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We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. As expected, the $S$-matrix of a single dressed gluon state ceases to be unitary if evolved to significant $\ln Q^2/Q_s^2$. Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.

We study the potential of $X(3872)$ at finite temperature in the Born-Oppenheimer approximation under the assumption that it is a tetraquark. We argue that, at large number of colors, it is a good approximation to assume that the potential consists in a real part plus a constant imaginary term. The real part is then computed adapting an approach by Rothkopf and Lafferty and using as input lattice QCD determinations of the potential for hybrids. This model allows us to qualitatively estimate at which temperature range the formation of a heavy tetraquark is possible, and to propose a qualitative picture for the dissociation of the state in a medium. Our approach can be applied to other suggested internal structures for the $X(3872)$ and to other exotic states., Comment: 12 pages, 7 figures. Numerical mistakes affecting two plots corrected, text changed accordingly; main conclusions unchanged