The low energy ππ amplitude to one and two loops

Abstract

The low-energy ππ amplitude is computed explicitly to two-loop accuracy in the chiral expansion. It depends only on six independent (combinations of) low-energy constants which are not fixed by chiral symmetry. Four of these constants are determined via sum rules which are evaluated using ππ scattering data at higher energies. Dependence of the low-energy phase shifts and of the threshold parameters on the remaining two constants (called α and β) are discussed and compared to the existing data from K l4 experiments. Using generalised χPT, the constants α and β are related to fundamental QCD parameters such as the quark condensate 0|qq|0 and the quark mass ratio m s / m. It is shown that forthcoming accurate low-energy ππ data can be used to provide, for the first time, experimental evidence in favour of or against the existence of a large quarkantiquark condensate in the QCD vacuum.

Towards a determination of the chiral couplings at NLO in 1/NC: L8r(μ) and C38r(μ)

“…The precision required in present phenomenological applications makes necessary to include corrections of O(p 6 ). While many two-loop χPT calculations have been already performed [7,8,9,10,11,12,13,14,15], the large number of unknown low-energy couplings (LECs) appearing at this order puts a clear limit to the achievable accuracy [16].…”

Testing chiral symmetry breaking at DAΦNE

“…This forces a 0 0 and a 2 0 to follow what is known as the universal curve of Morgan and Shaw [16], along which all phase-shift solutions and all models lie. Standard χPT [17] gives a 0 0 = 0.21 ± 0.01, for example, at 2 loops with electromagnetic corrections, while in generalized χPT a 0 0 is bigger [18]. For instance if α = 3 (Eq.…”

“…Clearly greater precision on the phases would be achieved if the [29] and Geneva-Saclay (solid dots) [30] experiments as a function of ππ mass. The curves are the predictions of two loop χPT : the Standard result [17] for which α ≃ 1.2 and for α = 2, 3 of Generalised χPT [18]. formfactors F , G, H were modelled as in χPT [28], but this would be prejudicing the result.…”

“…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).…”

A status report concerning theoretical predictions for various kaon decays

“…in 'generalized CHPT' [15], accurate data could tell us which is the behaviour of the quark condensate in the chiral limit [7,8].…”