Investigating the mass spectra of $1F$-wave singly heavy ${\mathrm{\Sigma }}_Q$, ${\mathrm{\Xi }}_Q^{\mathrm{\prime }}$, and ${\mathrm{\Omega }}_Q$ baryons

In this work, we enumerated the mass spectra of the experimentally unobserved $1F$-wave states with the the orbital angular momentum $L$ = 3 for the singly heavy ${\mathrm{\Sigma }}_Q$, ${\mathrm{\Xi }}_Q^{\mathrm{\prime }}$, and ${\mathrm{\Omega }}_Q$ $(Q=c,b)$ baryons in the framework of quark-diquark configuration using the Regge trajectory model and the scaling rules. To determine the effective masses of the heavy quark and two light quarks, the relativistic effective mass formula are employed by combining the Coulomb potential. Within the spin-dependent Hamiltonian, we construct the mass shift forms as a non-diagonal symmetric $6\times 6$ matrix for the $1F$-wave states of ${\mathrm{\Sigma }}_Q$, ${\mathrm{\Xi }}_Q^{\mathrm{\prime }}$, and ${\mathrm{\Omega }}_Q$ baryons. Our analysis of mass spectra provides valuable insights to guide future experimental investigations, and enhances the understanding of the spectroscopic properties of unobserved $1F$-wave orbital excitations for these singly heavy baryons.