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.