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Abstract
A new approach to study the mass spectrum of double heavy baryons ( QQ ′ q ) containing strange and charmed quarks is proposed. It is based on the separation of variables in the Schrodinger equation in the prolate spheroidal coordinates. Two nonrelativistic potential models are considered. In the first model, the interaction potential of the quarks is the sum of the Coulomb and non-spherically symmetrical linear confinement potential. In the second model it is assumed that the quark confinement provided by a spherically symmetric harmonic oscillator potential. In both models the mass spectrum is calculated, and a comparison with previous results from other models is performed.
Highlights
It is related to the fact that the masses of heavy quarks mQ define a new energy scale exceeding the the strong interaction scale ΛQCD: mQ mq, R ΛQCD 1, ΛQCD mQ
R is the distance between two heavy quarks, mq is the mass of light quark
In this approximation the wave function is split into heavy- and light-quark degree of freedom: Ψ(R, r) = anφn(R)ψn(R, r), n where R is the distance between two heavy quark and r is the distance between the light quark and center of mass of diquark
Summary
The study the properties of baryons containing two heavy quarks is of considerable interest for the solution the confinement problem in QCD. It is related to the fact that the masses of heavy quarks mQ define a new energy scale exceeding the the strong interaction scale ΛQCD: mQ mq , R ΛQCD 1 , ΛQCD mQ. R is the distance between two heavy quarks, mq is the mass of light quark. In theory, there is a small parameter mq/mQ, which can be used for the application of the perturbative approach. The baryons containing two heavy quarks are becoming the subject of extensive theoretical study in recent years. In 2002 the Selex Collaboration observed the baryon Ξ+cc(ccd) in the decay [1]. The mass of the state was measured to be: MΞ+cc = 3518.9 ± 0.9MeV
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