Whatπ−πscattering tells us about chiral perturbation theory

Abstract

We describe a rearrangement of the standard expansion of the symmetry-breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory (xPT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard xPT, and is more likely to converge rapidly. It provides a consistent framework for a measurement of the importance of additional "higher order" terms whose smallness is usually assumed but has never been checked. A method of measuring, among other quantities, the QCD parameters m(qq) and the quark mass ratio m,/m is elaborated in detail. The method is illustrated using various sets of available data. Both of these parameters might be considerably smaller than their respective leading-order standard xPT values. The importance of new, more accurate, experimental information on low-energy T-T scattering is stressed.

Testing chiral symmetry breaking at DAΦNE

“…Massless Goldstone bosons always result, but a large qq-condensate is not essential. Indeed, in analogy with an antiferromagnet, the condensate could be small or even zero, as Jan Stern and collaborators [10] have suggested. It is the difference between these two pictures that DAΦNE can test.…”

“…where in standard χPT with a large qq-condensate, α is close to unity [4], while in generalized χPT with a smaller condensate [10] α can be as large as 4, when the condensate goes to zero. Thus either the amplitude is approximately…”

“…It is at the symmetry point that the difference is maximal. This is because moving closer to the physical regions the parameters of the Chiral Lagrangians (ℓ i , λ i ) [4,10] are necessarily fixed from experiment and the different expansions inevitably become more similar. Thus it is the amplitude at the symmetry point, Eqs.…”

“…These can be translated into values of the amplitude at the symmetry point, Eq. (6), with [10,18] 1.30 ≤ α ≤ 3.02 (10) for the second values of a 0 0 in Eq. (9).…”

Light quark masses and condensates in QCD

“…GχP T provides a theoretical basis for a systematic search of possible experimental tests of the importance of qq-condensation. In this way, the best manner to control the GOR ratio X GOR = 2 mB 0 /M 2 π and the quark mass ratio r = m s / m experimentally, has been found sofar in the low-energy π − π scattering [FSS91], [SSF93]. The corresponding scattering amplitude at the leading [Wei66] and one loop [GL83] level has to be corrected including the twoloop contribution, in order to achieve the theoretical accuracy needed for a decisive test.…”