$\mathbf {D}^{\mathbf {0}} \rightarrow {\bar {\mathbf {K}}}^{\mathbf {0}}\mathbf {a}_{\mathbf {1}}^{\mathbf {0}} \mathbf {(1260)}$ Decay Within QCD Factorization Approach

Abstract

In this paper, we have analyzed the decay$D^{0}\to \bar {{K}}^{0}{a_{1}^{0}} (1260)_{\mathrm {~} }$in naïve factorization (NF) and QCD factorization (QCDF) schemes. Since, it is known from the data analysis based on the model-independent diagrammatic approach that weak annihilation in charm decays is quite sizable, so we have calculated weak annihilation contribution which is model-dependent in the QCD factorization approach. Indeed our obtained results of $D^{0}\to \bar {{K}}^{0}{a_{1}^{0}} (1260)$ decay show that the annihilation contribution is one of the key ingredients for understanding the data. Also we have calculated the branching ratio in two special scales of μ=m _c , 1 GeV and two different models for the charm to an axial-vector meson transition form factors. For ISGW2 model at scale μ=1 GeV, our calculated results of the branching ratio of $D^{0}\to \bar {{K}}^{0}{a_{1}^{0}} (1260)$ decay are$_{\mathrm {~} }\left (8.66_{-0.16}^{+0.15} \right )\times 10^{-6}_{\mathrm {~} }$and $\left (1.85_{-0.47}^{+0.58} \right )\times 10^{-2}_{\mathrm {~} }$in the NF and QCDF, respectively. The experimental data is less than 1.9×10⁻². The branching ratio obtained in NF is very smaller than the experimental data but in QCDF, it is compatible with experimental data.