Top-Quark Decay at Next-to-Next-to-Leading Order in QCD (1210.2808v3)

Abstract: We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and $W$ boson width effects. In particular, we also show the first results of the fully differential decay rates for top-quark semileptonic decay $t\to W^+(l^+\nu)b$ at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

• The paper significantly improves the precision in calculating top-quark decay widths by incorporating next-to-next-to-leading order QCD corrections.
• It employs a phase space slicing method rooted in SCET to accurately manage infrared singularities in two-loop, real-virtual, and double real contributions.
• The work delivers fully differential predictions for semileptonic decays, refining top-quark mass measurements and tests of the Standard Model.

Top-Quark Decay at Next-to-Next-to-Leading Order in QCD

The paper by Jun Gao, Chong Sheng Li, and Hua Xing Zhu provides a comprehensive exploration of top-quark decay, executed using next-to-next-to-leading order (NNLO) corrections in Quantum Chromodynamics (QCD). This work significantly enhances the precision in calculating the decay width of the top-quark, which is of paramount importance for theoretical and experimental investigations within the Standard Model (SM) and beyond.

This paper focuses on the top-quark decay process $t \to W^+ b + X$, incorporating $X$ as any additional parton in the final state. The authors meticulously account for several contributions to NNLO QCD corrections, including two-loop virtual contributions, one-loop real-virtual contributions, and tree-level double real contributions. A major aspect of this paper is its methodological approach to dealing with infrared singularities through a phase space slicing method, grounded in soft-collinear effective theory (SCET). This framework allows for accurate handling of the complexities in NNLO corrections by decomposing the decay width into integrals over regions defined by an invariant mass cutoff.

The paper's strong results include an updated calculation of top-quark decay incorporating not just NNLO corrections, but also next-to-leading order (NLO) electroweak corrections, and effects from the finite bottom quark mass and $W$ boson width. Numerical findings for the NNLO QCD corrections exhibit a $-2.09\%$ variation of the LO decay width, providing notable improvement over the previous order.

A significant portion of the research addresses the computation of fully differential decay rates of the semileptonic decay process $t \to W^+(\ell^+\nu)b$ at NNLO. This constitutes one of the pioneering efforts to derive differential distributions with such precision in perturbative QCD, involving complex angular and invariant mass observables within the decay products. Differential distributions are essential for refining top-quark mass measurements and evaluating the $tWb$ vertex structure for new physics insights—for instance, anomalous couplings possibly indicative of new physics scenarios.

In terms of theoretical implications, this work underscores the imperative of NNLO calculations for reducing theoretical uncertainties substantially, particularly in processes involving heavy quarks. Furthermore, the approach adopted here could be extended to other heavy-to-light decay processes, such as those in $B$ mesons, pointing towards broad applicability within flavor physics.

From a practical standpoint, the NNLO corrections provided in this paper can better guide experimental setups like the Large Hadron Collider (LHC) in their quest for precise top-quark property measurements and ensure more accurate comparisons between SM predictions and experimental data.

Overall, this paper represents an important stride towards mastering QCD corrections at NNLO, setting a benchmark for precision in top-quark decay analyses. Future developments in AI and computational physics may see this approach integrated into automated Monte Carlo event generators, thus facilitating even more precise and adaptable simulations in particle physics research.