201 research outputs found

### Group theoretical study of nonstrange and strange mixed symmetric baryon states $[N_c-1,1]$ in the $1/N_c$ 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.

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

### Baryon resonances in large $N_c$ QCD

The baryon spectra are discussed in the context of the $1/N_c$ expansion
approach, with emphasis on mixed symmetric states. The contributions of the
spin dependent terms as a function of the excitation energy are shown
explicitly. At large energies these contributions are expected to vanish.Comment: 6 pages, based on a talk given by Fl. Stancu at the Miniworkshop
"Progress in Quark Models" Bled, Slovenia, July 10-17, 2006, to be published
in Bled Workshops in Physics, vol. 7 no.

### Highly Excited Baryons in Large $N_c$ QCD

We use the $1/N_c$ expansion of QCD to analyse the spectrum of positive
parity resonances with strangeness $S = 0, -1, -2$ and -3 in the 2--3 GeV mass
region, supposed to belong to the $[\textbf{56},4^+]$ multiplet. The mass
operator is similar to that of $[\textbf{56},2^+]$, previously studied in the
literature. The analysis of the latter is revisited. In the $[\textbf{56},4^+]$
multiplet we find that the spin-spin term brings the dominant contribution and
that the spin-orbit term is entirely negligible in the hyperfine interaction,
in agreement with constituent quark model results. More data are strongly
desirable, especially in the strange sector in order to fully exploit the power
of this approach. We discuss possibilities of extending the calculations to
other excited baryons belonging to the N=2 or the N=4 band.Comment: 10 pages, Prepared for the Workshop "Three Days of Hadronics
Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock, December 16-18, 2004,
Spa, Belgium, to be published in AIP Proceedings. One reference adde

### Excited $[{\bf 70},\ell^+]$ baryon resonances in large $N_c$ QCD

We summarize results obtained in the $1/N_c$ expansion method for the masses
of baryon resonances belonging to the $[{\bf 70},\ell^+]$ multiplet. They
represent an extension of our previous studies from two to three flavors. A
better approach to mixed symmetric states of any angular momentum and parity is
also outlined.Comment: 4 pages, 1 figure, uses espcrc2.sty (included), based on a talk given
by N. Matagne at the 13th International QCD Conference, QCD06, Montpellier,
France, 3-7th July 200

### Negative parity baryons in the $1/N_c$ expansion: the quark excitation versus the meson-nucleon resonance picture

In order to better understand the fundamental issue regarding the
compatibility between the quark-shell picture and that of resonances in
meson-nucleon scattering in large $N_c$ QCD we extend the work of Cohen and
Lebed on mixed symmetric $\ell$ = 1 baryons to analyze excited states with
$\ell$ = 3. We give an explicit proof on the degeneracy of mass eigenvalues of
a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$
\emph{i. e.} neglecting $1/N_c$ corrections in the quark-shell picture in the
large $N_c$ limit. We obtain three degenerate multiplets formed of $\ell = 3$
states, as in the case of $\ell$ = 1 baryons. The compatibility between this
picture and that of resonances in meson-nucleon scattering is discussed in the
light of the present results.Comment: 18 pages, 4 tables. Published version. Note that Eqs. A1, A3 and A4
contain SO(3) Clebsch-Gordan coefficients, not Wigner 3j coefficient

### Matrix Elements of SU(6) Generators for Baryons at Arbitrary $N_c$

We present explicit formulas for the matrix elements of the SU(6) generators
for totally symmetric spin-flavor states, relevant for baryon spectroscopy in
large $N_c$ QCD. We rely on the interplay between two different methods to
calculate these matrix elements. As an outcome, general analytic formulas of
the corresponding SU(6) isoscalar factors are derived for arbitrary $N_c$.
These results can be used to study excited states of nonstrange and strange
baryons.Comment: 20 pages, 1 table, RevTeX4, version accepted for publication in Phys.
Rev.

### Updated $1/N_c$ expansion analysis of $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell^+}]$ baryon multiplets

The mass spectra of the $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell+}]$ multiplets,
both belonging to the $N$ = 2 band, is reviewed in the $1/N_c$ expansion
method. Previous studies, separately made for each multiplet, are presently
updated to the 2014 Particle Data Group. The mass formula including corrections
up to $\mathcal{O}(1/N_c)$ and first order in SU(3) flavor symmetry breaking,
has the same independent operator basis in both cases. A special emphasis is
made on the role of the SU(3) symmetry breaking operators $B_i$ $(i = 1,2,3)$.
This can allow for multiplet assignment of $\Lambda$ and $\Sigma$ hyperons,
which generally is quite difficult to make. Tentative assignments of hyperons
with two- and one-star resonances are made to the $[{\bf 70, \ell+}]$
multiplet. Another important aim is to find out whether or not a common value
of the coefficient $c_1$ of the dominant operator in the mass formula, can well
fit the present data in both multiplets. A negative answer, which is here the
case, implies distinct Regge trajectories for symmetric and mixed symmetric
states.Comment: 25 pages, to appear in Phys.Rev.

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