Role of square root threshold singularity in current algebra and chiral symmetry breaking calculations of Kℓ3, Kℓ4 and τ →πKν decays

It is shown that discrepancies between soft pion current algebra (or chiral symmetry) calculations in K?₄ and experiments are mostly due to the square root threshold singularity of the pion-pion interaction. For the same reason, chiral symmetry breaking calculations of the scalar K?₃ form factor cannot be extended to the threshold of τ → Kπν decay.