A statistical parameter referring to the standard deviation of a distribution where ‘one sigma' means one standard deviation away from the median (the square root of the variance). It is used for a bunch of particles approximated to a normal, or Gaussian distribution. For a normal distribution, 68 percent of the particles are within ‘one sigma,' 95 percent are within ‘two sigmas' and 99.7 percent within ‘three sigmas.' In a storage ring, the aperture should be at least eight sigmas for reasonable lifetimes.