Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.