RENORMALIZATION-GROUP STUDY OF FIELD-THEORETIC A+A-]CIRCLE-DIVIDE

We study field-theoretic A + A --> empty set in a perturbative renormalization-group framework. We calculate the reacted fraction and it is shown that, in addition to the reaction coupling constant, a second ''crossover'' parameter must be treated to all orders to obtain meaningful long-time results for spatial dimensions d less-than-or-equal-to 2. At d-2 the result is consistent with known rigorous long-time bounds, but the short-time behavior remains inconsistent (trivial) analogously to the Landau ghost [V. Rivasseau, From Perturbative to Constructive Renormalization (Princeton Univ. Press, Princeton, 1991)] of QED and phi4 theory. We argue that this inconsistency is true to all orders in the coupling constants.