v 1 1 1 Fe b 20 03 Triangular and Y - shaped hadrons with static sources

The structure of hadrons consisting of three static color sources in fundamental (baryons) or adjoint (three-gluon glueballs) representations is studied. The static potentials of glueballs as well as gluon field distributions in glueballs and baryons are calculated in the framework of field correlator method. 1. The study of the gluon field structure in hadrons is important for the deep understanding of the strong interaction physics. We demonstrate below how to perform such studies in gauge invariant way using the field correlator method relyed directly on QCD. The static potential in baryon was considered in detail in [1] at this conference, and we will extensively refer to this talk in what follows. We start with the calculations of static potentials in three-gluon glueballs. This part of the talk presents the results from [2]. In the rest of the talk the gluon field distributions in hadrons are discussed on the base of papers [3], [4], [5]. In contrast to baryons, the gauge-invariant extended wave function of glueballs may have both Y-type and triangular structure. In the former case it may be written as G (f) Here g a (x, Y) = g a (x)Φ ab (x, Y) denotes the extended gluon operator, g a (x) is the valence gluon operator and Φ ab (x, Y) = (P exp ig x Y A µ dz µ) ab is the parallel transporter or Schwinger line in the adjoint representation. The coordinates x, y, z and Y in (1) apply to the valence gluons and string junction positions respectively, f abc and g abc denote adjoint antisymmetric and symmetric symbols. The wave function of the triangular glueball has the form G ∆ (x, y, z) = G β α (x)Φ γ β (x, y)G δ γ (y)Φ ε δ (y, z)G ρ ε (z)Φ α ρ (z, x), (3) where G β α (x) = g a (x)(t a) β α , t is the generator of SU(3), and Φ β α is the parallel transporter in fundamental representation. According to (1), (2), a Wilson loop of Y-type glueball has the same structure as in the case of baryon, see eq. (2) and Fig. 1 of [1]. The difference is that the adjoint transporters should be substituted for the fundamental ones and symbols f abc or g abc for ǫ αβγ .