The strangeness form factors of the proton within nonrelativistic constituent quark model revisited

TL;DR

This paper revisits the nonrelativistic constituent quark model to analyze the proton's strangeness form factors, correcting previous assumptions and identifying the most plausible quark configuration that aligns with experimental data.

Contribution

It corrects prior claims about quark configurations and demonstrates that a symmetric uuds subsystem with a P-state ar{s} can explain empirical form factors, also highlighting the importance of center-of-mass motion removal.

Findings

The lowest-lying uudsar{s} configuration with symmetric spatial and flavor-spin symmetry fits data.

Removing center-of-mass motion significantly enhances transition current contributions.

A tiny probability (0.025%) for the uudsar{s} component can reasonably describe existing form factor data.

Abstract

We reexamine, within the nonrelativistic constituent quark model (NRCQM), a recent claim that the current data on the strangeness form factors indicates that the uuds\bar{s} component in the proton is such that the uuds subsystem has the mixed spatial symmetry [31]_X and flavor spin symmetry [4]_{FS}[22]_F[22]_S, with \bar{s} in S state (configuration I). We find this claim to be invalid if corrected expressions for the contributions of the transition current to G_A^s and G_E^s are used. We show that, instead, it is the lowest-lying uuds\bar{s} configuration with uuds subsystem of completely symmetric spatial symmetry [4]_X and flavor spin symmetry [4]_{FS}[22]_F[22]_S, with \bar{s} in P state (configuration II), which could account for the empirical signs of all form factors G_E^s, G_M^s, and G_A^s. Further, we find that removing the center-of-mass motion of the clusters will considerably enhance the contributions of the transition current. We also demonstrate that it is possible to give a reasonable description of the existing form factors data with a tiny probability P_{s\bar{s}}=0.025% for the uuds\bar{s} component. We further see that with a small admixture of configuration I, the agreement of our prediction with data for G_A^s at low-q^2 region can be markedly improved. We find that without removing CM motion, P_{s\bar{s}} would be overestimated by about a factor of four in the case when transition current dominates. We also explore the consequence of a recent estimate reached from analyzing existing data on \bar{d} -\bar{u}, s +\bar{s}, and \bar{u} + \bar{d} - s -\bar{s}, that P_{s\bar{s}} lies between 2.4-2.9%. It would lead to a large size for the five-quark system and a small bump in both G_E^s+\eta G_M^s and G_E^s in the region of q^2<=0.1 GeV^2 within the considered model.