Helicity amplitudes of $N(1520)$ and $N(1535)$ including pentaquark components

TL;DR

The paper tackles the problem of describing the helicity transitions in $\gamma^* p \to N^*$ for the $N(1520)$ and $N(1535)$ resonances, which are not fully captured by pure three-quark models. It extends a constituent quark framework to include $L=0$ symmetric $q^4\bar{q}$ pentaquark components alongside the $L=1$ three-quark core, constructs the pentaquark basis via group theory, and computes the helicity amplitudes $A_{1/2}$, $A_{3/2}$, and $S_{1/2}$ through both $q^3$ and $q^4\bar{q}$ configurations using the $\gamma^* \to q\bar{q}$ mechanism, with fits to data in $0 \le Q^2 \le 4.5 \,{\rm GeV^2}$. The results show a significantly improved description of the amplitudes with pentaquark fractions $B_{3q}^2: B_{5q}^2 = 0.91:0.09$ for N(1520) and $0.75:0.25$ for N(1535), particularly enhancing the low-$Q^2$ behavior and the $S_{1/2}$ amplitude in N(1535). Overall, the study supports non-negligible pentaquark components in these resonances, consistent with soft-wall AdS/QCD trends, while highlighting remaining discrepancies that point to meson-cloud and higher-order effects to be explored in future work.

Abstract

We investigate the helicity amplitudes of the $N(1520)$ and $N(1535)$ resonances in the electromagnetic transition process $γ^*p\to N^*$, where the $N(1520)$ and $N(1535)$ are assumed to include both the $L=1$ three-quark and $L=0$ spatial symmetric $q^4\bar q$ pentaquark components. The helicity transition amplitudes $A_{1/2}$, $A_{3/2}$ (for spin 3/2 states) and $S_{1/2}$ are computed within the constituent quark model. The inclusion of the $q^4 \bar q$ pentaquark components via the $γ^*\to q\bar q$ diagram significantly improves the theoretical description of the helicity amplitudes for both $N(1520)$ and $N(1535)$, yielding a closer agreement with experimental data compared to the pure three-quark picture. The work reveals that the $N(1520)$ and $N(1535)$ resonances may contain a considerable pentaquark components.