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 $\mathcal{O}(p^4)$ contributions within the Standard and Generalized Chiral Perturbation Theory frameworks. They are unitarized by means of Padé 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 $<\bar{q}q{>}_{{}_0}$.

Comments: 5 pages, 3 figures and 1 table