Revealing the mystery of the double charm tetraquark in $pp$ collision

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between $T_{\bar{c}\bar{c}}^-$ and $T_{cc}^+$ in $pp$ collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark's internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of $T_{\bar{c}\bar{c}}^-$ and $T_{cc}^+$ cross sections emerge, particularly at $p_\mathrm{T}\approx 2~\mathrm{GeV}$ and $y\approx \pm 6$ at a center-of-mass energy of 14$~\mathrm{TeV}$. The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.