Improved method to determine the $\Xi_c-\Xi_c'$ mixing

TL;DR

This paper introduces an improved nonperturbative method to determine the mixing angle between $\\Xi_c$ and $\ar{\Xi}_c'$ baryons by constructing flavor eigenstates, calculating matrix elements, and diagonalizing the Hamiltonian, confirming previous findings on SU(3) symmetry breaking.

Contribution

The paper presents a novel approach combining lattice QCD and Hamiltonian diagonalization to accurately determine the $\\Xi_c-\ar{\Xi}_c'$ mixing angle, accounting for flavor symmetry breaking effects.

Findings

Preliminary results support previous estimates of the mixing angle.

The mixing is insufficient to explain large SU(3) breaking in semileptonic decays.

Method improves nonperturbative determination of baryon mixing angles.

Abstract

We develop an improved method to explore the $\Xi_c- \Xi_c'$ 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 $\Xi_c'$, and estimating an off-diagonal matrix element, we extract the mixing angle between the $\Xi_c$ and $\Xi_c'$. 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.