Scalar Currents Research Articles

Regularization and Ward-Identity Anomalies

In the context of the free-quark model, we discuss the validity of the na\{\i}ve Ward identities (WI's) for arbitrary regularized $n$-point functions of scalar, pseudoscalar, vector, and axial-vector currents. In a simple version of the regularization procedure described by Pauli and Villars, we find that the na\{\i}ve vector WI's are all automatically satisfied, and that there is a compact necessary condition for the existence of an axial-vector anomaly. Subsequently, this version leads to a large number of anomalous axial-vector WI's (corresponding to the cases $n=2, 3, 4, \mathrm{and} 5$). It is shown that this number cannot be reduced, for example, to Bardeen's solution without additional counterterms beyond those possible in the general regularization framework---in spite of the framework's well-known ambiguities. We discuss other minimal sets, as well as a symmetry-breaking model in which no further anomalies are found. The explicit forms of the WI anomalies for the general minimal solution is given along with the necessary counterterms.

Nonstrong amplitudes in a veneziano-type model

We propose a general procedure for constructing the scattering amplitudes of hadrons with external currents. These are obtained from a representation of theN-point function for hadrons and leptons, in the lowest order of the weak constant. We consider a model with external scalar mesons and vector currents only. Current conservation is not required. We study the form factor, electroproduction and Compton scattering finding good analytic properties for the amplitudes.

Experimental Study ofK+→π0+e++νDecay

An analysis of 515 decays ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{+}+\ensuremath{\nu}$ in a Freon-filled bubble chamber is described. The events were kinematically overdetermined so that a complete reconstruction of each decay was possible. All decay configurations were detectable except for those with positron momentum less than 5 $\frac{\mathrm{MeV}}{c}$. The data are satisfactorily described by a pure vector interaction. The energy dependence of the vector form factor ${f}_{+}$ is given by $|{f}_{+}({q}^{2})|=|{f}_{+}(0)| \frac{{M}^{2}}{({M}^{2}\ensuremath{-}{q}^{2})}$, with $M={{810}_{\ensuremath{-}140}}^{+320}$ MeV, or equivalently, $|{f}_{+}({q}^{2})|=|{f}_{+}(0)|\ifmmode\times\else\texttimes\fi{}[1+\ensuremath{\lambda}(\frac{{q}^{2}}{{{M}_{\ensuremath{\pi}}}^{2}})]$, with $\ensuremath{\lambda}={{0.028}_{\ensuremath{-}0.014}}^{+0.013}$. In the Callan-Treiman relationship for ${K}_{l2}$ and ${K}_{l3}$ decays, this value of $\ensuremath{\lambda}$ leads to the prediction that $\ensuremath{\xi}=0.0\ifmmode\pm\else\textpm\fi{}0.1 or \ensuremath{-}2.0\ifmmode\pm\else\textpm\fi{}0.1$. Upper limits for scalar and tensor currents are given. Systematic biases inherent in the heavy-liquid-chamber technique are discussed.

The algebra of scalar and vector vertex strengths in Regge residues

An algebra of “strong” scalar and vector currents coupled to Regge residues accounts for the composite model predictions in high-energy elastic scattering. Some new relations are given; σ( K + N) = σ( K + P) is accounted for in a simple way.

Current-Generated Algebra and Mass Levels of the Hadrons

The mass splittings of the $U(3)$ [or $\mathrm{SU}(3)$] multiplets of the hadrons are investigated under the following assumptions: (i) The Hamiltonian decomposes into an invariant part plus an eighth component of an octet of $U(3)$, and the latter is a space integral of the scalar current transforming like $\frac{1}{2}({q}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\beta}{\ensuremath{\lambda}}_{8}q)$, where $q$ stands for the quark. (ii) An algebra of the positive parity operators generating a nonchiral $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ is a "good symmetry," where the generators consist of the scalar currents and the fourth components of the vector currents. It is shown that if a universal constant with the dimensions of a mass together with the average mass of the multiplet are given, then the splitting is calculated exactly for any multiplet under the above assumptions. A kind of competition of the kinematical group $U(3)$ and the dynamical group $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ can predict the average masses of $U(3)$ multiplets if they belong to the same multiplet of $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$. The multiplets that concern us are the ${\mathrm{\textonehalf{}}}^{+}$ octet, ${\frac{3}{2}}^{+}$ decuplet, ${\frac{3}{2}}^{\ensuremath{-}}$ octet, ${0}^{\ensuremath{-}}$ nonet, ${2}^{+}$ nonet, and ${1}^{\ensuremath{-}}$ nonet. The results show good agreement with experiment.

Zero-Mass Leptonic Decays ofWBosons

The leptonic decays of the intermediate vector bosons with radiative corrections is studied in the limit where the mass of the charged lepton tends to zero. By means of a simple rule of calculation, we show the independence of the problem on the boson spin. Thus the ratio of the decay rates $\frac{(W\ensuremath{\rightarrow}e\ensuremath{\nu})}{(W\ensuremath{\rightarrow}\ensuremath{\mu}{\ensuremath{\nu}}^{\ensuremath{'}})}$ is obtainable from the corresponding ratio for a spin-zero boson interacting with a weak scalar current. While the radiative correction to the ratio of total decay rates is zero in this approximation, the result is also given for the nonzero correction in the case where discrimination against high-bremsstrahlung photon energies is applied. The spin independence is shown to be true for all boson spins (to the lowest order in $\ensuremath{\alpha}$).