Bose-einstein Correlations in Heavy-ion Physics and Electron-positron Collisions

We shortly review recent successes in applying Bose-Einstein interferometry in heavy ion collisions and the proceed to some model calculations for 3-dimensional Bose-Einstein correlation functions in e + e − collisions at the Z 0 pole. 1 Theoretical Overview Bose-Einstein correlations (BEC) are a phase-space phenomenon: Symmetrization of the mul-tiparticle wave function affects the measured n-particle coincidence spectra and leads to an enhancement relative to the corresponding product of independent 1-particle spectra, if the emitted particles are close in phase-space (i.e. they occupy the same elementary phase-space cell). The spatial length of the elementary phase-space cells is limited by the geometric size of the source of particles with the considered momentum. The larger this size, the narrower these cells are in momentum space. By tuning the relative momenta and watching the onset of BEC effects one can thus measure the spatial length of the elementary phase-space cells and thereby the size of the source. Wigner Functions. A description of BEC effects among n particles thus involves the n-particle phase-space density. Since we are discussing a quantum mechanical phenomenon, we are not talking about a classical phase-space density (which has directly a probabilistic interpretation), but about the Wigner density (which is positive definite only when averaged over many elementary phase-space cells). If the particles are emitted independently, the (unsymmetrized) n-particle Wigner density factorizes, and all n-particle coincidence cross sections are expressible through the single-particle Wigner function S(x, p). The assumption of independent particle emission is justifiable in heavy ion collisions where the many unobserved particles serve as a reservoir for all kinds of conserved quantities. In e + e − collisions this is much less obvious and needs to be tested experimentally.