Precision measurement of the mass of the $\tau$ lepton

An energy scan near the $\tau$ pair production threshold has been performed using the BESIII detector. About $24{\mathrm{pb}}^{-1}$ of data, distributed over four scan points, were collected. This analysis is based on $\tau$ pair decays to $ee$, $e\mu$, $eh$, $\mu \mu$, $\mu h$, $hh$, $e\rho$, $\mu \rho$ and $\pi \rho$ final states, where $h$ denotes a charged $\pi$ or $K$. The mass of the $\tau$ lepton is measured from a maximum likelihood fit to the $\tau$ pair production cross-section data to be $m_{\tau }=(1776.91\pm {0.12}_{-0.13}^{+0.10})\mathrm{MeV}/c^2$, which is currently the most precise value in a single measurement.

Figure 1

Simplified schematic of the beam energy measurement system. The positron and electron beams are indicated. R1IAMB and R2IAMB are accelerator magnets, and the HPGe detector is represented by the dot at the center. The half-meter shielding wall of the beam tunnel is shown crosshatched. The laser and optics system is located outside the tunnel of the storage ring, where the optics system is composed of two lenses, mirrors and a prism denoted by the inverted solid triangle.

Figure 2

Energy spreads from the $J/\psi$ (left), $\tau$ (middle) and ${\psi }^{\prime }$ scans (right). Horizontal lines represent mean values, listed in Table 2.

Figure 3

(a) The scatter plot of PTEM versus acoplanarity for the $\tau$ pair candidate $ee$ event from the first scan energy point, which is below $\tau$ pair production threshold. The region above and to the right of the dashed line are the acceptance region. (b) The same scatter plot for $ee$ events obtained from the $\tau$ pair MC simulation corresponding to the second scan point, which is above $\tau$ pair production threshold, after applying the same selection criteria as used for data.

Figure 4

Fits of the $J/\psi$ (left) and ${\psi }^{\prime }$ (right) hadronic cross sections.

Figure 5

(left) The distribution in acoplanarity angle between two charged tracks and (right) the distribution in PTEM. Dots with error bars are data and the histogram is $\tau$ pair inclusive MC. The upper two plots are from the second scan point, the middle two are from the third scan point, and the lower two are from the fourth scan point.

Figure 6

(left) The c.m. energy dependence of the $\tau$ pair cross section resulting from the likelihood fit (curve), compared to the data (Poisson errors), and (right) the dependence of the logarithm of the likelihood function on $m_{\tau }$, with the efficiency and background parameters fixed at their most likely values.

Figure 7

Comparison of measured $\tau$ mass from this paper with those from the PDG. The green band corresponds to the $1\sigma$ limit of the measurement of this paper.