Extraction of the s-wave pi N scattering lengths from data on pionic atoms

Baru, V.; Hanhart, C.; Hoferichter, Martin; Kubis, B.; Nogga, A.; Phillips, D. R. (2012). Extraction of the s-wave pi N scattering lengths from data on pionic atoms. PoS - proceedings of science, QNP2012(133), pp. 1-6. Scuola Internazionale Superiore di Studi Avanzati SISSA

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For many years a combined analysis of pionic hydrogen and deuterium atoms has been known as a good tool to extract information on the isovector and especially on the isoscalar s-wave pN scattering length. However, given the smallness of the isoscalar scattering length, the analysis becomes useful only if the pion–deuteron scattering length is controlled theoretically to a high accuracy comparable to the experimental precision. To achieve the required few-percent accuracy one needs theoretical control over all isospin-conserving three-body pNN !pNN operators up to one order before the contribution of the dominant unknown (N†N)2pp contact term. This term appears at next-to-next-to-leading order in Weinberg counting. In addition, one needs to include
isospin-violating effects in both two-body (pN) and three-body (pNN) operators. In this talk we discuss the results of the recent analysis where these isospin-conserving and -violating effects have been carefully taken into account. Based on this analysis, we present the up-to-date values of the s-wave pN scattering lengths.

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