Pseudoscalar Currents Research Articles

ISOSPIN-BREAKING VACUUM-TO-π0, η PSEUDOSCALAR MATRIX ELEMENTS AT NEXT-TO-LEADING ORDER IN THE CHIRAL EXPANSION

We employ chiral perturbation theory (ChPT) to evaluate the complete set of pseudoscalar matrix elements, <0|Pf|π0,η>, with Pf any of the flavor-diagonal pseudoscalar currents (f=u,d,s) to [Formula: see text], and to next-to-leading order in the chiral expansion. These matrix elements represent the basic input to a QCD sum rule analysis of isospin breaking in the πNN couplings using the three-point function method. We also discuss how one could use the results to construct a one-parameter family of interpolating fields for the π0, all of whose members have zero vacuum-to-η matrix element, and explain how this could in principle be used to provide nontrivial tests of the reliability of the assumptions underlying the use of three-point function method. It is shown that the isospin-breaking mixing parameters required for this construction receive significant corrections beyond leading order in the chiral expansion.

Singlet polarization functions atO(αs2)

We consider the three-loop singlet diagrams induced by axial-vector, scalar, and pseudoscalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Pad\'e approximations in order to arrive at results for the polarization functions valid for all ${q}^{2}.$ Results are presented for the imaginary parts which are directly related to physical quantities such as the production of top quarks or the decay of scalar or pseudoscalar Higgs bosons.

Analytic calculation of two-loop corrections to heavy quark pair production vertices induced by light quarks

Non-singlet θ(α x 2) corrections from light quarks are calculated analytically for the massive quark-antiquark pair production rates through the vector, axial-vector, scalar and pseudoscalar currents for all energies above the threshold. The results are presented in terms of the moments of the absorptive part of the vacuum polarization function of the light quarks, which allows for an immediate determination of O( α s 2) corrections coming from other types of light particles. The kinematic regime close to the threshold is examined, and a comparison to results based on non-relativistic considerations is carried out.

Heavy quark current correlators to [formula omitted]( αs2

In this paper the three-loop polarization functions Π( q 2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section σ( e + e − → Z → hadrons) and to the Higgs decay rates, respectively.

π Nσ term and quark spin content of the nucleon

We report results of our calculation on the $\pi N\sigma$ term and quark spin content of the nucleon on the quenched $16^3 \times 24$ lattice at $\beta = 6.0$. The disconnected insertions which involve contributions from the sea quarks are calculated with the stochastic $Z_2$ noise algorithm. As a physical test of the algorithm, we show that the forward matrix elements of the vector and pseudoscalar currents for the disconnected insertions are indeed consistent with the known results of zero. We tried the Wuppertal smeared source and found it to be more noisy than the point source. With unrenormalized $m_q=4.42(17)$MeV, we find the $\pi N\sigma$ term to be $39.2\pm 5.2$ MeV. The strange quark condensate in the nucleon is large, i.e. $\langle N|\bar{s}s|N\rangle = 1.16 \pm 0.54$. For the quark spin content, we find $\Delta u =0.78\pm 0.07$, $\Delta d =-0.42\pm 0.07$, and $\Delta s = -0.13\pm 0.06$. The flavor-singlet axial charge $g_A^1 = \Delta \Sigma =0.22\pm 0.09 $.

Two-loop gluon-condensate contributions to heavy-quark current correlators: exact results and approximations

The coefficient functions of the gluon condensate 〈 G 2〉, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z = q 2 4m 2 . In the limiting cases z → 0, z → 1, and z → − ∞, comparison are made previous results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A single moment, combined with only the leading threshold and asymptotic behaviour, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields 〈 α s πG 2〉 ≈ 0.021 GeV 4 .

Two-loop coefficient functions in the large mass expansions of correlators of two (pseudo) scalar and (pseudo) vector currents

Coefficient functions of the operator G 2 in the large mass expansions of correlators of two (pseudo) scalar and (pseudo) vector currents are calculated in the two-loop approximation. The obtained results are numerically sizeable and could be important for the phenomenological determination of the value of the corresponding condensate 〈 G 2〉.

Calculation of the kaon B parameter using strictly local sum rules

The kaon B-parameter is computed in the framework of strictly local QCD sum rules for a threepoint function involving pseudoscalar currents. As an application of these sum rules we derive a low energy formula for the B-parameter. We show that strictly local QCD sum rules yield more reliable results than other QCD sum rules, since they need less phenomenological information and do not suffer from stability problems. Our result for the B-parameter isB=0.74±0.17.

Instantons and the QCD sum rule for the pion

We try to extend the QCD sum rules for the two-point functions of the quark currents to the case of the pseudoscalar current of the «up» and «down» quarks. The essential ingredient is the coupling of this current to the instantons, whose effect is to make the sum rule more sensitive to the mass of the pion. A phenomenological approach to the problem yields an effective instanton Lagrangian which is consistent with the one required for reproducing quantitatively the ΔI=1/2 rule in the nonleptonic K-meson decay.

Two-loop effects in QCD sum rules for light mesons

We calculate two-loop corrections to the coefficient functions of the dim ≤ 4 contributions to the vacuum correlator of two flavour-diagonal vector, scalar, and pseudoscalar currents. We formulate the renormalization-group invariant criteria for the convergence of the perturbation theory series for the coefficient functions. We also study effects of the calculated corrections on the sum rules for the ϱ, ϕ, δ(980) and ε(1300) mesons.

Isospin violation in heavy quark pseudoscalar currents

It is shown that, to preserve the SU(3) L×SU(3) R current algebra, it is necessary to have strong isospin violation in heavy quark pseudoscalar densities. This result is obtained without invoking the strong pseudoscalar anomaly.

Leptonic decay constant fB of the B(bd-bar) meson and the b-quark mass.

We determine the value of the current b-quark mass using the existing detailed experimental information in moment and Borel-transformed sum rules for the vector b-quark current b\ifmmode\bar\else\textasciimacron\fi{}${\ensuremath{\gamma}}_{\ensuremath{\mu}}$b. The resulting value (${m}_{b}$=4.17\ifmmode\pm\else\textpm\fi{}0.02 GeV at ${p}^{2}$=-${m}_{b}^{2}$) is used for calculating the decay constant ${f}_{B}$ and the mass of the B meson via two sum rules: one constructed from the correlation function of two pseudoscalar currents and the other from the correlation function of a pseudoscalar and an axial-vector current. We find ${f}_{B}$=170\ifmmode\pm\else\textpm\fi{}20 MeV.

QCD Calculation of $$K^0 - \bar K^0 $$ mixing from three-point function sum rules

We calculate theB parameter for\(K^0 - \bar K^0 \) mixing in the framework of QCD sum rules for a three-point function involving pseudoscalar currents, and contrast our results with other calculations. We findB=0.5±0.1±0.2, where the first error reflects uncertainties in the various QCD parameters and the second one is an estimate of uncalculated three-loop radiative and higher order quark mass corrections.

A QCD sum rule calculation of the [formula omitted] mixing parameter B

We present a QCD sum rule calculation of the K 0 − K 0 mixing parameter B, employing pseudoscalar currents for the currents coupling to the K-meson in the three-point function related to B. Our calculation shows that there is a large cancellation between factorizable and non-factorizable terms of order 1/ N. The result for the parameter B is B = 0.84 ± 0.08. In addition we obtain an excellent sum rule for the K-meson parameters.

Radiative corrections to pseudoscalar meson decays

QED radiative corrections to the decay of a pseudoscalar meson into a lepton pair have been estimated. The results are applied to the decay of the neutral pion into electron and positron. Formulas are also given for a pseudoscalar Higgs-like particle decaying to a lepton or quark pair. The results are also of relevance for QCD sum rules for the pseudoscalar current, where conflicting calculations exist in the literature.

Pseudoscalar mesons and instantons

We discuss the QCD sum rules for the correlators of pseudoscalar currents with quantum numbers of π, K, η, η′ mesons. In the framework of the instanton model of the QCD vacuum suggested earlier by the author, we calculate SU(3) breaking effects such as K, η masses and ηη′ mixing, as well as the U(1) breaking effect, the η′ mass. We conclude that all these phenomena are very well reproduced by this model.

η c puzzle in quantum chromodynamics

The mass of the η c meson is calculated by means of QCD sum rules. If the spectrum of the 0 − states of charmonium contains a single prominent resonance, like the J ψ in the case of vector states, then the η c mass is 3.0 GeV, not 2.83. There is a possibility however that there are two mixed 0 − states with close masses. Then the X(2.83) could be one of them. The other one however has a much larger coupling to the pseudoscalar current of c quarks and is a “true” η c. The η c mass in the case of two mixed states is 3.0–3.2 GeV.

Asymmetry of Beta-Ray Angular Distribution in Polarized 12B and 12N and Second-Class Current

An explicit formula for beta-ray angular distribution in the decay of polarized nuclei is given by taking into account the radiative corrections, Coulomb corrections of the finite-size nucleus, weak magnetisim, induced pseudoscalar, second-class induced tensor, and contributions of the d-wave leptons. Generally speaking, the radiative corrections are almost the same for P0 (cosθ) and P1 (cosθ) terms. In particular, the logarithmic divergence disappears for the asymmetry factor in the case of the Gamow-Teller transitions. And the effect of the induced pseudoscalar current is extremely small. Experimental data on the beta decays of polarized 12B and 12N are carefully investigated, and it is shown that these data are in favor of the existence of the second-class induced tensor current. Contributions of the ∫(σ·r)r and ∫σr2 terms, which are evaluated with available nuclear models, are found to be negligible. The effect of the exchange currents is also discussed in connection with the elementary particle treatment of the nuclear beta decay.

Application of current-algebra techniques to soft-pion production by the weak neutral current:S,P,Tcase

We develop the cross-section formulas needed to correlate information on neutral currents obtained from deep-inelastic neutrino scattering, neutrino-proton elastic scattering, and neutral-current-induced soft-pion production, in the case of neutral currents with $S$, $P$, $T$ spatial structure. (The necessary $S$, $P$, $T$ current renormalization constants were estimated by us in a previous paper.) The pion-emission amplitude is obtained by current-algebra soft-pion techniques, with the effects of (3,3)-resonance excitation taken into account to leading nonvanishing order in the static approximation. We analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar $S$, $P$, $T$ neutral current, while simultaneously imposing existing bounds on neutrino-proton elastic scattering and fitting existing data on neutral-current-induced deep-inelastic scattering. If all $S$, $P$, $T$ renormalization constants are given their central quark-model values, the elastic-scattering and deep-inelastic restrictions constrain the pion-production cross section to be too low compared with experiment; if apparently reasonable deviations of the parameters from the quark-model values are permitted, satisfactory fits to all data are obtained with $S$, $T$, with $P$, $T$ or with $S$, $P$, $T$ mixtures. An isovector tensor or pseudoscalar neutral current is found to lead to a strong (3,3) peak in $\ensuremath{\pi}N$ invariant-mass plots, but an isovector scalar neutral current can be present without producing a visible (3,3) peak, even when ratios of the various $\ensuremath{\pi}N$ charge states produced by the neutral current are appreciably changed from the values which they have in the isoscalar-current case. Two other interesting qualitative features of $\mathrm{CP}$-conserving $S$, $P$, $T$ structures are the following: (1) constructive $T$ interference with $S$ (or $S$ and $P$) in $\ensuremath{\nu}+N\ensuremath{\rightarrow}\ensuremath{\nu}+N+\ensuremath{\pi}$ can accompany destructive interference in $\ensuremath{\nu}+p\ensuremath{\rightarrow}\ensuremath{\nu}+p$, and vice versa, and (ii) observation of unequal neutrino- and antineutrino-induced neutral-current cross sections would not be accompanied by neutral-current-induced parity-violating effects in the $\mathrm{pp}$, $\mathrm{ep}$, and $\ensuremath{\mu}p$ interactions.

Renormalization constants for scalar, pseudoscalar, and tensor currents

We calculate the renormalization constants describing nucleon and pion matrix elements of scalar, pseudoscalar, and tensor ($S, P, T$) current densities. For certain of the constants, expressions can be obtained using standard S${\mathrm{U}}_{3}$ and chiral S${\mathrm{U}}^{3}$\ensuremath{\bigotimes}S${\mathrm{U}}^{3}$ methods. To get the remaining constants, we employ the quark model with spherically symmetric quark wave functions to relate the $S$, $P$, $T$ renormalization constants to known parameters of the usual vector and axial-vector ($V,A$) currents. We also evaluate the renormalization constants using the MIT "bag" model quark wave functions. We summarize our results in tabular form, compare the results of the various calculational methods used, and attempt to estimate the accuracy of our predictions.