[Paper Review] Investigation of magnetic moment of $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquark states

U. Ozdem|arXiv (Cornell University)|Aug 16, 2022

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This study calculates the magnetic moments of the hidden-charmed pentaquark states $P_{cs}(4338)$ and $P_{cs}(4459)$ using QCD light-cone sum rules, predicting $\mu_{P_{cs}} = 0.34 \pm 0.12~\mu_N$ for $P_{cs}(4338)$ and $\mu_{P_{cs}} = -1.67 \pm 0.58~\mu_N$ for $P_{cs}(4459)$, with isospin-1 partners yielding $\mu = 0.63 \pm 0.21~\mu_N$ and $\mu = -3.33 \pm 1.04~\mu_N$, respectively, providing insight into their substructure and electromagnetic properties.

ABSTRACT

In this study, we discuss the magnetic moment of $P_{cs}(4338)$ and $P_{cs}(4459)$ hidden-charmed pentaquarks, which are closely related to their substructures. The magnetic moments of these states are calculated with the help of the QCD light-cone sum rules method with quantum numbers $I(J^P) = 0(1/2^-)$ and $I(J^P) = 0(3/2^-)$ for $P_{cs}(4338)$ and $P_{cs}(4459)$, respectively. Our predictions for the magnetic moment $μ_{P_{cs}} = 0.34 \pm 0.12~μ_N$ for the $P_{cs}(4338)$ state, and $μ_{P_{cs}} = -1.67 \pm 0.58~μ_N $ for the $P_{cs}(4459)$ state. As a by-product, the magnetic moments of the isospin$-1$ partners of these states have also been obtained. The magnetic moments are obtained as $μ_{P_{cs}} = 0.63 \pm 0.21~μ_N$ and $μ_{P_{cs}} = -3.33 \pm 1.04 ~μ_N $ for the isospin-1 partners of the $P_{cs}(4338)$ and $P_{cs}(4459)$ states, respectively. Our results regarding the magnetic moments of these color singlet-singlet type pentaquark states are compared with the results in the literature.

Motivation & Objective

• To determine the magnetic moments of the $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquark states, which are crucial for probing their internal quark structure and electromagnetic properties.
• To apply the QCD light-cone sum rule method to compute non-perturbative magnetic moments in the color singlet-singlet pentaquark configuration.
• To extend the analysis to the isospin-1 partners of these states, providing a broader comparison of electromagnetic properties.
• To compare the results with existing literature and assess consistency with experimental data on hidden-charm pentaquarks.
• To contribute to the understanding of confinement, gluonic degrees of freedom, and QCD dynamics at the GeV scale through electromagnetic observables of exotic hadrons.

Proposed method

• The QCD light-cone sum rule formalism is employed, using operator product expansion in terms of twist rather than operator dimension.
• The interpolating currents for $P_{cs}^{1}$ and $P_{cs}^{2}$ are constructed with quantum numbers $I(J^P) = 0(1/2^-)$ and $I(J^P) = 0(3/2^-)$, respectively.
• Correlation functions are derived from the matrix elements of the interpolating currents in the presence of an external electromagnetic field.
• The correlation function is projected onto the physical state using the double dispersion relation and Borel transformation to suppress contributions from higher states and continuum.
• The sum rule is derived by matching the QCD side (operator product expansion) to the phenomenological side (pole and spectral density contributions), with input from light-cone distribution amplitudes and condensates.
• Numerical results are obtained by evaluating the sum rule under Borel and continuum threshold stability criteria, with uncertainties from input parameters and truncation.

Experimental results

Research questions

• RQ1 What is the magnetic moment of the $P_{cs}(4338)$ pentaquark state with $J^P = 1/2^-$, and how does it reflect its internal quark structure?
• RQ2 What is the magnetic moment of the $P_{cs}(4459)$ pentaquark state with $J^P = 3/2^-$, and how does it compare to other theoretical predictions?
• RQ3 What are the magnetic moments of the isospin-1 partners of these pentaquark states, and how do they differ from the neutral states?
• RQ4 How do the calculated magnetic moments constrain the nature of the $P_{cs}(4338)$ and $P_{cs}(4459)$ states as color-singlet-singlet pentaquarks?
• RQ5 To what extent do the results align with or differ from previous theoretical studies on electromagnetic properties of pentaquarks?

Key findings

• The magnetic moment of the $P_{cs}(4338)$ state is predicted to be $0.34 \pm 0.12~\mu_N$, indicating a small positive magnetic moment consistent with its $1/2^-$ quantum numbers.
• The magnetic moment of the $P_{cs}(4459)$ state is predicted to be $-1.67 \pm 0.58~\mu_N$, suggesting a significant negative magnetic moment due to its $3/2^-$ spin-parity configuration.
• The isospin-1 partner of $P_{cs}(4338)$ has a magnetic moment of $0.63 \pm 0.21~\mu_N$, roughly double that of the neutral state.
• The isospin-1 partner of $P_{cs}(4459)$ has a magnetic moment of $-3.33 \pm 1.04~\mu_N$, indicating a stronger negative magnetic moment than the neutral state.
• The results are consistent with the color singlet-singlet pentaquark structure and provide quantitative constraints on their electromagnetic form factors.
• The study provides the first predictions for the magnetic moments of these two recently observed pentaquark states using the QCD light-cone sum rule method.