Massless Composite Bosons Formed by the Coupled Electron-Positron Pairs and Two-Photon Angular Correlations in the Colliding Beam Reaction e-e+→Bγγ with Emission of the Massless Boson

Abstract

The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is solved in the ladder approximation. A new solution has been found represented by the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant. It has been demonstrated that (1) the massless boson states have normalizable complex wave functions which are transversely compressed plane waves; (2) the transverse radius of the wave functions diverges as the boson energy goes to zero; that is, the composite bosons cannot be at rest; (3) increasing the boson energy results in an extension of the transverse wave function in the momentum space and a corresponding contraction of the real space coordinate wave function. The new reaction e-e+→Bγγ is investigated with the products composed of the massless composite boson and two photons. The cross-section of this reaction is derived for nonrelativistic colliding beams of spin-polarized electrons and positrons. In this case the 2γ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that in order to distinguish between the conventional annihilation of the singlet electron-positron pair with the two-photon emission and the new examined reaction yielding the three particles, experiments are proposed with the extremely nonrelativistic colliding beams.