Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture

Electroexcitation of nucleon resonances

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proven to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.

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The quantum N-body problem and the auxiliary field method

Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.

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The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles \textit{a priori}. This equivalence leads to a deeper understanding of both frameworks.

Some equivalences between the auxiliary field method and the envelope theory

A connection is establisehd between the results of a potential quark model with dynamical masses and the 1/Nc expansion mass formula used in the description of baryon resonances. It is shown that a remarkable compatibility exists between the two methods.

Baryonic mass formula in large N c QCD versus quark model

A good agreement between a flux tube-based quark model of light baryons (strange and nonstrange) and the 1/N{sub c} expansion mass formula has been found in previous studies In the present work a larger connection is established between the quark model and the 1/N{sub c} and 1/m{sub Q} expansion method by extending the previous procedure to baryons made of one heavy and two light quarks The compatibility between both approaches is shown to hold in this sector too

Charm and bottom baryon masses in the combined 1/N{sub c} and 1/m{sub Q} expansion versus the quark model

A previous work establishing a connection between a quark model, with relativistic kinematics and a Y-confinement plus one gluon exchange, and the 1/N{sub c} expansion mass formula is extended to strange baryons. Both methods predict values for the SU(3)-breaking mass terms which are in good agreement with each other. Strange and nonstrange baryons are shown to exhibit Regge trajectories with an equal slope, but with an intercept depending on the strangeness. Both approaches agree on the value of the slope and of the intercept, and on the existence of a single good quantum number labeling the baryons within a given Regge trajectory.

Mass formula for strange baryons in large N(c) QCD versus quark model

We establish a connection between the quark model and the 1/Nc expansion mass formulas used in the description of baryon resonances. We show that a remarkable compatibility exists between the two methods in the light and heavy baryon sectors. In particular, the band number used to classify baryons in the 1/Nc expansion is explained by the quark model and the mass formulas for both approaches are consistent.

Florica Stancu

Papers

Baryonic mass formula in large N c QCD versus quark model

Charm and bottom baryon masses in the combined 1/N{sub c} and 1/m{sub Q} expansion versus the quark model

Mass formula for strange baryons in large N(c) QCD versus quark model

Light and heavy baryon masses: the 1/N c expansion and the quark model