Bose-Einstein correlations

[Bose] [Einstein]

In the beginning of 1920s, when the quantum theory was developing intensively to describe the structure of atoms, the theory of quantum statistics became an important tool in describing ensembles of subatomic particles. Considering identical and indistinguishable particles, the theory of quantum statistics differentiates two kinds of particles, according to the way in which they may be distributed among the available wave functions associated with each energy state.

The statistics which concerns particles satisfying the exclusion principle ad hence described by antisymmetric wave functions, is called Fermi-Dirac statistics, and the particles are called fermions. In particle physics, fermions are characterised by the spin values J=n(h/2), where n is an odd integer. Leptons and quarks, for example, are fermions.

The second kind of statistics was first studied in 1921 by indian mathematician and physicist Satyendra Nath Bose in a paper on the statistics of photons. It concerns particles not restricted by the exclusion principle, and described by symmetric wave functions. Dirac invented the name bosons for such particles, and the statistics got the name of Bose-Einstein statistics. Bosons have an integral spin, therefore not only photons do obey the Bose-Einstein statistics, but also gluons, W and Z intermediate vector fields, and mesons.

When in 1950s, both in particle physics experiments and astronomical observations, it had been discovered that bosons emitted from the same source show the tendency to have close space-time or energy-momentum characteristics, this behaviour was ascribed to the particles obeying the Bose-Einstein statistics. The phenomenon of increasing probability for emission of identical bosons from similar regions of space and time due to the imposition of Bose symmetry, has been called Bose-Einstein correlations.

Presuming that only particles emitted from the same or close sources contribute to the probability enhancement of producing particles with small relative momentum, it is expected that from studies of Bose-Einstein correlations one could obtain important information about the space-time extension and the coherence of sources. This approach to estimating the source size proved to be a reliable tool in astronomy, where the so-called HBT (after Hanbury-Brown and Twiss, - astronomers who first reported of it) effect is used to measure stellar sizes by analysing correlations between detected photons.

In particle physics, the hadron interferometry fulfils the similar task of defining the size, the shape, and the evolution in time of a microscopic source of mesons. The process of hadron production, or fragmentation, in high energy physics is less understood. It can not be described by an appropriate theory, and only phenomenological models are used so far to reproduce it. Studies of the space-time characteristics of a hadron source give an important information about the hadronization process as a whole and also provide tests of fragmentation models.

Since fragmentation models are mostly of probabilistic nature, it is very difficult to incorporate the Bose symmetrization into them. Thus effects of Bose-Einstein correlations are often absent in event generators, which apparently does not affect significantly their performance. However, it was shown recently that in events like e+e- -> W+W-, where two hadron sources are produced close to each other, the Bose-Einstein effects can lead to interference between particles produced by neighbouring sources. From the experimental point of view, this will affect the observed W masses. To account to such an effect and describe it properly in event generators, the Bose-Einstein correlations have to be well understood, which requires more profound studies.

BE Correlations

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