Dr. Melissa Van Beekveld

Abstract:

We present methods to achieve NLL+NLO accurate parton showering for processes with two coloured legs: neutral- and charged-current Drell-Yan, and Higgs production in pp collisions, as well as DIS and e+e− to jets. The methods include adaptations of existing approaches, as well as a new NLO matching scheme, ESME, that is positive-definite by construction. Our implementations of the methods within the PanScales framework yield highly competitive NLO event generation speeds. We validate the fixed-order and combined resummation accuracy with tests in the limit of small QCD coupling and briefly touch on phenomenological comparisons to standard NLO results and to Drell-Yan data. The progress reported here is an essential step towards showers with logarithmic accuracy beyond NLL for processes with incoming hadrons.

Abstract:

Using invariant-mass threshold resummation, we compute the invariant-mass distribution and the total cross section for tt¯tt¯ production at the LHC with centre-of-mass energy of 13.6 TeV at NLL^′ accuracy. This accuracy includes next-to-leading logarithmic contributions together with relative O(αs) non-logarithmic terms present in the threshold limit. We match the NLL^′ results to NLO in QCD and to complete NLO with electroweak corrections. We find that the inclusion of NLL^′ soft-gluon corrections significantly reduces the size of the theoretical uncertainties and greatly improves the convergence of the predictions when considering various choices of renormalisation and factorisation scales.

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.