Pentaquarks on the light front, and their mixture with baryons

TL;DR

This work extends the light-front quark framework to multi-quark states by formulating pentaquark wave functions on the 4-simplex $A_4$ and enforcing permutation symmetry with $S_4$. It derives both variational Ritz and exact Laplacian solutions to obtain S- and P-shell pentaquark WFs, and classifies them using LF analogues of orbital-color-spin-flavor structures. The study then explores baryon-pentaquark mixing, computing 5-quark admixtures in the proton through overlaps with $p\sigma$, $N\pi$, and $\Delta\pi$ channels, predicting distributions of antiquarks and their spin/isospin content. By linking these admixtures to parton distributions, the paper connects hadronic spectroscopy to observable PDFs, including the antiquark flavor asymmetry and the high-$x$ behavior, and discusses implications for instanton-driven chiral dynamics at low resolution scales.

Abstract

In previous papers we developed the light front formulation for Hamiltonians and wave functions (WFs) for mesons and baryons, with both confinement and chiral symmetry breaking. For baryons limited to the lowest Fock component with three quarks, the longitudinal WF is valued in an equilateral triangle with momentum fractions $x_i,i=1,2,3$. The WF was developed both numerically and using a basis function that diagonalizes the Laplacian with Dirichlet boundary conditions. In this paper we extend this analysis to $n$ quark states, and specialize to pentaquarks ($n=5$). We determine their masses and WFs, and address the mixing between baryons and pentaquarks, the issue central to understanding the observed antiquark sea of baryons.

Figures (14)

• Figure 1: equilateral triangle formed by cube $x_1,x_2,x_3\in [0,1]^3$ cut by momentum normalization condition $x_1+x_2+x_3=1$
• Figure 2: Effective potential for equilateral triangular domain for $N=3$.
• Figure 3: The shape of the $\Psi 0^2$, at $\alpha=\beta=0$ at the $\gamma,\delta$ plane. Note that this plane contains two corners $a_4,a_5$, but not the opposite center of the face 123: thus it does not sit on an equilateral triangle.
• Figure 4: The antiquark PDF in pentaquarks versus the momentum fraction $x$ (arbitrary units). The upper and lower plots show the same distributions, in linear and logarithmic plots. The lower plot is used to magnify the larger $x$ region, with a fit to a form $\sim (1-x)^8$.
• Figure 5: Upper: The lowest Laplacian eigenfunction $\psi[1,1,1,1]$ at $\alpha=\beta=\gamma=0$ versus $\delta$ (solid line) compared to our simplest variational function (\ref{['eqn_ansatz_faces']}) (dotted line), and its improvement by the Ritz variational procedure (dashed line). For comparison all eigenfunctions are normalized to their value at the origin. Lower: The same $\psi[1,1,1,1]$ (blue) compared to the numerically exact wave function (red) obtained in PENTAX and normalized.