Momentum subtraction and the $R$ ratio

We determine the $R$ ratio for massless quarks in several renormalization schemes to various loop orders. These are the momentum subtraction schemes of Celmaster and Gonsalves as well as the minimal momentum subtraction scheme. The dependence of the $R$ ratio on the schemes is analyzed.

Figure 1

Comparison of $a_{33}^{\mathcal{S}}(x)$ for the various schemes for $N_f=3$, 4, 5 and 6.

Figure 2

Comparison of $a_{44}^{\mathcal{S}}(x)$ for $\overline{\mathrm{MS}}$ and mMOM for $N_f=3$, 4, 5 and 6.

Figure 3

Plots of $a_{LL}^{\overline{\mathrm{MS}}}(x)$ for $L=2$, 3 and 4.

Figure 4

Plots of $a_{LL}^{\mathrm{MOMggg}}(x)$ for $L=2$ and 3.

Figure 5

Plots of $a_{LL}^{\mathrm{MOMh}}(x)$ for $L=2$ and 3.

Figure 6

Plots of $a_{LL}^{\mathrm{MOMq}}(x)$ for $L=2$ and 3.

Figure 7

Plots of $a_{LL}^{\mathrm{mMOM}}(x)$ for $L=2$, 3 and 4.

Figure 8

Plots of $a_{22}^{\mathrm{MOMq}}(x)$ for various gauges.

Figure 9

Plots of $a_{33}^{\mathrm{MOMq}}(x)$ for various gauges.