Negative parity baryons in the 1/Nc1/N_c expansion: the three towers of states revisited

We discuss the compatibility between the quark-shell picture and the meson-nucleon scattering picture in large $N_c$ QCD for mixed symmetric $\ell$ = 1 states previously analyzed by using a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$ defined in the standard ground state symmetric core + excited quark procedure. Here we introduce a Hamiltonian of order $\mathcal{O}(N^0_c)$ defined in a new approach where the separation of the system into two parts is not required. Three degenerate sets of states (towers) with the same quantum numbers as in the scattering picture and in the standard procedure are obtained. Thus the 0 is equally achieved. The eigenvalues of the presently chosen Hamiltonian also have simple analytic expressions, depending linearly on the three dynamical coefficients entering the Hamiltonian. This reinforces the validity of the new approach which had already 0 described excited negative parity baryons in a large energy range.Comment: 13 page

SU(6) [70,1−][{\bf 70},1^-] baryon multiplet in the 1/Nc1/N_c expansion

The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest $[{\bf 70},1^-]$ multiplet are calculated in the $1/N_c$ expansion to order $1/N_c$ with a new method which allows to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.Comment: 26 pages, 11 tables, to be published in PR

Group theoretical study of nonstrange and strange mixed symmetric baryon states [Nc−1,1][N_c-1,1] in the 1/Nc1/N_c expansion

Using group theory arguments we extend and complete our previous work by deriving all SU(6) exact wave functions associated to the spectrum of mixed symmetric baryon states $[N_c-1,1]$ in the $1/N_c$ expansion. The extension to SU(6) enables us to study the mass spectra of both strange and nonstrange baryons, while previous work was restricted to nonstrange baryons described by SU(4). The wave functions are specially written in a form to allow a comparison with the approximate, customarily used wave functions, where the system is separated into a ground state core and an excited quark. We show that the matrix elements of the flavor operator calculated with the exact wave functions acquire the same asymptotic form at large $N_c$, irrespective of the spin-flavor multiplet contained in $[N_c-1,1]$, while with the approximate wave function one cannot obtain a similar behaviour. The isoscalar factors of the permutation group of $N_c$ particles derived here can be used in any problem where a given fermion system is described by the partition $[N_c-1,1]$, and one fermion has to be separated from the rest.Comment: 19 pages, 7 tables, comments added in the introduction and in the section 3, to be published in Phys. Rev.

Mass formula for strange baryons in large NcN_c QCD versus 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 $1/N_c$ 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.Comment: 2 figure

Probabilities in nonorthogonal basis: Four--quark systems

Four-quark states may exist as colorless meson-meson molecules or compact systems with two-body colored components. We derive an analytical procedure to expand an arbitrary four--quark wave function in terms of nonorthogonal color singlet--singlet vectors. Using this expansion we develop the necessary formalism to evaluate the probability of physical components with an arbitrary four-quark wave function. Its application to characterize bound and unbound four--quark states as meson-meson, molecular or compact systems is discussedComment: Accepted for publication in PR

Anti-charmed pentaquark from B decays

We explore the possibility of observing the anti-charmed pentaquark state from the $\Theta_c \bar{n} \pi^+$ decay of $B$ meson produced at $B$-factory experiments. We first show that the observed branching ratio of the $B^+$ to $\Lambda^-_c p \pi^+$, as well as its open histograms, can be remarkably well explained by assuming that the decay proceeds first through the $\pi^+ \bar{D}^0$ (or $\bar{D}^{*0}$) decay, whose branching ratios are known, and then through the subsequent decay of the virtual $\bar{D}^0$ or $\bar{D}^{*0}$ mesons to $\Lambda_c^- p$, whose strength are calculated using previously fit hadronic parameters. We then note that the $\Theta_c$ can be similarly produced when the virtual $\bar{D}^0$ or $\bar{D}^{*0}$ decay into an anti-nucleon and a $\Theta_c$. Combining the present theoretical estimates for the ratio $g_{D N \Lambda_c} / g_{D N \Theta_c} \sim 13$ and $g_{D^* N \Theta_c} \sim {1/3} g_{D N \Theta_c}$, we find that the anti-charmed pentaquark $\Theta_c$, which was predicted to be bound by several model calculations, can be produced via $B^+ \to \Theta_c \bar{n} \pi^+$, and be observed from the $B$-factory experiments through the weak decay of $\Theta_c \to p K^+ \pi^- \pi^-$.Comment: 4 pages, 4 figures, Revised version to be published in Physical Review Letter

k-String tensions and the 1/N expansion

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.Comment: RevTeX4, 21 pages. Typos corrected, references added, some discussions expanded; conclusions unchanged. Version to appear on PR