Measurements of the Lifetimes of Positive and Negative Pions

The experiment described here compares the lifetimes of ${\pi }^{+}$ and ${\pi }^{-}$ by measuring the fraction of surviving pions at several positions along a 1000-cm (one-half lifetime) decay path. The result of the measurement, $\frac{\tau \left({\pi }^{+}\right)}{\tau \left({\pi }^{-}\right)=1.00055\mathrm{}\pm 0.00071}$, is consistent with the $\mathrm{CPT}$ theorem, which predicts that a particle and its antiparticle have equal lifetimes. The beam polarity was alternated frequently between positive and negative particles, and many precautions were taken to ensure that the ${\pi }^{+}$ and ${\pi }^{-}$ beams were identical in their spatial and momentum distributions. Most of the running time was spent investigating possible sources of systematic bias which might make the lifetimes appear to be different, and a number of these systematic errors were found and eliminated. Using a time-of-flight determination of the pion velocity, we obtain a value of the charged-pion lifetime $\tau =26.02\mathrm{}\pm 0.04$ nsec. The good agreement between this value for pions in flight and the result of independent measurements with pions at rest provides the most precise verification of time dilation. In the model of Lundberg and Rédei this comparison sets an upper limit on a fundamental length of 3×${10}^{-15\mathrm{}}$ cm. The velocities of the ${\pi }^{+}$ and ${\pi }^{-}$ beams were compared by time of flight and the momenta by use of a magnetic spectrometer. Together the measurements determine $\frac{m\left({\pi }^{+}\right)}{m\left({\pi }^{-}\right)}=1.0002\mathrm{}\pm 0.0005$.