Azimuthal Asymmetries in Hadronic Final States at HERA

The distribution of hadrons produced in deeply inelastic electron–proton collisions depends on the azimuthal angle between lepton scattering plane and hadron production plane in the photon-proton centre-of-mass frame. In addition to the well known up-down asymmetry induced by the azimuthal dependence of the Born level subprocess, there is also a non-vanishing left-right asymmetry, provided the incoming electron is polarized. This asymmetry is time-reversal-odd and induced by absorptive corrections to the Born level process. We investigate the numerical magnitude of azimuthal asymmetries in semi-inclusive hadron production at HERA with particular emphasis on a possible determination of the time-reversal-odd asymmetry. The increase in the statistical accuracy of deep inelastic scattering (DIS) data at the HERA collider will soon allow to investigate hadronic final state observables which go beyond hadron multiplicity distributions [1] and jet rates that have been studied up to now. Observables of particular interest are angular correlations between the lepton scattering plane, defined by the incoming and outgoing lepton momenta and the hadron production plane, defined by incoming proton and outgoing hadron momentum. These correlations probe the dynamics and colour flow of the underlying partonic interaction at a detailed level, such that they can be used to test the perturbative description of hadron production via partonic fragmentation. An accurate prediction of the perturbatively induced asymmetries is in particular desirable since azimuthal correlations in semi-inclusive DIS have been suggested as probes of non-perturbative effects in various places in the literature [2]. In this paper, we estimate the magnitude of the different azimuthal asymmetries for kinematical conditions at the HERA collider, using parton model expressions at leading order. Particular emphasis is put on time-reversal-odd (T -odd) asymmetries, resulting from absorptive contributions to the parton level scattering amplitudes [3]. These T odd effects manifest in left-right asymmetries of the hadron distribution with respect to the lepton scattering plane [6, 7]. Corresponding to antisymmetric contributions to the hadronic tensor, their observation requires either the contribution from parity violating weak interactions or polarization of the initial lepton beam. Given that lepton beam polarization will soon be realized for the HERA collider experiments, both cases shall be investigated below. Perturbative T -odd effects have up to now only been studied experimentally in polarized electron-positron annihilation at SLAC [4], where the expected asymmetries [5] are however too small to be measured directly, such that only upper limits could be determined [4]. The kinematics of the semi-inclusive reaction l(k) + p(p) −→ l(k) + h(P ) +X are described by the following invariant variables Q = −q = −(k − k) ,