Twist-3 gluon fragmentation contribution to polarized hyperon production in unpolarized proton-proton collision

Twist-3 gluon fragmentation contribution to transversely polarized hyperon production in semi-inclusive deep-inelastic scattering

“…We work in the hadron frame in which the momenta of the initial proton and the virtual photon are collinear [10]. Following the formalism developed for 𝑝 𝑝 → Λ ↑ 𝑋 in [6], we could obtain the LO cross section as…”

“…S 1,2,3,4 = sin Ψ 𝑠 and S 8,9 = cos Ψ 𝑠 , where Ψ 𝑠 denotes the azimuthal angle of the transverse spin vector of the final hyperon. According to the formalism developed in [6], intrinsic, kinematical, and the dynamical twist-3 FFs as well as the derivative of kinematical FFs appear in the cross section. By using the QCD equation-of-motion relations and the Lorentz invariance relations [9], one can eliminate the intrinsic FF, Δ Ĝ3 T (𝑧), and the derivative of the kinematical FFs, 𝜕 Ĝ (1) 𝑇 (𝑧)/𝜕 (1/𝑧) and 𝜕Δ Ĥ (1) 𝑇 (𝑧)/𝜕 (1/𝑧), in favor of the other twist-3 FFs.…”

“…In this framework, the transverse polarization of hyperons appear as a twist-3 observable to which nonperturbative multi-parton correlation functions contribute. The complete leading-order (LO) cross sections contributing to 𝑝 𝑝 → Λ ↑ 𝑋 were derived in [2][3][4][5][6].…”

Transverse Polarization of Hyperons Produced in Semi-Inclusive Deep Inelastic Scattering

“…Derivation of the twist-3 cross sections for SSAs required lots of technical development. By now the collinear twist-3 formalism for all kinds of the twist-3 distribution functions (DFs) and the fragmentation functions (FFs) has been well established in the leading order (LO) with respect to the QCD coupling constant [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Those functions are, in general, not independent from each other but obey some constraint relations based on the operator identities.…”

“…In this paper, we study the transverse polarization of hyperons produced in semi-inclusive deep inelastic scattering (SIDIS), ep → eΛ ↑ X, in the LO collinear twist-3 factorization. As for the case of pp → Λ ↑ X [20,[27][28][29][30], two kinds of the twist-3 cross sections contribute. One is from the twist-3 DF in unpolarized proton combined with the "transversity" FF for the polarized Λ.…”