Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension

Abstract: We present a factorization formula for the production of pairs of heavy coloured particles in hadronic collisions at the production threshold, which forms the basis for the resummation of soft gluons and Coulomb gluons. We construct a basis in colour space that diagonalizes the soft function appearing in the factorization formula to all orders in perturbation theory. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.

• The paper presents a novel color diagonalization method that simplifies the computation of soft functions in heavy-particle pair production.
• The derivation of an analytic two-loop soft anomalous dimension enhances precision in threshold cross section calculations.
• The framework integrates soft and Coulomb gluon resummation, improving predictive accuracy for collider experiments like the LHC and Tevatron.

Overview of the Paper on Soft Radiation in Heavy-Particle Pair Production

The paper under review presents an in-depth analysis of the soft radiation effects in the context of heavy-particle pair production at hadronic colliders, focusing on the production threshold. The authors, M. Beneke, P. Falgari, and C. Schwinn, introduce a comprehensive framework to address the complexities associated with soft gluon emissions and Coulomb gluon interactions in such processes. The study extends existing theoretical models by formulating an enhanced factorization approach that incorporates both types of gluon resummation, lending new insights into the computation of heavy colored particle pair production cross sections.

Key Contributions

1. Color Space Diagonalization: The paper introduces a novel color basis that diagonalizes the soft function across all orders in perturbation theory. This advances the understanding of soft anomalous dimensions, facilitating a more systematic calculation approach for threshold production processes.
2. Two-Loop Soft Anomalous Dimension: The authors successfully derive an analytic expression for the two-loop soft anomalous dimension, a critical component for the precision calculation of production cross sections at threshold. This is framed within the context of arbitrary production processes, enhancing the applicability of the results.
3. Extended Factorization Formula: By employing effective field theory techniques, the paper develops an extended factorization formula represented as $\hat \sigma = H \otimes J \otimes S$. This accounts for both soft and Coulomb gluon effects, thereby providing a unified framework for their resummation. The inclusion of the function $J_{R_\alpha}$ allows for the summation of Coulomb gluon exchanges.

Technical Details

• Soft Function Analysis: The derived expression for the soft function involves vacuum expectation values of Wilson line operators, preserving information about the color and directions of both massive and light-like particles. The representation is specifically constructed to be coherent at threshold conditions.
• Color Strategy: The analysis identifies a robust color decomposition strategy, permitting the use of Clebsch-Gordan coefficients to build projection operators on irreducible heavy particle pair color representations. This methodological refinement underscores the paper's contribution to clarifying the color structure in soft function evaluations.
• Phenomenological Implications: The theoretical insights delivered by the paper have practical implications for experiments conducted at the LHC and Tevatron. In particular, processes such as the production of top-quark pairs, supersymmetric colored particles, and color-octet scalars can be analyzed with heightened precision, improving the predictive capability of QCD calculations.

Future Directions

The rigorous framework established in this paper opens several avenues for future research. One notable direction is the exploration of non-leading terms in the velocity (β) expansion and their implications on NNLL (next-to-next-to-leading logarithmic) resummation. Additionally, given the rigorous foundation laid for soft gluon and Coulomb interaction factorization, further theoretical development and empirical testing can significantly enhance precision heavy-particle collider physics.

The methodology and results presented in this manuscript provide a roadmap for researchers aiming to achieve higher accuracy in the modeling of complex QCD processes at colliders, ensuring that theoretical predictions keep pace with the precision afforded by modern experimental results. As the understanding of these processes deepens, so too will the landscape of particle physics, offering sharper tools for probing the intricacies of the quantum world.