  Precision measurements of cosmic microwave background (CMB) polarization
require extreme control of instrumental systematics. In a companion paper we
have presented cosmological constraints from observations with the BICEP2 and
Keck Array experiments up to and including the 2015 observing season (BK15),
resulting in the deepest CMB polarization maps to date and a statistical
sensitivity to the tensor-to-scalar ratio of $\sigma(r) = 0.020$. In this work
we characterize the beams and constrain potential systematic contamination from
main beam shape mismatch at the three BK15 frequencies (95, 150, and 220 GHz).
Far-field maps of 7,360 distinct beam patterns taken from 2010-2015 are used to
measure differential beam parameters and predict the contribution of
temperature-to-polarization leakage to the BK15 B-mode maps. In the
multifrequency, multicomponent likelihood analysis that uses BK15, Planck, and
WMAP maps to separate sky components, we find that adding this predicted
leakage to simulations induces a bias of $\Delta r = 0.0027 \pm 0.0019$. Future
results using higher-quality beam maps and improved techniques to detect such
leakage in CMB data will substantially reduce this uncertainty, enabling the
levels of systematics control needed for BICEP Array and other experiments that
plan to definitively probe large-field inflation.
