  The Standard Model (SM) of particle physics, comprised of the unified
electro-weak (EW) and Quantum Chromodynamic (QCD) theories, accurately explains
almost all experimental results related to the micro-world, and has made a
number of predictions for previously unseen particles, most notably the Higgs
scalar boson, that were subsequently discovered. As a result, the SM is
currently universally accepted as the theory of the fundamental particles and
their interactions. However, in spite of its numerous successes, the SM has a
number of apparent shortcomings including: many free parameters that must be
supplied by experimental measurements; no mechanism to produce the dominance of
matter over antimatter in the universe; and no explanations for gravity, the
dark matter in the universe, neutrino masses, the number of particle
generations, etc. Because of these shortcomings, there is considerable
incentive to search for evidence for new, non-SM physics phenomena that might
provide important clues about what a new, beyond the SM theory (BSM) might look
like. Although the center-of-mass energies that BESIII can access are far below
the energy frontier, searches for new, BSM physics are an important component
of its research program. Here we describe ways that BESIII looks for signs of
BSM physics by measuring rates for processes that the SM predicts to be
forbidden or very rare, searching for non-SM particles such as dark photons,
making precision tests of SM predictions, and looking for violations of the
discrete symmetries $C$ and $CP$ in processes for which the SM-expectations are
immeasurably small.
