Abstract
I study the behavior of the gauge-invariant gluon bi-local operator with space- like separation at large longitudinal distances. Performing the Fourier transform, I also calculate the behavior of the pseudo and quasi gluon PDF at low Bjorken x and compare it with the leading and next-to-leading twist approximation. I show that the pseudo-PDF and quasi-PDF are very different at this regime and that the higher twist corrections of the quasi-PDF come in not as inverse powers of P but as inverse powers of xBP.
Highlights
Using the light-ray operators, obtained as analytic continuation of local twist-two operators [16–20], we will calculate the behavior of the leading twist (LT) and next-toleading twist (NLT) contributions for the gluon Ioffe-time distribution at large longitudinal distances as well as for the pseudo-PDF and quasi-PDF at low-xB, and compare them with the behavior given by the BFKL resummation result
When we move into the low-xB region, we notice a strong disagreement which confirms the necessity of a ln x1B resummation represented by BFKL eq
The main result is that the pseudo-PDF and the quasi-PDF have a very different behavior at low-xB
Summary
We review the HE-OPE formalism applied to the T-product of two electromagnetic currents in deep inelastic scattering (DIS). Performing the functional integration over the spinor fields using the quark propagator (3.1), the T-product of two electromagnetic currents is given in terms of the impact factor, which is related to the probability for the virtual photon to split into a quark-antiquark pair, and matrix elements of Wilson line which takes into accounts the recoil of the target. To complete the HE-OPE procedure applied to DIS case, we need to find, employing the background field method, the evolution equation of the operator Tr{Uzη1Uz†2η} with respect to the rapidity parameter. [28–31] where the notion of composite conformal Wilson line operator is introduced The motivation for this transition is to restore conformal invariance of the NLO BK evolution equation and of the NLO impact factor.
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