Dr. Melissa Van Beekveld

Abstract:

We formulate a collinear partonic shower algorithm that achieves next-to-single-logarithmic (NSL, αsnLn−1) accuracy for collinear-sensitive non-singlet fragmentation observables. This entails the development of an algorithm for nesting triple-collinear splitting functions. It also involves the inclusion of the one-loop double-collinear corrections, through a z-dependent NLO-accurate effective 1 → 2 branching probability, using a formula that can be applied more generally also to future full showers with 1 → 3 splitting kernels. The specific NLO branching probability is calculated in two ways, one based on slicing, the other using a subtraction approach based on recent analytical calculations. We close with demonstrations of the shower’s accuracy for non-singlet partonic fragmentation functions and the energy spectrum of small-R quark jets. This work represents an important conceptual step towards general NNLL accuracy in parton showers.

Abstract:

We study the collinear fragmentation of highly energetic jets defined with a small jet radius. In particular, we investigate how the corresponding fragmentation functions differ from their hadronic counterpart defined in the common MS¯ scheme. We find that the anomalous dimensions governing the perturbative evolution of the two fragmentation functions differ starting at the two loop order. We compute for the first time the new anomalous dimensions at two loops and confirm our predictions by comparing the inclusive small-R jet spectrum against a fixed order perturbative calculation at O(αs2). To investigate the dependence of the anomalous dimension on the kinematic cutoff variable, we study the fragmentation functions of Cambridge jets defined with a transverse momentum cutoff as opposed to an angular cutoff R. We further study the evolution of the small-R fragmentation function with an alternative cutoff scale, proportional to zR, representing the maximum possible transverse momentum of emissions within a jet. In these cases we find that the two-loop anomalous dimensions coincide with the MS¯ DGLAP ones, highlighting a correspondence between the MS¯ scheme and a transverse-momentum cutoff.

Abstract:

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.

Abstract:

We introduce the first family of parton showers that achieve next-to-leading logarithmic (NLL) accuracy for processes involving a t-channel exchange of a colour-singlet, and embed them in the PanScales framework. These showers are applicable to processes such as deep inelastic scattering (DIS), vector boson fusion (VBF), and vector boson scattering (VBS). We extensively test and verify the NLL accuracy of the new showers at both fixed order and all orders across a wide range of observables. We also introduce a generalisation of the Cambridge-Aachen jet algorithm and formulate new DIS observables that exhibit a simple resummation structure. The NLL showers are compared to a standard transverse-momentum ordered dipole shower, serving as a proxy for the current state-of-the-art leading-logarithmic showers available in public codes. Depending on the observable, we find discrepancies at NLL of the order of 15%. We also present some exploratory phenomenological results for Higgs production in VBF. This work enables, for the first time, to resum simultaneously global and non-global observables for the VBF process at NLL accuracy.