A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT

We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega similar or equal to upsilon(0)k+a+b/k+..., where the limiting velocity upsilon(0) is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m(q). We compute a and b in terms of the meson quantum numbers and T/m(q). The limiting meson velocity upsilon(0) becomes much smaller than the speed of light at temperatures below but close to T-diss, the temperature above which no meson bound states at rest in the plasma are found. From our result for upsilon(0)( T/mq), we find that the temperature above which no meson bound states with velocity upsilon exist is T-diss(upsilon) similar or equal to (1 - upsilon(2))T-1/4(diss), up to few percent corrections. We thus confirm by direct calculation of meson dispersion relations a result inferred indirectly in previous work via analysis of the screening length between a static quark and antiquark in a moving plasma. Although we do not do our calculations in QCD, we argue that the qualitative features of the dispersion relation we compute, including in particular the relation between dissociation temperature and meson velocity, may apply to bottomonium and charmonium mesons propagating in the strongly coupled plasma of QCD. We discuss how our results can contribute to understanding quarkonium physics in heavy ion collisions.