1/Nc expansion and the spin-flavor structure of the quark interaction in the constituent quark model

Abstract

We study the hierarchy of the coefficients in the 1/Nc expansion for the negative parity L=1 excited baryons from the perspective of the constituent quark model. This is related to the problem of determining the spin-flavor structure of the quark interaction. The most general two-body scalar interaction between quarks contains the spin-flavor structures $t_1^a{t}_2^a,{\vec{s}}_1\cdot {\vec{s}}_2$ and ${\vec{s}}_1\cdot {\vec{s}}_2{t}_1^a{t}_2^a$. We show that in the limit of a zero range interaction all these structures are matched onto the same hadronic mass operator $S_c^2$, which gives a possible explanation for the dominance of this operator in the 1/Nc expansion for the L=1 states and implies that in this limit it is impossible to distinguish between these different spin-flavor structures. Modeling a finite range interaction through the exchange of a vector and pseudoscalar meson, we propose a test for the spin-flavor dependence of the quark forces. For the scalar part of the quark interaction we find that both pion exchange and gluon exchange are compatible with data.

arXiv comment20 pages, 4 figures

References in corpus (23)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics
• Glueball Spectrum and Matrix Elements on Anisotropic Lattices
• The Physics of Glueballs
• Spin-Flavor Structure of Large N Baryons
• Baryons from Quarks in the $1/N$ Expansion
• On Spin Independence in Large $N_c$ Baryons
• Masses of the 70- Baryons in Large Nc QCD
• Operator Analysis of L=1 Baryon Masses in Large N_c QCD
• Large N_c Limit of Spin-Flavor Breaking in Excited Baryon Levels
• Negative Parity 70-plet Baryon Masses in the 1/Nc Expansion
• Analysis of the [56,2^+] Baryon Masses in the 1/Nc Expansion
• Lattice calculation of $1^{-+}$ hybrid mesons with improved Kogut-Susskind fermions
• The $[56,4^{+}]$ baryons in the $1/N_c$ expansion
• The Gluon Propagator
• S_3 and the L=1 Baryons in the Quark Model and the Chiral Quark Model
• Baryonic mass formula in large $N_c$ QCD versus quark model
• Decays of Non-strange Negative Parity Baryons in the 1/Nc Expansion
• Analysis of Negative Parity Baryon Photoproduction Amplitudes in the $1/N_c$ Expansion
• The permutation group S_N and large Nc excited baryons
• Mass formula for strange baryons in large $N_c$ QCD versus quark model
• Quark Forces from Hadron Spectroscopy
• The Isgur-Karl model revisited

Cited by in corpus (6)

• Baryon resonances in large $N_c$ QCD
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Operator analysis of effective spin-flavor interactions for L=1 excited baryons
• Towers of positive parity excited baryons and their mixing in the large $N_c$ limit
• Testing for three-body quark forces in L=1 excited baryons
• Exploration of hyperfine interaction between constituent quarks via eta productions