Resummation of the hadronic tau decay width with the modified Borel transform method

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Pade approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.} +- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead.Comment: 32 pages, 2 eps-figures, revtex; minor changes in the formulations; a typo in Eq.(47) corrected; version as appearing in Phys. Rev.

Remediation of fluency: Word specific or generalised training effects?

The present study examines whether reading fluency benefits more from repeated reading of a limited set of words or from practicing reading with many different words. A group of 37 reading delayed Dutch children repeatedly read the same 20 words with limited exposure duration, whereas another group of 37 poor readers received the same reading exercises with 400 different words. Results demonstrated that improvements in accuracy and speed of trained words were larger for the repeated reading group than for the children who had only practiced with these words once. No difference in generalisation of effects to untrained neighbour and control words was found between the two conditions. Furthermore, rapid naming skill was unrelated to improvements in reading fluency and transfer effects in both training conditions. Results demonstrate that the practical value of repeated reading lies in its word specific training effects. © Springer 2006