Investigations into the BFKL mechanism with a running QCD coupling

Abstract

We present approximations of varying degree of sophistication to the integral equations for the ͑gluon͒ structure functions of a hadron ͑''the partonic flux factor''͒ in a model valid in the leading log approximation with a running coupling constant. The results are all of the BFKL type, i.e., a power in the Bjorken variable x B Ϫ with the parameter determined from the size ␣ 0 of the ''effective'' running coupling ␣ ϵ3␣ s / ϭ␣ 0 /ln(k Ќ 2 ) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k Ќ ) fluctuations along the emission chains and we obtain an exponential falloff in the relevant ϵln(k Ќ 2 ) variable, i.e., an inverse power (k Ќ 2 ) Ϫ(2ϩ) with the same parameter . This is different from the BFKL result for a fixed coupling, where the distributions are Gaussian in the variable with a width as in a Brownian motion determined by ''the length'' of the emission chains, i.e., ln(1/x B ). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change. ͓S0556-2821͑98͒00811-X͔ PACS number͑s͒: 12.38.Bx, 12.38.Aw

Small-x phenomenology – Summary of the 3rd Lund small-x workshop in 2004

“…Therefore there is no singularity for the minimum k ⊥ -value. This result agrees exactly with the result in the Linked Dipole Chain model, LDC [203,207], which is a reformulation of the CCFM model [24,25], interpolating between DGLAP and BFKL for non-k ⊥ -ordered chains.…”

“…In ref. [206] similarities between the Linked Dipole Chain model (LDC) [203,207] in momentum space and the Mueller dipoles in transverse coordinate space [134,135,154] are used to derive a scheme for implementing energy momentum conservation in Mueller's dipole formalism. It is conjectured that only those gluon emissions, which satisfy energy-momentum conservation, can correspond to real final state gluons, and that keeping only these (with a corresponding modification of the Sudakov form factor) will not only give a better description of the final states, but also account for essential parts of the NLO corrections to the BFKL equation.…”

Expanding running coupling effects in the hard Pomeron

“…(66) (or its analogues with various forms of higher-order correction) with a regularised running coupling, see for example [26,27] . A measure of the perturbative uncertainty on the prediction can then be made by comparing different regularisations and seeing how they affect the Green's function.…”

“…Current practice in numerical solutions of the small-x evolution equations (see for example [26,27]) is to evaluate a perturbative result with an infrared regularised coupling (e.g. with a cutoff) and then define the perturbatively accessible region in Y as that insensitive to the choice of regularisation.…”

Tunneling transition to the pomeron regime

“…This resummation was initially considered for fixed coupling [1], but subsequently interest developed in its extension to the (more physical) running coupling case [2,3]. One of the conclusions of these studies was that regardless of the hardness of the probes, there always exists a centre of mass energy beyond which the problem becomes entirely non-perturbative, see for example [4,5].…”