Extraction and validation of a set of HERWIG 7 tunes from CMS underlying-event measurements

This note presents a new set of parameters ("tunes") for the underlying-event model of the HERWIG$\,$7 event generator. The parameters control the description of multiple-parton interactions (MPI) and colour reconnection in HERWIG$\,$7, and are obtained from a fit to underlying-event and minimum-bias data collected by the CMS experiment at $\sqrt{s}=$ 0.9, 7, and 13 TeV. The tunes are based on the NNPDF3.1 next-to-next-to-leading-order PDF set for the parton shower, and either a leading-order or next-to-next-to-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event-shape observables, and minimum-bias, dijet, top quark pair, and weak boson events, and are compared to data. Each of the new tunes describe the data to a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI are found to provide the best description of the data.