The singular part of the Borel transform of a QCD amplitude near the infrared renormalon can be expanded in terms of higher order Wilson coefficients of the operators associated with the renormalon. In this paper we observe that this expansion gives nontrivial constraints on the Borel amplitude that can be used to improve the accuracy of the ordinary perturbative expansion of the Borel amplitude. In particular, we consider the Borel transform of the Adler function and its expansion around the first infrared renormalon due to the gluon condensate. Using the next-to-leading order ͑NLO͒ Wilson coefficient of the gluon condensate operator, we obtain an exact constraint on the Borel amplitude at the first IR renormalon. We then extrapolate, using judiciously chosen conformal transformations and Padé approximants, the ordinary perturbative expansion of the Borel amplitude in such a way that this constraint is satisfied. This procedure allows us to predict the O(␣ s 4 ) coefficient of the Adler function, which gives a result consistent with the estimate by Kataev and Starshenko using a completely different method. We then apply this improved Borel amplitude to the tau decay width and obtain the strong coupling constant ␣ s (M z 2 )ϭ0.1193Ϯ0.0007 exp. Ϯ0.0010 EWϩCKM Ϯ0.0009 meth. Ϯ0.0003 evol. . We then compare this result with those of other resummation methods.

We show that the Borel resummed perturbative static potential at N f = 0 converges well, and is in a remarkable agreement with the quenched lattice calculation at distances 1/r > ∼ 660 MeV. This shows that Borel resummation is very good at handling the renormalon in the static potential (and in the pole mass), and allows one to use the pole mass in perturbative calculation of heavy quark physics. * Electronic address: tlee@muon.kaist.ac.kr

We study the cosmological gravitino production in gauge mediated supersymmetry breaking models, while properly taking into account the existence of the messenger mass scale. It is found that for sizable parameter range of the model the messenger sector contribution leads to more stringent upper bound on the reheat temperature obtained from the condition that the universe should not be overclosed by relic gravitinos. However it turns out that in the limit of relatively low messenger scale and large gravitino mass, the relic gravitino mass density can be smaller than the critical density independently of the reheat temperature, suggesting the possibility in this limit to have a high reheat temperature without the dilution of gravitinos at late time.

Higher order renormalons beyond the chain of one-loop bubbles are discussed. A perturbation method for the infrared renormalon residue is found. The large order behavior of the current-current correlation function due to the first infrared renormalon is determined in both QED and QCD to the first three orders.

In models of spontaneously broken supersymmetry, certain light gravitino processes are governed by the coupling of its Goldstino components. The rules for constructing SUSY and gauge invariant actions involving the Goldstino couplings to matter and gauge fields are presented. The explicit operator construction is found to be at variance with some previously reported claims. A phenomenological consequence arising from light gravitino interactions in supernova is reexamined and scrutinized.