Investigations of Azimuthal Asymmetry in Semi-Inclusive Leptoproduction

We consider the azimuthal asymmetries in semi-inclusive deep inelastic leptoproduction arising due to both perturbative and nonperturbative effects at HERMES energies and show that the k2 T /Q 2 order corrections to 〈cos φ〉 and 〈cos 2φ〉 are significant. We also reconsider the results of perturbative effects for 〈cosφ〉 at large momentum transfers [1] using the more recent sets of scale-dependent distribution and fragmentation functions, which bring up to 18% difference in 〈cosφ〉. In the same approach we calculate the 〈cos 2φ〉 as well. On leave of absence from Yerevan Physics Institute, Alikhanian Br.2, 375036 Yerevan, Armenia e-mail: [email protected] On leave of absence from Yerevan Physics Institute, Alikhanian Br.2, 375036 Yerevan, Armenia e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] 1 The semi-inclusive deep inelastic process l(k1) + p(P1) → l ′ (k2) + h(P2) +X, where l and l ′ are charged leptons and h is a observed hadron, has been recognized [2] as an important testing ground for QCD. In particular, measurement of the azimuthal angle φ of the detected hadron around the virtual photon direction (Fig.1) provides information on the production mechanism. Different mechanisms to generate azimuthal asymmetries 〈cosφ〉 and 〈cos 2φ〉 have been discussed in the literature. Georgi and Politzer [2] found a negative contribution to 〈cosφ〉 in the first-order in αS perturbative theory and proposed the measurement of this quantity as a clean test of QCD. However, partons have nonzero transverse momenta (kT ) as a consequence of being confined by the strong interactions inside hadrons. As Cahn [3] showed, there is a contribution to 〈cosφ〉 from the lowest-order processes due to this intrinsic transverse momentum. Therefore the perturbative QCD alone does not describe the observed azimuthal angular dependence. In connection with this Chay, Ellis and Stirling [1] combined these perturbative and nonperturbative mechanisms and analyzes the quantity 〈cosφ〉 as a function of the detected hadron’s transverse momentum cutoff PC . In this paper we reconsider the results obtained in Ref. [1] at HERMES energies and show that the k T/Q 2 order corrections to 〈cosφ〉 and 〈cos 2φ〉 are significant, whereas at E665 energies in Fermilab [4] these contributions are less then 10% [1]. We also recalculate the behavior of 〈cosφ〉 in the kinematic regime at HERA where perturbative QCD effects should dominate, by using the new sets of scale-dependent distribution and fragmentation functions which bring up to 18% difference to quantity 〈cosφ〉 obtained in Ref. [1]. In the same approach the quantity 〈cos 2φ〉 is calculated as well. The quantities 〈cosφ〉 and 〈cos 2φ〉 are defined as 〈cosφ〉 = ∫ dσ cosφ+ ∫ dσ cos φ ∫ dσ(0) + ∫ dσ(1) , (1) 〈cos 2φ〉 = ∫ dσ cos 2φ+ ∫ dσ cos 2φ ∫ dσ(0) + ∫ dσ(1) , (2) where dσ (dσ) is the lowest-order (first-order in αS) hadronic scattering cross section expressed as dσ ∼ Fi(ξ, Q )⊗ dσij ⊗Dj(ξ ′ , Q), where Fi(ξ, Q ) is the probability distribution describing an i-type parton with a fraction ξ of the target momentum, pμ1 = ξP μ 1 , dσij describes the partonic semi-inclusive process (Fig.2) and Dj(ξ ′ , Q) is the probability distribution for a j-type parton to fragment producing a hadron with a fraction ξ ′ of the partons momentum, P μ 2 = ξ ′ pμ2 . In Eqs.(1, 2) the integrations are over P2T , φ, xH , y and zH . These usual set of kinematic variables are defined as: xH = Q 2(P1q) , y = (P1q) (P1k1) , zH = (P1P2) (P1q) , where q-momentum of the virtual photon (Q = −q), and the parton variables x = xH ξ = Q 2(p1q) , z = zH ξ′ = (p1p2) (p1q) .