Recent progress in hadronic τ decays

Abstract

The determination of αs from hadronic τ decays is impeded by the fact that two choices for the renormalisation group resummation, namely fixed-order (FOPT) and contour-improved perturbation theory (CIPT), yield systematically differing results. On the basis of a model for higher-order terms in the perturbative series, which incorporates well-known structure from renormalons, it is found that FOPT smoothly approaches the Borel sum for the τ hadronic width, while CIPT is unable to account for the resummed series. An example for the behaviour of QCD spectral function moments, displaying a similar behaviour, is presented as well.

Determination ofαs(Mτ2)from improved fixed order perturbation theory

“…For the RGS improved FOPT we have used the expressions of D n given in the Appendix, setting k ¼ 0 for k ! 4 as in the previous similar analyses of higher order expansions [6,7,14,16].…”

“…We mention however that, as discussed in [14,16], for other models the CI expansion may give better results than the standard FOPT at low orders. In particular, this is true for models with a residue d IR 2 of the first IR renormalon smaller than the value quoted in (23).…”

“…It is of interest to see whether this behavior is preserved to higher orders. To this end we consider a class of physical models of the Adler function used for testing various expansions in [6,7,13,14,16].…”

“…The recent calculation of the Adler function to four loops [1], the same order to which the -function of the renormalization-group (RG) equation is known [2,3], renewed interest in the determination of s ðM 2 Þ [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The intriguing remark [6] that the inclusion of a higherorder term increased, instead of reducing, the theoretical error on the resulting s ðM 2 Þ stimulated many investigations aimed at understanding this fact.…”