Massless and massive Jets in the in the large-$\beta_0$ limit
In this talk I will discuss an alternative way of organising
perturbative computations in QCD, using $1/\beta_0$ as the small
expansion parameter. The leading correction in this expansion can be
computed in an exact form and is very useful to study the convergence
properties of series, in particular so-called renormalons. I will
present a formalism to compute renormalised matrix elements to all
orders in alphaS in this particular limit, adapting the existing
formalism to account for quantities with cusp anomalous dimensions. We
will apply this result to various short-distance masses, as well as the
hard and jet functions in SCET (massless quarks) and bHQET (massive
quarks), finding closed expressions for them as well as for their cusp
and non-cusp anomalous dimensions, reproducing known results up to
O[alphaS * (nf * alphaS)^3]. Some phenomenological applications will be
presented.