Current-current Interaction Research Articles

A new approach to the chiral transition in lattice QED

Evidence is presented that the chiral transitions in non-compact lattice QED and a fermion model with only a current-current interaction are in the same universality class, both having mean-field scaling laws with logarithmic corrections. The finite-size effects in the present QED data are explainable from the corrections. The effective field theory in the chirally broken phase is discussed.

Seeking signs of a second Z.

Principles of minimality and unifiability lead us to a unique family of mutants of the electroweak theory which are parametrized solely by the mass of a heavy Z' boson. These models generate an additional vectorial current-current interaction at low energy, and modify the properties of the observed Z boson in a way that would appear (in the context of the standard model) as an apparently fractional number (exceeding three) of light neutrino species. Such alternative theories offer a foil against which to test our confidence in the orthodox theory.

Radiative corrections for forward coherent neutrino scattering

We have calculated radiative corrections of the order α to forward coherent\(\nu _e - e\) scattering assuming the model of the current-current interaction. We have also calculated corrections to the finite W-boson mass. Some implications of these calculations on neutrino oscillations in the matter are discussed.

A CHIRALLY SYMMETRIC EFFECTIVE ACTION FOR VECTOR AND AXIAL VECTOR FIELDS IN A GLOBAL COLOR SYMMETRY MODEL OF QCD

We consider the quantum field theory of a model of an extended Nambu-Jona-Lasinio type with a QCD based nonlocal fermion current-current interaction which has global SU(Nc) symmetry. We obtain an exact bosonization of this model in four Euclidean dimensions using auxiliary bilocal fields and discuss the dynamical breakdown of chiral symmetry in the massless fermion limit. A local field bosonization is obtained by decomposing the bilocal fields in terms of complete orthonormal sets of functions with the expansion coefficients, which are local functions, identified as the local meson fields. Retaining the ground state pseudoscalar, vector and pseudovector local fields we obtain a local effective action for this sector of the theory. The derivative expansion of the fermionic determinant necessary to obtain this local action is self-regularizing because of the bilocal substructure present in the model which is manifest in the form factors that are associated with the local fields. In our local action the value of each coefficient depends critically on the underlying fermionic dynamics through these form factors and the vacuum functions. As a consequence of this the vector and pseudovector fields in the theory are best interpreted as simple fermion-antifermion bound states rather than as massive Yang-Mills fields or exotic composites of the pseudoscalars; interpretations that we find are not in general admitted when models such as the GCM are treated correctly. Identifying then the physical vector and pseudovector fields with the linearly transforming chiral partners introduced by the bosonization, we obtain an effective action for this sector of the meson spectrum which predicts values for the kinematic and dynamic quantities associated with these fields.

Non-abelian Bose-Fermi equivalence in the background of Kaluza-Klein scalars and compactifications of closed bosonic strings

The two-dimensional non-abelian Bose-Fermi equivalence in the presence of background gauge fields and “Kaluza-Klein” scalar fields is derived. It is shown that a current-current interaction linear in the background scalar field in the Fermi version leads to interactions which involve all orders in the background scalar fields in the Bose version of the theory. Implications for the possible embedding of the heterotic string in the closed bosonic string with a special choice of background fields are discussed.

A STUDY OF ρ→ππ DECAY IN A GLOBAL COLOR MODEL FOR QCD

We show how a meson effective action, in which all of the meson parameters are finite, arises from a “global color symmetry” model involving a nonlocal current-current (four-quark) interaction. As an application of this general approach we present a covariant analysis of the ρ-π system and thus obtain estimates for the ρ meson mass and the coupling constant gρππ.

Systematic search of Abelian gauge theories.

We make a systematic search of all the possible field theories in n-dimensional Minkowski space with an Abelian gauge invariance and bosonic gauge fields. They include the usual cases of Maxwell theory and spontaneously broken gauge theories but also less known cases such as a conserved current-current interaction and a massive Abelian vector boson coupled to a conserved current, as well as a description of any symmetry breaking as coming from a spontaneous breakdown. Special cases in one, two, or three space-time dimensions are also considered.

Investigation of the weak interaction from general relativity

The flat—space-time limit of a generalized covariant field theory of electrodynamics in general relativity is explored. The generalized force, expressed in terms of Hermitian products of spinor functions, is a complex variable. Its real part corresponds to the standard (Lorentz) force in electrodynamics; its imaginary part corresponds to reflection nonsymmetric forces, some that can be identified with the weak interaction—particularly applied to neutron decay, within the context of this theory. To test the theory, the effective charge compared with the electron charge,ew/e, is computed, found to be the order 7.10−4. This result is compared with Fermi’s result for this ratio for the pseudoscalar, current-current interaction, which gave the order of 3.10−4.

Final polarizations in quasielastic neutrino-nucleon scattering.

The purposes of this paper are (1) to suggest a set of useful parameters for analysis of cross section and output polarization in the reaction ..nu../sub ..mu../n..--> mu../sup -/p and (2) to use the established ideas that explain the cross section to predict the final polarizations. In setting up the parameters, the general case, with only current-current interaction and V-A lepton current assumed, is treated. The parameters come from a consideration of the Jacob and Wick single-particle helicity states. They are linear in the form factors F(Q/sup 2/) but are not functions of Q/sup 2/ alone. They lead to brief formulas for the cross section and polarizations of the output particles and they facilitate some of the discussions of the process.

Small correction to the quantization of Hall conductance due to current-current interactions and charge redistribution.

Small correction to the quantization of Hall conductance due to current-current interactions and charge redistribution.

Effects of compositeness in deep inelastic scattering

It is conjectured that leptons and quarks are composites of more fundamental constituents bound together by a new confining force with a typical confinement radius ∼1/GL H. Assuming that the effective low energy lagrangian is given by the lagrangian of the standard model plus induced lepton and quark current-current interactions, the effects of the latter remnants of the new force on the deep inelastic structure function, F 2( x, Q 2), are investigated at Q 2 ≲ H 2. It is shown that these signatures of compositeness should be detectable at HERA if GL H ≲ 2−3 TeV.

Feynman rules for processes involving composite bound systems

A set of Feynman rules is developed to deal with any Bethe-Salpeter model description of baryons and mesons interacting through any effective current-current interaction. The rules follow from the Mandelstam generalisation of the Gell-Mann-Low method to compute matrix elements and are used to evaluate the Delta T=1/2 enhancement in the process K to 2 pi .

Weak radiative decays of hyperons and charmed baryons in a quark model

The weak radiative decays of 1/2/sup +/ baryons are studied in a quark model as arising through single-quark spectator and nonspectator quark transitions. These decays seem to occur predominantly through nonspectator processes, where the quarks may interact through the exchange of colored gauge bosons. We compare the decay-amplitude sum rules in left x left and left x right current-current interaction pictures.

Equivalence of (super-) renormalizable fermion-boson interactions and nonlinear fermion interactions

Using well-defined cutoff theories it is shown that many (super-) renormalizable fermion-boson interactions are equivalent to nonlinear fermion interactions which are local when the cutoffs are removed. The reason is that the Dirac sea has antiscreening effects which generate long-range interactions from short-range interactions. Thus, for example, an Abelian current-current interaction is equivalent to quantum electrodynamics for $2<d\ensuremath{\le}4$, where $d$ is the space-time dimension. The eigenvalue condition on the four-fermion coupling constant corresponds to choosing the critical point of the transition to the phase in which Lorentz invariance is spontaneously broken. Thus the photon can be regarded as the Goldstone excitation of a spontaneously broken Lorentz symmetry. Also it is possible to regard fundamental interactions as due to self-interactions of a fermionic "matter" field.

Comment on the inelastic scattering of relativistic charged particles

It has long been known that the cross section for the inelastic scattering of relativistic charged particles by atoms rises logarithmically with increasing energy. I rederive this result without introducing the current-current interaction (and hence without quantizing the electromagnetic field). This is done by working in the projectile frame in which the projectile current vanishes. The advantage of using the projectile frame is emphasized. A rough heuristic derivation of the logarithmic divergence is also given with the collision viewed in the projectile frame.

Nonleptonic decays of charm mesons

We investigate the possibility that both nonleptonic strange-particle and charm-particle decays can be understood in terms of one effective nonleptonic Hamiltonian ${H}_{\mathrm{eff}}={H}_{0}+{H}_{\mathrm{COR}}$. ${H}_{0}$ is a usual four-fermion current-current interaction term and the ${H}_{\mathrm{COR}}$ is the color-radius interaction term. The color-radius interaction is known to explain the $\ensuremath{\Delta}I=\frac{1}{2}$ rule in strange-particle decays. The effects of ${H}_{\mathrm{COR}}$ as well as those of final-state interaction on two-body charm-meson decays are examined. The theory is in qualitative agreement with all measured branching ratios. Predictions for charm-meson decays into two pseudoscalar mesons are presented.

Elementary Particle Physics: An Introduction

This textbook is intended for graduate-level courses for students specializing in the study of matter and energy at the extremes of high energy and small distance. It is organized into these subject areas: electromagnetic interactions of the leptons; electromagnetic form factors of the hadrons; inelastic electron-proton scattering; historical development of weak interation physics; the V-A current-current interaction theory; strangeness-changing and charm-changing weak interactions; K/sup 0/ mesons; high energy neutrino interactions; dispersion relations; the strong interaction coupling constant; classification of hadrons; SU-2 and SU-3; the octet in SU-3; SU-3 applications and SU-4; the quark model; SU-6 and symmetrization; quark model applications; and Regge poles. (GHT)

Diffractive dissociation processes in a field-theoretic quark model

We consider here diffractive dissociation processes like $A+B\ensuremath{\rightarrow}A+X$ in a field-theoretic quark model with a phenomenological current-current interaction in quark space used earlier for discussing diffraction scattering in the same model. The process $A+B\ensuremath{\rightarrow}A+X$ is interpreted as being diffractive for the hadron $A$ with correlation to the form factor of $A$, and is incoherent for the hadron $B$ with correlation to the structure function of $B$. These assumptions in the quark model yield that the cross sections $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}d{M}^{2}$ have the same structure as is otherwise derived on the basis of the more established triple-Pomeron coupling, which could probably be partly anticipated since the Pomeron corresponds to a spin-1 object with vacuum quantum numbers. The results are compared with experiments, and broad agreement at high energies is observed. With these ideas, in the region of small mass of the dissociated system, the contributions to the cross section from diffractive dissociation and from diffractive production of resonances can be separated, where a limitation for the incoherent scattering in quark-parton models is used.

Deviations from the [formula omitted] rule and nonlocal effect on the weak current-current interaction

Sum rules for deviations from the ΔI = 1 2 rule are discussed both for S- and P-wave hyperon decay amplitudes. The observed deviations for the P-wave decay amplitudes suggest that a nonlocal effect on the weak current-current interaction is not negligible.

Spin structure of proton-proton scattering in the current-current interaction picture

Using the current-current interaction picture for elastic pp scattering, excellent fits are obtained for all data above 12Gev/ c which covers twelve orders of magnitude. It can fit all polarization data, and imply considerable structure in spin-dependent differential cross sections.