  By finding rare (but not exponentially rare) large-angle deflections of
partons within a jet produced in a heavy ion collision, or of such a jet
itself, experimentalists can find the weakly coupled short-distance quark and
gluon particles (scatterers) within the strongly coupled liquid quark-gluon
plasma (QGP) produced in heavy ion collisions. This is the closest one can come
to probing QGP via a scattering experiment and ultimately learning how a
strongly coupled liquid emerges from an asymptotically free gauge theory. The
short-distance, particulate, structure of liquid QGP can be revealed in events
in which a jet parton resolves, and scatters off, a parton from the droplet of
QGP. The probability for picking up significant transverse momentum via a
single scattering was calculated previously, but only in the limit of infinite
parton energy which means zero angle scattering. Here, we provide a leading
order perturbative QCD calculation of the Moli\`ere scattering probability for
incident partons with finite energy, scattering at a large angle. We set up a
thought experiment in which an incident parton with a finite energy scatters
off a parton constituent within a "brick" of QGP, which we treat as if it were
weakly coupled, as appropriate for scattering with large momentum transfer, and
compute the probability for a parton to show up at a nonzero angle with some
energy. We include all relevant channels, including those in which the parton
that shows up at a large angle was kicked out of the medium as well as the
Rutherford-like channel in which what is seen is the scattered incident parton.
The results that we obtain will serve as inputs to future jet Monte Carlo
calculations and can provide qualitative guidance for how to use future
precise, high statistics, suitably differential measurements of jet
modification in heavy ion collisions to find the scatterers within the QGP
liquid.
