The electromagnetic properties of the light pseudoscalar mesons via the Primakoff effect

Abstract

The PrimEx (Primakoff Experiment) Collaboration is currently preparing to perform a high precision (1.4%) measurement of the two photon decay width of the neutral pion, Γ π o →γγ . The proposed 12 GeV upgrade of the CEBAF accelerator will enable a significant enlarging of the scope of these studies to include measurements of the two photon decay widths of the η and η mesons, as well as of the transition form factors of all the light pseudoscalar mesons (π o , η, η ). These precision measurements would have a significant impact on the experimental determination of the ratios of the light quark masses (m u , m d , m s ), and on our understanding of some fundamental issues in QCD. The Radiative WidthsThe two-photon decay mode of the π 0 involves the explicit breaking of a classical symmetry by the quantum fluctuations of the quark fields coupling to a gauge field [1]. This phenomenon, called anomalous symmetry breaking, is of pure quantum mechanical origin, and in this case involves the coupling of the quarks to photons[2]. In the limit of vanishing quark masses, the anomaly leads to the π 0 → γγ decay width[1, 2]:where F π = 92.42 ± 0.25M eV is the pion decay constant [3]. The current experimental value, summarized in figure 1, is 7.84 ± 0.56 eV [3] and is in good agreement with the predicted value in the chiral limit. Stimulated by the PrimEx proposal, next to leading order calculations have been performed giving Γ π 0 →γγ = 8.10 eV with an estimated uncertainty of less than 1%[4] [5]. With its 1.4% level of precision, such effects will be tested in the PrimEx experiment. The availability of 12 GeV beams at Jefferson Lab will also enable measurements of the η radiative width. One decay that is particularly important is the decay η → πππ, which is driven by isospin breaking, and thus gives access to the quark mass ratio (m u − m d )/m s . In a very elegant analysis, Leutwyler[11] constructed a relation, now called Leutwyler's ellipse, given by:where the semi-major axis Q is given by the ratio:withm = (m u + m d )/2. One way to determine Q is given by a ratio of meson masses: