Perturbative and Nonperturbative Renormalization in Lattice QCD

Abstract

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.

Figures (17)

• Figure 1: $Z^{{\mathrm{RI}^\prime - \mathrm {MOM}}}$ for the operator $\overline{{\cal O}}_T$ at $\beta = 5.29$, $\kappa = 0.1362$ on a $24^3 \times 48$ lattice. The curves represent splines with two interior knots fitted to the data and to the data $\pm$ the statistical error.
• Figure 2: Chiral extrapolation for ${\cal O}_{a_2}$ at $\beta = 5.40$.
• Figure 3: Chiral extrapolation for ${\cal O}^S$ (subtracted data, as explained in Sec. \ref{['sec.subtraction']}) at $\beta = 5.40$.
• Figure 4: Chiral extrapolation of $1/Z_P$ (subtracted data, as explained in Sec. \ref{['sec.subtraction']}) at $\beta = 5.40$. The symbols at $am = 0$ represent the chirally extrapolated values, i.e., the quantity $s_1$.
• Figure 5: $a^2 \mu_p^2 \, s_0$ (from a fit to subtracted data, as explained in Sec. \ref{['sec.subtraction']}) as a function of $\mu_p^2$ for the pseudoscalar density at $\beta = 5.40$.