Belle II early physics program of bottomonium spectroscopy

The Belle II experiment at the SuperKEKB collider is a major upgrade of the KEK "$B$ factory" facility in Tsukuba, Japan. Phase 1 commissioning of the main ring of SuperKEKB has started in February 2016 and first physics data will be recorded in 2017 during the so-called Phase 2 commissioning, when the partial Belle II detector will be operated still without its vertex detector. In 2018, the full Belle II detector will be rolled in and physics run will start. In this proceeding, a possible physics program for this early data run at different center-of-mass energies is described, in particular at the $\Upsilon(3S)$ and $\Upsilon(6S)$ resonances, amongst other energy points.Comment: 6 pages, XXIV International Workshop on Deep-Inelastic Scattering and Related Subject

Single soft gluon emission at two loops

We study the single soft-gluon current at two loops with two energetic partons in massless perturbative QCD, which describes, for example, the soft limit of the two-loop amplitude for $gg\to Hg$. The results are presented as Laurent expansions in $\epsilon$ in $D=4-2\epsilon$ spacetime dimension. We calculate the expansion to order $\epsilon^2$ analytically, which is a necessary ingredient for Higgs production at hadron colliders at next-to-next-to-next-to-leading order in the soft-virtual approximation. We also give two-loop results of the single soft-gluon current in ${\cal N}=4$ Super-Yang-Mills theory, and find that it has uniform transcendentality. By iteration relation of splitting amplitudes, our calculations can determine the three-loop single soft-gluon current to order $\epsilon^0$ in ${\cal N}=4$ Super-Yang-Mills theory in the limit of large $N_c$.Comment: typos corrected; journal versio

On Braided Linear Gr-categories

We provide explicit and unified formulae for the normalized 3-cocycles on arbitrary finite abelian groups. As an application, we compute all the braided monoidal structures on linear Gr-categories.Comment: 14 pages; typos correcte