Effect of higher orbital angular momenta in the baryon spectrum

We have performed a Faddeev calculation of the baryon spectrum for the chiral constituent quark model including higher orbital angular momentum states. We have found that the effect of these states is important, although a description of the baryon spectrum of the same quality as the one given by including only the lowest-order configurations can be obtained. We have studied the effect of the pseudoscalar quark-quark interaction on the relative position of the positive-and negative-parity excitations of the nucleon as well as the effect of varying the strength of the color-magnetic interaction. 1 In a recent paper [1] we calculated the nonstrange baryon spectrum within a Faddeev approach for the chiral constituent quark model [2,3,4,5]. This model, besides a confining interaction and a perturbative one-gluon exchange, includes a pseudoscalar and a scalar boson exchange between quarks. In Ref. [1] only the lowest-order configurations (ℓ, λ, s, t) (ℓ is the orbital angular momentum of a pair, λ is the orbital angular momentum between the pair and the third particle, while s and t are the spin and isospin of the pair) were included., while for the ∆3/2 + state (the ∆) we included the single configuration (0,0,1,1). We have now extended our calculation to include all the configurations (ℓ, λ, s, t) with ℓ and λ up to 5. The objective of the present work is to evaluate the effects of the higher orbital angular momentum components in a model including gluon as well as Goldstone boson exchanges To study the convergence behavior with respect to the number of (ℓ, λ, s, t) configurations we give in Table I the results for the ∆, N(1535), N, and N(1440), corresponding to Fig. 4 of Ref. [1]. In this table we give the mass difference with respect to the nucleon ground state including 12 (ℓ, λ, s, t) configurations, i.e. with ℓ and λ up to 5, considered to be the converged result for the nucleon ground state and therefore our mass reference. As can be seen, the convergence with respect to the number of configurations is different for different states, so that, for example, the ∆ comes down by only 5 MeV while the N(1535), N, and N(1440) they all come down by approximately 100 MeV when one includes the higher orbital angular momentum configurations. It is also interesting to notice that while in the lowest-order calculation the N(1440) lies below …