ar X iv : h ep - p h / 04 01 15 7 v 1 2 1 Ja n 20 04 PROBING TRANSVERSITY IN ELECTROPRODUCTION OF TWO VECTOR MESONS

Electroproduction of two vector mesons with a large rapidity gap between them provides the first feasible selective access to chiral-odd GPDs [1]. The scattering amplitude of the process γ * N → ρ 0 L ρ + T N ′ may be represented as a convolution of an impact factor describing the γ * → ρ 0 L transition and an amplitude describing the N → ρ + T N ′ transition, analogously to deeply exclusive electroproduction of a meson, the virtual photon being replaced by a Pomeron. The production of a transversely polarized vector meson ρ + T selects a chiral-odd GPD in the proton. The study of transversity [2] is of fundamental interest for understanding the spin structure of nucleons. Generalized Parton Distributions (GPDs) are the non-perturbative objects encoding the information about the quark and gluon proton structure in the most complete way [3]. While the chiral even GPD may be probed in various hard exclusive processes, no single one has yet be proven to be sensitive to transverse spin dependent chiral-odd GPDs [4, 5]. In the massless quark limit, the chiral-odd functions may appear only in pairs in a non-vanishing scattering amplitude, so that chirality flip encoded in one of them is compensated by another. The natural probe for the forward chiral-odd distributions is the Drell-Yan process, containing the convolution of chiral-odd distributions of quark and antiquark [6]. Its nonforward analog is provided by the hard exclusive production of a transversely polarized vector meson, where the quark transversity distribution in the nucleon is substituted by the chiral-odd GPD. The generalized (skewed) transversity distribution in nucleon target F T ζ (x) described by the polarization vector n µ is defined by the formula N(p 2 ′ , n)|¯ q(0)σ µ ν q(y)|N(p 2 , n) = (1) = ¯ u(p 2 ′ , n)σ µ ν u(p 2 , n) 1 0 d x 1 e −ix 1 (p 2 y) F T q ζ (x 1) − e ix 2 (p 2 y) F T ¯ q ζ (x 1) , where σ µ ν = i/2[γ µ , γ ν ], x 2 = x 1 − ζ. However, the simplest realization of this idea, namely the hard exclusive electropro-duction of a transversely polarized vector meson, results in a zero contribution [7], [8]. We suggest another process which allows to access the chiral-odd GPD's by " …