Particle theory

Abstract:

Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our algorithm reproduces the full set of reflexive polytopes in two and three dimensions, and in four dimensions with a small number of vertices and points. Motivated by this result, we construct five-dimensional reflexive polytopes with the lowest number of vertices and points. By calculating the normal form of the polytopes, we establish that many of these are not in existing datasets and therefore give rise to new Calabi–Yau four-folds. In some instances, the Hodge numbers we compute are new as well.

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.