Leading Quark Distribution Functions

Current fragmentation in semiinclusive deep inelastic leptoproduction offers, besides refinement of inclusive measurements such as flavor separation and access to the chiral-odd quark distribution functions hq1(x) = δq(x), the possibility to investigate intrinsic transverse momentum of hadrons via azimuthal asymmetries. LEADING QUARK DISTRIBUTION FUNCTIONS In deep-inelastic leptoproduction (DIS), the soft hadron structure enters via the quark distribution functions. These distribution functions for a quark can be obtained from the lightcone correlation functions [1–4]. Φij(x) = ∫ dξ 2π e 〈P, S|ψj(0)ψi(ξ)|P, S〉 ∣ ∣ ∣ ∣ ∣ ξ=ξT=0 , (1) depending on the lightcone fraction of a quark (with momentum p), x = p/P. In particular the At leading order, the relevant part of the correlator is Φγ (Φγ)ij = ∫ dξ 2π √ 2 e 〈P, s|ψ +j(0)ψ+i(ξ)|P, s〉 ∣ ∣ ∣ ∣ ∣ ξ=ξT=0 (2) where ψ+ ≡ P+ψ = 12γγψ is the good component of the quark field [5]. 1) For inclusive leptoproduction the lightlike directions n± and lightcone coordinates a ± = a ·n∓ are defined through hadron momentum P and the momentum transfer q, P = Q xB √ 2 n+ + xBM 2 Q √ 2 n−, q = − Q xB √ 2 n+ + Q √ 2 n−. Explicitly, the matrix M = (Φγ) in Dirac space using a chiral representation becomes for a spin 0 target the following 4 × 4 matrix, Mij =    f1(x) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f1(x)    (3) In hard processes only two Dirac components are relevant, one of them righthanded and one lefthanded (ψR/L = 1 2 (1± γ5)ψ). Restricting ourselves to those states, the matrix for a spin 0 target becomes Mij =    f1(x) 0 0 f1(x)    R