Marco Bonvini, Stefano Forte, Margherita Ghezzi, Giovanni Ridolfi
We compare threshold resummation in QCD, as performed using soft-collinear
effective theory (SCET), to the standard perturbative QCD formalism based on
factorization and resummation of Mellin moments of partonic cross-sections. We
consider various forms of the SCET result, which correspond to different
choices of the soft scale mu_s that characterizes this approach. We derive a
master formula that relates the SCET resummation to the QCD result for any
choice of mu_s. We then use it first, to show that if SCET resummation is
performed in N-Mellin moment space by suitable choice of mu_s it is equivalent
to the standard perturbative approach. Next, we show that if SCET resummation
is performed by choosing for mu_s a partonic momentum variable, the
perturbative result for partonic resummed cross-sections is again reproduced,
but like its standard perturbative counterpart it is beset by divergent
behaviour at the endpoint. Finally, using the master formula we show that when
mu_s is chosen as a hadronic momentum variable the SCET and standard approach
are related through a multiplicative (convolutive) factor, which contains the
dependence on the Landau pole and associated divergence. This factor depends on
the luminosity in a non-universal way; it lowers by one power of log the
accuracy of the resummed result, but it is otherwise subleading if one assumes
the luminosity not to contain logarithmically enhanced terms. Therefore, the
SCET approach can be turned into a prescription to remove the Landau pole from
the perturbative result, but the price to pay for this is the reduction by one
logarithmic power of the accuracy at each order and the need to make
assumptions on the parton luminosity.
View original:
http://arxiv.org/abs/1201.6364
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