Using Phenomenological Formulae,Deducing the Masses and Flavors of the Quarks, Baryons and Mesons from Two Elementary Quarks

A combined expansion in the number of QCD colors 1/N_c and SU(3) flavor breaking parameter epsilon has long been known to provide an excellent accounting for the mass spectrum of the lightest spin-1/2, 3/2 baryons when the quarks are taken to transform under the fundamental SU(N_c) representation, and in the final step N_c \to 3 and epsilon is set to its physical value ~0.3. Subsequent work shows that placing quarks in the two-index antisymmetric SU(N_c) representation leads ...

The standard procedure to determine (analytically) the values of the quark masses is to relate QCD two-point functions to experimental data in the framework of QCD sum rules. In the case of the light quark sector, the ideal Green function is the pseudoscalar correlator which involves the quark masses as an overall multiplicative factor. For the past thirty years this method has been affected by systematic uncertainties originating in the hadronic resonance sector, thus limiti...

We perform a preliminary study of the 1/2+ and 3/2+ ground-state baryons containing a heavy quark in the framework of the chiral SU(3) quark model. By using the calculus of variations, masses of Lambda_Q, Sigma_Q, Xi_Q, Omega_Q, Sigma_Q^*, Xi_Q^* and Omega_Q^*, where Q means c or b quark, are calculated. With taking reasonable model parameters, the numerical results of established heavy baryons are generally in agreement with the available experimental data, except that those...

We show that application of quantum unitary groups, in place of ordinary flavor SU(n_f), to such static aspects of hadron phenomenology as hadron masses and mass formulas is indeed fruitful. The so-called q-deformed mass formulas are given for octet baryons (1/2)^+ and decuplet baryons (3/2)^+, as well as for the case of vector mesons 1^- involving heavy flavors. For deformation parameter q, rigid fixation of values is used. New mass sum rules of remarkable accuracy are prese...

The use, for flavor symmetries, of the quantum (or q-) analogs of unitary groups SU(n_f) yields new, very accurate, baryon mass sum rules. We show, in the 3-flavor case, that such approach accounts for nonpolynomial SU(3)-breaking effects in the octet and decuplet baryon masses. A version of this approach with manifestly q-covariant mass operator is given. The obtained new version of the q-deformed mass relation is simpler than those derived before, but, for its empirical val...

We establish a connection between the quark model and the 1/N_c 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/N_c expansion is explained by the quark model and the mass formulas for both approaches are consistent.

I give a short historical and a critical review of the determinations of light quark masses from QCD at dawn of the next millennium. QCD spectral sum rules combined with ChPT give, to order $\alpha_s^3$, the world average for the running masses: $\bar{m}_s$(2 GeV)= $(118.9\pm 12.2)$ MeV, $\bar{m}_d(2~{GeV})=(6.3\pm 0.8)$ MeV, $\bar{m}_u(2~{GeV})=(3.5\pm 0.4)$ MeV and the corresponding values of the invariant masses given in Eq. 24. Lower and upper bounds derived from the posi...

We compute masses of positive parity spin-$1/2$ and $3/2$ baryons composed of $u$, $d$, $s$, $c$ and $b$ quarks in a quark-diaquark picture. The mathematical foundation for this analysis is implemented through a symmetry-preserving Schwinger-Dyson equations treatment of a vector-vector contact interaction, which preserves key features of quantum chromodynamics, such as confinement, chiral symmetry breaking and low energy Goldberger-Treiman relations. This study requires a com...

We discuss several highly accurate theoretical predictions for masses of baryons containing the b quark which have been recently confirmed by experimental data. Several predictions are given for additional properties of heavy baryons. We also discuss the two charged exotic resonances Z_b with quantum numbers of a (b bbar u ddbar) tetraquark, very recently reported by Belle in the channel [Upsilon(nS) \pi^+, n=1,2,3]. Among possible implications are deeply bound I=0 counterpar...

We have studied the three quark systems in an Effective Hamiltonian approach in QCD. With only two parameters: the string tension sigma and the strong coupling constant alpha_s we obtain a good description of the ground state light and heavy baryons. The prediction of masses of the doubly heavy baryons not discovered yet are also given. In particular, a mass of 3620 MeV for the lightest (ccu) baryon is found by employing the hyperspherical formalism to the three quark confini...