Twist decomposition of nonlocal light-ray operators and harmonic tensor functions

Light–cone(LC) dominated hard scattering processes, like deep inelastic scattering and deeply virtual Compton scattering, and various hadronic wave functions, e.g., vector meson amplitudes, appearing in (semi) exclusive processes are most effectively described by the help of the nonlocal light–cone expansion [1].Thereby, the same nonlocal LC–operator, and its anomalous dimension, is related to different phenomenological distribution amplitudes, and their Q–evolution kernels [2]. Growing experimental precision requires the consideration of higher twist contributions. Therefore, it is necessary to decompose the nonlocal LC–operators according to their twist content. Unfortunately, ‘geometric’ twist (τ) = dimension (d)− spin (j), introduced for the local LC–operators [3] cannot be extended directly to nonlocal LC–operators. Therefore, motivated by LC–quantization and by kinematic phenomenology the notion of ‘dynamic’ twist (t) was introduced counting powers Q of the momentum transfer [4]. However, this notion is defined only for matrix elements of operators, is not Lorentz invariant and its relation to ‘geometric’ twist is complicated, cf. [5]. Here, we carry on a systematic procedure to uniquely decompose nonlocal LC– operators into harmonic operators of well defined geometric twist, cf. Ref. [6]. This will be demonstrated for tensor operators of low rank, namely (pseudo)scalars, (axial) vectors and (skew)symmetric tensors Thereby, various harmonic tensor operators (in D = 2h space-time dimensions) are introduced being related to specific infinite series of symmetry classes which are defined by corresponding Young tableaus. In the scalar case these LC–operators are series of the well-known harmonic polynomials corresponding to (symmetric) tensor representations of the orthogonal group SO(D), cf. [7]. Symmetric tensor operators of rank 2 are considered as an example.