Doubly charmed baryon production in heavy ion collisions

We give an estimate of $\Xi_{cc}^{++}$ production rate and transverse momentum spectra in relativistic heavy ion collisions. We use Boltzmann transport equations to describe the dynamical evolution of charm quarks and diquarks inside quark-gluon plasma. In-medium formation and dissociation rates of charm diquarks are calculated from potential non-relativistic QCD for the diquark sector. We solve the transport equations by Monte Carlo simulations. For $2.76$ TeV Pb-Pb collisions with $0-10\%$ centrality, the number of $\Xi_{cc}^{++}$ produced in the transverse momentum range $0-5$ GeV and rapidity from $-1$ to $1$ is roughly $0.02$ per collision. We repeat the calculation with a melting temperature $250$ MeV above which no diquarks can be formed. The number of $\Xi_{cc}^{++}$ produced in the same kinematic region is about $0.0125$ per collision. We discuss how to study diquarks at finite temperature on a lattice and construct the anti-triplet free energy in a gauge invariant but path dependent way. We also comment on extensions of the calculation to other doubly heavy baryons and doubly heavy tetraquarks and the feasibility of experimental measurements.