Taming of preasymptotic small x evolution within resummation framework

Abstract

It is well understood that the leading logarithmic approximation for the amplitudes of high energy processes is insufficient and that the next-to-leading logarithmic effects are very large and lead to instability of the solution. The resummation at low $x$, which includes kinematical constraints and other corrections leads to stable result. Using previously established resummation procedure we study in detail the preasymptotic effects which occur in the solution to the resummed BFKL equation when the energy is not very large. We find that in addition to the well known reduction of the intercept, which governs the energy dependence of the gluon Green's function, resummation leads to the delay of the onset of its small $x$ growth. Moreover the gluon Green's function develops a dip or a plateau in wide range of rapidities, which increases for large scales. The preasymptotic region in the gluon Green's function extends to about $8$ units in rapidity for the transverse scales of the order of $30-100\mathrm{GeV}$. To visualize the expected behavior of physical processes with two equal hard scales we calculate the cross section of the process ${\gamma }^{\ast }+{\gamma }^{\ast }\to X$ to be probed at future very high-energy electron-positron colliders. We find that at ${\gamma }^{\ast }{\gamma }^{\ast }$ energies below $100\mathrm{GeV}$ the BFKL Pomeron leads to smaller value of the cross section than the Born approximation, and only starts to dominate at energies about $100\mathrm{GeV}$. This pattern is significantly different from the one which we find using LL approximation. We also analyze the transverse momentum contributions to the cross section for different virtualities of the photons and find that the dominant contributions to the integral over the transverse momenta comes from lower values than the the external scales in the process under consideration.

arXiv comment27 pages, 17 figures

References in corpus (53)

• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• The BFKL Equation from the Wilson Renormalization Group
• BFKL pomeron in the next-to-leading approximation
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Energy Scale(s) and Next-to-leading BFKL Equation
• NLO evolution of color dipoles
• A resummation of large sub-leading corrections at small x
• Renormalization Group Improved Small-x Equation
• A unified BFKL and GLAP description of $F_2$ data
• Resumming double logarithms in the QCD evolution of color dipoles
• Renormalisation group improved small-x Green's function
• Collinearly-improved BK evolution meets the HERA data
• Mueller Navelet jets at LHC - complete NLL BFKL calculation
• Improving the kinematics for low-x QCD evolution equations in coordinate space
• Small x Resummation with Quarks: Deep-Inelastic Scattering
• Factorization and Resummation of Small x Scaling Violations with Running Coupling
• Photon impact factor and $k_T$-factorization for DIS in the next-to-leading order
• An anomalous dimension for small x evolution
• Resummation of Singlet Parton Evolution at Small x
• Virtual photon scattering at high energies as a probe of the short distance pomeron
• An "all-poles" approximation to collinear resummations in the Regge limit of perturbative QCD
• NLO Corrections to the Photon Impact Factor: Combining Real and Virtual Corrections
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Probing the QCD pomeron in e+ e- collisions
• A Global Fit to Scattering Data with NLL BFKL Resummations
• Constraints on gluon evolution at small x
• A collinear model for small-x physics
• The Running Coupling BFKL Anomalous Dimensions and Splitting Functions
• Physics at the CLIC Multi-TeV Linear Collider
• NLO JIMWLK evolution unabridged
• The gluon splitting function at moderately small x
• Small-$x$ resummation from HELL
• Small-x Resummation and HERA Structure Function Data
• A matrix formulation for small-x singlet evolution
• The Process γ^{*}_L+ q \to q\bar{q}g + q: Real Corrections to the Virtual Photon Impact Factor
• Exact kinematics in the small x evolution of the color dipole and gluon cascade
• Extending QCD perturbation theory to higher energies
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• The (gamma^*-q\bar q)-Reggeon Vertex in Next-to-Leading Order QCD
• High Energy QCD at NLO: from light-cone wave function to JIMWLK evolution
• BFKL at Next-to-Next-to-Leading Order
• Probing the QCD pomeron in doubly tagged e^+ e^- collisions
• Solution of the NLO BFKL Equation and a Strategy for Solving the All-Order BFKL Equation
• BFKL resummation effects in the gamma* gamma* total hadronic cross section
• The ${\gamma }^{\ast }{\gamma }^{\ast }$ total cross section in next-to-leading order BFKL and LEP2 data
• BFKL pomeron in the next-to-next-to-leading approximation in the planar N=4 SYM theory
• On the different forms of the kinematical constraint in BFKL
• Diffractive phenomena in high energy processes

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