Mixing and Heavy Baryon Masses

We examine the ΞQ-Ξ ′ Q mixing and heavy baryon masses in the heavy quark effective theory with the 1/mQ corrections. In the conventional baryon assignment, we obtain the mixing angle cos θ = 0.87 ± 0.03 in virtue of the GellMann−Okubo mass relation. On the other hand, if we adopt the new baryon assignment given by Falk, the allowed region of the Σc mass is upper from 2372MeV. The heavy quark effective theory(HQET) is an efficient approach to investigating the properties of hadrons containing a single heavy quark Q[1,2]. One of the most important application will be to the semileptonic decay of hadrons with a heavy flavor. In particular, this effective theory leads to the model independent determination of the Kobayashi-Maskawa matrix[3] element |Vcb| by use of experimental data for the semileptonic decay B → Dlν̄l[4]. On the other hand, heavy hadron mass spectra have been studied in the HQET by taking account of 1/mQ corrections[5]. In the heavy quark symmetry limit, the total spin of the heavy hadron J and the spin of the light degrees of freedom sl (i.e., the angular momentum of the light degrees of freedom in the heavy quark rest frame) are separately conserved under the strong interactions, because the heavy quark spin sQ decouples from the hadron dynamics. The hadron containing a heavy quark is the simultaneous eigenstate of the energy, the total angular momentum-parity J and the spin-parity of the light degrees of freedom sl . Therefore, the heavy hadrons can be classified by s P l instead of the relative internal orbital angular momentum[6]. At infinite quark mass limit(i.e., ΛQCD/mQ → 0), the states with the same sl degenerate. By incorporating the effect of the 1/mQ correction, this degeneracy is resolved. In this case the mixing between two states with a same total spin-parity is unavoidable in general since they are no longer eigenstates of sl . For instance, ΞQ and Ξ ′ Q mix with each other. In this paper, we discuss the ΞQ-Ξ ′ Q mixing and heavy baryon mass spectra in the both cases of the conventional assignment and the new assignment given by Falk[7]. The HQET Lagrangian with 1/mQ corrections is L = h̄v(iv ·D)hv + 1 2mQ h̄v(iD) hv + ZQ 1 2mQ h̄vσ Gμνhv, (1) where v is the four velocity of the heavy quark h, ZQ is a renormalization factor and Gμν is the gluon field strength[8]. Neglecting the higher order corrections, we have a