[Paper Review] Exclusive central production of heavy quarks at the LHC

Grigorios Chachamis, Martin Hentschinski+2 more|ArXiv.org|Nov 13, 2009

Particle physics theoretical and experimental studies1 references10 citations

TL;DR

This paper proposes a next-to-leading order (NLO) $k_T$-factorisation framework for exclusive central production of heavy quark-antiquark pairs at the LHC, using NLO unintegrated gluon densities in transverse momentum space. It enables Monte Carlo-compatible simulations by iteratively solving the NLO BFKL evolution kernel, offering a precision tool to probe small-$x$ gluon dynamics in bottom quark pair production.

ABSTRACT

We study the exclusive production of heavy flavors at central rapidities in hadron-hadron collisions within the kT factorisation formalism. Since this involves regions of small Bjorken x in the unintegrated gluon densities, we include the next-to-leading order BFKL contributions working directly in transverse momentum representation. Our results are presented in a form suitable for Monte Carlo implementation.

Motivation & Objective

• To develop a theoretical framework for exclusive central production of heavy quarks at the LHC using $k_T$-factorisation at NLO.
• To test the applicability of high-energy $k_T$-factorisation in the small Bjorken-$x$ regime, particularly for bottom quark pairs.
• To provide a numerically implementable formalism for Monte Carlo event generation of exclusive heavy flavor production.
• To probe unintegrated gluon densities at small $x$ via exclusive heavy quark pair production, enabling validation of theoretical approximations.
• To lay the groundwork for future fits of unintegrated gluon densities to HERA data and LHC predictions.

Proposed method

• Formulates the differential cross-section in a Sudakov basis using light-like momenta $p_1$ and $p_2$ for incoming protons.
• Applies $k_T$-factorisation with unintegrated gluon densities that include $k_T$ dependence and are evolved via the NLO BFKL kernel.
• Uses an iterative solution of the NLO BFKL Green function in transverse momentum space to compute the gluon density.
• Incorporates NLO corrections to the BFKL kernel, including real emission and collinear terms, with explicit dependence on the running coupling $\bar{\alpha}_s$.
• Constructs the NLO unintegrated gluon density as a convolution of the BFKL Green function with the proton impact factor.
• Derives a representation of the NLO kernel in transverse momentum space that allows for Monte Carlo integration and event-by-event simulation.

Experimental results

Research questions

• RQ1 Can exclusive central production of bottom quark pairs at the LHC serve as a clean probe of small-$x$ gluon dynamics via $k_T$-factorisation?
• RQ2 How do NLO corrections to the BFKL evolution kernel affect the differential cross-section for exclusive heavy quark pair production?
• RQ3 To what extent can the iterative structure of the NLO BFKL Green function be implemented numerically for Monte Carlo event generation?
• RQ4 What is the role of the $\overline{\text{MS}}$ vs. Gluon-Bremsstrahlung (GB) renormalisation scheme in stabilizing predictions for exclusive heavy flavor production?
• RQ5 How well can the NLO $k_T$-factorised framework describe the kinematic regime of small-$x$ gluon densities probed in bottom quark pair production?

Key findings

• The NLO BFKL kernel is expressed in transverse momentum space with explicit dependence on the running coupling $\bar{\alpha}_s$, allowing for scheme-invariant predictions.
• The iterative solution of the NLO BFKL Green function enables a numerical implementation suitable for Monte Carlo event generation.
• The formalism treats the kinematics of the heavy quark-antiquark pair exclusively, avoiding approximations from collinear factorisation.
• The inclusion of NLO corrections to the BFKL kernel accounts for asymmetric energy scale choices and early collinear evolution effects in hadronic collisions.
• The framework allows for a precise determination of the $x$ values probed in the unintegrated gluon densities, enabling validation of small-$x$ approximations.
• The model is stable under renormalisation scheme changes (e.g., $\overline{\text{MS}}$ to GB), providing a robust tool for theoretical predictions.