QCD Sum Rule Calculation for the Tensor Charge of the Nucleon

Abstract

The nucleon's tensor charges (isovector $g^v_T={\delta}u-{\delta}d$ and isoscalar $g^s_T={\delta}u+{\delta}d$) are calculated using the QCD sum rules in the presence of an external tensor field. In addition to the standard quark and gluon condensates, new condensates described by vacuum susceptibilities are induced by the external field. The latter contributions to $g^v_T$ and $g^s_T$ are estimated to be small. After deriving some simplifying formulas, a detailed sum rule analysis yields $g^v_T=1.29 \pm 0.51$ and $g^s_T = 1.37 \pm 0.55$, or ${\delta}u=1.33 \pm 0.53$ and ${\delta}d = 0.04 \pm 0.02$ at the scale of 1 GeV$^2$.