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In the framework of QCD sum rules, we present an improved study of ourprevious work [Phys. Rev. D {\bf80}, 056004 (2009)] particularly on the$\bar{D}D^{*}$ molecular state to investigate that the possibility of the newlyobserved $Z_{c}(3900)$ as a $S$-wave $\bar{D}D^{*}$ molecular state. To ensurethe quality of QCD sum rule analysis, contributions of up to dimension nine arecalculated to test the convergence of operator product expansion (OPE). We findthat the two-quark condensate $<\bar{q}q>$ is very large and makes the standardOPE convergence (i.e. the perturbative at least larger than each condensatecontribution) happen at very large values of Borel parameters. By releasing therigid OPE convergence criterion, one could find that the OPE convergence isstill under control. We arrive at the numerical result $3.86\pm0.27 {GeV}$ for$\bar{D}D^{*}$, which agrees with the mass of $Z_{c}(3900)$ and could supportthe explanation of $Z_{c}(3900)$ in terms of a $S$-wave $\bar{D}D^{*}$molecular state.

Improved QCD sum rule study of $Z_{c}(3900)$ as a $\bar{D}D^{*}$ molecular state