ar X iv : h ep - p h / 02 11 40 2 v 1 2 6 N ov 2 00 2 Perturbative and Nonperturbative Aspects of Azimuthal Asymmetries in Polarized ep

We discuss the possibilities of testing of perturbative quantum chromodynamics through azimuthal asymmetries in polarized ep in the context of future collider and fixed target facilities, such as Electron Ion Collider and TESLA-N. It is widely recognized that the study of the distributions in the azimuthal angle φ of the detected hadron in hard scattering processes provide interesting variables to study in both non-perturbative and perturbative regimes. They are of great interest since they test perturbative quantum chromodynamics (QCD) predictions for the short-distance part of strong interactions and yield an important information on the long-distance internal structure of hadrons which computed in QCD by non-perturbative methods. We discuss here the perturbative aspects of spin-independent, singleand doublespin azimuthal symmetries in leptoproduction processes. The non-perturbative aspects of some of them have been discussed in these proceedings (see Refs. [1-5]). Spin-independent cosφ , cos2φ asymmetries Different mechanisms to generate spin-independent azimuthal asymmetries in semiinclusive processes have been discussed in the literature. Georgi and Politzer [6] 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, as Cahn [7] showed, there is a contribution to 〈cosφ〉 from the lowest-order processes due to this intrinsic transverse momentum. The measurements indicate large negative cosφ asymmetry [8, 9] and the simple QCD-improved parton model rather well describes the data, where essential contribution comes from non-perturbative intrinsic transverse momentum effects. Recently, the expectation values of cosφ and cos2φ in the deep inelastic electroproduction of single particles in the high Q2 region have been observed by ZEUS detector at HERA [10] for the first time. For hadrons produced at large transverse momenta the results are in agreement with QCD predictions [11, 12, 13]. Since the non-perturbative 1 Presented at the 15th International Spin Physics Symposium (Spin 2002), Brookhaven National Laboratory, September 9-14, 2002. contributions to 〈cos2φ〉 are of 1/Q2, its precise measurement may provide clear evidence for a pQCD and an alternative possibility to measure FL(x,Q 2) [14]. Double-spin cosφ , cos2φ asymmetries The cosφ and cos2φ asymmetries arise also in semi-inclusive DIS of longitudinally polarized electrons off longitudinally polarized protons. Recently, the non-perturbative phenomena of these asymmetries has been considered [15] and a sizable negative cosφ asymmetry for π+ electroproduction was predicted. Perturbative contributions proportional to αs(Q) . . .g1 . . . will likely appear at the same point where the twist-3 function (M/Q) . . .gL appears [15, 16, 17], like contributions proportional to αs(Q) . . . f1 . . . appear at the same point where the function (M/Q) . . . f⊥ 1 appears [6, 15, 16]. Then the cosφ dependence of the double longitudinal spin asymmetry, ALL = dσ++ +dσ−−−dσ+−−dσ−+ dσ++ +dσ−− +dσ+− +dσ−+ , (1) for charged pion electroproduction have been examined [18]. The subscript LL denotes the longitudinal polarization of the beam and target, and the superscripts ++,−− (+−,−+) denote the helicity states of the beam and target respectively, corresponding to antiparallel (parallel) polarization. In general, due to parity conservation in the electromagnetic and strong interactions, Eq.(1) can be written in terms of the spin-independent (σ ) and double-spin (∆σ ) cross sections of semi-inclusive DIS ALL = 2 ∑m=1 ∆σ m LL cos([m−1] ·φ) 4 ∑m=1 σ m UU cos([m−1] ·φ) , (2) Up to sub-leading order 1/Q the Eq.(2) can be rewritten as ALL = ∆σ 1 LL/2σ 1 UU + 〈cosφ〉LL · cosφ 1+2〈cosφ〉UU · cosφ , (3) where 〈cosφ〉UU and 〈cosφ〉LL are unpolarized and double polarized cosφ moments, respectively. The ALL depends on and allows the simultaneous determination of the spinindependent and double-spin cosφ -moments of the cross section. A cos2φ asymmetry only appears at order 1/Q2, unless one allows for T-odd structure functions [2, 4]. Beam/target single-spin azimuthal asymmetries The interest in the single beam asymmetry in the pion electroproduction in semiinclusive deep inelastic scattering of longitudinally polarized electrons off unpolarized nucleon resides in the fact that they probe the antisymmetric part of the hadron tensor, which entirely due and particularly sensitive to final state interactions (FSI). In longitudinally polarized electron scattering it shows up as a < sinφ > asymmetry for the produced hadron and expressed as 〈sinφ〉 = ±〈 ~s× ~k′ ·Ph⊥ |~s×~k||~Ph⊥| 〉, (4) where ~s denoted the spin vector of the electron (the upper (lower) sign for right (left) handed electrons), ~k (~k′) and Ph⊥ are three vectors of incoming (outgoing) electron and the produced hadrons transverse momentum about virtual photon direction. This asymmetry is related to the left-right asymmetry in the hadron momentum distribution with respect to the electron scattering plane, A = ∫ π 0 dφdσ − ∫ 2π π dφdσ ∫ π 0 dφdσ + ∫ 2π π dφdσ , (5) which is 4/π times < sinφ >. Among various proposed tests to measure the gluon self-coupling, the tests based on observation of time-reversal-odd (T-odd) processes, which are highly sensitive to FSI, are particularly promising. In the one-loop order, which is the leading order for T-odd quantities in pQCD [19], the left-right asymmetry is quite sensitive to the gluon selfcoupling [20], and even the qualitative observation of such effects is sufficient to establish its existence. Furthermore, they are fairly insensitive to the poorly known gluon distribution and fragmentation functions [20]. The magnitude of this asymmetry for kinematical conditions (assuming √ s = 300 GeV) at HERA collider have been evaluated using parton model expressions at leading order [21]. Although the asymmetry appears small at first sight, their measurement may still be possible. An experimental determination of it is therefore a challenging task. In particular by including only hadrons above a minimal transverse momentum in the measurement, the asymmetries can be suppressed to O (α(1) S ). It is worthy to not that in the electromagnetic scattering the difference in magnitude between the opposite helicity measurements and the asymmetry < sin2φ > is proportional the parity-violating effects. Within the last few years, after appearance of experimental results from HERMES [22, 23] and SMC [24] collaborations on single target-spin azimuthal asymmetries in semi-inclusive pion electroproduction the subject obtained much more attention. It is considered as one of the ways to access and measure third, completely unknown distribution function, so-called, transversity. This twist-2 function is equally important for the description of quarks in nucleons as the more familiar function g1(x); their information is complementary (for a review of transversity see Refs. [25, 26]). In the perturbative regime the single target-spin asymmetries also should be different from zero in the one-loop order. They are remaining out of attention, while they may give a valuable information about the behavior of QCD interactions under discrete symmetry operations and may test our understanding of FSI at the perturbative level. The future collider and fixed target facilities, such as Electron Ion Collider (EIC) [27] and TESLA-N [28] will be very important for deeper study of considered azimuthal asymmetries. In particular, the wide and tunable range of collision energies at EIC will allow to study the nonperturbative and perturbative effects of azimuthal asymmetries consistently. Polarization of electron and proton spins will allow to measure all discussed asymmetries as well as their different combinations simultaneously. Some of the asymmetries are expected to be small, thus the facilities with high luminosity, such as EIC, TESLA-N are required. From the theoretical side, a realistic estimates of these azimuthal asymmetries for the future collider and fixed target facility kinematics are needed. I am grateful to Abhay Deshpande and Werner Vogelsang for many valuable discussions and the Physics Department at Brookhaven National Laboratory for hospitality.