Mass and decay angles in the $\Xi_c$--$\Xi_c'$ mixing tension: Virtual hybrids and a single-direction criterion

Abstract

We compare three definitions of $\Xi_c$--$\Xi_c'$ mixing within a constituent-quark model: a spin-component probability angle, a common-source overlap angle, and an SU(3)-breaking mass-operator angle. The probability angle is $3.11^\circ$, while the two operator-based definitions give $2.48$--$2.58^\circ$; a second parameter set gives $2.38$--$2.49^\circ$. The operator-based angles are closer to the lattice determinations $1.2(1)^\circ$ and $0.810(50)(200)^\circ$, but remain larger. We then couple conventional $qsQ$ states to virtual $qsQg$ configurations, where $q=u,d$ and $Q=c,b$. An orbital-$S$-wave chromomagnetic transition containing both $j_{Qg}=1/2$ and $3/2$ raises the source and mass-operator charm angles to $2.67$--$3.16^\circ$ when normalized to reference short-range mass shifts. The hybrid probability stays below $1.7\%$, and the corresponding bottom angles are $0.42$--$0.48^\circ$. Eliminating the hybrid sector gives a rank-one mass correction precisely when all weighted transitions select the same retained-state combination. The mode-resolved calculation separates the flavor-breaking response that changes the mixing angle from the response that generates a second transition direction. The accompanying effective-current relation connects this mass analysis to radiative and semileptonic amplitudes through their current matrix elements.