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Quark-diquark effective mass formalism for heavy baryon spectroscopy

Binesh Mohan, Rohit Dhir

Abstract

We present a comprehensive study of heavy flavor baryons within a quark-diquark effective mass formalism, formulated using the effective masses of quarks and diquarks inside baryons. We predict the masses of $J^P=\frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ states under two complementary scenarios: the quark-quark interaction picture (Scenario I) and the quark-diquark interaction picture (Scenario II). Scenario I considers all possible quark-quark correlations, while Scenario II employs fixed spin-flavor diquark configurations, treating the baryon as an effective quark-diquark system. Using current experimental data, we estimate constituent quark masses, diquark masses, and hyperfine interactions, and include a mass-dependent binding energy term to account for short-range chromoelectric effects. The analysis shows that the binding energy plays a crucial role in describing heavy-heavy diquarks. The predicted baryon masses show excellent agreement with experimental and lattice QCD results across the charm and bottom sectors.

Quark-diquark effective mass formalism for heavy baryon spectroscopy

Abstract

We present a comprehensive study of heavy flavor baryons within a quark-diquark effective mass formalism, formulated using the effective masses of quarks and diquarks inside baryons. We predict the masses of and states under two complementary scenarios: the quark-quark interaction picture (Scenario I) and the quark-diquark interaction picture (Scenario II). Scenario I considers all possible quark-quark correlations, while Scenario II employs fixed spin-flavor diquark configurations, treating the baryon as an effective quark-diquark system. Using current experimental data, we estimate constituent quark masses, diquark masses, and hyperfine interactions, and include a mass-dependent binding energy term to account for short-range chromoelectric effects. The analysis shows that the binding energy plays a crucial role in describing heavy-heavy diquarks. The predicted baryon masses show excellent agreement with experimental and lattice QCD results across the charm and bottom sectors.
Paper Structure (11 sections, 16 equations, 3 figures, 8 tables)

This paper contains 11 sections, 16 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Quark-diquark effective mass formalism
  4. Binding energy
  5. Numerical results and discussions
  6. Diquark masses in Scenario I and II
  7. $J^P=\frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ heavy baryon masses
  8. Summary and Conclusions
  9. $SU(6)$ diquark wave functions
  10. Quark-diquark wave functions of $J^P = \frac{1}{2}^+$ and $J^P = \frac{3}{2}^+$ $SU(3)$ baryons
  11. Mass expressions of $J^P = \frac{1}{2}^+$ and $J^P = \frac{3}{2}^+$ $SU(3)$ baryons

Figures (3)

  • Figure 1: Two scenarios in QDEMF: (a) quark-quark interaction picture (Scenario I), (b) quark-diquark interaction picture (Scenario II).
  • Figure 2: Variation of hyperfine splitting, $\Delta M= M_A - M_S$ in scenarios I and II with corresponding diquark masses.
  • Figure 3: Lower half illustrates the diquark binding energies, while the upper half shows the hyperfine mass splittings for different diquark flavors in scenarios I and II.