On the large order behavior of Φ 4 4

We continue the rigorous study of the large order behavior of the perturbation series for the ⁴ model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ₄ ⁴ is greater than or equal to the expected value given by the position of the first renormalon [2]. This result holds for any vector (²)² model withN components, and makes use of the Lipatov bound of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.     

Ellagitannin chemistry. Evolution of a three-component coupling strategy for the synthesis of the dimeric ellagitannin coriariin A and a dimeric gallotannin analogue

The total synthesis of the dimeric ellagitannin coriariin A is reported. The key reaction to access the dimeric framework was realized early in the synthesis pathway via a bis acylation reaction of a dehydrodigalloyl diacid with 2 equiv of a glucopyranose trichloroacetimidate. The glucose rings were subsequently functionalized, culminating in a double oxidative cyclization to form stereoselectively both (S)-HHDP ester units. This bis acylation strategy was also employed to prepare a gallotannin analogue of coriariin A whose earlier synthesis by orthoquinone dimerization was plagued by yield-limiting side reactions.