Quartic mass corrections to R_had at order α_s^3

Abstract

The total cross section for the production of massive quarks in electron positron annihilation can be predicted in perturbative QCD. After expansion in m^2/s the quartic terms, i.e. those proportional to m^4/s^2, are calculated up to order α_s^3 for vector and axial current induced rates. Predictions relevant for charm, bottom and top quarks production are presented. The α_s^3 corrections are shown to be comparable to terms of order α_s and α_s^2. As a consequence, the predictions exhibit a sizeable dependence on the renormalization scale. The stability of the prediction is improved and, at the same time, the relative size of the large order terms decreases by replacing the running mass \bar{m}(μ) with the scheme independent invariant one \hat{m}. By combining these results with the prediction for massless case and the quadratic mass terms the cross section for massive quark production at electron positron colliders is put under control in order α_s^3 from the high energy region down to fairly low energies.

Figures (9)

• Figure 1: The massless approximation $r_0$ in three different energy ranges, relevant for (a) charm, (b) bottom and (c) top production.
• Figure 2: Mass corrections to the non-singlet contribution of $r_q$ for $c$, $b$, and $t$ production (1. ,2., and 3. row, respectively), arising from diagrams where the external current couples to massless quarks only. Left column: quadratic, starting to be non-zero in ${\cal O}\left(\alpha_s^3\right)$; right column: quartic mass corrections, starting to be non-zero in ${\cal O}\left(\alpha_s^2\right)$.
• Figure 3: Quadratic mass corrections ($\propto m^2$) to the non-singlet contribution of $r_Q$ for $Q=c,b,t$, arising from diagrams where the external current couples directly to the massive quark. Upper row: vector current for $c$ and $b$ quarks; lower row: vector and axial currents for $t$ quark.
• Figure 4: Quartic mass corrections ($\propto m^4$) to the non-singlet contribution of $r_Q$ for $Q=c,b,t$, arising from diagrams where the external current couples directly to the massive quark. Upper row: vector currents for $c$ and $b$ quarks; lower row: vector and axial currents for $t$ quark.
• Figure 5: Variation of $r_0$ with $\mu$. $s$ is fixed to values relevant for the production of (a) charm, (b) bottom, and (c) top quarks. The abscissa ranges from $\mu=\sqrt{s}/2$ to $\mu=2\sqrt{s}$.