Muonium and positronium potentials

Abstract

Muonium and positronium potentials with radiative corrections are derived from the scattering operator, and general results for the spectra of these systems to order a 3~, are obtained. We also compare our results with those obtained earlier with the Bethe-Salpeter approach, and find a discrepancy in the case of the 1S state. Our theoretical results are in good agreement with the available experimental data. -(3) of this reference should be s.

Effective-field theories for heavy quarkonium

“…In order to obtain the spectrum at order m␣ s 4 , ␣ V s has to be calculated to order ␣ s 3 ͑two loops͒, V s ͑1͒ to order ␣ s 2 ͑one loop͒, and the remaining potentials to order ␣ s ͑tree level͒. They are and the complete V s ͑2͒ have been computed over the years ͑Buchmüller et al, 1981;Gupta andRadford, 1981, 1982;Pantaleone et al, 1986;Titard and Yndurain, 1994;Pineda and Soto, 1999;Manohar and Stewart, 2000b;Kniehl et al, 2002a͒ and can be found in the article by Kniehl et al ͑2002a͒. Several comments are in order concerning these calculations.…”

“…At lowest order in the weak-coupling regime ͉͑p͉ ӷ⌳ QCD ͒, the potential is Coulombic. Higherorder corrections to the potential in perturbation theory were obtained over the years ͑Buchmüller et al, 1981;Gupta andRadford, 1981, 1982;Pantaleone et al, 1986;Titard and Yndurain, 1994͒ even though the computations were difficult due to the several scales involved. It was also not clear how to systematically incorporate US effects.…”

Mass and theE1 decay rate of the singletPstate of charmonium

“…(2) for calculating the hyperfine (1 1) is also the spin-independent part of the nonsingular Hamiltonian used by Gupta, Repko, and Suchyta [7] In Eq. (5), V ( p , p l ) is given by (GRS).…”

“…Even the sign of the hyperfine splitting then changes. We also used the nonsingular Hamiltonian of Gupta, Repko, and Suchyta [7] obtained by means of the improved quasistatic approximation of Gupta [4] in a nonperturbative variational calculation to obtain the hyperfine splitting AMp of the P states. Now all the terms in the nonsingular Hamiltonian, including the spin-independent, tensor, and spin-orbit terms, contribute to the hyperfine splitting since the wave functions for the triplet and the singlet states are different in a nonperturbative variational calculation using the full Hamiltonian.…”

“…We also calculated the electric dipole ( E 1 ) one-photon transition rate for the process 'PI + 'so + y for charmonium. The E 1 decay rate for this process is given by the formula [8] where a is the fine structure constant, w',,=M('P, ) --M ( ' s 0 ) , batively by the variational method in the GRS model [7]. In Eq.…”