Current Algebra Sum Rules Research Articles

Current and constituent quarks: Their implications for resonance excitations polarized and unpolarized inelastic structure functions

The transformation between constituent and current quarks is discussed and applied to the calculation of matrix elements for nucleon to resonance transitions induced by arbitrary currents belonging to an octet. In particular, previous results on πN and γN transitions are subsumed while weak interactions ( ΔQ = 0 or 1) and longitudinal photon induced transitions are discussed for the first time. The implications of a non-trivial Melosh transformation upon previous calculations in quark parton models of the non-diffractive component of the deep inelastic structure functions are discussed. The magnitudes of the unpolarized structure functions are found to be unchanged but for the polarized structure functions significant corrections to previous calculations are discovered. In particular it is found that it is not necessary that the polarization asymmetry A γ P be positive in the deep inelastic region. Our approach is valid for all Q 2, even for photoproduction, and is not restricted to deep inelastic scattering in contrast to earlier parton model calculations. The saturation of various current algebra sum rules is discussed.

Causality, current algebra, and fixed poles

We study the causality restrictions on the structure of the nonforward matrix element of the commutator of two conserved isovector currents. We give a fixed-pole interpretation of the noncausal contribution, derive a set of causality and current-algebra sum rules, and determine the structure of the equal-time commutator.

Light-cone expansion, current algebra and σ-commutators

It has been shown recently that, in order to have consistency between some current algebra sum rules, the light-cone expansion leading to Bjorken scaling has to be modified. The required modifications are shown to be consistent with current algebra, but lead to a new scaling regime and to Schwinger terms in σ-commutators. These Schwinger terms appear only in commutators involving nonconserved currents, and may, therefore, provide a natural explanation for the large value of ξ in Kt3-decay, without destroying any of the successful predictions based on current algebra.

A narrow-resonance approach to current algebra sum rules: Meson-nucleus low-energy scattering

su3⊗su3 chiral algebra and PCAC have been employed to derive pion and kaon scattering amplitudes on nuclei from sum rules of the Fubini-Furlan type. The nuclear states are described as finite systems in a simple, nonrelativistic impulse approximation. The effects of the break down of chiralSU3⊗SU3 symmetry are described in a (3, 3*)+(3*, 3) model. The πN sigma-term turns out to be about 46 MeV and we find good agreement between the model by Gell-Mann, Oakes and Renner and both pion and kaon-nucleus data.

Current algebra determination of K −-nuclear scattering lengths

We make use of the Fubini-Furlan current algebra sum rules to calculate the real part of the K −-nuclear ( A ⪅ 24) scattering lengths a. Re a is expressed in terms of equal-time commutators of currents and a dispersive integral over the off-mass-shell scattering amplitude. In evaluating the dispersion integral we assume that kaon capture occurs predominantly on a single nucleon. The kaon nucleus sigma term is written as a coherent sum of kaon nucleon sigma terms σ KN. Due to inconsistencies in the determinations of σ KN we present our results for different values of σ KN.

Spin sum rules for inelastic (anti) neutrino-nucleon scattering

We present a systematic discussion of the equal-time current-algebra sum rules for the structure functions in inelastic (anti) neutrino-nucleon scattering. Our emphasis is on spin-dependent results. All sum rules, both at fixed- q 2 and in the Bjorken scaling limit, are obtained by a single procedure which presumes Bjorken scaling. In particular, the procedure yields sensible results in the cases where the familiar infinite momentum method yields nonsense. Our procedure requires a complete characterization of the ν-behaviour of the structure functions in the presumed scaling limit. For definiteness, we achieve this characterization by giving the complete quark light-cone scaling behaviour together with the complete set of positivity restrictions on the structure functions. After having derived the sum rules, we give, following the approach of Callan, et al., the spin generalization of the ΔS = 0 Nachtmann relations, as these relations, together with the sum rules, may eventually be use in determining the precise light-cone formalism.

Scalar-Meson Pole Model for Weak Parity-Violating Baryon-Baryon-Meson Vertices

We apply a scalar-meson pole model to the parity-violating hyperon decays and to the parity-violating $\mathrm{NN}\ensuremath{\pi}$ vertex. In this model we obtain the usual octet-dominance results for the hyperon decay amplitudes: the $I=\frac{1}{2}$ rule, the Lee-Sugawara triangle, and a vanishing amplitude for $s$-wave ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$ decay. The model is distinguished from the vector-meson pole models by the fact that it gives the current-algebra sum rule for the parity-violating $\mathrm{NN}\ensuremath{\pi}$ amplitude whereas the vector pole model predicts that this amplitude vanishes in the limit of isospin symmetry. Using the SU(3)\ifmmode\times\else\texttimes\fi{}SU(3) $\ensuremath{\sigma}$ model for the currents we compute the amplitudes without arbitrary constants and find that they are about half the observed amplitudes.

Pion charge radius from current algebra sum rule and short range correlation model

Starting from the Fubini-Dashen-Gell-Mann sum rule, we relate the slope of the pion electromagnetic form factor at t = 0 to the rotational properties of the photopion production amplitudes. When the pion's charge radius is calculated with a simple short range correlation model for the production amplitudes (diffractive processes being forbidden), the result is 〈r π 2〉 1 2 = 0.8 fm .

Quantum Field Theories in the Infinite-Momentum Frame. I. Quantization of Scalar and Dirac Fields

Renormalizable coupled scalar and Dirac field theories are quantized in equal-${x}^{+}$ surfaces (called light fronts). Schwinger's action principle is employed to deduce the correct canonical equal-${x}^{+}$ (anti-) commutation relations. These theories are shown to be Lorentz-invariant. Generalized Schwinger conditions for a quantum field theory to be Lorentz-invariant are given and discussed in an appendix. Spectral sum rules are derived. Leading singularities of Green's functions and products of field operators near the light cone are studied and the implications to current algebra sum rules are discussed. We also discuss some of the delicate features of the light-front formulation.

Current algebra sum rules for reggeons

The interplay between the constraints of chiralSU2×SU2 symmetry and Regge asymptotic behaviour is investigated. We review the derivation of various current algebra sum rules in a study of the reaction π+α→π+β. These sum rules imply that all particles may be classified in multiplets ofSU2×SU2 and that each of these multiplets may contain linear combinations of an infinite number of physical states. Extending our study to the reaction π+α→π+π+β, we derive new sum rules involving commutators of the axial charge with the reggeon coupling matrices of the ρ and f Regge trajectories. Some applications of these new sum rules are noted, and the general utility of these and related sum rules is discussed.

Form factors and equal-time commutators

We study the equal-time commutator of the charge and current sandwiched between states of unequal momenta, considering the momentum transfer between the two states as a new independent variable. One notes that usual current algebra sum rules are obtained at zero momentum transfer, probing the equal-time commutator by usingq2 (the 4-momentum square of the current) as a variable, namely, the Adler-Weisberger and the Cabibbo-Radicati sum rules. By our new approach, we study the dispersion method (Dashen-Fubini-Gell-Mann sum rule) and the current algebra method (using Ward identity, specifically the Weisberger approach). We find that they give the same result for the pion, but different results for the nucleon. The difference (due to spin) is traced down to the question of subtraction. We comment on that at the end.

Current algebraic sum rules and Veneziano model for photoproduction of pions off nucleons

Sum rules relating the proton and the neutron magnetic moments to amplitudes for γ+N→π+N are analysed in the framework of the dual-resonance model and reasonably good agreement is obtained.

Light-cone aspect of inelastic neutrino scattering

The hypothesis of universal light-cone behaviour of current commutators formulated previously is applied to the deep inelastic neutrino-nucleon scattering. It is shown that it yields the scaling laws of the parton model and, provided the nonleading light-cone singularities are of certain type, it reproduces the current algebra sum rules for the scaling functions. One new sum rule is obtained relating the longitudinal scaling function to the equal-time commutator of the weak-current charge with the weak-current divergence. Particular attention is paid to the light-cone aspect of an eventual vanishing of the longitudinal scaling functionFs(ξ). It is shown thatFs(ξ)=0 both in electron and neutrino inelastic scattering would imply that the currents might satisfy theU3⊗U3 algebra at equal « lightlike times »x⊥=(1/√2)(x0−x3) without operator Schwinger terms, as is suggested by the quark model.

Current algebra sum rules, veneziano model and K l3 form factors

The Kl3 form factorsf±(t) are obtained by means of current algebra dispersive sum rules. After introducing a simple Veneziano formula with satellites for the relevant amplitudes, and using the normalizationf+(0)=1, an expression with no free parameters is found for bothf±(0). In the decay region they turn out to bef+(t)=1+0.06(t/mπ2),f−(t)=−1.7(1+0.02(t/mπ2). Thus, the model predicts the following values for the Kl3 parameters: ξ(0)=−1.7, λ+=0.06, λ−=0.02 andΛ=0.07. The agreement with experiment is found to be excellent.

Current algebra sum rule by the hard-meson technique

Current algebra sum rule by the hard-meson technique

Quarks, Sum Rules, and Low-Energy Parameters inπNScattering

Finite-energy sum rules and current-algebra sum rules are shown to work at the quark level. Making use of these rules, and of a factorization assumption for the basic mesonquark amplitudes above threshold, some well-known SU(6) results are derived. Low-energy parameters in $\ensuremath{\pi}Q$ and $\ensuremath{\pi}N$ scattering are also evaluated. Using our model for the $\ensuremath{\pi}N {a}_{1\ifmmode\pm\else\textpm\fi{}}^{(\ensuremath{-})}$ $p$-wave scattering lengths, an inconsistency is found between the usual PCAC (partially conserved axial-vector current) or $\ensuremath{\rho}$-exchange-model treatments and dispersion relations. It can be removed if double counting of resonances and $\ensuremath{\rho}$-exchange terms is avoided. This provides good agreement with experiment.

Current-Algebra Sum Rules in Neutrino Scattering and Scale Dimension of the Chiral-Symmetry-Breaking Hamiltonian

Current-algebra sum rules for the structure functions ${W}_{4}$ and ${W}_{5}$ which occur in neutrino scattering because of the nonconservation of the axial-vector current are derived and used to get information about the scaling behavior of ${W}_{4}$ and ${W}_{5}$. This information together with the light-come analysis is used to determine the scale dimension of the chiral-symmetry-breaking Hamiltonian.

Current Algebra in Two-Particle Bases and Single-Particle Inclusive Processes

We discuss several problems involved in the current-algebra sum rules derived by Suzuki and his collaborators. In particular we discuss the ambiguities related to soft-current insertion to the external lines. Alternative prescriptions to get similar sum rules are also discussed. An application of the sum rule to the $W$-production process is briefly discussed.

Local Current-Algebra Sum Rules in the Rest Frame

Local Current-Algebra Sum Rules in the Rest Frame

Determination of πN sigma term from pion nucleus scattering

We make use of the current algebra sum rules developed by Fubini and Furlan for pion-nucleon scattering to evaluate π −-nucleus scattering lengths. Assuming that the pion-nucleus sigma term Σ can be written as a coherent sum of pion-nucleon sigma terms S and using experimental data we determine S for each reaction tested averaging 22 ± 1 MeV. With S = 22 ± 1 we calculate π −-nucleus scattering lengths and our results indicate a good agreement with experimental data.