Tests of current algebra and partially conserved axial-vector current in the subthreshold region of the pion-nucleon system

Abstract

Current algebra and partially controlled axial-vector current ~PCAC! make powerful predictions in the threshold and subthreshold regions of the pN system @1#. Some of the most important examples are the Adler consistency condition @2# ~which predicts a zero in the pole-subtracted isospin-even amplitude for one soft pion!, the Weinberg-Tomozawa prediction of pN scattering lengths @3#, the Adler-Weisberger sum rule @4# ~which constrains the isospin-odd amplitude at n5t50 for massless pions!, and the pN s term ~which measures the chiral-symmetry breaking in the pN system!. The values of these quantities are determined from amplitudes evaluated within the small subthreshold ‘‘crescent’’ region in the Mandelstam diagram shown in Fig. 1 @5#. Because the crescent lies below the physical threshold of all of the crossed reactions (pN→pN , pN→pN , and NN→pp!, the invariant amplitudes are real in this region. In this article we report on an application of a recent Virginia Polytechnic Institute phase-shift analysis SP98 @6# and interior dispersion relations ~IDR’s! @7# to map the relevant amplitudes within the entire crescent @8#. Hence, this analysis provides current tests of several predictions of chiral symmetry. The present work is an extension and update of work done at the beginning of the era of the meson factories @9#; since then, new high-precision pN data have been obtained, from which improved low-energy phase shifts have been extracted. The general structure of the pion-nucleon invariant amplitudes has long been known @10#, of course, but the IDR method is especially well suited for studies of the subthreshold region, especially when coupled with the high-precision VPI phase-shift analyses.