H.R. Rubinstein

QCD sum rules for heavy quark systems

Abstract In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2++. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the 1P1 level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-ηb splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p2 = −mq2: mc = 1.28 GeV and mb = 4.25 GeV.

L = 1 light quark mesons in QCD

Abstract Using the Borel transformed QCD sum rule formalism, the masses of L = 1 light quark mesons with isospin I = 1 and I = 0 are calculated. Non-perturbative effects from higher dimensional operators up to dimension d = 6 in the operator product expansion are taken into account.

Scaling and duality in electro- and photoproduction

Abstract Using new sum rules and a new scaling variable we show that scaling holds even for small q 2 and for physical photons. We also discuss local duality in electro production and show that to a good approximation it holds in all directions in the ν − q 2 plane. In particular, we are able to construct the high energy electroproduction structure function curve from photoproduction data, Thus, we present a unified, “scale invariant” picture of photon-nucleon total cross sections that adds to the challenge of determining the origin of scaling.

Hadron Couplings to Goldstone Bosons in {QCD}

Abstract We calculate coupling constants in QCD by extrapolating from the asymptotic freedom regime using QCD sum rules. The novel feature is that these amplitudes are dominated by the quark condensate when one leg is a pseudoscalar Goldstone boson. We find many couplings and in particular the remarkable formulas g π NN 2 /4π≌2 5 π 3 ⨍ π 2 /M N 2 and g ωρπ = (2⨍ ρ /m ρ )(e/2√2) .

Estimate of the gluon condensate from Monte Carlo calculations

Using existing Monte Carlo data we estimate the value of the gluon condensate φ = 〈0|(β(g)/g)Fμν2|0〈. Given the limitations of the method and the available data we find reasonable agreement in both sign and magnitude with the value needed in QCD sum rule calculations.

Masses and Couplings of Open Beauty States in {QCD}

Abstract Masses and couplings of open beauty states (strange and non-strange) with J pC - 0 ++ , 0 −+ , 1 −− , and 1++ are calculated using the QCD sum rule formalism. Non-perturbative effects due to quark and gluon condensate operators are shown to be important, confirming earlier calculations for equal quark mass systems.

QCD contribution to vacuum polarization: The pseudoscalar unequal mass case

Abstract We have computed to first order in α s the perturbative and non-perturbative contributions to the vacuum polarization from the pseudoscalar current in the unequal mass case.

Analysis of photo and electroproduction data against ωW

A detailed analysis is made of scaling and local duality of the two structure functions W1 and νW2 characterizing inelastic electron scattering, against the variable ωW = 2Mυ + MW2q2 + a2 For this purpose a compilation of world data spanning the resonance and deep inelastic region and including photoproduction has been used. It is shown that to the accuracy allowed by present experiments, ωW is a good variable for all ν and q2 values, including real photons.

Two-point functions for flavour changing currents in QCD

Abstract We complete the calculations of two-point functions in QCD by presenting the results for the flavour changing vector current, including perturbative and non-perturbative contributions (to first order in αs).

QCD contributions to vacuum polarization

Abstract We have computed to lowest non-trivial order the perturbative and non-perturbative contributions to the vacuum polarization from all currents up to and including spin 2++. These expressions are important, for example to evaluate QCD sum rules for heavy and light quark systems as shown by Shifman, Vainshtein and Zakharov. Most of the known ones are verified, one slightly changed, and many new ones are displayed.