Few-particle lepton bound states in variational approach

TL;DR

This work tackles the calculation of ground-state energies and hyperfine splittings for three-particle and four-particle lepton bound states in QED. It employs a stochastic variational method with Gaussian basis functions in Jacobi coordinates, transforming the problem into a generalized eigenvalue equation $H C = E^eta B C$ with analytically evaluable matrix elements and explicit hyperfine corrections from spin-spin delta interactions. The authors develop a complete variational framework for four-body Coulomb systems, including spin-coupled bases for HPs and MuPs, and provide numerical results that agree with prior calculations to within ~0.04%, highlighting the potential impact of relativistic corrections of order $O( olinebreak[4]alpha^2)$. The study also discusses experimental prospects for observing such bound states (e.g., HPs, Ps2, MuPs) and the relevance of these results for tests of bound-state QED in few-body systems.

Abstract

The energy levels of the ground states of the three-particle and four-particle bound states of leptons in quantum electrodynamics are calculated. For the calculation, the variational method with Gaussian basis functions is used. The hyperfine structure of the spectrum is taken into account due to the pairwise spin-spin interaction of particles.

Figures (1)

• Figure 1: Jacobi coordinates for a system of four particles.