Phenomenology of the BFKL pomeron and Unitarity Corrections at low x

TL;DR

The paper investigates the phenomenology and unitarity corrections of the perturbative QCD description of the BFKL Pomeron at low $x$. It first demonstrates how the leading-log resummation governs DIS processes, diffractive vector-meson production, and photon diffractive dissociation, while highlighting diffusion in transverse momentum and infrared sensitivity. It then develops the first nonleading unitarity corrections via a compact two-to-four reggeon transition vertex, proves its conformal invariance, and analyzes the twist expansion of the four-gluon state, linking anomalous dimensions to the spectrum $oldsymbol{ abla} abla$ of the four-gluon system. The work emphasizes that unitarity corrections, though perturbative, are essential to tame the BFKL growth and to approach a unitary QCD Pomeron, with implications for DIS observables and diffractive processes. Overall, it provides a framework to connect conformal-field-theory ideas with reggeon dynamics in QCD and outlines the path toward a full unitarization of high-energy scattering in perturbative QCD.

Abstract

The low $x$ limit of deep inelastic electron proton scattering is considered using methods of perturbative QCD. In the first part we investigate the phenomenological consequences of the resummation of leading logarithms in $1/x$ given by the BFKL pomeron. We apply the BFKL pomeron to the inclusive structure function $F_2$, to the diffractive production of vector mesons at large momentum transfer, to inclusive photon diffractive dissociation in DIS and to quark-antiquark production with large transverse momenta in DIS diffractive dissociation. For the last process we perform extensive numerical calculations based on the double logarithmic approximation. The BFKL pomeron is known to violate unitarity. In the second part the first next-to-leading corrections which have to be taken into account to restore unitarity of the scattering amplitude are investigated. A compact configuration space representation of the two to four gluon transition vertex is derived. Conformal symmetry of the vertex is proven and its relation to a conformal covariant three point function is established. The important role of the spectral function $χ_4$ of the four gluon state is pointed out. We relate this function to the twist expansion of the four gluon amplitude. Motivated by this relation we develop a method to perform the twist expansion of the amplitude. Based upon first results of our analysis we draw conclusions concerning the singularity structure of the function $χ_4$.

Figures (31)

• Figure 3.1: Results of the BFKL-based $F_2$-calculation for $Q^2 = 8.5, 15, 25$ and $50 \,\hbox{GeV}^2$. Displayed are the non-modified solution (solid line) and the modified solution with ${\bf k}_a^2 = 1 \,\hbox{GeV}^2$ (dotted line) and ${\bf k}_a^2 = 2 \,\hbox{GeV}^2$ (dashed line) in comparison with data from the H1 h1, ZEUS zeus and E665 e665 collaborations.
• Figure 3.2: Mean value $<\xi>$ and width $\Delta(\xi)$ of the distribution of $\xi=\log {\bf k}^2/{\bf k}_0^2$ inside the non-modified BFKL evolution for $F_2$ with $x=10^{-4},x_0=10^{-2}$ and $Q^2=8.5\,\hbox{GeV}^2$ (left diagram) resp. $Q^2=50 \,\hbox{GeV}^2$ (right diagram).
• Figure 3.3: The same as in fig. \ref{['fig21b']} but with the BFKL evolution modified in the infrared region with ${\bf k}_a^2 = 1\,\hbox{GeV}^2$.
• Figure 3.4: The $\xi$-distributions in the central rapidity region for different values of $x_B$ and the corresponding transverse energy distributions.
• Figure 3.5: Width of the $\xi$-distributions and mean value of the $E_T$ distributions for $Q^2=25 \,\hbox{GeV}^2$ and $Q^2=50 \,\hbox{GeV}^2$.