The Minlo
0
implementation presented here can be readily promoted to a Nnlops
simulation of W
+
W
−
production following the same procedure employed to build Nnlops
H [64, 65], Z [66], and HW [62] generators. The present work can be regarded as a main
theoretical step towards such a Nnlops simulation of W
+
W
−
production.
An Nnlops generator could also be achieved through matching an NNLO + NNLL
0
resummed calculation of this process to a parton shower using the Geneva matching formal-
ism [67–70]. In addition, it would appear to be a straightforward matter to merge the same
NNLO calculation with a parton shower according to the UN
2
LOPS prescription [71, 72].
The paper is structured as follows. In section 2 we give details on the construction of
our underlying NLO calculation for W -pair production in association with a jet, as well
as details on the validation of our implementation. We then proceed to exemplify the
extension of the Minlo
0
method to a generic colour-singlet process. Many aspects of the
Minlo
0
approach follow unchanged from refs. [57, 73], and so we focus on presenting the
key differences and their practical implementation. Section 3 presents a phenomenological
study of kinematic distributions for the decay mode of the W -bosons to e
+
ν
e
µ
−
ν
µ
. We
summarize our findings and conclude in section 4. We have made our simulation publicly
available within the Powheg-Box code.
4
2 Method and technical details
In this section we first give all details concerning the construction of the pure Nlops
simulation of jet-associated W -pair production (henceforth WWj), including the treatment
of heavy fermions and the CKM matrix. We subsequently detail the validation of this
construction. Following this, we go on to describe how we have modified and extended
the original Minlo
0
method, such that our WWj-Minlo simulation also recovers NLO
accurate results for 0-jet and inclusive W -pair production observables (henceforth WW).
2.1 Nlops construction
We have generated Born and real matrix elements using the Powheg-Box interface to
Madgraph 4 [74] developed in ref. [75]. The virtual matrix elements have been obtained
using GoSam 2.0 [76]. Our code is based on matrix elements for the following Born sub-
processes and all of their associated NLO counterparts:
5
q¯q → e
+
ν
e
µ
−
ν
µ
g , qg → e
+
ν
e
µ
−
ν
µ
q , ¯qg → e
+
ν
e
µ
−
ν
µ
¯q . (2.1)
Hence, while we refer to our simulation as being one of WWj production, we do in fact
include full spin correlations and all related off-shell and single-resonant contributions. That
is, while no ZZ or Zγ contributions exist for the unequal flavour choice, we include all other
Z, W or γ intermediate exchanges. We have not included the Higgs contribution.
We have chosen to work throughout in the four-flavour scheme (4FNS), as employed,
for instance, in the NNLO calculations of W
+
W
−
production in refs. [23, 30]. Thus, we do
4
Instructions to download the code can be obtained at http://powhegbox.mib.infn.it.
5
In section 2.2 we will also discuss the impact of removing the gauge-invariant set of fermionic loop
corrections.
– 4 –