Improved method to determine the ${\Xi }_c-{\Xi }_c^{\prime }$ mixing

Abstract

We develop an improved method to explore the ${\Xi }_c-{\Xi }_c^{\prime }$ mixing which arises from the flavor SU(3) and heavy quark symmetry breaking. In this method, the flavor eigenstates under the SU(3) symmetry are at first constructed and the corresponding masses can be nonperturbatively determined. Matrix elements of the mass operators which break the flavor SU(3) symmetry sandwiched by the flavor eigenstates are then calculated. Diagonalizing the corresponding matrix of Hamiltonian gives the mass eigenstates of the full Hamiltonian and determines the mixing. Following the previous lattice QCD calculation of ${\Xi }_c$ and ${\Xi }_c^{\prime }$, and estimating an off-diagonal matrix element, we extract the mixing angle between the ${\Xi }_c$ and ${\Xi }_c^{\prime }$. Preliminary numerical results for the mixing angle confirm the previous observation that such mixing is incapable to explain the large SU(3) symmetry breaking in semileptonic decays of charmed baryons.

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Cited by in corpus (5)

• Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD
• First lattice QCD calculation of $J/\psi$ semileptonic decay containing $D$ and $D_s$ particles
• ${\Xi }_c\to \Xi$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of ${\Xi }_c^0$ decay rates
• Revisiting heavy-flavor conserving weak decays of charmed baryons within the nonrelativistic quark model
• The nonleptonic decays ${\Xi }_{cc}^{++}\to {\Xi }_c^{(\prime )+}{\pi }^{+}$ within the nonrelativistic quark model