Indirect production of doubly charmed tetraquarks $T_{cc}$ at high energy colliders

The indirect production mechanisms of doubly charmed tetraquark $T_{cc}$ through three decay channels, Higgs$/Z^{0}\to \langle cc\rangle_{\bar{3}} +\bar{c}+\bar{c} \to T_{cc}^{\bar{q}\bar{q^{\prime}}} +\bar{c}+\bar{c} $ and $W^+\to \langle cc\rangle_{\bar{3}}+\bar{c}+\bar{s} \to T_{cc}^{\bar{q}\bar{q^{\prime}}} +\bar{c}+\bar{s} $, are analyzed within the framework of nonrelativistic QCD. The intermediate $\langle cc\rangle_{\bar{3}}$ diquark cluster in color antitriplet evolves into tetraquark components via the fragmentation process by trapping two light antiquarks ($\bar{q}$ and $\bar{q^{\prime}}$) from the vacuum. After the considered doubly charmed tetraquark components are summed, including $T_{cc}^{\bar{u} \bar{u}}$, $T_{cc}^{\bar{u} \bar{d}}$, $T_{cc}^{\bar{d} \bar{d}}$, $T_{cc}^{\bar{u}\bar{s}}$, and $T_{cc}^{\bar{d}\bar{s}}$, the decay widths, branching ratios, and produced events each year for the production of $T_{cc}$ can be predicted at LHC and CEPC, respectively. The differential distributions and two main sources of theoretical uncertainty are also discussed. The results show that the produced events each year for $T_{cc}$ via $W^{+}$ decays is $1.80\times10^5$, nearly $2$ orders of magnitude larger than that by Higgs decays ($1.11\times10^{3}$) and $Z^{0}$ decays ($4.81\times10^3$) at LHC. However at CEPC, the largest contribution for the production of $T_{cc}$ is through $Z^{0}$ decays, about $1.63\times10^6$. There are only $4.79\times10^{-1}$ and $2.03\times10^{2}$ $T_{cc}$ events produced each year at CEPC through Higgs and $W^+$ decay, respectively.