Hyperon Polarization from Unpolarized pp and ep Collisions

Cross section formulas for the Λ polarization in pp → Λ↑(`T )X and ep→ Λ↑(`T )X are derived and its characteristic features are discussed. In this report we discuss the polarization of Λ hyperon produced in unpolarized pp and ep collisions relevant for the ongoing RHIC-SPIN, HERMES and COMPASS experiments. According to the QCD factorization theorem, the polarized cross section for pp→ Λ↑X consists of two twist-3 contributions: (A) Ea(x1, x2)⊗ qb(x′)⊗ δq̂c(z)⊗ σ̂ab→c, (B) qa(x)⊗ qb(x′)⊗ Ĝc(z1, z2)⊗ σ̂′ ab→c, where the functions Ea(x1, x2) and Ĝc(z1, z2) are the twist-3 quantities representing, respectively, the unpolarized distribution in the nucleon and the polarized fragmentation function for Λ↑. δq̂c(x) is the transversity fragmentation function for Λ↑. a, b and c stand for the parton’s species, sum over which is implied. Ea and δq̂c are chiral-odd. Corresponding to the above (A) and (B), the polarized cross section for ep → Λ↑X (final electron is not detected) receives two twist-3 contributions: (A′) Ea(x1, x2)⊗ δq̂a(z)⊗ σ̂ea→a, (B′) qa(x)⊗ Ĝa(z1, z2)⊗ σ̂′ ea→a. The (A) contribution for pp→ Λ↑X has been analyzed in [1], where it was shown that (A) gives rise to growing PΛ at large xF as observed experimentally. Here we extend the study to the (B) term (see also [2]) at RHIC energy and also for the ep collision. The unpolarized twist-3 distribution EF,D(x1, x2) is defined in [1]. Likewise the twist-3 fragmentation function for a polarized Λ (with momentum `) is defined as the lightcone correlation function as (w = 0, ` · w = 1) 1 Nc ∑ X ∫ dλ 2π ∫ dμ 2π e −i λ z1 e −iμ( 1 z2 − 1 z1 〈0|ψi(0)|πX〉〈πX|gF (μw)wβψ̄j(λw)|0〉 = MN 2z2 (/̀)ij ⊥ĜF (z1, z2) + i MN 2z2 (γ5/̀)ij S α ⊥Ĝ 5 F (z1, z2) + · · · . (1)