Baryon properties in the relativistic quark model
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aryon Properties in the Relativistic Quark Model1 D. Eberta, R. N. Faustovb, and V. O. Galkinb, * aInstitut
für Physik, Humboldt–Universität zu Berlin, Newtonstrasse 15, Berlin, D-12489 Germany b Institute of Informatics in Education, FRC CSC RAS, Moscow, 119333 Russia *e-mail: [email protected]
Abstract⎯Properties of heavy and strange baryons are investigated in the framework of the relativistic quarkdiquark picture. It is based on the relativistic quark model of hadrons, which was previously successfully applied for the calculation of meson properties. It is assumed that two quarks in a baryon form a diquark and baryon is considered as the bound quark-diquark system. The relativistic effects and diquark internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of heavy and strange baryons. On this basis the Regge trajectories are constructed. The rates of semileptonic decays of heavy baryons are calculated. The obtained results agree well with available experimental data. DOI: 10.1134/S1063779617050148
The convincing evidence of the existence of diquark correlations in hadrons has been collected. Recently several charged charmonium- and bottomonium-like states were discovered. They should be inevitably multiquark, at least four quark states. One of the most successful pictures of such tetraquark states is the diquarkantidiquark model [1]. In the light meson sector it has been argued for a long time that mesons forming the inverted lightest scalar nonet can be well described as tetraquarks treated as diquark-antidiquark bound states [2]. In the baryon sector it is well known that the number of observed excited states both in the light and heavy sectors is considerably lower than the number of excited states predicted in the three-quark picture [3]. The introduction of diquarks significantly reduces this number since in such a picture some of degrees of freedom are frozen and thus the number of possible excitations is substantially smaller. Here we study spectroscopy and weak decays of heavy and strange baryons in the relativistic quarkdiquark picture in the framework of the quasipotential approach. The interaction of two quarks in a diquark and the quark-diquark interaction in a baryon are described by the diquark wave function Ψ d of the bound quark-quark state and by the baryon wave function Ψ B of the bound quark-diquark state respectively, which satisfy the relativistic quasipotential equation of the Schrödinger type [4]
⎛ b 2(M ) p 2 ⎞ − ⎜ ⎟ Ψ d ,B (p) 2μ R ⎠ ⎝ 2μ R d 3q V (p, q; M )Ψ d ,B (q), = 3 (2π)
where the relativistic reduced mass and the centerof-mass system relative momentum squared on mass shell are
M − (m1 − m2 ) , 3 4M 2 2 2 2 [M − (m1 + m2 ) ][M − (m1 − m2 ) ] b 2(M ) = , 2 4M μR =
4
2
2 2
and M is the bound state mass (diquark or baryon), m1,2 are the masses of quarks (q1 and q 2 ) which form the diquark or of the diquark (d ) and quark (q ) which form the baryon (B ), and p is their relative momentum. The kernel V (
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