DIRAC Experiment - Tests of nonperturbative QCD predictions

The strong interaction dynamics is still an open question within the Standard Model (SM) of elementary particles. Quantum Chromodynamics (QCD), responsible for the strong interaction sector of SM, exhibits two distinct features: asymptotic freedom and quark color confinment. Only the asymptotic freedom, has successfully been tested so far. This is evident at high momentum transfers (Q > 1 GeV), or equivalently at short relative distance $\Delta r \sim \hbar/Q$ ( $\Delta r < 0.2~fm$) and can be described within perturbative QCD approach. Here the constituent quarks behave as weakly interacting, nearly massless particles. The QCD in the perturbative region, as any gauge theory with massless fermions, presents chiral symmetry.

In the nonperturbative region of low momentum transfer, say Q < 100 MeV, or equivalently at large distance ( $\Delta r > 2~fm$), asymptotic freedom is absent, and quark confinment takes place. In this region the chiral symmetry of QCD must be spontaneously broken.

The Chiral Perturbation Theory (ChPT) seems to be the candidate theory for low momentum transfer processes. It exploits the mechanism of spontaneous breaking of chiral symmetry (SBChS), or in other words, the existence of a quark condensate. In order to test the existence of the quark condensate, the particularly significant symmetry effect refers to the S-wave $\pi \pi$ scattering lengths. Within ChPT, Gasser and Leutwyler[1,2,3] and also Bijnens and collaborators[4] as well within the Generalized Chiral Perturbation Theory (GChPT), Stern and collaborators[5], have obtained expressions for the $\pi \pi$ scattering amplitude in the chiral expansion. The values predicted for the isospin I=0 and I=2 S-wave scattering lengths a₀⁰ and a₀² can be confronted with the future experimental values of the DIRAC Experiment[6]. It aims to determine the difference of the scattering lengths $\Delta = \left\vert a_0^0 - a_0^2 \right\vert$ with 5% accuracy, by measuring the lifetime of pionium ($\pi^+ \pi^-$ bound state). For the first time experimental evidence in favour of or against the existence of a strong quark condensate in the QCD vacuum could be within reach.

The experimental setup (Fig.1) has been designed to detect pion pairs and to select pairs from pionium breakup, with low relative momentum, with a resolution better than 1 MeV/c. It was installed and commissioned in 1998 at the ZT8 beam area of the PS East Hall at CERN. After a calibration run in 1998, DIRAC has been collecting data since summer 1999.

Figure 1: Experimental setup