Pion-Pion Phase-Shifts and the Value of Quark-Antiquark Condensate in the Chiral Limit

Abstract

We use low energy pion-pion phase-shifts in order to make distinction between the alternatives for the value of the quark-antiquark condensate $B_0$ in the chiral limit. We will consider the amplitude up to and including ${\cal O}(p^4)$ contributions within the Standard and Generalized Chiral Perturbation Theory frameworks. They are unitarized by means of Pad\'e approximants in order to fit experimental phase-shifts in the resonance region. As the best fits correspond to $\alpha = \beta = 1$, we conclude that pion-pion phase-shift analysis favors the standard ChPT scenario, which assumes just one, large leading order parameter $_{_0}$.Comment: 5 pages, 3 figures and 1 tabl