ar X iv : h ep - p h / 99 06 26 1 v 1 4 J un 1 99 9 1 Hard exclusive production of two pions :

The leading twist parametrization of dipion mass distribution in hard exclusive reactions is proposed. Its parameters are related to quark distributions (usual and skewed) in the pion and to distributions amplitudes of mesons (π, ρ, etc.). We show that measurements of the shape of dipion mass distribution in hard exclusie reactions can give important information about partonic structure of the pion. The expression for the amplitude of the reaction γ * γ → ππ near the threshold in terms of singlet quark distribution in the pion is presented. 1. Dipion mass distribution in γ * + p → π + π − + p Recently it became possible to measure with good precision two pion hard exclusive production in the deeply virtual photon fragmentation region in the range of dipion masses 0.4 ≤ m ππ ≤ 1.5 GeV (see talks at this conference [ 1] and refs. [ 2, 3]). Owing to QCD factorization theorem for hard exclusive reaction [ 4] the dependence of the amplitude of the reactions γ * L + T → ππ + T ′ (1) on the dipion mass m ππ factorizes at leading order into the universal (independent of the target) factor: 1 0 dz z Φ I (z, ζ, m ππ ; Q 2). (2) Here Φ I (z, ζ, m ππ ; Q 2) is two-pion light cone distribution amplitude (2πDA), which depends on z–longitudinal momentum carried by the quark, ζ characterizing the distribution of longitudinal momentum between the two pions, and the invariant mass of produced pions m ππ , superscript I stands for isospin of produced pions (I = 0, 1). The dependence on the virtuality of the incident photon Q 2 is governed by the evolution equation. The 2πDA's were introduced recently in [ 5] in the context of the QCD description of the process γ * γ → 2π, its detailed properties were studied in [ 6], we refer to these papers for details. For the process (1) at small x Bj (see e.g. recent measurements [ 2, 3]) the production of two pi-ons in the isoscalar channel is strongly suppressed relative to the isovector channel, because the former is mediated by C-parity odd exchange. At asymptotically large Q 2 QCD predicts the following simple form for the isovector 2πDA [ 7, 6]: Φ I=1 as (z, ζ, m ππ) = 6z(1 − z)(2ζ − 1)F π (m …