Résumé des résultats (Abstract)
(Anglais)
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1. We have completed the work on pp scattering in the framework of the Roy equations that we started at the beginning of this network activity, and on which we had reported in the previous annual summaries. In Ref.[1], we match the known chiral perturbation theory representation of the pp scattering amplitude to two loops with a phenomenological description that relies on the Roy equations. On this basis, the corrections to Weinberg's low energy theorems for the S-wave scattering lengths are worked out to second order in the expansion in powers of the quark masses. The resulting predictions, a0 = 0.220±0.005, a2 = -0.0444±0.0010, contain remarkably small uncertainties and thus allow a very sensitive experimental test of the hypothesis that the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry. In Ref. [2], we show that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave pp scattering lengths. A detailed analysis [3] of the new Ke4 data by the BNL-goup has beautifully confirmed our prediction [2]. The main conclusion is that the quark condensate is large, and that generalized chiral perturbation theory [4] has served its purposes and can be dismissed
2. In recent years, experimental progress has made it mandatory to determine hadronic amplitudes to previously unknown accuracy. An example is the anomalous magnetic moment of the muon, which requires knowledge of the e+e- ®p+p- cross section at the one percent level in the low-energy region. Therefore, the inclusion of electromagnetic interactions in the effective theory of QCD is required. This is a subtle affair. We have investigated the problem in a model where everything is under control: The linear sigma-model, coupled to photons through minimal coupling. We have evaluated several Green functions at one loop order and have then performed the low-energy expansion, where the pion momenta are considered to be small compared to the sigma-meson mass. In this manner, one generates the standard low-energy effective representation, where now, however, the dependence of the low-energy couplings on the renormalization scale is under control. The model illustrates many features that we expect to remain true in the full theory [5].
3. We have organized two workshops dedicated to Hadronic Atoms on October 14-15, 1999 [6] and on October 11-12, 2001 [7], both in Bern.
We have been invited to several international conferences, where we have reported on our work, among them Bangalore (IN), Dubna (RU), Frascati (I), Jefferson Lab (USA), Jülich (D), Marseille (F), Vienna (A), Washington DC (USA), Jefferson Lab (USA), Uppsala (S).
A full account of the activities of the Bern node as well as of the full network is given in the final report of the network.
[1] G. Colangelo, J. Gasser and H. Leutwyler, Phys. Lett. B 488 (2000) 261 [arXiv:hep-ph/0007112].
[2] G. Colangelo, J. Gasser and H. Leutwyler, Phys. Rev. Lett. 86 (2001) 5008 [arXiv:hep-ph/0103063].
[3] S. Pislak et al. [BNL-E865 Collaboration], Phys. Rev. Lett. 87 (2001) 221801 [arXiv:hep-ex/0106071].
[4] M. Knecht, B. Moussallam, J. Stern and N.H. Fuchs, Nucl. Phys. B 457 (1995) 513 [arXiv:hep-ph/9507319]; ibid. B 471 (1996) 445 [arXiv:hep-ph/9512404.
[5] J. Gasser et al., in preparation.
[6] J. Gasser, A. Rusetsky and J. Schacher, arXiv:hep-ph/9911339.
[7] J. Gasser, A. Rusetsky and J. Schacher, arXiv:hep-ph/0112293.
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