Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

TL;DR

This work applies the Principle of Maximum Conformality (PMC) to the NLL BFKL Pomeron intercept, transforming from the MS-bar to the physical MOM scheme and absorbing β-dependent terms into the running coupling to achieve improved perturbative convergence. The authors derive the PMC-scale μ_R^PMC and show the intercept ω_MOM^PMC has weak dependence on the reggeized gluon virtuality and reduced gauge sensitivity, enabling more reliable high-energy phenomenology. Numerical results yield constrained intercept ranges across gauges and Q^2, and comparisons with photon-photon collision data illustrate both the strengths of PMC and the need for full NLO impact-factor calculations. The extended renormalization group further refines scheme-scale relations, suggesting robust predictions for future collider energies and providing a framework for precision high-energy QCD analyses.

Abstract

We apply the principle of maximum conformality (PMC) to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron intercept at the next-to-leading logarithmic (NLL) accuracy. The PMC eliminates the conventional renormalization scale ambiguity by absorbing the non-conformal $\{β_i\}$-terms into the running coupling, and a more accurate pQCD estimation can be obtained. After PMC scale setting, the QCD perturbative convergence can be greatly improved due to the elimination of renormalon terms in pQCD series, and the BFKL Pomeron intercept has a weak dependence on the virtuality of the reggeized gluon. For example, by taking the Fried-Yennie gauge, we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2},0)\in [0.149,0.176]$ for $Q^2\in[1,100]\;{\rm GeV}^2$. This is a good property to apply to the high-energy phenomenology. Further more, to compare with the data, it is found that the physical ${\rm MOM}$-scheme is more reliable than the $\overline{\rm MS}$-scheme. The ${\rm MOM}$-scheme is gauge dependent, which can also be greatly suppressed after PMC scale setting. We discuss the MOM-scheme gauge dependence for the Pomeron intercept by adopting three gauges, i.e. the Landau gauge, the Feynman gauge and the Fried-Yennie gauge, and we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2}=15\;{\rm GeV}^2,0) = 0.166^{+0.010}_{-0.017}$; i.e. about $10\%$ gauge dependence is observed. We apply the BFKL Pomeron intercept to the photon-photon collision process, and compare the theoretical predictions with the data from the OPAL and L3 experiments.

Figures (3)

• Figure 1: The error analysis of the NLO BFKL Pomeron intercept $\omega(Q^{2},0)$ versus $Q^2$ under the ${\rm MOM}$ scheme and the conventional scale setting. The shaded band shows the conventional renormalization scale uncertainty by varying the renormalization scale $\mu_R (\equiv\mu_R^{\rm init})$ within the region of $[Q/2, 2Q]$. The left diagram is for the Landau gauge with $\xi=0$ and the right one is for the Fried-Yennie gauge with $\xi=3$.
• Figure 5: The energy dependence of the total cross section for the highly virtual photon-photon collisions with $Q^2=17\;{\rm GeV}^2$ predicted by NLO BFKL under PMC and PMS scale setting compared with OPAL OPAL ($\langle Q^2\rangle =18 GeV^2$) and L3 L3 ($\langle Q^2\rangle =16\; {\rm GeV}^2$) data from the previous LEP-2 experiment at CERN.
• Figure 6: The energy dependence of the total cross section of highly virtual photon-photon collisions with $\langle Q^2\rangle\equiv 20\; {\rm GeV}^2$ predicted by NLO BFKL under PMC scale setting for future linear colliders with the collision energy up to 2 TeV ILC.