Physics Letters B 781 (2018) 161–168
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Matching factorization theorems with an inverse-error weighting
Miguel G. Echevarria
a,∗
, Tomas Kasemets
b
, Jean-Philippe Lansberg
c
, Cristian Pisano
d
,
Andrea Signori
e
a
INFN, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy
b
PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Gutenberg University, 55099 Mainz, Germany
c
IPNO, CNRS-IN2P3, Univ. Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, France
d
Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy
e
Theory Center, Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
12 January 2018
Received
in revised form 27 March 2018
Accepted
28 March 2018
Available
online 3 April 2018
Editor:
A. Ringwald
We propose a new fast method to match factorization theorems applicable in different kinematical
regions, such as the transverse-momentum-dependent and the collinear factorization theorems in
Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition
and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using
the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate
the unknown complete matched cross section from an inverse-error-weighted average. The method is
simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated
with the uncertainties from the power corrections to the factorization theorems (additional uncertainties,
such as the nonperturbative ones, should be added for a proper comparison with experimental data).
Its usage is illustrated with several basic examples, such as Z boson, W boson, H
0
boson and Drell–
Yan
lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–
Sterman
subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can
straightforwardly be extended to match any (un)polarized cross section differential in other variables,
including multi-differential measurements.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Motivation
In processes with a hard scale Q and a measured transverse
momentum q
T
, for instance the mass and the transverse momen-
tum
of an electroweak boson produced in proton–proton collisions,
the q
T
-differential cross section can be expressed through two dif-
ferent
factorization theorems. For small q
T
Q , the transverse-
momentum-dependent
(TMD) factorization applies and the cross
section is factorized in terms of TMD parton distribution/frag-
mentation
functions (TMDs thereafter) [1–3]. The evolution of the
TMDs resums the large logarithms of Q /q
T
[4–6]. For large q
T
∼
Q m, with m a hadronic mass of the order of 1GeV, there is
only one hard scale in the process and the collinear factorization
is the appropriate framework. The cross section is then written
in terms of (collinear) parton distribution/fragmentation functions
*
Corresponding author.
E-mail
address: mgechevarria @pv.infn .it (M.G. Echevarria).
(PDFs/FFs). In order to describe the full q
T
spectrum, the TMD and
collinear factorization theorems must properly be matched in the
intermediate region.
Many
recent works on TMD phenomenology and extractions
of TMDs from data did not take into account the matching with
fixed-order collinear calculations for increasing transverse momen-
tum
(see e.g. Refs. [7,8]). Such a matching is one of the compelling
milestones for the next generation of TMD analyses and more gen-
erally
for a thorough understanding of TMD observables [9]. In
addition, it has recently been shown that the precisely measured
transverse-momentum spectrum of Z boson at the LHC does not
completely agree with collinear-based NNLO computations,
1
hint-
ing
at possible higher-twist contributions at the per-cent level.
Thus having a reliable estimation of the matching uncertainty from
power corrections is very opportune.
1
See https://gsalam .web .cern .ch /gsalam /talks /repo /2016 -03 -SB +SLAC -SLAC -
precision
.pdf.
https://doi.org/10.1016/j.physletb.2018.03.075
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.