relatively small.     

Systematic study of horizontal gauge theories

We analyze all the possible continuous horizontal gauge groups G _H in relation with their possibility to explain m _b ? m _t. We assume that the only effective fermionic degrees of freedom correspond to the known fermions but allow the possibility of adding a right handed neutrino to each family. We assume that the Higgs fields which generate masses for these fermions, trough renormalizable Yukawa couplings, transform as an irreducible representation of SU(3)_c ? SU(2)_L ? U(1)_Y ? G_H. Under these assumptions we find two U(1)_H or U(1) _H1 ? U(1) _H2 models free of anomalies and able to guarantee that only the top has a renormalizable mass-generating Yukawa coupling.     

Nonlinear σ-model and nucleon structure

The nonlinear σ-model with the Wess-Zumino action describes the nucleon as a soliton and incorporates the non-abelian chiral anomalies. Several studies have shown that the model works well except for the nucleon mass, which comes out consistently too large. We investigate this question beginning with the more general framework of the linear σ-model, which has besides a pseudoscalar meson sector, a fermion or quark sector, a scalar field and an interaction between the fermions via the scalar field. Using a path integral formulation, we express the fermion measure of the model as the product of a Jacobian and an invariant measure. Identifying this Jacobian as exp[iΓ _wz] , we find that the model breaks up into two parts, when in the pseudoscalar meson sector the scalar field is replaced by its vacuum value. The pseudoscalar part of the model becomes the nonlinear σ-model with the Wess-Zumino actionΓ _wz. The other part involves chiral fermions, the scalar field and their interaction. We continue this part back to the Minkowski space to determine its ground state and energy levels. We find that for a scalar field that vanishes at smallr, but rises sharply to its vacuum value at someR, the ground state energy of the interacting quark-scalar-field system can be lower than the ground state energy of the non-interacting quark system. This means the interaction between quarks and the scalar field can lead to a condensed ground state or vacuum and can reduce the overall energy of the system (a phase transition as in superconductivity). It is, therfore, not surprising that the nonlinear σ-model predicts too large a nucleon mass, since it implicitly assumes a normal non-interacting vacuum in the quark sector. Quarks are now quasiparticles that appear as excitations of the condensed vacuum. The nucleon structure that emerges from this investigation agrees fully with the phenomenological nucleon structure found from analysis of high energy elasticpp and \(\bar p\) p scattering at CERN ISR and SPS Collider.