D 0 − D ¯ 0 mixing in the Dyson-Schwinger approach

In view of difficulty to reproduce observables in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>D</a:mi> <a:mn>0</a:mn> </a:msup> <a:mo>−</a:mo> <a:msup> <a:mover accent="true"> <a:mi>D</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mn>0</a:mn> </a:msup> </a:math> mixing via the operator product expansion, we discuss the Dyson-Schwinger approach to this process. Formulated by the parametrization of quark propagators, SU(3) breaking relevant to charm mixing is evaluated in such a way that properly takes account of dynamical chiral symmetry breaking. The <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mover accent="true"> <e:mi>D</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mn>0</e:mn> </e:msup> <e:mo stretchy="false">→</e:mo> <e:msup> <e:mi>D</e:mi> <e:mn>0</e:mn> </e:msup> </e:math> transition is discussed in the vacuum-insertion approximation with locality of the light valence-quark field, represented by the decay constant of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msup> <j:mi>D</j:mi> <j:mn>0</j:mn> </j:msup> </j:math> meson as well as relevant momentum integrals. It is found that dimensionless mass-difference observable in this approach leads to <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mo stretchy="false">|</l:mo> <l:mi>x</l:mi> <l:mo stretchy="false">|</l:mo> <l:mo>=</l:mo> <l:mo stretchy="false">(</l:mo> <l:mn>1.3</l:mn> <l:mtext> </l:mtext> <l:mi>–</l:mi> <l:mtext> </l:mtext> <l:mn>2.9</l:mn> <l:mo stretchy="false">)</l:mo> <l:mo>×</l:mo> <l:msup> <l:mn>10</l:mn> <l:mrow> <l:mo>−</l:mo> <l:mn>3</l:mn> </l:mrow> </l:msup> </l:math> , the order of magnitude comparable to the HFLAV data, and thereby offering a certain improvement as a theoretical framework.