Se p 19 96 Vector Meson production in ep → epV

The diffractive production of vector mesons in ep interactions at low x is a subject of heated debates. This chapter consists of four contributions written by the original authors and expresses the possible scenarios which are to be investigated experimentally. 1 Hard diffractive vector meson production contributed by L. Frankfurt, W. Koepf and M. Strikman The derivation of our QCD formulas [1] consists of three essential steps: (i) The process factorizes into three stages: the creation of a quark-gluon wave packet, the interaction of this packet with the target, and the formation of the vector meson. The wave packet’s large coherence length, 1 2mNx , justifies using completeness over the intermediate states. (ii) For longitudinal polarization, the end point contribution is suppressed by 1/Q, which supports applying the factorization theorem. This important result follows from the well known light-cone wave function of a photon and conformal symmetry of pQCD, which dictates the dependence of the vector meson’s asymptotic wave function on the momentum fraction carried by the quarks. For transverse polarizations, the onset of the hard regime is expected at much larger Q since large distance effects are suppressed only by the square of a Sudakov type form factor, exp(−s 3π ln Q 2 k t ). (iii) As a result of the QCD factorization theorem, the hard amplitude factorizes from the softer blob [2]. Thus, within the leading αs lnQ 2 approximation, the cross section of hard diffractive processes can be written in terms of the distribution of bare quarks within the vector meson and the gluon distribution in the target. The respective cross section can thus be expressed through the light-cone wave function of the vector meson, ψV (z, b = 0), a well defined and intensively researched object in QCD. In addition, there is not much freedom in the choice of this wave function since the absolute normalization of the cross section is related to the vector meson’s leptonic decay width, ΓV→e+e−. Our numerical analysis has found a number of distinctive features of these hard diffractive processes (see Ref.[3] and references therein): 1. A significant probability of small transverse size (bqq̄ ≈ 3/Q) minimal Fock qq̄ configurations within the vector meson’s light-cone wave function. 2. A fast increase of the cross section at small x and a relatively slow Q dependence, both resulting from the Q evolution of the parton distributions. 3. To avoid contradiction with b-space unitarity, the increase of the cross section with decreasing x should slow down. For Q ∼ 5 GeV, this is expected at x ∼ 10 [3]. 4. For longitudinal polarization, an almost flavor and energy independent t-slope, while for transverse polarizations, soft QCD may reveal itself in a larger value as well as an energy dependence of the latter. 5. At large Q, the diffractive electroproduction ratio of ρ and φ mesons follows from the form of the e.m. current in the standard model, i.e. restoration of SU(3) symmetry. Some enhancement of the relative yield of the φ meson is expected due to its smaller size. 6. The diffractive photoproduction of J/ψ mesons is dominated by relativistic cc̄ configurations. Significant diffractive photoproduction of Υ mesons. 7. Large cross sections for the production of excited states, ep → epV , with a ratio proportional to MV ′ ΓV ′→e+e−, in qualitative difference from photoproduction processes. 8. Model estimates found large 1/Q corrections to the basic formulas resulting from quark Fermi motion within the vector meson and from shadowing effects evaluated within the eikonal approximation. However, the reliability of these estimates is still unclear since similar corrections follow from the admixture of qq̄g components to the vector meson’s wave function and because the elastic eikonal approximation is inappropriate. Note that, in an exact calculation, the contribution of more than two rescatterings by the qq̄ pair should be zero due to energy-momentum conservation. 2 γ p → V p at small t contributed by P. V. Landshoff All models [4, 5, 6, 7, 8, 9] couple the γ to the vector meson V through a simple quark loop, to which is attached a pair of gluons which interact with the proton. The models differ in two essentials: what they assume about the wave function that couples V to the qq̄, and what they assume about how the gluons interact with the proton. Because the models have the same quark loop, there is general agreement that the γ and the V should have the same helicity, and that