Mass spectrum of heavy hybrid mesons in the QCD string model

نویسنده

  • D. S. Kuzmenko
چکیده

Using adiabatic hybrid meson potentials calculated in the QCD string model, the mass spectrum of heavy hybrid mesons is calculated in Born-Oppenheimer approximation within the accuracy of 100 MeV. INTRODUCTION A phenomenon of valence glue is very interesting from theoretical point of view, since it is directly related to the phenomenon of confinement. It is well known that states consisting of quark, antiquark, and valence gluon are present in QCD spectrum. In particular, the adiabatic spectrum of valence gluon excitations in the presence of static quark and antiquark was calculated with high accuracy in lattice QCD [1]. However, there is no established conception of valence gluon up to now. Several kinds of models with different treatments of excited glue exist, and precise lattice results [1] have to be used to distinguish the correct one. A QCD string approach, or QCD string model considered below treats hybrid meson as a system of point valence gluon joined by straight strings of confining field to quark and antiquark. It is based on the background field method and uses the Fock-FeynmanSchwinger proper time – path integral formalism [2] to derive the string Hamiltonian of hybrid meson [3]. In the recent paper [4] hybrid adiabatic potentials were calculated in the QCD string model and were shown to match well lattice data [1]. Since preliminary results have already been reported at this Conference held in Protvino two years ago [5], I shall only present final results and make estimations of an accuracy of the variational procedure been used. Relying on adiabatic potentials, I shall then calculate masses of heavy hybrid mesons in Born-Oppenheimer approximation. STRING HAMILTONIAN OF HYBRID MESON When the calculations of the spectrum of heavy hybrid mesons are concerned, one is interested first of all in dynamics of valence glue at small and intermediate distances between quark and antiquark. It is shown in the QCD string model, see [4] and refs. therein, that in this region the inertia J of the strings, joining the valence gluon with quark and antiquark, is much smaller than the “constituent mass” of valence gluon μ , appearing as einbein field in Fock-Feynman-Schwinger formalism. String Hamiltonian of valence gluon takes the form [4] H = μ 2 + p2 2μ +V conf +V OGE (1) where first two terms describe the kinetic energy of valence gluon and contain the einbein μ which has to be eliminated through the stationary point condition, and last two terms are confining and one-gluon-exchange potentials, V conf = σr1 +σr2, V OGE = − 3αs 2r1 − 3αs 2r2 + αs 6R , (2) where r1 and r2 are distances from quark and antiquark to valence gluon, R is the quarkantiquark separation, and σ ≈ 0.18 GeV2 is the string tension. V conf emerges from the area law for Wilson loop, while V OGE represents the color-Coulomb perturbative OGE interaction. String inertia is taken into account in the order J/μ , Hstring = − σ 6μ2 (

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تاریخ انتشار 2003