  Within the first 10 days after Swift discovered the jetted tidal disruption
event (TDE) Sw J1644+57, simultaneous observations in the radio, near-infrared,
optical, X-ray and gamma-ray bands were carried out. These multiwavelength data
provide a unique opportunity to constrain the emission mechanism and make-up of
a relativistic super-Eddington jet. We consider an exhaustive variety of
radiation mechanisms for the generation of X-rays in this TDE, and rule out
many processes such as SSC, photospheric and proton synchrotron. The infrared
to gamma-ray data for Sw J1644+57 are consistent with synchrotron and
external-inverse-Compton (EIC) processes provided that electrons in the jet are
continuously accelerated on a time scale shorter than ~1% of the dynamical time
to maintain a power-law distribution. The requirement of continuous electron
acceleration points to magnetic reconnection in a Poynting flux dominated jet.
The EIC process may require fine tuning to explain the observed temporal decay
of the X-ray lightcurve, whereas the synchrotron process in a magnetic jet
needs no fine tuning for this TDE.
