Measurement of the $p\overline{p}\to WZ+X$ cross section at $\sqrt{s}=1.96\mathrm{TeV}$ and limits on $WWZ$ trilinear gauge couplings

We present measurements of the process $p\overline{p}\to WZ+X\to {\ell }^{\prime }{\nu }_{{\ell }^{\prime }}\ell \overline{\ell }$ at $\sqrt{s}=1.96\mathrm{TeV}$, where $\ell$ and ${\ell }^{\prime }$ are electrons or muons. Using $1{\mathrm{fb}}^{-1}$ of data from the D0 experiment, we observe 13 candidates with an expected background of $4.5\pm 0.6$ events and measure a cross section $\sigma (WZ)={2.7}_{-1.3}^{+1.7}\mathrm{pb}$. From the number of observed events and the $Z$ boson transverse momentum distribution, we limit the trilinear $WWZ$ gauge couplings to $-0.17\le {\lambda }_Z\le 0.21(\Delta {\kappa }_Z=0)$ at the 95% C.L. for a form factor scale $\Lambda =2\mathrm{TeV}$. Further, assuming that $\Delta g_1^Z=\Delta {\kappa }_Z$, we find $-0.12\le \Delta {\kappa }_Z\le 0.29({\lambda }_Z=0)$ at the 95% C.L. These are the most restrictive limits on the $WWZ$ couplings available to date.