Abstract
The precision measurement of the hyperfine splitting, ΔHF(1P, c-c) = M cog(xcJ) — M(h c), in the Fermilab-E835 and CLEO experiments allows one to determine the gluonic condensate G 2 with high accuracy if the gluonic correlation length T g is fixed. In our calculations, the negative value of ΔHF = −0.5 ± 0.4 MeV, as in the E835 experiment, is obtained only if the relatively small T g = 0.16 im and G 2 = 0.060(3) GeV4 are taken. For T g ≥ 0.2 fm, the hyperfine splitting is positive and grows for increasing T g. In particular, for T g = 0.2 fm and G 2 = 0.045(2) GeV4, the splitting ΔHF = 1.0(5) MeV is just in accordance with the recent CLEO result. The values of G 2 taken correspond to the “physical” string tension σ ≈ 0.18 GeV2.
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Badalian, A.M., Bakker, B.L.G. The gluonic condensate from the hyperfine splitting M cog(XcJ) — M(h c) in charmonium. Phys. Atom. Nuclei 69, 734–738 (2006). https://doi.org/10.1134/S106377880604017X
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DOI: https://doi.org/10.1134/S106377880604017X