Measurement and interpretation of the $W$-pair cross-section in $e^+e^-$ interactions at 161 GeV

In 1996 LEP ran at a centre-of-mass energy of 161~GeV, just above the threshold of W-pair production. DELPHI accumulated data corresponding to an integrated luminosity of $9.93 {\mathrm{~pb^{-1}}}$, and observed 29 events that are considered as candidates for W-pair production. From these, a cross-section for the doubly resonant $e^+e^-\to\mathrm{WW}$ process of $3.67~^{+0.97}_{-0.85} \pm 0.19{\mathrm{~pb}}$ has been measured. Within the Standard Model, this cross-section corresponds to a mass of the W-boson of ${\mathrm{80.40~\pm~0.44~(stat.)~\pm~0.09~(syst.) ~\pm 0.03~(LEP)~GeV}}/c^2$. Alternatively, if $m_{\mathrm{W}}$ is held fixed at its current value determined by other experiments, t…