### Speaker

Prof.
Kazuhiro Tanaka
(Juntendo University)

### Description

In the conventional b_* model for the Collins–Soper–Sterman resummation,
the resummed form factor is accompanied by the nonperturbative gaussian form factor, and
it is known that the nonperturbative parameter associated with the latter exhibits the strong dependence on the logarithm of
the vector boson invariant mass.
On the other hand, an another approach to treat the impact parameter (b space) transform in the
resummation formalism has been developed as the ``minimal prescription (MP)'' based on an analytic continuation procedure.
By contrast to the b_* approach, the MP has advantages that it leaves unchanged the perturbative
expansion to any (and arbitrarily-high) fixed order in \alpha_s and it does not require any infrared cut-off to avoid the
Landau pole in the b-space integration. In the framework of the MP, however, the behavior of
the corresponding nonperturbative form factor as a function of the vector boson invariant mass has been unknown.
In this work, we present a first systematic study of the nonperturbative form factor associated with the resummed form factor in the MP.
The matching of the b-space resummation formulas between the MP and the b_* model indicates that the
nonperturbative form factor in the MP has the milder dependence on the vector boson invariant mass
than that in the b_* model . To clarify this point quantitatively, we perform a global fit of the nonperturbative form factor in the MP resummation
at the next-to-leading logarithmic accuracy, with the Z boson production data at the Tevatron
and the low energy Drell-Yan data. We obtain good description of the transverse momentum distribution of vector bosons using a gaussian form of the
nonperturbative form factor and find
the weak dependence of the corresponding nonperturbative parameter on the vector boson invariant mass,
which in turn allows an interpretation as arising from the intrinsic transverse momentum of partons inside the proton.

### Primary author

Prof.
Kazuhiro Tanaka
(Juntendo University)

### Co-authors

Dr
Hiroyuki Kawamura
(KEK)
Prof.
Masanori Hirai
(Tokyo University of Science)