Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

Plane-wave,coordinate-space,and moment techniques in the operator-product expansion: Equivalence,improved methods,and the heavy quark expansion

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.     

The ratios among condensates from e+e− (I=1) data

We calculate the ratios among condensates from the ρ channel (I=1) e⁺e⁻ data in a systematic way. We use quotients of SVZ sum rules for different moments of the correlation functions. The results turn out to be very accurate. A factor of 1.6 for the ratio of the four quark condensate over the gluon condensate compared with the standard value is predicted.     

Analysis of (1/2)~+ baryon states containing fourth-family quarks from QCD sum rules

When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks, the hadrons made up from these quarks can be long-lived enough. We analyze the (1/2)⁺ baryon states containing fourth-generation quarks and standard-model quarks, i.e. the charm or bottom quarks, in the QCD sum rules approach. Considering the perturbative and two gluon condensate contributions in the calculation, we give the numerical results of the masses and pole residues.     

Light 0- Meson Solution of Bethe-Salpeter Equation Involving the Vacuum Condensates in QCD

We dkcuss the Bethe-Salpeter equation involving the vacuum condensates in QCD in the backgrouud fields. The bound state equation for the light 0^- meson (π and K) is solved in the ladder approximation of single gluon exchange, where the gluon propagator is calculated in tree level of a gluon condensate and a quark condensate. The kernel is divided into two parts: perturbative and non-pert,urbative. The non-perturbative part is determined by the vacuum condensate. Pseudo-scalar meson spectrum and decay constants are in good agreement with data.     

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

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Analysis of (1/2)+ baryon states containing fourth-family quarks from QCD sum rules

When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks, the hadrons made up from these quarks can be long-lived enough. We analyze the (1/2)⁺ baryon states containing fourth-generation quarks and standard-model quarks, i.e. the charm or bottom quarks, in the QCD sum rules approach. Considering the perturbative and two gluon condensate contributions in the calculation, we give the numerical results of the masses and pole residues.     

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that the mixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded as an additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from some ansatz for the gluon propagator are compared with those determined from QCD sum rules.     

Gluon condensation and the bag model of hadrons

Migdal's scheme for gluon condensation is applied to a model where gluons are dynamically confined by coloured Higgs fields and are also subjected to ac-number colour field due to external “semiclassical” quarks. We show that, no matter how strong the external field becomes, stabilization of the gluonic ground state is guaranteed by the formation of an inhomogeneous gluon condensate. The contribution to the total energy from the condensate is computed semiclassically using a variational approximation. A physical interpretation of the results obtained is given in terms of a renormalization of the MIT bag model input parameters in particular the zero point energy coefficientZ and the bag constantB.

     

Solution of the Schwinger-Dyson Equation Involving the Gluon condensate Kernel

The form of the quantum chromodynamic Schwinger-Dyson (SD) equation modified by the nonperturbative kernel associated with the gluon condensate is obtained. It is shown that the eolution for the renormalisation group invariant quark condensate from the SD equation is in agreement with that obtained from the consistent equation for quark condensate when the leading behavior of the dynamical quark mass is concerned^[1]. It is also found that the gluon condensate kernel makes the critical coupling constant above which the chiral symmetry breaks smaller and increases the value of the quark condensate.     

Finding charm at RHIC

Dileptons produced by hard scatterings, such as heavy quark decays and the Drell-Yan mechanism, probe the gluon and sea quark distributions in hadrons. In nucleus-nucleus collisions, these processes are the thermal ‘back-ground’. To determine the magnitude and behavior of this background, we calculate the hard scattering contribution to next to leading order in perturbative QCD at RHIC. We compare these results to optimistic estimates of thermal dilepton production and find that initial charm production is dominant. However, experimental cuts can reduce the charm background, enhancing thermal information.     

Quark-diquark model description for double charm baryons

We report here the mass spectrum and magnetic moments of ccq(q ∈ u,d,s) systems in the potential model framework by assuming the inter-quark potential as the colour coulomb plus power form with power index ν varying between 0.1 to 2.0.Here the two charm quarks are considered for the diquark states.The conventional one gluon exchange interaction has been employed to get the hyperfine and the fine structure between different states.We have predicted many low-lying states whose experimental verification can exclusively support the quark-diquark structure of the baryons.     

Shifman-Vainshtein-Zakharov moments and quark-antiquark potentials

From the SVZ moments, for heavy quark-antiquark systems, we extract an “equivalent” non-relativistic potential. It increases as the fourth power of the distance and linearly with the quark mass. Numerical integration of the “equivalent” Schrödinger equation leads to much higher estimates of the gluon condensate parameter ø₁ than the original inverse power moment method or even the Borel transformed exponential version.     

Instanton liquid at finite temperature and chemical potential of quarks

Instanton liquid in heated and strongly interacting matter is studied using the variational principle. The dependence of the instanton liquid density (gluon condensate) on the temperature and the quark chemical potential is determined under the assumption that, at finite temperatures, the dominant contribution is given by an ensemble of calorons. The respective one-loop effective quark Lagrangian is used.     

Correction to Goldstein Equation from the Gluon Condensate Diagram

An exact Goldstein solution of the Bethe-Salpeter equation including the gluon condensate in the background field QCD is discussed.We find that the gluon condensate diagram makes quark and anti-quark more close to form a bound state.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

Effective dilaton lagrangian and gluon condensate in a nucleon medium

The gluon condensate as a function of temperature and baryon density in a nucleon medium is obtained from an effective dilaton Lagrangian. It is shown that, at a normal nuclear density of nucleons, n ₀ = 0.17 fm^?3, the gluon condensate decreases by about 10%.     

Trends in Polarized Lepton Nucleon Scattering

The thoery of scattering between polarized leptons and polarized nucleons is reviewed in a comprehensive and pedagogical way. The polarized structure functions are introduced and their interpretation in the framework of the QCD parton model is discussed, including the gluon contribution. Sum rules ( = relations between moments of the structure functions) are derived and critically considered. They are then contrasted to recent experimental results.     

The proton''s gluon distribution

The gluon distribution is dominated by the hard pomeron at small x and all Q², with no soft-pomeron contribution. This describes well not only the DGLAP evolution of the hard-pomeron part of F₂(x,Q²), but also charm photoproduction and electroproduction, and is consistent with what is known about the longitudinal structure function.