Comments on the relation between the mass of Υ(11P1) and the QCD scale parameterΛMS¯

We study how the mass of the Υ${(1\mathrm{}\mathrm{}}^1$ $P_1$) depends on the QCD scale parameter ${\Lambda }_{\mathrm{MS}\mathrm{¯}}$ (MS¯ denotes the modified minimal-subtraction scheme). We find that the mass differences between the center of gravity of the Υ${(1\mathrm{}\mathrm{}}^3$ $P_{J=0\mathrm{}}$,1,2) and Υ${(1\mathrm{}\mathrm{}}^1$ $P_1$) are 3.7, 4.8, and 5.8 MeV for ${\Lambda }_{\mathrm{MS}\mathrm{¯}=200\mathrm{}}$, 300, and 400 MeV, respectively. A recent experimental value for this mass difference is 5.4±1.7 MeV.