  Based on an exact expression for the self-energy of the Jahn-Teller polaron,
we find that symmetry of pseudospin rotation makes the vertex correction much
less effective than that for the Holstein polaron. This ineffectiveness brings
about a smaller effective mass m^* and a quantitatively differenent
large-to-small polaron crossover, as examined by exact diagonalization in a
two-site system. In the strong-coupling and antiadiabatic region, a rigorous
analytic expression is found for m^*.
