Non-perturbative QCD corrections beyond leading-order for jet observables

Abstract

In this thesis, we investigate non-perturbative effects, specifically hadronisation, in processes in Quantum Chromodynamics (QCD) using analytical methods. Following a brief introduction, we present an initial chapter on QCD that discusses the construction of the Standard Model with a particular emphasis on QCD. This chapter also delves into the factorisation properties of QCD matrix elements and examines examples of infrared-collinear (IRC) safe observables calculated within QCD. Subsequently, in Chapter 3, we examine the relationship between hadronisation and the asymptotic nature of the perturbative expansion by exploring renormalons and the associated power-behaved corrections. This includes a concise overview of analytic methods used to determine the magnitude of leading power corrections to QCD observables. The chapter concludes with a discussion of universality in the context of hadronisation corrections. We review and motivate the "Milan factor", a multiplicative factor arising at 2-loops necessary to unambiguously determine the magnitude of power corrections computed at 1-loop, providing important context for work presented in Chapters 4 and 6. Upon concluding this review, in Chapter 4, we analyse dispersively generated power corrections to jet observables in the small R limit, where the leading power correction behaves as 1/R. We utilise the Dokshitzer-Marchesini-Webber dispersive approach to power corrections, wherein infrared effects are encapsulated by an effective coupling valid at low scales. Our calculation employs a different parametrisation compared to previous studies. This parametrisation leverages the soft and triple-collinear limit of the QCD matrix element and phase space, which is crucial for capturing the coefficient of the leading 1/R power correction. At the two-loop level, we determine the change in jet p_t after applying a jet clustering algorithm. We perform a consistency check on the known result after applying the k_t algorithm with our new parametrisation. We then fill in a gap in the literature by evaluating p_t after applying the Cambridge-Aachen sequential clustering algorithm. We frame the calculation to connect with the conventional Milan factor. In Chapter 5 we study non-perturbative power corrections to the mean value of event shapes within the Dokshitzer-Webber model. We highlight that, in the strongly energy ordered limit, the presence of soft but perturbative radiation enhances hadronisation corrections by logarithms of Q/Lambda_QCD, which appear at arbitrarily high orders in the perturbative expansion. These enhanced terms are formally of the same order as the leading 1/Q power correction, underscoring the necessity of resumming them. In Chapter 6 we extend the analysis of Chapter 4 to the anti-k_t algorithm. We briefly investigate the presumed universality of the anti-k_t Milan factor. We identify two potential mechanisms by which universality can be spoiled. The first is due to recoil effects. The second involves the decay products of a "massive" gluon carrying energies that are comparable to the hard scale, while the angle between the decay products remains small. As a result, the mass of the parent gluon remains small, allowing such configurations to contribute to hadronisation corrections within a dispersive model. We briefly comment on recoil effects, and focus in more detail on the impact of an energetic massive gluon on universality. Preliminary results suggest that within a formal dispersive approach, the Milan factor remains universal. However, we also find that soft-parton clustering effects are visible close to the boundary of the non-perturbative region, i.e., k_t ~ 1 GeV, and we find that the anti-k_t Milan factor may be sensitive to these soft-parton clustering effects at phenomenologically relevant jet p_t values, warranting a more comprehensive investigation.

Date of Award	12 Aug 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Mrinal Dasgupta (Main Supervisor) & Jonathan Gaunt (Co Supervisor)