Improved method to determine the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="normal">Ξ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi mathvariant="normal">Ξ</mml:mi><mml:mi>c</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:math> mixing
Hang Liu, Wei Wang, Qi-An Zhang
Abstract
We develop an improved method to explore the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Ξ</a:mi><a:mi>c</a:mi></a:msub><a:mo>−</a:mo><a:msubsup><a:mi mathvariant="normal">Ξ</a:mi><a:mi>c</a:mi><a:mo>′</a:mo></a:msubsup></a:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi mathvariant="normal">Ξ</e:mi><e:mi>c</e:mi></e:msub></e:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msubsup><h:mi mathvariant="normal">Ξ</h:mi><h:mi>c</h:mi><h:mo>′</h:mo></h:msubsup></h:math>, and estimating an off diagonal matrix element, we extract the mixing angle between the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="normal">Ξ</k:mi><k:mi>c</k:mi></k:msub></k:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mi mathvariant="normal">Ξ</n:mi><n:mi>c</n:mi><n:mo>′</n:mo></n:msubsup></n:math>. 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. Published by the American Physical Society 2024