The maximum possible value of a quantity consistent with observations, often used when no signal is detected.An upper limit is the maximum value a physical quantity can take while still being consistent with experimental observations, typically used when a signal is not detected. It defines the boundary of what is possible given the data, often expressed as a confidence interval (e.g., 95% upper limit). This concept is crucial in searches for rare or hypothetical phenomena, such as new particles, gravitational waves, or dark matter interactions, where absence of evidence is quantified rather than taken as proof of nonexistence.
The formal concept of upper limits in particle physics emerged in the mid-20th century with the development of statistical methods for hypothesis testing, notably by Neyman and Pearson. It became standard practice in high-energy physics during the 1960s and 1970s, particularly in searches for new particles.
When an experiment looks for a signal, it records background events and compares them to the expected signal. If no excess is found, scientists set an upper limit by determining the maximum signal strength that could be hidden within the statistical fluctuations of the background. This involves statistical methods like the CLs technique or Bayesian inference, which account for uncertainties and produce a limit that can be compared across experiments.
Upper limits are used in particle physics (e.g., LHC searches for supersymmetry), astrophysics (e.g., limits on gravitational wave backgrounds), and cosmology (e.g., constraints on dark matter cross-sections).
The strongest upper limit on the electron's electric dipole moment is so small that it would be like measuring a displacement of less than a thousandth of the width of a proton on an object the size of the Earth.
