Perturbative Quantum Chromodynamics α_s⁴-Order Corrections to the Ratio R for τ Decay

The perturbative quantum chromodynamics correction to the semihadronic decay rate R of the heavy lepton τ was expressed by Braaten as an expansion in powers of α_s to order α_s³. Braaten had found the α_s³ order correction to be significant and conjectured that the α_s⁴ order corrections might also be significant. Braaten et al. later corrected the α_s³-order result. We have extended the analytic calculations to order α_s⁴; it involves an unknown constant K₃ which occurs in α_s⁴ order. In order to estimate the effect of α_s⁴ order correction, we have chosen K₃ to range from -1000 to +1000 and we find that the value of R changes by about -11% to +10%, respectively, compared to the value of R = 3.5 obtained to α_s³-order result.