Light S-wave pentaquarks on the light front

TL;DR

This work develops a CM-free light-front framework for light quark pentaquarks by building an explicit eigenbasis on a regular 4-simplex. The longitudinal and transverse degrees of freedom are treated with Jacobi coordinates, using an einbein trick to linearize confinement and enforcing Dirichlet boundary conditions that reflect parton momentum vanishing at simplex faces. A mapping to impenetrable fermions on a circle yields a complete Slater-determinant basis, which, together with a four-oscillator transverse basis, enables diagonalization of the light-front Hamiltonian; ultra-local color-spin and flavor-spin hyperfine interactions lift the degeneracy and yield spectra that are in fair agreement with nucleon excitations. The ground-state pentacstates produce an antiquark PDF peaking near $x\approx 0.2$ with a hard tail $\sim(1-x)^{15}$, illustrating a consistent momentum sharing among five constituents. Overall, the approach demonstrates a CM-free Basis Light-Front Quantization of multi-quark systems and provides concrete predictions for the light-quark pentaquark spectrum and PDFs.

Abstract

We construct an explicit basis set for pentaquark states on a regular 4-simplex, that diagonalizes the Hamiltonian for light pentaquarks with confinement on the light front (LF). The ensuing eigenstates are free of the center of mass motion and satisfy exact Dirichlet boundary conditions. Hyperfine interactions in the form of color-spin or flavor-spin are shown to lift the degeneracy of the 16 pentastates, with a spectrum that compares fairly with some of the empirical nucleon excited states. The quark PDF for the light pentastates is discussed.

Figures (1)

• Figure 1: The ground state of the Laplacian operator obtained by diagonalizing the operator using the basis defined in Eq. (\ref{['SLAT4']}). The variables $x_\gamma$ and $x_\delta$ are set to $x_\gamma=x_\delta=-0.2$.