Pseudoscalar Correlator Research Articles

On the reliable measurement of the gluon condensate in lattice QCD

We propose to calculate the gluon condensate in lattice QCD in an indirect way by extracting it from the correlator of hadronic currents of heavy quarks. Moments (derivatives with respect to momentum at vanishing momentum) of the vector and pseudoscalar correlators are evaluated. The contribution of the continuum spectrum in addition to the low-lying resonance is observed in accordance with qualitative expectations. Finite size effects are observed and shown to be insignificant for heavy quarks and moderate lattices. A practical definition of the nonperturbatively renormalized heavy quark mass is given.

Pseudoscalar correlators and the problem of the chiral limit in the compact lattice QED with Wilson fermions

The phase diagram for the compact lattice QED with Wilson fermions is shown. We discuss different methods for the calculation of the 'pion' mass $m_{\pi}$ near the chiral transition point $\kappa_c(\beta )$.

Exploring lattice quantum chromodynamics by cooling.

The effect of cooling on a number of observables is calculated in SU(2) lattice gauge theory. The static quark-antiquark potential and spin-dependent interactions are studied, and the topological charge is monitored. The chiral symmetry breaking order parameter $\langle \overline{\chi}\chi \rangle$ and meson correlators are calculated using staggered fermions. Interactions on the distance scale of a few lattice spacings are found to be essentially eliminated by cooling, including the spin-dependent potentials. $\langle \overline{\chi}\chi \rangle$ and meson correlators up to time separations of several lattice spacings relax very quickly to their free-field values. At larger times, there is evidence of a difference between the pseudoscalar and vector channels. A fit to the pseudoscalar correlation function yields ``mass'' values about $2/3$ (in lattice units) of the uncooled masses. These results raise the question of how to reconcile the large-time behavior of the hadron correlators with the fact that the spin-dependent potentials and $\langle \overline{\chi}\chi \rangle$ essentially disappear (in lattice units) after only a small amount of cooling.

Nonperturbative propagators for scalars and fermions to all orders in their masses

The contribution of fermion and scalar condensates,\(\left\langle {\bar \psi \psi } \right\rangle \) and 〈φ+φ〉 to their propagators is calculated exactly in their masses. The ensuing contributions to the photon propagator and the pseudoscalar correlation function are then evaluated.

Next-next-to-leading perturbative QCD corrections and light quark masses

We present the next-next-to-leading three-loop perturbative QCD corrections to the (pseudo) scalar quark current correlator. They amount to about 20% of the leading term at α s ≈ 0.25 . Taking them into account and exploiting finite energy sum rules, we find the following values of light quark masses: m u ≈ 5 MeV , m d ≈ 11 MeV , m s ≈ 195 MeV . We also discuss the phenomenological predictions of “linear dual models” for radial excitations of the K, δ and κ mesons.

Determination of light quark masses

Using the finite energy sum rule or the Shifman-Vainshtein-Zakharov technique for the scalar correlation function, it is shown that m ̂ d − m ̂ u = 10 MeV (for Λ QCD = 150 MeV and three flavours) where the m ̂ 's are the invariant masses. Using ( m ̂ d − m ̂ u ) ( m ̂ d + m ̂ u ) = 0.29 we deduced that m ̂ d = 22 MeV . The question of the determination of the sum of the light quark masses with the pseudoscalar correlation function is discussed.

Superconvergence relations for axial-vector pseudoscalar meson scattering

We consider the effect of the predictions of the superconvergence sum rules for axial-vector pseudoscalar meson scattering on axial-vector meson decays into one vector and one pseudoscalar meson. AssumingSU 3 invariance it is shown that these rules implys-wave decay phase space for both axial-vector nonets known experimentally to exist. For those processes where the vector meson decays into two pseudoscalar mesons ans-wave angular correlation is implied. These predictions are compared with the higher symmetry group predictions and with indirect theoretical estimates for angular correlations.

Interference Effects in Leptonic Decays

It is proven that in any leptonic decay experiment in which the lepton masses and charges may be neglected, and in which no pseudoscalar correlations are measured, all $V\ifmmode\cdot\else\textperiodcentered\fi{}A$ interference terms will be antisymmetric under exchange of the two leptons, while the pure $V$ and $A$ terms will be symmetric. If the experiment measures a pseudoscalar correlation, these conclusions are reversed. Even if the lepton masses cannot be ignored (e.g., for ${\ensuremath{\Lambda}}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+\overline{\ensuremath{\nu}}+p$, or low-energy $\ensuremath{\beta}$ decay) it is still true that no $V\ifmmode\cdot\else\textperiodcentered\fi{}A$ interference may appear when scalars are measured, and only $V\ifmmode\cdot\else\textperiodcentered\fi{}A$ interference may contribute when pseudoscalars are measured, providing that the lepton spins and momenta are not directly observed. Thus experiments can be devised that involve no interference effects, or only interference effects. This theorem holds independently of the strangeness change, spin change, energy transfer, or of any particular assumptions about the form of the $V$ and $A$ currents. It proves most useful when it is difficult or tedious to calculate transition rates directly. Applications are discussed, including possible tests of the Feynman-Gell-Mann theory in nonunique forbidden $\ensuremath{\beta}$ decay, of the nature of the leptonic ${\ensuremath{\Lambda}}^{0}$ and ${K}^{0}$ decay interaction, and of the charge symmetry properties of weak interactions.