Hadronic molecules in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math> decays

Abstract

There are eighteen possibly existing ${D}^{(*)}{\overline{D}}^{(*)}$, ${D}^{(*)}{\overline{K}}^{(*)}$, and ${D}^{(*)}{D}_{s}^{(*)\ensuremath{-}}$ hadronic molecular states. We construct their corresponding interpolating currents and calculate their decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in $B$ and ${B}^{*}$ decays through the current algebra, and calculate their relative branching ratios through the Fierz rearrangement, as summarized in Table III. Our results support the interpretations of the $X(3872)$, ${Z}_{c}(3900{)}^{0}$, ${Z}_{c}(4020{)}^{0}$, and ${X}_{0}(2900)$ as the molecular states $D{\overline{D}}^{*}$ of ${J}^{PC}={1}^{++}$, $D{\overline{D}}^{*}$ of ${J}^{PC}={1}^{+\ensuremath{-}}$, ${D}^{*}{\overline{D}}^{*}$ of ${J}^{PC}={1}^{+\ensuremath{-}}$, and ${D}^{*}{\overline{K}}^{*}$ of ${J}^{P}={0}^{+}$, respectively. Our results also suggest that the ${Z}_{cs}(3985{)}^{\ensuremath{-}}$, ${Z}_{cs}(4000{)}^{+}$, and ${Z}_{cs}(4220{)}^{+}$ are strange partners of the $X(3872)$, ${Z}_{c}(3900{)}^{0}$, and ${Z}_{c}(4020{)}^{0}$, respectively. In the calculations we estimate the lifetime of a weakly coupled composite particle $A=|BC⟩$ to be $1/{t}_{A}\ensuremath{\approx}1/{t}_{B}+1/{t}_{C}+{\mathrm{\ensuremath{\Gamma}}}_{A\ensuremath{\rightarrow}BC}+\ensuremath{\cdots}$, with $\ensuremath{\cdots}$ partial widths of other possible decay channels.

Topics & Concepts