Observation of Upsilon(3S)-->tau+tau- and tests of lepton universality in Upsilon decays

Kendall's tau test, also known as the Kendall rank coefficient test, is a nonparametric method for assessing association between two variables. This test is particularly useful for identifying significant correlations when the distributions of the sample and population are unknown. Developed in 1938 by the British statistician Sir Maurice George Kendall, the tau coefficient (denoted as τ) serves as a rank correlation coefficient, with values ranging from -1 to +1.
A τ value of +1 indicates that...

In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform particle speeds. An arrangement known as a velocity selector uses electric and magnetic fields to pick particles with a particular speed from the beam.
A particle with charge q, speed v, and mass m enters an area from the top, where the magnetic and electric fields are perpendicular both to the particle's motion and to one another. The magnetic...

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to determine this direction with Lenz's law, named in honor of its discoverer, Heinrich Lenz (1804–1865). Lenz's law states that the direction of the induced emf drives the current around a wire loop always to oppose the change in magnetic flux that causes the emf.
If a bar magnet is moved toward a coil such that the magnetic flux through the coil...

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their closest cousins are neutron stars, which are composed almost entirely of neutrons packed against each other, making them extremely dense. A neutron star has the same mass as the Sun but its diameter is only a few kilometers. Therefore, the escape velocity from their surface is close to the speed of light.
Not until the 1960s, when the first neutron...

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.