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High Energy Physics - Phenomenology
Title: New method for the solution of the two-body Dirac equation: Estimation of the weights of $C$, $P$ and $CP$ symmetry violating terms in positronium
(Submitted on 30 Mar 2024 (v1), last revised 17 Apr 2024 (this version, v3))
Abstract: A new theoretical method is developed for the solution of the two-body bound-state Dirac equation for positronium. Only Coulomb potential was included in the Dirac Hamiltonian. It is shown that the two-body Dirac Hamiltonian can be written in the Hermitian matrix form of the $4\times 4$ size and contains terms, responsible for the violation of the $P$, $C$, and $CP$ symmetries. Numerical results for the energy spectrum of the para- and ortho-positronium ground states performed within the variational method using the harmonic oscillator basis functions are in good agreement with a high-precision finite-element method of T.C. Scott et al. The weights of the $P$ and $CP$ symmetry-violating components in the para-positronium ground state are identical to the weight of the $P$ symmetry-violating component of the ortho-Ps and are estimated to be 6.6E-6. The weights of the $C$ and $CP$ symmetry-violating components of the ortho-Ps are equal to the 2/3 and 1/3 parts of this value, respectively. These numbers are less by two orders of magnitude than the precision limit of current experimental facilities.
Submission history
From: Ergash M. Tursunov [view email][v1] Sat, 30 Mar 2024 18:18:27 GMT (78kb)
[v2] Thu, 11 Apr 2024 17:30:23 GMT (78kb)
[v3] Wed, 17 Apr 2024 04:56:54 GMT (78kb)
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