Two-loop soft anomalous dimensions for single top quark associated production with a W- or H-

Abstract: I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a W boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for bg -> tW- and bg -> tH- at LHC energies of 7, 10, and 14 TeV.

• The paper provides precise calculations of two-loop soft anomalous dimensions for associated single top production, enhancing NNLL accuracy.
• Using the eikonal approximation and cusp angle formalism, the analysis predicts approximate NNLO corrections that improve tW− and tH− cross sections by up to 20%.
• The study sets a benchmark for collider physics by sharpening theoretical predictions in electroweak and Higgs boson searches.

Overview of the Two-loop Soft Anomalous Dimensions for Single Top Quark Associated Production

This paper by Nikolaos Kidonakis provides an in-depth analysis and calculation of two-loop soft anomalous dimensions relevant to the associated production of a single top quark with a $W^-$ boson or a charged Higgs boson ($H^-$) at the LHC. The analysis leverages known expressions for the massive cusp anomalous dimension to advance soft-gluon resummation at the next-to-next-to-leading-logarithm (NNLL) level, enabling the approximation of next-to-next-to-leading-order (NNLO) cross sections for the processes $bg \rightarrow tW^-$ and $bg \rightarrow tH^-$ at multiple LHC energy levels—specifically, 7, 10, and 14 TeV.

Main Contributions

The salient contributions of this paper lie in the precise calculation of two-loop soft anomalous dimensions, which are critical for attaining NNLL accuracy in soft-gluon resummation for QCD processes involving top quark production. The main technical foundation is anchored in the eikonal approximation, facilitating the resummation through renormalization group evolution of the soft function. This approach reveals the two-loop soft anomalous dimensions in a manageable analytical form while incorporating the cusp angle formalism.

Key findings include:

• Calculation of two-loop soft (cusp) anomalous dimensions for heavy quark-antiquark pairs.
• Introduction of a framework assessing associated production of a single top quark with a $W^-$ or $H^-$ boson via enhanced resummation accuracy.
• Derivation of approximate NNLO cross sections which embody the utility of the computed NNLL resummation.

Numerical Results

The NNLL enhancement achieves a pivotal role in estimating higher-order corrections, significantly elevating the accuracy and reliability of predicted cross-sections. For example, the approximate NNLO corrections improve the NLO cross section for $tW^-$ production by approximately 8% and $tH^-$ production by 15% to 20%.

Implications and Speculations on Future Development

The paper deepens the theoretical understanding required for precise prediction of cross sections pertinent to single top quark processes—a fundamental block in the broader endeavors of electroweak and Higgs boson searches at the LHC. The analyses and methodology presented could substantially influence future explorations into associated top production channels and may elucidate underlying physics beyond the Standard Model indicated by potential deviations from predicted cross-sections.

This contribution underscores the importance of NNLL resummation in sharpening our toolkit for collider physics, setting a standard for future studies on resummation in complex processes involving electroweak particles and potential beyond-SM scenarios.

Additionally, as researchers refine computational techniques and theoretical models, further studies might explore more generalized scenarios or consider higher energy frontiers that might also benefit from these refinements.

In summary, this paper offers a pivotal advancement in the precision physics of top quarks associated production at colliders, presenting a robust approach that aids in pushing the boundaries of our current theoretical frameworks.