Evidence against naive truncations of the OPE from e+ e- → hadrons below charm

The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, alpha(s), from hadronic tau-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes nonperturbative contributions to the I = 1 vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of alpha(s) is tantamount to the assumption that the lowdimension part of the OPE converges rapidly with increasing dimension near the tau mass. Were this assumption valid, it would certainly have to be valid at energies above the t mass as well. It follows that the method can be tested using data obtained from e(+) e(-) -> hadrons, as they are not limited by the kinematic constraints of tau decays. We carry out such an investigation using a recent high-precision compilation for the R ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related, channel. We find that e(+) e(-) -based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the tau mass and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.