Massless composite bosons formed by the coupled electron-positron pairs, and two-photon angular correlations in the colliding beam reaction $e^{-}e^{+}\to B\gamma\gamma$ with emission of the massless boson

TL;DR

This paper introduces a symmetric approach to electron-positron interactions, revealing a new branch of massless composite bosons with unique wave functions and proposing a reaction with distinct two-photon angular correlations for experimental detection.

Contribution

It develops a symmetric Dirac particle representation, finds a new class of massless composite bosons, and predicts a specific two-photon correlation signature in electron-positron collisions.

Findings

Massless composite bosons have transversely compressed plane wave functions.

The transverse radius of these bosons diverges as energy approaches zero.

The two-photon angular correlation spectrum shows a narrow peak, aiding experimental identification.

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 studied in the ladder approximation. A new branch of the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant, has been found. It has been obtained that: 1) the massless bosons have the normalized 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) the extension of the transverse wave function in the momentum space and the compression of the coordinate wave function are continuously occurred with increasing the boson energy. The reaction $e^{-}e^{+}\to B\gamma\gamma$ products of which are the massless composite boson and two photons, is investigated. The cross-section of this reaction is derived for the non-relativistic colliding beams of the spin-polarized electrons and positrons. In this case the $2\gamma$ 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 to establish whether there is the conventional annihilation of singlet electron-positron pair with the two-photon emission or the investigated reaction, products of which are the three particles, experiments with the extremely non-relativistic colliding beams should be conducted.