Using Z$\gamma$ Events

The emission of a hard ISR $\gamma$ reduces the effective centre-of-mass energy of e⁺e^- interactions, such that the effective interaction can be at the Z resonance. Kinematic reconstruction of these so-called ``Z$\gamma$'' events, with Z $\rightarrow$ q$\overline{q}$, can provide a cross-check to W mass measurements, by measuring either m_Z or E_beam, and comparing these values to independent measurements.

L3 measure m_Z from q$\overline{q}$$\gamma$ events [10] at $\sqrt{s}$ = 189 GeV using $\sim$ 10K events. This is a check of detector calibration, jet reconstruction, fitting method etc., and uses a kinematic fit and a reweighting technique as in their W mass analysis. The fitted value from Z$\gamma$ events is m_Z = 91.106 $\pm$ 0.062 GeV (prel.), in good agreement with m_Z extracted from their cross-section measurements at the Z-pole of m_Z = 91.195 $\pm$ 0.009 GeV. This represents an important test of the complete mass analysis method.

Since the beam energy is used in the kinematic fits of WW events, the uncertainty on it propagates through to the W mass measurement. The error on the beam energy is very precise at LEP1, less than 1 MeV, as it is measured by resonant depolarisation. Polarisation has not been achieved above a beam energy of 60 GeV, so the same technique does not work at LEP2. Instead, beam energy measurements at lower beam energies are extrapolated to higher energies, resulting in a larger beam energy error (25 MeV at $\sqrt{s}$ = 183 GeV [12]). As a cross-check of the LEP determination of E_CM, ALEPH use the q$\overline{q}$$\gamma$ events by providing the precise ( m_Z,$\Gamma_{\rm Z}^{}$) information and using the jet angles to extract E_CM. The average LEP centre-of-mass energy at ALEPH for the $\sqrt{s}$ = 183 GeV run of 1997 is measured to be 182.50 $\pm$ 0.19(stat) $\pm$ 0.08(syst) GeV [13], which is consistent with the estimate from the LEP energy working group [12] of 182.652 $\pm$ 0.050 GeV.