Measurement of the W-pair cross-section and of the W mass in $e^+ e^-$ interactions at 172 GeV

From a data sample of $9.98 {\mathrm{~pb^{-1}}}$ integrated luminosity collected by DELPHI at a centre-of-mass energy of 172 GeV, 118 events were selected as W-pair candidates. From these, the branching fraction ${\mathrm Br}({\mathrm W} \rightarrow {\mathrm q}\bar{\mathrm q})$ was measured to be $0.660^{+0.036}_{-0.037} (\mathrm{stat.}) \pm 0.009 (\mathrm{syst.})$ and the cross-section for the doubly resonant process $\mathrm{e^+ e^- \rightarrow W^+ W^-}$ to be $11.58^{+1.44}_{-1.35} (\mathrm{stat.}) \pm 0.32 (\mathrm{syst.})$ pb. The mass of the W boson, obtained from direct reconstruction of the invariant mass of the fermion pairs in the decays $\mathrm{ WW \rightarrow \ell\nu q \bar{q}}$ and $\mathrm{ WW \rightarrow q\bar{q}q\bar{q}}$, was determined to be $m_{\mathrm W} = \: 80.22 \: \pm \: 0.41 (\mathrm{stat.}) \: \pm 0.04 (\mathrm{syst.}) \: \pm 0.05 (\mathrm{int.}) \: \pm 0.03 (\mathrm{LEP})\: \mathrm{GeV}/c^2$, where ``int.'' denotes the uncertainty from interconnection effects like colour reconnection and Bose-Einstein interference. Combined with the W mass obtained from the cross-sections measured by DELPHI at threshold, a value of $m_{\mathrm W} = \: 80.33 \: \pm \: 0.30 (\mathrm{stat.}) \: \pm 0.05 ({\mathrm syst.}) \: \pm \: 0.03 (\mathrm{int.}) \: \pm \: 0.03 (\mathrm{LEP}) \: \mathrm{GeV}/c^2$ was found.