We present a scheme-independent calculation of the infrared value of the anomalous dimension of the fermion bilinear, ${\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}}_{\overline{\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}}\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>},IR}$ in an SU(3) gauge theory as a function of the number of fermions, $N_f$, via a series expansion in powers of ${\mathrm{<ruby><rb>\Delta </rb><rt>でるた</rt></ruby>}}_f$, where ${\mathrm{<ruby><rb>\Delta </rb><rt>でるた</rt></ruby>}}_f=(16.5-N_f)$, to order ${\mathrm{<ruby><rb>\Delta </rb><rt>でるた</rt></ruby>}}_f^4$. We perform an extrapolation to obtain the first determination of the exact ${\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}}_{\overline{\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}}\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>},IR}$ from continuum field theory. The results are compared with calculations of the $n$-loop values of this anomalous dimension from series in powers of the coupling and from lattice measurements.

• Received 30 July 2016

DOI:https://doi.org/10.1103/PhysRevD.94.105014