arXiv subjects
Publications and source records attributed to Fl. Stancu.
The mass splittings of the baryons belonging to the $[{\bf 70},1^-]$-plet are derived by using a simple group theoretical approach to the matrix elements of the mass formula. The basic conclusion is that the first order correction to the baryon masses is of order $1/N_c$ instead of order $N^0_c$, as previously found. The conceptual difference between the ground state and the excited states is therefore removed.
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.
The masses of positive $[{\bf 70},0^+]$ and $[{\bf 70},2^+]$ nonstrange and strange baryons are calculated in the $1/N_c$ expansion. The approach is based on the separation of a system of $N_c$ quarks into an excited core and an excited quark. The previous work for two flavor baryons is now extended to include strange baryons, to first order in SU(3)-flavor breaking. We show that the extension to $N_f = 3$ maintains the regularities previously observed in the behaviour of the linear term in $N_c$, of the spin-spin and of the spin-orbit terms. In particular the contribution of the spin-dependent terms decrease with the excitation energy, the dominant term remaining the spin-spin term.
Previous work is extended from SU(2) to SU(3) and we present results for the mass spectrum of the $[{\bf 70},\ell^+]$ ($\ell=0,2$) nonstrange and strange baryons in the $1/N_c$ expansion. We show that the dominant term is the spin-spin interaction and its contribution vanishes at large excitations.
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.
Using the $1/N_c$ expansion of QCD we analyze 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.
The dynamics of two heavy quarks inside the same hadron is probed against the double charm baryon results of SELEX. This can be seen as a part of the mechanism to bind tetraquarks with two heavy quarks and two light antiquarks. In the framework of potential models, it is possible to test the role of different effects: relativistic corrections, confinement, hyperfine forces, etc. It is conjectured that an additional interaction rescaled from the nucleon--nucleon system and acting between light quarks only, can help in bringing extra, possibly required, binding in tetraquarks.
The masses of the positive parity $[{\bf 70},0^+]$ and $[{\bf 70},2^+]$ non-strange baryons are calculated in large $N_c$ QCD by considering the most dominant operators in an $1/N_c$ expansion. The approach is based on the introduction of an excited core, obtained after the last particle (an excited quark) has been removed. Configuration mixing is neglected, for simplicity. Although being a sub-leading $1/N_c$ order, we find that the spin-spin interaction plays a dominant role in describing the data. The role of $N_c^ 0$ operators is also pointed out. We show how the contribution of the linear term in $N_c$, of the spin-spin and spin-orbit terms vary with the excitation energy.
We review results for the mass spectrum of orbitally excited baryons obtained in the $1/N_c$ expansion. We show the dependence of various contributions to the mass operator as a function of the excitation energy.
Light and heavy pentaquarks are described within a constituent quark model based on a spin-flavor hyperfine interaction. In this model the lowest state acquires positive parity. The masses of the light antidecuplet members are calculated dynamically using a variational method. It is shown that the octet and antidecuplet states with the same quantum numbers mix ideally due to SU(3)$_F$ breaking. Masses of the charmed antisextet pentaquarks are predicted within the same model.
Some recent developments in the study of light and heavy pentaquarks are reviewed, mainly within constituent quark models. Emphasis is made on results obtained in the flavor-spin model where a nearly ideal octet-antidecuplet mixing is obtained. The charmed antisextet is reviewed in the context of an SU(4) classification.
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.
Dynamical calculations are performed for all members of the flavor antidecuplet to which the pentaquark $Θ^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavor-spin structure. From symmetry considerations the lowest state acquires a positive parity. By fitting the mass of $Θ^+$ of minimal content $uudd\bar{s}$, the mass of $Ξ^{--}$, of minimal content $ddss \bar{u}$, is predicted to be approximately 1960 MeV. It is shown that the octet and antidecuplet states with the same quantum numbers mix ideally due to SU(3)$_F$ breaking.
We use the $1/N_c$ expansion of QCD to analyze 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.}
Dynamical calculations are performed for all isomultiplets of the flavour antidecuplet to which the newly discovered pentaquark $Θ^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavour-spin structure. In this model the lowest pentaquarks have positive parity. Each antidecuplet member is described by a variational solution with the Pauli principle properly taken into account. By fitting the mass of $Θ^+$ of minimal content $uudd\bar{s}$, the mass of $Ξ^{--}$, of minimal content $ddss \bar{u}$, is predicted at approximately 1960 MeV. The influence of the octet-antidecuplet mixing on the masses of the $Y = 1$ and 0 pentaquarks is considered within the same model and the role of the kinetic energy plus the hyperfine interaction in this mixing is pointed out.
The pentaquarks are exotic baryons formed of four quarks and an antiquarks. Their existence has been discussed in the literature over the last 30 years or more, first in connection with kaon nucleon scattering data. The subject has been revived by the end of 2002 when experimental evidence of a narrow baryon of strangeness $S$ = + 1, and mass $M \simeq$ 1530 MeV has been found. This is interpreted as the lightest member of an SU(3)-flavor antidecuplet. Here we shall mainly review the predictions of pentaquark properties as e.g. mass, spin and parity, within constituent quark models. Both light and heavy pentaquarks will be presented.
We discuss the mass splittings of the pentaquark $10_F$-, and ${\bar {10}}_F$-plet due to the quark mass differences, as well as %We discuss the $10_F$-plet's median mass relative to that of the ${\bar {10}}_F$% -plet of pentaquarks for both the flavour-spin and the colour-spin hyperfine interactions, and for both parities of the pentaquark ground states. We show that the colour-spin interaction leads to degenerate $10_F$- and ${\bar {10}}_F$-plets when the parity is even, and a median mass splitting of 75 MeV for odd parity. The flavour-spin interaction leads to $10_{F}-{\bar {10}}_F$ median mass splittings of 200 MeV and 40 MeV, for even and odd parities, respectively. We display mass relations between $10_F$- and ${\bar {10}}_F$-plets and analyze the presently known baryon resonances in this light.
We show that in realistic constituent quark models based on a two-body confinement interaction color states appear in the middle of the experimentally known spectrum. To avoid this situation we implement a three-body confinement interaction, introduced on an algebraic basis, into a semirelativistic version of the Goldstone-boson-exchange constituent quark model and by solving the Faddeev equations we show that this interaction can increase the gap between singlet and colour states, such as the latter can be ignored and the known baryons can be described as $q^3$ systems. We analyze the effect of a $Δ$- and a Y-shape three-body interaction.