Current Algebra Sum Rules Research Articles

Collective modes and current-algebraic sum rules in nuclear medium

In-medium sum rules following from the chiral charge algebra of QCD are reviewed, and new sum rules are derived. The new sum rules relate the I g (J pc ) = 1 −(0 ++) excitations (quantum numbers of a 0(980)) to the scalar and isovector densities, and are non-trivial for the isospin-asymmetric medium. We present an extensive illustration of the sum rules with the help of quark matter in the Nambu-Jona-Lasinio model. Collective excitations different from the usual meson branches (spin-isospin sound modes) are shown to contribute significantly to the sum rules and to play a crucial role in the limit of vanishing current quark masses.

Constraint on the Isgur-Wise function for semileptonic decays

A current algebra sum rule for the inclusive decays by Bjorken et al is used to obtain constraints on the Isgur-Wise function for the decays.

Current algebra and soft pionic modes in asymmetric quark matter

Pionic excitations are analyzed in isospin-asymmetric Fermi gas of constituent quarks. It is found that in addition to the usual pionic excitations, there exists a very low collective mode with quantum numbers of the charged pion (spin-isospin sound). In the chiral limit the excitation energy of one of the modes scales as the current quark mass, and the mode saturates current-algebraic sum rules. This is in agreement with predictions of current algebra for isospin-asymmetric medium.

Chiral Lagrangian with vector and axial vector meson for π+ - π0 mass difference

It is shown that the simple expression for the forward virtual Compton scattering on a soft pion for the π + - π 0 electromagnetic mass difference calculation usually obtained from Current Algebra and Weinberg sum rules can be derived in a simple manner from a chiral Lagrangian with vector and axial vector mesons. We also discuss the relation between the chiral Lagrangian approach and the dispersion relation for the Compton amplitude.

Low-energy sum rules and large- Nc consistency conditions

The large- N c consistency conditions for axial-vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of low-energy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial-vector and isovector magnetic coupling constants get corrections only at the order 1/ N c 2 follows from the N c-counting of appropriate cross sections. This counting is performed using various approaches at the quark and hadronic level. Other implications of our method are also presented.

Pi -p--> pi 0 pi 0n near threshold and chiral symmetry breaking.

Total cross sections, angular, and mass distributions for the reaction {pi}{sup {minus}}{ital p}{r arrow}{pi}{sup 0}{pi}{sup 0}{ital n} have been measured for {ital p}{sub {pi}}{sup {minus}}(lab)=7--140 MeV/{ital c} above threshold. The threshold amplitude was used to determine a value for the chiral-symmetry-breaking parameter, {xi}, of {minus}0.98{plus minus}0.52. The {pi}{pi} scattering lengths {ital a}{sub {ital I}} for isospin {ital I}=0 and 2 are derived from this result, together with a current-algebra sum rule. The results are {ital a}{sub 0}=(0.207{plus minus}0.028){ital m}{sub {pi}}{sup {minus}1} and {ital a}{sub 2}=({minus}0.022{plus minus}0.011){ital m}{sub {pi}}{sup {minus}1}. These values are consistent with chiral symmetry broken by the Weinberg {pi}{pi} interaction and the effects of the {ital f}{sub 0}(975) scalar meson.

Technicolor corrections to electroweak parameters

The isospin conserving effect of technicolor on the electroweak parameters is studied using a current algebra sum rule. It is found that the main contributions are through the low-lying weak isotriplet vector meson states. Large technicolor models are already excluded by current data, in agreement with previous estimates.

LIMITS SET BY ANALYTICITY AND CURRENT ALGEBRA ON THE EXISTENCE OF A HEAVY NUCLEON

We estimate through the analysis of dispersion relations and current algebra sum rules that the experimentally searched excited state of nucleon with mass below pion-nucleon threshold must have a coupling one order of magnitude smaller than the normal pion-nucleon one [Formula: see text] as an upper bound.

A current algebra description of kaon-nucleus scattering lengths

Current algebra sum rules for kaon-nucleus elastic-scattering amplitudes are re-written as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the meson-nucleus continua and in the bound-state spectra, we produce a general formula for the dependence of the real parts of kaon-nucleus scattering lengths on the target quantum numbers. We introduce explicitly a shell-model description of nuclear ground-states, which was instrumental in reproducing with satisfactory accuracy the corresponding pion-nucleus data: most of the effects observed there (up to and including the 2s−1d shell) were consistent with a naive spherical-harmonic-oscillator picture. An output of this analysis is the (average) kaon-nucleon sigma-term: the value derived here stays as large as found in two previous estimates by ourselves, the first from a slightly less sophisticated analysis of (mostly) the same data, the second derived from the dispersion-relation evaluations of the zero-energy, fixed-t kaon-nucleon scattering amplitudes made by Oades. Such a large value (about 640 MeV) confirms the hypothesis, advanced by Donoghue and Nappi, of a large, nonperturbative, strange-quark scalar density in the nucleon.

Threshold pion-nucleus amplitudes as predicted by current algebra. Systematic dependence on target quantum numbers and chiral-symmetry breaking parameters

We re-express current-algebra sum rules for pion-nucleus elastic-scattering amplitudes as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the continua and in the bound-state spectra, we analyse all available data on the real parts of pion-nucleus scattering lengths. We find that a good description of these data requires introducing explicitly a shell-model picture of the nuclear ground states: indeed, most of the effects observed in light nuclei (up to and including the 2s-1d shell) are described by a very naive, spherical-harmonic-oscillator picture, save for the few-nucleon systems lighter than4He, which behave as loosely bound nucleon clusters (and for6Li, a loosely bound d-α cluster). An output of this analysis is the pion-nucleon sigma-term, which turns out smaller than, but still consistent with, the estimate by the Karlsruhe-Helsinki collaboration from pion-proton scattering amplitudes: this originates in a reduction in the pion decay constantfπ from the mass-shell toq2=0, needed to reproduce the isospin dependence in the data; the accord between the two estimates is recovered by extrapolating the πN amplitude inboth the variablest andq2 and imposing elastic unitary.

Decay constants and SU(2) mass splittings of pseudoscalar mesons

Borel-transformed QCD sum rules are applied to pseudoscalar mesons containing a light antiquark and a light or heavy quark. We determine the decay constants and the SU(2) mass splittings of these mesons. A suitable method of extracting the hadronic parameters from the sum rules is discussed in detail. The relationship of these sum rules to the current algebra sum rules is p emphasized. Our results are in good agreement with the experimental results, where available.

Hadronic Couplings of Open b-Flavour States

l) is based on quantum chromodynamics (QCD) which is the candidate theory for strong interactions. This analysis is based on the fact that hadrons are composite objects of constituent quarks. It assigns binding of constituents together in the long distance scale. However, these attempts suffer from the lack of proper understanding of the binding mechanism, i.e., confinement. An alternative approach, which has so far played a central role in the strong interaction physics, is based on the S matrix phenomenology. This approach has given us many calculational tools in the form of current algebra sum rules, superconvergence relations, etc. Recently hadronic couplings of charmed particles have been calculated using these techniques by many authors. 2 )-8) In this paper we want to use these techniques to calculate hadronic couplings of open beauty particles. This theoretical study of hadronic parameters of beauty particles will throw considerable light on the dynamics of flavour symmetry breaking as well as on the hadronic production of these particles.

Pionic decays and saturation of current-algebra sum rules in a nonrelativistic expansion of the quark shell model

Pionic decays of hadrons are calculated using a PCAC (partial conservation of axial-vector current) prescription and a quark shell model with quarks bound by a central potential, described by the Dirac equation. The Dirac Hamiltonian and operators are expanded in $\frac{v}{c}$, the internal quark velocity. Then, one finds an exact saturation of the current-algebra sum rules as defined in the SU(2) \ensuremath{\bigotimes} SU(2) symmetry of Gilman-Harari and Weinberg up to order $\frac{{v}^{4}}{{c}^{4}}$. The saturation is obtained without need of exotics, with the usual excitations of the ground state. The relation with the $P=\ensuremath{\infty}$ approach is clarified. The corrections found with respect to previous quark models in $L=2$ decays are discussed. They do not solve the problem of $\mathrm{SU}{(6)}_{W}$ coupling signs. Finally, the whole Weinberg scheme of linear SU(2) \ensuremath{\bigotimes} SU(2) symmetry is completed by the expression of the chiral-breaking part of the mass operator ${{m}_{4}}^{2}$.

Nonpointlike-parton model with asymptotic scaling and with scaling violation at moderateQ2values

A nonpointlike-parton model is formulated on the basis of the assumption of energy-independent total cross sections of partons and the current-algebra sum rules. No specific strong-interaction Lagrangian density is introduced in this approach. This model predicts asymptotic scaling for the inelastic structure functions of nucleons on the one hand and scaling violation at moderate ${Q}^{2}$ values on the other hand. The predicted scaling-violation patterns at moderate ${Q}^{2}$ values are consistent with the observed scaling-violation patterns. A numerical fit of ${F}_{2}$ functions is performed in order to demonstrate that the predicted scaling-violation patterns of this model at moderate ${Q}^{2}$ values fit the data, and to see how the predicted asymptotic scaling behavior sets in at various $x$ values. Explicit analytic forms of ${F}_{2}$ functions are obtained from this numerical fit, and are compared in detail with the analytic forms of ${F}_{2}$ functions obtained from the numerical fit of the quantum-chromodynamics (QCD) parton model. This comparison shows that this nonpointlike-parton model fits the data better than the QCD parton model, especially at large and small $x$ values. Nachtman moments are computed from the ${F}_{2}$ functions of this model and are shown to agree with data well. It is also shown that the two-dimensional plot of the logarithm of a nonsinglet moment versus the logarithm of another such moment is not a good way to distinguish this nonpointlike-parton model from the QCD parton model.

Reformulation of chiral dynamics in infinite-Ncquantum chromodynamics

We present a formulation of chiral dynamics suitable for the large-${N}_{c}$ (number of colors) limit of quantum chromodynamics (QCD). The formulation is in terms of current amplitudes with cyclic crossing symmetry. We derive the chiral Ward identities for these "cyclic current amplitudes" and illustrate how they can be used to obtain low-energy theorems and current-algebra sum rules. We suggest that the Dashen---Gell-Mann program of saturating current-algebra sum rules with narrow resonances be reexamined within the framework of infinite-${N}_{c}$ QCD. We discuss several possible escapes from no-go results obtained by Chang, Dashen, and O'Raifeartaigh.

Spectral-function sum rules in a relativistic quark model

The current-meson couplings are calculated using a relativistic quark model. It is shown that the couplings of the highly excited pseudoscalar mesons are inversely proportional to the particle mass, whereas couplings of vector and axial-vector mesons are proportional to the masses. Spectral functions obtained from these couplings approximate the quark-parton results and satisfy current-algebra sum rules to the leading order in mass.

Parameter-free hard-meson prediction of theKl3form factors

Using the results of a previous on-mass-shell analysis of current-algebra sum rules for K..pi.. scattering we are able to make parameter-free predictions for the K/sub l//sub 3/ form factors. The results are compared with recent experiments and found to be in reasonably good agreement.

Residue sum rules for inelastic (anti) neutrino nucleon scattering

We discuss the complete set of current algebra sum rules for the Regge residues and asymptotic constant S limits of the structure functions of inelastic (anti) neutrino nucleon scattering.

Fixed mass and scaling sum rules: Generalized truncation and current algebra constraints on Regge residues

Using the correspondence principle (continuity in dynamics), we extend the approach of Keppel-Jones-Ward-Taha to fixed mass and scaling current algebraic sum rules so as to consider explicitly the contributions of all classes of intermediate states. A natural, generalized formulation of the truncation ideas of Cornwall, Corrigan, and Norton is introduced as a by-product of this extension. The formalism is illustrated in the familiar case of the spin independent Schwinger term sum rule. New sum rules are derived which relate the Regge residue functions of the respective structure functions to their fixed hadronic mass limits for q 2 → ∞.

Current-algebra theorems forKπscattering

On-mass-shell current-algebra sum rules for $K\ensuremath{\pi}$ scattering are investigated. At threshold these sum rules relate the combinations ${a}^{\frac{1}{2}}\ensuremath{-}{a}^{\frac{3}{2}}$ and ${a}^{\frac{1}{2}}+{2a}^{\frac{3}{2}}$ of $I=\frac{1}{2} \mathrm{and} \frac{3}{2}$ $S$-wave scattering lengths to their soft-meson predictions plus "correction" terms. A dispersion-theoretic approach is used to calculate the corrections to both the soft-koan and soft-pion values for each of these scattering length combinations. The dispersion relations are assumed to be dominated by the ${K}^{*}(890)$ and a ${J}^{P}={0}^{+}\ensuremath{\kappa}$ meson. The correction to the soft-pion value ${a}^{\frac{1}{2}}\ensuremath{-}{a}^{\frac{3}{2}}=0.210{{m}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$ is found to be very small, thus suggesting that the on-mass-shell current-algebra prediction for ${a}^{\frac{1}{2}}\ensuremath{-}{a}^{\frac{3}{2}}$ is nearly equal to the soft-pion value. Self-consistency requirements of the analysis favor $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}\ensuremath{\simeq}1.22$; this implies that a fairly large (\ensuremath{\sim}30%) correction to the corresponding soft-koan prediction of ${a}^{\frac{1}{2}}\ensuremath{-}{a}^{\frac{3}{2}}\ensuremath{\approx}0.14{{m}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$ is needed. The ${K}^{*}$ and $\ensuremath{\kappa}$ contributions to the latter correction increase this value to $0.177{{m}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$. Furthermore, since the ${K}^{*}$ and $\ensuremath{\kappa}$ corrections to and the soft-koan value of ${a}^{\frac{1}{2}}\ensuremath{-}{a}^{\frac{3}{2}}$ decrease with increasing $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}$, a value of $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}\ensuremath{\gtrsim}1.3$ seems, at least in the context of the present study, to be rather unlikely.