Construction of nonlocal light–cone operators with definite twist

With the growing precision of data for light– cone dominated hard scattering processes like DIS, DVCS and various (semi) exclusive processes a better perturbative understanding of QCD concerning higher twist contributions is required. Thereby the nonlocal light–cone expansion (LCE) is optimally adapted since the same nonlocal LC operator, and its anomalous dimension, are related to different phenomenological distribution amplitudes, and their Q–evolution kernels [ 1, 2]. But, ‘geometric’ twist = dimension − spin, τ = d − j, introduced for the local LC–operators [ 3] cannot be extended directly to the nonlocal LC– operators. On the other hand, motivated by LC– quantization where the quark fields may be decomposed into ‘good’ and ‘bad’ components [ 4] and by kinematic phenomenology [ 5] the notion of ‘dynamic’ twist (t) was introduced counting powers Q of the momentum transfer. However, this notion is defined only for matrix elements of operators, is not Lorentz invariant and its relation to ‘geometric’ twist is quite complicated, cf. [ 6]. Here, we introduce a systematic procedure to uniquely decompose nonlocal LC–operators into harmonic operators of well defined geometric twist, cf. Ref. [ 7]. This will be demonstrated for the case of (pseudo)scalar, (axial) vector and (skew) tensor bilocal quark light–ray operators.