  We have established a relation between the brightest super star cluster
magnitude in a galaxy and the host star formation rate (SFR) for the first time
in the near infrared (NIR). The data come from a statistical sample of ~ 40
luminous IR galaxies (LIRGs) and starbursts utilizing K-band adaptive optics
imaging. While expanding the observed relation to longer wavelengths, less
affected by extinction effects, it also pushes to higher SFRs. The relation we
find, M_K ~ - 2.6 log SFR, is similar to that derived previously in the optical
and at lower SFRs. It does not, however, fit the optical relation with a single
optical to NIR color conversion, suggesting systematic extinction and/or age
effects. While the relation is broadly consistent with a size-of-sample
explanation, we argue physical reasons for the relation are likely as well. In
particular, the scatter in the relation is smaller than expected from pure
random sampling strongly suggesting physical constraints. We also derive a
quantifiable relation tying together cluster-internal effects and host SFR
properties to possibly explain the observed brightest SSC magnitude vs. SFR
dependency.
