Measurement of $\sigma (p\overline{p}\to Z)·\mathcal{B}(Z\to \tau \tau )$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We present a measurement of the inclusive production cross section for $Z$ bosons decaying to tau leptons in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. We use a channel with one hadronically-decaying and one electronically-decaying tau. This measurement is based on $350{\mathrm{pb}}^{-1}$ of CDF Run II data. Using a sample of 504 opposite sign $e\tau$ events with a total expected background of 190 events, we obtain $\sigma (p\overline{p}\to 4Z)·\mathcal{B}(Z\to \tau \tau )=264\pm 23(\mathrm{stat})\pm 14(\mathrm{syst})\pm 15(\mathrm{lumi})\mathrm{pb}$, in agreement with the next-to-next-to-leading order QCD prediction. This is the first CDF cross section measurement using hadronically-decaying taus in Run II.

Figure 1

Efficiency of the hadronic tau reconstruction and fiducial selections as a function of the true visible (neutrino contribution excluded) transverse momentum of ${\tau }_h$ for $Z/{\gamma }^{*}\to \tau \tau$ events as obtained using the pythia MC and CDF II detector simulation. The efficiency is calculated for generated hadronic tau decays with $|\eta |<0.9$.

Figure 2

Comparison of the true hadronic tau transverse energy (as obtained from MC) and the reconstructed tau candidate energy using CDF II detector simulation for $Z\to \tau \tau$ events. The dashed line corresponds to using only calorimeter energy, while the solid line corresponds to the combination of track and ${\pi }^0$ energies with appropriate corrections.

Figure 3

Distribution of $M_{\tau \tau }$ for pythia $Z/{\gamma }^{*}\to \tau \tau \to e\nu \nu {\tau }_h\nu$ process for all generated events (open histogram) and events passing acceptance requirements (shaded histogram). The latter is scaled by a factor of 10 for illustration purposes. Note that the events were generated with the lower cutoff of $\sqrt{\widehat{s}}=20\mathrm{GeV}$.

Figure 4

Density of charged tracks $2\pi d{N}_{\mathrm{trk}}/d\Omega$ per unit of solid angle plotted as a function of the angle $\theta$ with respect to the direction of the electron in a clean sample of $Z\to ee$ events. Data (points) is compared to MC simulation using pythia (shown as shaded rectangles); the MC prediction has an added constant (10% of the plateau level) to have the plateau level agree with data.

Figure 5

Distribution $dN/d\xi$ for electrons (shaded histogram) and hadronically-decaying taus (points) illustrating discriminating power of variable $\xi$. Both distributions are obtained using pythia MC and normalized to a unit area.

Figure 6

The density $2\pi d{N}_{\mathrm{trk}}/d\Omega$ of charged tracks with $p_{\mathrm{T}}>1\mathrm{GeV}/c$ per unit of solid angle plotted as a function of the angle $\theta$ with respect to the direction of (i) electron in a clean sample of $Z\to ee$ events (data points), (ii) electron in pythia MC $Z\to ee$ events (line), and (iii) hadronically-decaying tau lepton in pythia MC $Z\to \tau \tau$ (shaded rectangles).

Figure 7

Comparison of the reconstructed missing transverse energy with the true value obtained at the generator level in the pythia MC $Z\to {\tau }_e{\tau }_h$ events. Dashed line shows the ${\mathrm{E̸}}_{\mathrm{T}}^{\mathrm{Rec}}-{\mathrm{E̸}}_{\mathrm{T}}^{\mathrm{Gen}}$ distribution prior to the correction procedure, and the solid line shows the same distribution when all corrections have been applied.

Figure 8

Distribution of $M_{\mathrm{T}}$ vs $p_{\mathrm{T}}$ for: (a) signal $Z\to \tau \tau$ events obtained using the pythia MC simulation; (b) like sign (LS) data after all cuts. The latter sample is dominated by QCD and $\gamma +\mathrm{\text{jets}}$ backgrounds. The area bounded by the solid lines and including the right bottom quadrant on the plots indicates the signal region.

Figure 9

(a) Distribution of the electron track isolation, $I_{\mathrm{trk}}^{\Delta R<0.4}$ for OS (points) and LS (histogram) $Z\to \tau \tau$ candidates after all analysis cuts except the track isolation cut, which is dropped. (b) The same distribution, but with additional cuts, $M_{\mathrm{T}}<10\mathrm{GeV}/c^2$, $10<E_{\mathrm{T}}^e<20\mathrm{GeV}$ that suppress $W+\mathrm{\text{jets}}$ and $\gamma +\mathrm{\text{jets}}$ backgrounds. LS events in this case are a nearly pure sample of QCD jet events.

Figure 10

Logarithmic likelihood function $-\log d\mathcal{L}/d{N}_{\mathrm{A}-\mathrm{I}}^{Z\to \tau \tau }$ for the rate of $Z\to \tau \tau$ events in the primary signal region A-I under the constraint $f_{\mathrm{OS}}^W=f_{\mathrm{LS}}^W$. All variables other than the signal rate are considered nuisance parameters and are integrated out. The fit yields $N_{\mathrm{A}-\mathrm{I}}^{Z\to \tau \tau }=315\pm 27$ at 68% C.L.

Figure 11

Distribution of the hadronic tau candidate transverse momentum, $p_{\mathrm{T}}$, for events passing all selections in data (points) compared to the sum of background and signal contributions. Note that this is only visible part of the momentum, as the neutrino escapes undetected. The $Z\to \tau \tau$ and background predictions are normalized to the number of events extracted from the fit.

Figure 12

Distribution of the electron candidate transverse energy, $E_{\mathrm{T}}$, for events passing all selections in data (points) compared to the sum of background and signal contributions. The $Z\to \tau \tau$ and background predictions are normalized to the number of events extracted from the fit.

Figure 13

Distribution of the invariant mass of $e-\tau -{\mathrm{E̸}}_{\mathrm{T}}$ system for opposite sign events in data (points) compared to the sum of background and signal contributions. The $Z\to \tau \tau$ and background predictions are normalized to the number of events extracted from the fit.

Figure 14

Distribution of the prong multiplicity of hadronic tau candidates with the OS and $N_{\mathrm{trk}}=1,3$ requirements dropped. Data (points) are compared to the sum of background and signal contributions. The $Z\to \tau \tau$ and background predictions are normalized to the number of events extracted from the fit (with all cuts applied).

Figure 15

Distribution of the transverse mass of the electron and missing transverse energy with the $M_T(e,{\mathrm{E̸}}_{\mathrm{T}})<50\mathrm{GeV}/c$ requirement dropped. Data (points) are compared to the sum of background and signal contributions. The $Z\to \tau \tau$ and background predictions are normalized to the number of events extracted from the fit (with all cuts applied).