The pion-pion scattering lengths from DIRAC

The scattering lengths of a two pion system are the golden magnitudes to test the QCD predictions in the low energy sector. The DIRAC (PS-212) experiment at CERN will obtain a particular combination of the S-wave isospin 0 and 2 scattering lengths by measuring the lifetime of pionium, the hydrogen-like π+π− atom. This measurement tests the accurate predictions of the Chiral Perturbation Theory. The most recent experimental results are presented. INTRODUCTION DIRAC experiment, conducted at CERN, is measuring the lifetime of the ground state of pionium, the hydrogen-like π+π− atom [1]. The decay of pionium is dominated by the strong channel π+π− → π0π0 (BR=94%). The ground state lifetime is related to the S-wave isospin 0 and 2 scattering length difference by the Deser type formula known to NLO [2]: 1 τ = 2 9 α3 √ M2 π −M 2 π0 −α 2M2 π/4 ∣ ∣a0 −a 2 0 ∣ ∣ 2 (1+δ ), (1) where α is the fine structure constant, Mπ the mass of the charged pions, Mπ0 the mass of the neutral pion and δ the correction to NLO (δ = 0.058). The Chiral Perturbation Theory has a precise prediction to O(p6) for this difference and hence for the lifetime of pionium [3]: