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

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.

💡 Research Summary

The paper introduces a unified quark‑diquark effective‑mass formalism (QDEMF) that simultaneously describes heavy baryons, tetraquarks, and pentaquarks with a minimal set of parameters. The authors first calibrate effective scalar and axial‑vector diquark masses using the well‑established heavy‑baryon spectrum (e.g., Λ_c, Σ_c, Λ_b, Σ_b). Independently, they determine the chromomagnetic coupling constant κ from the hyperfine splittings of vector–pseudoscalar mesons (D*–D, B*–B, etc.). These two inputs—diquark masses and κ—are then propagated unchanged to exotic multiquark configurations, ensuring that the same one‑gluon‑exchange (OGE) color‑spin dynamics that govern conventional hadrons also control the residual interaction between composite color sources in multiquark states.

In the tetraquark sector the system is treated as a bound state of an effective diquark and an antidiquark. Both color‑antisymmetric (\bar{3}_c) and color‑symmetric (6_c) diquarks are retained, leading to two distinct color‑singlet channels: (\bar{3}_c\otimes3_c) and (6_c\otimes\bar{6}_c). The authors construct explicit color, spin, and flavor wave functions, enforce Pauli antisymmetrization within each cluster, and classify the resulting states into scalar‑scalar, scalar‑axial, and axial‑axial configurations (J^P = 0^+, 1^+, 2^+). The hyperfine interaction between the diquark and antidiquark is written as \