Heavy-quarkonium systems and the QCD scale parameterΛMS¯

We study how the properties of t-quarkonium states depend on the scale parameter ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$, where MS¯ is the modified minimal subtraction scheme. We find that if ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$ is as small as 100 MeV the shape of the QQ¯ potential for the low-lying tt¯ states with $m_t$∼40 GeV is already almost uniquely determined while if ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$ is as large as 500 MeV the ambiguity in E(2S)-E(1S), e.g., becomes much larger (∼20%). We also study the difference of predictions of t-quarkonium spectra between nonrelativistic and relativistic models. Finally we show that hyperfine and fine splittings are sensitive to the value of ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$, and hence the allowed range of ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$ may be restricted from the data of already known quarkonia, cc¯ and bb¯.