Power corrections in the dispersive model for a determination of the strong coupling constant from the thrust distribution

Abstract

In the context of the dispersive model for non-perturbative corrections, we extend the leading renormalon subtraction to NNLO for the thrust distribution in e ⁺ e ⁻ annihilation. Within this framework, using a NNLL+NNLO perturbative description and including bottom-quark mass effects to NLO, we analyse data in the centre-of-mass energy range $\sqrt{s}=14\mbox{--}206~\mbox{GeV}$ in view of a simultaneous determination of the strong coupling constant and the non-perturbative parameter α ₀. The fits are performed by matching the resummed and fixed-order predictions both in the R and the log-R matching schemes. The final values in the R scheme are $\alpha_{s}(M_{Z}) = 0.1131^{+0.0028}_{-0.0022}$, $\alpha_{0}(2~\mathrm{GeV}) = 0.538^{+0.102}_{-0.047}$.

Appendix: Explicit resummation formulae

In the present section we report the full resummation formulae used in the main text. The QCD β-function is defined by the renormalisation group equation for the QCD coupling constant

(A.1)

where the first two coefficients read

(A.2)

Following these conventions, the perturbative functions h _i (α _s L) have the following expressions [34, 45], as a function of $\lambda=\frac{\alpha_{s}(\mu)}{\pi}\beta_{0}\log N$:

(A.3)

(A.4)

(A.5)

The resummation coefficients read

(A.6a)

(A.6b)

(A.6c)

(A.6d)

Additional contributions to the functions g _i (α _s L) (8) arise from the function H(1,α _s (Q)) which accounts for hard virtual corrections as well as the hard collinear $\tilde{J} (1, \alpha_{s}(\sqrt{\frac{N_{0}}{N}}Q) )$ and soft $\tilde{S} (1,\alpha_{s}(\frac{N_{0}Q}{N}) )$ constant functions. The latter functions contribute to the perturbative logarithmic structure since their strong couplings are evaluated at the collinear ($\sqrt{\frac{N_{0}}{N}}Q$) and soft ($\frac {N_{0}Q}{N}$) scales, respectively. Their perturbative expansions can be found for example in the appendix of [44, 45].