Measurements of the $\tau$ mass and the mass difference of the ${\tau }^{+}$ and ${\tau }^{-}$ at BABAR

We present the result from a precision measurement of the mass of the $\tau$ lepton, $M_{\tau }$, based on $423{\mathrm{fb}}^{-1}$ of data recorded at the ${\rm Y}(4S)$ resonance with the BABAR detector. Using a pseudomass endpoint method, we determine the mass to be $1776.68\pm 0.12(\mathrm{stat})\pm 0.41(\mathrm{syst})\mathrm{MeV}$. We also measure the mass difference between the ${\tau }^{+}$ and ${\tau }^{-}$, and obtain $(M_{{\tau }^{+}}-M_{{\tau }^{-}})/M_{\mathrm{AVG}}^{\tau }=(-3.4\pm 1.3(\mathrm{stat})\pm 0.3(\mathrm{syst}))\times {10}^{-4}$, where $M_{\mathrm{AVG}}^{\tau }$ is the average value of $M_{{\tau }^{+}}$ and $M_{{\tau }^{-}}$.

Figure 1

Pseudomass distribution. The points are data, the solid area is the background estimated from MC, and the dashed vertical line represents the PDG average value of the $\tau$ mass [8]. Note the sharp edge of the distribution at the $\tau$ mass.

Figure 2

Pseudomass endpoint distributions from the three MC samples. The open squares, dots, and open triangles are for generated $\tau$ mass values of 1774, 1777, and 1780 MeV, respectively, and the curves are the results of the fits to the samples.

Figure 3

The fitted value of $p_1$ as a function of $M_g$, the value of $M_{\tau }$ in the simulation. These fit results are used in the determination of $M_{\tau }$ from the endpoint fit to the data.

Figure 4

Fitted $K_S^0$ mass vs decay-vertex radius (top panel) and $K_S^0$ lab momentum (bottom panel). On the vertical axis, the PDG average value of the $K_S^0$ mass [8] has been subtracted from the fitted value. The points show the normally reconstructed data events, the open circles show the data reconstructed with 20% more SVT material, and the shaded region is the error on the nominal $K_S^0$ mass [8]. The dependence of the $K_S^0$ mass on the decay-vertex radius and momentum is due to the underestimation of the energy loss by the reconstruction procedure.

Figure 5

Fitted $K_S^0$ mass vs decay-vertex radius (top panel) and lab momentum (bottom panel). On the vertical axis, the PDG average value of the $K_S^0$ mass [8] has been subtracted from the fitted value. The points show the normally reconstructed data events, the squares show the data reconstructed with 10% more material in the tracking volume, and the shaded region is the error on the nominal $K_S^0$ mass [8].

Figure 6

Fitted $K_S^0$ mass vs lab momentum. On the vertical axis, the PDG average value of the $K_S^0$ mass [8] has been subtracted from the fitted value. The points show the normally reconstructed data, the open squares show the data reconstructed with the solenoid field increased by 0.02%, the crosses show the data reconstructed with magnetization field increased by 20%, and the shaded region is the error on the nominal $K_S^0$ mass [8].

Figure 7

Fitted $K_S^0$ mass vs decay-vertex radius (top panel) and lab momentum (bottom panel). On the vertical axis, the PDG average value of the $K_S^0$ mass [8] has been subtracted from the fitted value. The points show the normally reconstructed data, the triangles show the data after the correction from the increased material and magnetic-field strengths has been applied, and the shaded region is the error on the nominal $K_S^0$ mass [8].

Figure 8

Combined ${\tau }^{+}$ and ${\tau }^{-}$ pseudomass endpoint distribution. The points show the data, the curve is the fit to the data, and the solid area is the background. The inset is an enlargement of the boxed region around the edge position showing the fit quality where $p_1$ is most sensitive.

Figure 9

Resulting pseudomass distribution from subtracting the ${\tau }^{-}$ distribution from the ${\tau }^{+}$ distribution.

Figure 10

Pseudomass distributions for the ${\tau }^{+}$ and ${\tau }^{-}$ in the region around the pseudomass threshold region. The open circles and solid points show the ${\tau }^{+}$ and ${\tau }^{-}$ distributions, respectively. The curves show the results of the fits to the data.