A baryon-calibrated unified quark-diquark effective mass formalism for heavy multiquarks

Abstract

We present a unified framework for heavy tetraquark and pentaquark systems within the quark-diquark effective mass formalism, extending its baryon-calibrated construction to multiquark states without introducing sector-dependent parameters. Intra-diquark color-spin correlations are encoded in effective diquark masses fixed from baryon spectroscopy, while the inter-cluster chromomagnetic scale, independently determined from vector-pseudoscalar meson splittings, is propagated unchanged to exotic configurations, ensuring residual one-gluon exchange dynamics only between composite color sources. Within this framework, we compute the complete spectra for both $\bar{\mathbf{3}}_c\otimes\mathbf{3}_c$ and $\mathbf{6}_c\otimes\bar{\mathbf{6}}_c$ configurations in tetraquarks, whereas the pentaquark analysis focuses on the dominant $\bar{\mathbf{3}}_c\otimes\bar{\mathbf{3}}_c\otimes\bar{\mathbf{3}}_c$ clustering. Heavy-quark spin symmetry and flavor-symmetry breaking across light, charm, and bottom sectors emerge naturally through the explicit $1/(m_{D_1}m_{D_2})$ scaling of the calibrated couplings. The resulting spectra exhibit a coherent dynamical hierarchy spanning baryons and multiquark states. Established exotic candidates are reproduced within hadronic uncertainties, while the unified calibration enables quantitative predictive control across flavor sectors. The framework thus provides a parameter-economical, systematically constrained baseline with unified dynamical consistency for heavy multiquark spectroscopy.

Figures (9)

• Figure 1: Schematic representation of the tetraquark as an effective diquark–antidiquark bound state.
• Figure 2: Diquark-diquark-antiquark interaction picture of a pentaquark.
• Figure 3: Mass spectra of singly-charm tetraquark states: $cn\bar{n}\bar{n}, cn\bar{n}\bar{s}, cn\bar{s}\bar{s}$ (left panel) and $cs\bar{n}\bar{n}, cs\bar{n}\bar{s}, cs\bar{s}\bar{s}$ (right panel). The $\bar{\mathbf{3}}\otimes\mathbf{3}~(\mathbf{6}\otimes\bar{\mathbf{6}})$ configurations are shown in blue (red), while black diamonds correspond to available experimental states. The relevant thresholds are indicated by dashed lines. The same legend is followed throughout.
• Figure 4: Mass spectra of singly-bottom tetraquark states: $bn\bar{n}\bar{n}, bn\bar{n}\bar{s}, bn\bar{s}\bar{s}$ (left panel) and $bs\bar{n}\bar{n}, bs\bar{n}\bar{s}, bs\bar{s}\bar{s}$ (right panel).
• Figure 5: Mass spectra of doubly charm and doubly bottom tetraquark states: $cc\bar{u}\bar{d}, cc\bar{u}\bar{s}, cc\bar{s}\bar{s}$ (left panel) and $bb\bar{u}\bar{d}, bb\bar{u}\bar{s}, bb\bar{s}\bar{s}$ (right panel).