Testing the mode of quark condensation

If unconventional quark condensates are considered as possibilities, pions may acquire mass mπ≠0 only after d orders of perturbation in the quark-mass operator. Then ππ scattering amplitudes are given by Fπ-2 {(qi+zj)2+ξdmπ2} for small pion momenta qi (Fπ ≅ 93 MeV), where ζ=-1 and ξ2=0 are fixed by chiral symmetry, but not ζd for d≥3. The O(mπ4 ln mπ2) corrections also depend on d. (orig.)