Quantum Chromodynamics in Exclusive Processes

Abstract

According to Brodsky and Lepage[1] the helicity amplitude for an exclusive reaction AB → CD at large momentum transfer is expressed by a convolution of universal process independent distribution amplitudes (DA) with an amplitude representing the scattering of constituents. The DA’s specify the distribution of the longitudinal momentum fractions the constituents carry inside their parent hadrons. They are the wave functions of constituent Fock states integrated over the intrinsic transverse (Fermi) momentum up to a soft scale. The convolution integral manifestly factorizes long (DA’s) and short (constituent scattering) distance physics. Explicitly, a helicity amplitude reads

$$ {{M}_{CDAB}}(s,t)=\int\limits_{i=A,B.C.D}{[d{{x}_{i}}]}\phi _{c}^{*}({{x}_{C}},{{Q}^{2}})\phi _{D}^{*}({{x}_{D}},{{Q}^{2}})\hat{T}({{x}_{i}},s,t){{\phi }_{A}}({{x}_{A}},{{Q}^{2}}){{\phi }_{B}}({{x}_{B}},{{Q}^{2}}) $$

(1.1)

where helicity labels are omitted for convenience. [dx _i ] is a multi-index defined as

$$ [d{{x}_{i}}]=\prod\limits_{j=1}^{n}{d{{x}_{ij}}}\delta (1-\sum\limits_{j}{{{x}_{ij}}}) $$

(1.2)

x _ij is the momentum fraction the constituent j of hadron i carries.

Supported in part by the Bundesministerium für Forschung und Technologie, FRG under contract number 06 WÜ 765.