GEN-17-001

$HeadURL$ $Id$

GEN-17-001

# Extraction and validation of a new set of CMS pythia8 tunes from underlying-
event measurements

###### Abstract

New sets of CMS underlying-event parameters (“tunes”) are presented for the
pythia8 event generator. These tunes use the NNPDF3.1 parton distribution
functions (PDFs) at leading (LO), next-to-leading (NLO), or next-to-next-to-
leading (NNLO) orders in perturbative quantum chromodynamics, and the strong
coupling evolution at LO or NLO. Measurements of charged-particle multiplicity
and transverse momentum densities at various hadron collision energies are fit
simultaneously to determine the parameters of the tunes. Comparisons of the
predictions of the new tunes are provided for observables sensitive to the
event shapes at LEP, global underlying event, soft multiparton interactions,
and double-parton scattering contributions. In addition, comparisons are made
for observables measured in various specific processes, such as multijet,
Drell–Yan, and top quark-antiquark pair production including jet substructure
observables. The simulation of the underlying event provided by the new tunes
is interfaced to a higher-order matrix-element calculation. For the first
time, predictions from pythia8 obtained with tunes based on NLO or NNLO PDFs
are shown to reliably describe minimum-bias and underlying-event data with a
similar level of agreement to predictions from tunes using LO PDF sets.

##  0.1 Introduction

Monte Carlo (MC) simulation codes describe hadron-hadron collisions with
models based on several components. The hard scattering component of the event
consists of particles from the hadronization of partons whose kinematics are
predicted using perturbative matrix elements (MEs), along with partons from
initial-state radiation (ISR) and final-state radiation (FSR) that are
simulated using a showering algorithm. The underlying event (UE) consists of
the beam-beam remnants (BBR) and the particles that arise from multiple-parton
interactions (MPI). The BBR are what remains after a parton is scattered out
of each of the two initial beam hadrons. The MPI are additional soft or semi-
hard parton-parton scatterings that occur within the same hadron-hadron
collision. Generally, observables sensitive to the UE also receive
contributions from the hard-scattering components. Accurately describing
observables that are sensitive to the UE not only requires a good description
of BBR and MPI, but also a good modeling of hadronization, ISR, and FSR.
Standard MC event generators, such as pythia8 [1], [2, 3], and [4] have
adjustable parameters to control the behavior of their event modeling. A set
of these parameters, which has been adjusted to better fit some aspects of the
data, is referred to as a tune.

In a previous study [5], we presented several pythia8 and UE tunes constructed
for a center-of-mass energy $\sqrt{s}$ lower than 13. The CMS pythia8 tune
CUETP8M1 is based on the Monash tune [6], using both the NNPDF2.3LO parton
distribution function (PDF) set [7]. The CMS pythia8 tune CUETP8S1-CTEQ6L1 is
based instead on the tune 4C [8]. Both tunes CUETP8M1 and CUETP8S1-CTEQ6L1
were constructed by fitting the CDF UE data at $\sqrt{s}=900\GeV$ and 1.96 [9]
together with CMS UE data at $\sqrt{s}=7\TeV$ [10]. A similar procedure was
used for the determination of the tune (CUETHppS1) with the CTEQ6L1 PDF set
[11]. A collection of previously published tunes is documented in [6, 12, 8,
13, 14, 12, 15].

In this paper, a new set of tunes for the UE simulation in the pythia8
(version 8.226) event generator is obtained by fitting various measurements
sensitive to soft and semi-hard MPI at different hadron collision energies [9,
10], including data from $\sqrt{s}=13\TeV$ [16]. These tunes are constructed
with the leading order (LO), next-to-leading order (NLO), and next-to-next-to-
leading order (NNLO) versions of the NNPDF3.1 PDF set [17] for the simulation
of all UE components. Typically, the values of strong coupling used for the
simulation of the hard scattering are chosen consistent with the order of the
PDF set used.

The new tunes are obtained by fitting CDF UE data at $\sqrt{s}=1.96\TeV$ [9],
together with CMS UE data at $\sqrt{s}=7\TeV$ [10] and at 13 [16, 18]. For the
first time, we show that predictions obtained with tunes based on higher-order
PDF sets are able to give a reliable description of minimum-bias (MB) and UE
measurements with a similar level of agreement to predictions from tunes using
LO PDF sets. We also compare the predictions for multijet, Drell–Yan, and top-
antiquark () processes from pythia8 with new tunes in ME-parton shower (PS)
merged configurations.

In Section 2 we describe observables that are sensitive to MB and UE:
diffractive processes [19], where one or both protons remain intact after the
collision; and double-parton scattering (DPS), where two hard scatterings
occur within the same collision. In Section 3, we compare the tunes that were
constructed before the data at $\sqrt{s}=13\TeV$ were available (“Pre-13”
tunes) with UE data measured at 13. Section 4 is dedicated to a general
discussion of the choice of PDF sets and strong coupling values for the UE
simulation. In Section 5 we describe the new tunes. Section 6 shows the
validation of the new CMS pythia8 tunes for multijet, Drell–Yan, , and DPS
processes. Section 7 is the summary and conclusions.

##  0.2 Observables for characterizing minimum bias, underlying event, and
double-parton scattering

Minimum bias is a generic term that refers to inelastic events that are
collected with a loose event selection that has the smallest bias possible.
The MB observables are constructed from data with little or no additional
selection requirements. The majority of MB collisions are soft, with a typical
transverse momentum scale $\pt\lesssim 2\GeV$. The UE is defined as the
activity that is not associated with the particles originating from the hard
scattering of two partons and is generally studied in events that contain a
hard scattering with $\pt\gtrsim 2\GeV$. The main contribution to the UE comes
from color exchanges between the beam partons and is modeled in terms of MPI,
BBR, and color reconnection (CR). The MB and UE observables have quite
different kinematic properties because they are affected by different mixtures
of hard and soft scattering processes.

As illustrated in Fig. 1, one can use the topological structure of a typical
hard hadron-hadron collision to study the UE experimentally. On an event-by-
event basis, a leading object is used to define regions of $\eta\text{-}\phi$
space that are sensitive to the modeling of the UE, where $\eta$ is the
pseudorapidity and $\phi$ is the azimuthal scattering angle defined in the
$xy$ plane. The azimuthal separation between charged particles and the leading
object, $\Delta\phi\ =\phi-\phi_{\text{max}}$, is used to define the UE-
sensitive regions. Here $\phi_{\text{max}}$ is the azimuth of the leading
object and $\phi$ is the azimuth angle of an outgoing charged particle. The
regions are labelled as ‘toward’ ($\abs{\Delta\phi}\leq 60^{\circ}$), ‘away’
($\abs{\Delta\phi}<120^{\circ}$), and ‘transverse’
($60^{\circ}<\abs{\Delta\phi}\leq 120^{\circ}$).

Figure 1: Illustration of several $\phi$ regions relative to the leading
object that are sensitive to the underlying event. See the text for the
details on the definitions of the regions.

The transverse region can further be separated into transMAX and transMIN. On
an event-by-event basis, transMAX (transMIN) is defined as the transverse
region having the maximum (minimum) of either the number of charged particles,
or scalar sum of charged particles ($\pt^{\text{sum}}$), depending on the
quantity under study.

Published UE studies used the charged-particle jet with the largest [16], the
dilepton system in DY [20, 21], or [22] events as the leading (, the highest )
objects. The tunes from CDF and CMS data [9, 10] made use of the charged
particle with the largest ($\pt^{\text{max}}$) as the “leading object”, and
use only charged particles with $\pt>0.5\GeV$ and $\abs{\eta}<0.8$ to
characterize the UE. The toward region contains the leading object, and the
away region is expected to include the object recoiling against the leading
one. Most of the UE contributions, , PS and MPI, are contained in the two
transverse regions. For events with multiple ISR or FSR emissions, transMAX
often contains a third hard jet, while both transMAX and transMIN receive
contributions from the MPI and BBR components. Typically, the transMIN
observables are more sensitive to the MPI and BBR components of the UE.

Observables sensitive to UE contributions are the charged-particle
multiplicity and the charged-particle scalar-sum densities in the
$\eta\text{-}\phi$ space, measured in transMIN and transMAX. The tunes that
are constructed by fitting such UE-sensitive observables are referred to as
“UE tunes”.

The pythia8 MC event generator also simulates single-diffractive (SD)
dissociation, double-diffractive (DD) dissociation, central-diffractive (CD),
and nondiffractive (ND) processes [23], which contribute to the inelastic
cross section in hadron-hadron collisions. In SD, CD, and DD events, one or
both of the beam particles are excited into color singlet states, which then
decay. The SD and DD processes correspond to color singlet exchanges between
the beam hadrons, while CD corresponds to double color singlet exchange with a
diffractive system produced centrally. For ND processes, color exchanges
occur, the outgoing remnants are no longer color singlets, and a multitude of
particles is produced. All processes except SD are defined as nonSD (NSD)
processes. An NSD-enhanced sample is required to have an energy deposit in
both the backward ($-5<\eta<-3$) and the forward ($3<\eta<5$) regions of the
detector. The details of the selection for different types of diffractive
events can be found in Ref. [24].

Generally, MC models such as pythia8 regularize the contributions of the
primary hard-scattering processes and MPI to the differential cross section by
using a threshold parameter $\pt^{0}$. The primary hard-scattering processes
and the MPI are regularized in the same way with this parameter. This
threshold is expected to have a dependence on the center-of-mass energy of the
hadron-hadron collision, $\sqrt{s}$. The threshold at a reference center-of-
mass energy $\sqrt{s}=7\TeV$ is called pT0Ref. In pythia8 the energy
dependence is parameterized using a power law function with a reference energy
parameter $s_{0}$ and an exponent $\epsilon$. At a given center-of-mass
energy, the amount of MPI depends on the threshold $\pt^{0}$, the PDF, and the
overlap of the matter distributions of the two colliding hadrons. Smaller
values of $\pt^{0}$ result in larger MPI contributions because of a higher MPI
cross section. Each MPI adds colored partons to the final state, creating a
dense net of color lines that spatially overlap with the fields produced by
the partons of the hard scattering and with each other. All the generated
color lines may connect to each other according to the CR model.

Since pythia8 regularizes both the cross section for MPI and the cross section
of collisions with low-exchange using the $\pt^{0}$ parameter, one can model
the overall ND cross section by letting the of the primary hard scattering
become small. In this simple approach, the UE in a hard-scattering process is
related to MB collisions. At the same center-of-mass energy, the activity in
the UE of a hard-scattering process is greater than that of an average MB
collision. In pythia8, this is caused by the higher MPI activity in hard-
scattering processes compared to a typical MB collision. By demanding a hard
scattering, one forces the collision to be more central, , with a small impact
parameter between the protons, and this increases the probability of MPI. For
MB collisions, peripheral collisions, where the impact parameter between the
two colliding protons is large, are most common.

Typically MPI interactions contain particles with substantially lower
(“softer”). However, occasionally two hard 2-to-2 parton scatterings can occur
within the same hadron-hadron collision. This is referred to as DPS. Tunes
that are constructed by fitting DPS-sensitive observables are referred to as
“DPS tunes”. Ultimately, one universal tune that simultaneously accurately
describes observables in hard scattering events, as well as MB collisions, is
desirable.

The goals of this paper are to produce improved 13 pythia8 tunes with well-
motivated parameters, and to provide an investigation of the possible choices
that can be made in pythia8 which simultaneously describe a wide range of UE
and MB measurements and are suitable for merged configurations, where a ME
calculation is interfaced to the simulation of UE contributions.

##  0.3 Comparisons of predictions for UE observables from previous tunes to
measurements at 13

In this section, comparisons are presented between data collected at
$\sqrt{s}=13\TeV$ and predictions from tunes obtained using fits to
measurements performed at lower center-of-mass energies. Figure 2 displays
comparisons of CMS data at 13 [16] for the transMIN and transMAX charged-
particle $\pt^{\text{sum}}$ densities, as functions of the leading charged-
particle $\pt^{\text{max}}$. The data are compared with predictions from the
pythia8 tunes CUETP8S1-CTEQ6L1 [5], CUETP8M1 [5], and Monash [6].

The CMS Monash-based tune CUETP8M1 does not describe the central values of the
data at $\sqrt{s}=13\TeV$ well, nor does the original Monash tune. For
example, CUETP8M1 and Monash tunes do not predict enough UE activity in the
region with $\pt^{\text{max}}>5\GeV$ (the “plateau” region) of transMIN at 13,
with a disagreement of $\approx$10% and $\approx$5%, respectively. The
transMIN observables are very sensitive to MPI, which suggests that tune
CUETP8M1 does not produce enough charged particles at 13. In addition,
CUETP8M1 does not provide a good fit to the jet multiplicity in production
either at 8or at 13 [25, 26]. High jet multiplicity events are sensitive to
the modeling of the ISR. Hence, CUETP8M1 may not have the proper mixture of
MPI and ISR. The ATLAS collaboration has also observed some discrepancies
between the predictions of the A14 tune [12], used as standard tune for
analyses of 7 and 8data, and the data at 13 [27]. The CMS UE tunes were
constructed by fitting CDF UE data at $\sqrt{s}=900\GeV$ and 1.96, together
with CMS UE data at $\sqrt{s}=7\TeV$.

In Fig. 2 the CMS UE tunes provide a fairly good description of the 13UE data.
Because the CMS UE tunes were obtained by fitting UE observables at various
collision energies ($\sqrt{s}=900$, 1960, and 7000), they underestimate the
data at $\sqrt{s}=13\TeV$. This might be an indication of the need to improve
the energy extrapolation function implemented in pythia8 [28]. Predictions
obtained with the Monash tune, which is the default pythia8 tune, slightly
better reproduce the 13UE data, but is somewhat worse at describing the UE
observables at $\sqrt{s}=900$ and 1960than the CMS UE tunes.

Predictions from the 7.1 tune UE-MMHT [3] are also shown. The H7-UE-MMHT tune
was obtained by fitting UE data at $\sqrt{s}=0.9$ and 7. This tune is based on
the MMHT2014 PDF set [29] and is able to describe the plateau region of the UE
observables at $\sqrt{s}=13\TeV$. The part of the spectrum at
$\pt^{\text{max}}>5\GeV$ is not well reproduced in the range of the leading
charged-particle $\pt^{\text{max}}$ between 2 and 7, with differences of up to
30% with respect to the data. The predictions from 7 achieve an overall good
agreement with measurements at $\sqrt{s}=7\TeV$ [30], while the disagreement
observed for measurements at $\sqrt{s}=13\TeV$ might indicate the need for
further tuning of the new soft MPI model [30]. Since many parameters related
to PS changed between and 7, the CMS tunes extracted for with the CTEQ6L1 PDF
set and documented in Ref. [5] are not updated and should not be used with 7.

Since no currently available tune is able to optimally reproduce the UE data
at $\sqrt{s}=13\TeV$, we aim to produce improved pythia8 UE tunes.

Figure 2: The (left column) transMIN and (right column) transMAX charged-
particle $\pt^{\text{sum}}$ (upper row), and multiplicity (lower row)
densities for particles with $\pt>0.5\GeV$ in $\abs{\eta}<2.0$, as a function
of the transverse momentum of the leading charged particle
($\pt^{\text{max}}$), from the CMS $\sqrt{s}=13\TeV$ analysis [16]. The data
are compared with the pythia8 tune Monash, the CMS pythia8 tunes
CUETP8S1-CTEQ6L1 and CUETP8M1, and the 7 (labelled as “H7”) tune UE-MMHT. The
ratios of the simulations to the data (MC/Data) are also shown, where the
shaded band indicates the total experimental uncertainty in the data. Vertical
lines drawn on the data points refer to the total uncertainty in the data.
Vertical lines drawn on the MC points refer to the statistical uncertainty in
the predictions. Horizontal bars indicate the associated bin width.

##  0.4 PDF and strong coupling values for the tunes

Two of the basic input parameters to the predictions are the choice of the
order of the PDF sets and values of the strong coupling $\alpS$. These appear
in the hard partonic MEs, the PS model, and the MPI model. The $\alpS$ values
used in simulations at LO or NLO are typically different. Traditionally, the
perturbative order of the PDF is matched to the order of the ME calculation.
Merged calculations capture some higher-order corrections with respect to the
formal order of the ME calculation. Merging schemes, such as the –MLM [31] or
CKKW [32, 33], allow the combination of predictions of jet production using ME
calculations with those from PS emissions for soft and collinear parton
radiation at leading-log accuracy without double counting or dead regions.
Merging can be applied also for processes generated at NLO. Using the same PDF
set and $\alpS$ value in the ME calculations and in the simulation of the
various components of the PS is advocated in Ref. [34], and by the 7 and
Collaborations, especially when the PS simulation is merged with calculations
of higher-order MEs. The PDF used for the hard process is constrained by the
accuracy of the ME calculation. If we require the PDF to match between the ME
and PS, simulations with a (N)NLO ME will also require a (N)NLO PDF in the PS.
Depending on the process, this may not have a significant effect. For PS MC
event generators, different strategies are adopted; CMS [5] and ATLAS [12]
tunes are traditionally based on LO PDFs, pythia8 [6] tunes are mostly based
on LO PDFs, new [4] tunes are based on NNLO PDFs, and 7 [30] provide tunes
based on NLO PDFs. The usage of a LO PDF set in the UE simulation is motivated
by the fact that MPI processes occur at very low energy scales, where a
physical (positive) gluon distribution is required by the parton shower.
However, there is no consensus on the choice of the order of the PDF. For
example, in the NNPDF3.1 set at NNLO, the gluon distribution remains physical
even at very low scales.

In the pythia8 tunes produced prior to this paper, the values used for $\alpS$
were often not the same as those used in the PDFs. For example, in the Monash
tune, the FSR $\alpS(m_{\cPZ})$, set to 0.1365, is obtained by fitting pythia8
predictions to LEP event-shape measurements [6], the ISR $\alpS(m_{\cPZ})$ is
assumed to be equal to FSR $\alpS(m_{\cPZ})$, and the hard scattering and MPI
$\alpS(m_{\cPZ})$ is set to 0.13 according to the value used in the LO PDF
set. Even though the $\alpS$ values are free parameters in event generators
and various possibilities are viable, the usual course is to choose them
consistent with the value used by the PDF set.

In this paper, a collection of new tunes is presented for PDF sets that are
evaluated at different accuracies and tested against observables of MB, UE,
and hard processes. The NNPDF3.1 PDF sets at the LO, NLO, and NNLO accuracy
are used [17]. The LO PDF set uses an $\alpS(m_{\cPZ})$ value of 0.13, while
0.118 [35] is the $\alpS(m_{\cPZ})$ value used for the NLO and NNLO PDF sets.
None of the central values of the PDF sets have negative values for any parton
flavor in the phase space relevant for comparisons. Special care is required
when applying these tunes at high-x regions, where the parton distributions in
NNPDF3.1 NLO and NNLO PDF may become negative, which implies an unphysical
(negative) value of the calculated cross sections.

The UE simulation is performed by pythia8, together with PS merged with a
calculation of a higher-order or a multileg ME provided by external programs,
such as [36] or madgraph5_amc@NLO (mg5_amc) [37]. The issue of combining
external ME calculations with PS contributions is addressed by the merging
procedure. The procedures considered in this paper are the “FxFx” [38] or the
“POWHEG” [39] methods for merging higher-order (NLO) MEs to PS and the “MLM”
method [31].

During this study, we also investigated the effect of imposing an additional
rapidity ($y$) ordering to ISR in these merging calculations. The pythia8
Monash tune includes a rapidity ordering for both ISR and MPI. The rapidity
ordering acts as an extra constraint on the -ordered emissions, thus reducing
the phase space for parton emission.

##  0.5 New CMS pythia8 tunes at 13

In the following, a set of new 13pythia8.226 tunes is presented with different
choices of values of the strong coupling used in the modeling of the ISR, FSR,
hard scattering, and MPI, as well as the order of its evolution as a function
of the four-momentum squared $Q^{2}$. We distinguish the new tunes according
to the order of the PDF set used: LO-PDF, NLO-PDF, or NNLO-PDF. The tunes are
labeled as CPi, where CP stands for “CMS pythia8” and i is a progressive
number from 1 to 5. Only five parameters related to the simulation of MPI, to
the overlap matter distribution function [40], and to the amount of CR are
constrained for the new CMS tunes. In all tunes, we use the MPI-based CR model
[41]. The CP tunes are multipurpose tunes, aiming for a consistent description
of UE and MB observables at several collision energies and a reliable
prediction of the UE simulation in various processes when merged with higher-
order ME calculations.

The settings, used in the determination of the new CMS pythia8 UE tunes, are
as follows:

  * •

Tune CP1 uses the NNPDF3.1 PDF set at LO, with $\alpS$ values used for the
simulation of MPI, hard scattering, FSR, and ISR equal to, respectively, 0.13,
0.13, 0.1365, and 0.1365, and running according to an LO evolution.

  * •

Tune CP2 is a slight variation with respect to CP1, uses the NNPDF3.1 PDF set
at LO, with $\alpS$ values used for the simulation of MPI, hard scattering,
FSR, and ISR contributions equal to 0.13, and running according to an LO
evolution.

  * •

Tune CP3 uses the NNPDF3.1 PDF set at NLO, with $\alpS$ values used for the
simulation of MPI, hard scattering, FSR, and ISR contributions equal to 0.118,
and running according to an NLO evolution.

  * •

Tune CP4 uses the NNPDF3.1 PDF set at NNLO, with $\alpS$ values used for the
simulation of MPI, hard scattering, FSR, and ISR contributions equal to 0.118,
and running according to an NLO evolution.

  * •

Tune CP5 has the same settings as CP4, but with the ISR emissions ordered
according to rapidity.

The parameters related to the simulation of the hadronization and beam
remnants are not varied in the fits and are kept fixed to the values of the
Monash tune. The overlap distribution between the two colliding protons is
modeled according to a double-Gaussian functional form with the parameters
coreRadius and coreFraction. This parametrization of the transverse partonic
overlap of two protons identifies an inner, denser part, the so-called core,
and an outer less dense part. The coreRadius parameter represents the width of
the core and the coreFraction, the fraction of quark and gluon content
enclosed in the core. A double-Gaussian function is preferred for modeling the
proton overlap over the negative exponential used in some previous tunes.
Tunes using a double-Gaussian function tend to better reproduce the cross
sections measured by the CMS experiment at $\sqrt{s}=7\TeV$ [10],
simultaneously as a function of charged-particle multiplicity and transverse
momenta.

The parameter that determines the amount of simulated CR in the MPI-based
model is varied in the fits. A small (large) value of the final-state CR
parameter tends to increase (reduce) the final particle multiplicities.

The new CMS pythia8 tunes are extracted by varying the parameters listed in
Table 0.5 and by fitting UE observables at various collision energies. In the
fitting procedure, we use the charged-particle and $\pt^{\text{sum}}$
densities, measured in transMIN and transMAX regions as a function of
$\pt^{\text{max}}$, as well as the charged-particle multiplicity as a function
of pseudorapidity $\eta$, measured by CMS at $\sqrt{s}=13\TeV$ [16, 18]. In
addition, we also use the charged-particle and $\pt^{\text{sum}}$ densities as
a function of the leading charged-particle , measured in transMIN and transMAX
by CMS at $\sqrt{s}=7\TeV$ [10] and by CDF at $\sqrt{s}=1.96\TeV$ [9].

Parameters in the pythia8 MC event generator together with the PDFs determine
the energy dependence of MPI, the overlap matter distribution function, and
the amount of simulated color reconnection. The parameter ranges used for the
fits are also listed.  Parameter description Name in pythia8 Range considered
MPI threshold [], pT0Ref, at $\sqrt{s}=\sqrt{s_{0}}$
MultipartonInteractions:pT0Ref 1.0–3.0 Exponent of $\sqrt{s}$ dependence,
$\epsilon$ MultipartonInteractions:ecmPow 0.0–0.3 Matter fraction contained in
the core MultipartonInteractions:coreFraction 0.1–0.95 Radius of the core
MultipartonInteractions:coreRadius 0.1–0.8 Range of color reconnection
probability ColorReconnection:range 1.0–9.0

Tunes are determined by generating sets of predictions using the rivet [42]
(version 2.5.2) and the professor [43] (version 1.4.0) frameworks with around
150 different choices of the five parameter values used in the event
simulation. The predictions form a grid in the five-dimensional parameter
space which is fitted using a third-order polynomial function. The uncertainty
introduced in the fitted parameters due to the interpolation procedure is
negligible compared with the quoted tune uncertainty. Results are found to be
stable if one decreases this number to 100 or increases to 200, or uses a
fourth-order polynomial function for the grid interpolation. The generated
inelastic events include ND and diffractive (DD$+$SD$+$CD) contributions. The
UE observables used to determine the tunes are sensitive to diffractive
contributions only at very small $\pt^{\text{max}}$ values ($<$3). The ND
component is dominant for $\pt^{\text{max}}$ values greater than $\approx$3.0,
since the cross section of the diffractive components rapidly decreases as a
function of the exchanged . Minimum-bias observables, such as the inclusive
charged-particle multiplicity as a function of $\eta$, are sensitive to all
contributions over the whole spectrum.

The fit is performed by minimizing the $\chi^{2}$ function

$\chi^{2}(p)=\sum_{\textrm{O}_{j}}\sum_{i}\frac{(f_{i,\textrm{O}_{j}}(p)-R_{i,\textrm{O}_{j}})^{2}}{\Delta_{i,\textrm{O}_{j}}^{2}}$
(1)

where the sum runs over each bin $i$ of every observable Oj. The
$f_{\mathrm{i}}(p)$ functions represent a parametrization of the dependence of
the predictions in bin $i$ on the tuning parameters, $R_{\mathrm{i}}$ is the
value of the measured observable in bin $i$, and $\Delta_{\mathrm{i}}$ is the
total experimental uncertainty of $R_{\mathrm{i}}$. The best fit values of the
tuned parameters are shown in Table 0.5 for CP1 and CP2, , the tunes using LO
PDF sets, and in Table 0.5 for CP3, CP4, CP5, , the tunes using NLO or NNLO
PDF sets. Uncertainties in the parameters of these tunes are discussed in
Appendix A. No correlation across bins is included in the minimized $\chi^{2}$
function.

The value of pT0Ref and its energy dependence is very different between tunes
based on LO PDF sets and tunes based on NLO or NNLO PDFs. While pT0Ref is
around 2.3–2.4for CP1 and CP2 tunes with $\epsilon\approx 0.14$–0.15, CP3,
CP4, and CP5 tunes prefer much lower values for both pT0Ref ($\approx$1.4–1.5)
and $\epsilon$ ($\approx$0.03–0.04). A value of $\epsilon$ of
$\approx$0.03–0.04 corresponds to a very weak energy dependence of the
threshold of the MPI cross section. These results can be understood by
considering the shapes of the gluon densities at small $x$ for the different
PDF sets. In order to describe the UE observables, the rapidly increasing
gluon densities at small $x$ in LO PDF sets favor large values of pT0Ref.
Meanwhile NLO and NNLO PDF sets, whose gluon densities are more flat at low
$x$, need higher contributions of MPI, , a small value of pT0Ref. Figure 3
shows the number of MPI observed for the various tunes and the gluon
distribution at a reference scale of $\mu=3\GeV$ for various NNPDF versions.
The larger number of simulated MPI for NLO and NNLO tunes with respect to LO
tunes is apparent.

Figure 3: Distribution of number of MPI simulated by the tunes Monash, CP2,
CP3, CP4, and CP5 (left). Gluon distribution function at a reference scale of
$\mu=3\GeV$ (right) for the NNPDF2.3LO PDF set and the different versions of
the NNPDF3.1 PDF set: LO, NLO, and NNLO. The ratio of NNPDF3.1 gluon
distribution functions to the NNPDF2.3LO gluon distribution function are also
shown.

We have found that the values of pT0Ref and $\epsilon$ also depend on the
order of the running used for $\alpS$. In particular, fits based on NLO or
NNLO PDF sets, , CP3, CP4, or CP5, with an LO $\alpS$ running prefer even
smaller values for both pT0Ref and $\epsilon$ than the ones in the tunes
obtained with an NLO $\alpS$ running. This is because $\alpS$ runs faster at
NLO than at LO. When $\alpS$ is run from the same value at the same scale
($m_{\cPZ}$), the effective coupling at low scales is larger for NLO running
than for LO running. Therefore, a lower pT0Ref is needed for NLO $\alpS$
running than for LO $\alpS$ running to obtain a similar number of MPI.

For tunes based on NLO and NNLO PDF sets, the value of pT0Ref is as low as the
initial scale of the PDF $Q_{\text{min}}^{2}$. For interactions occurring at
$Q^{2}$ which are lower than $Q_{\text{min}}^{2}$, the value of the PDF is
left frozen to the value assumed at the initial scale.

CMS pythia8 LO-PDF tunes CP1 and CP2. Both the values at $Q=m_{\cPZ}$ and the
order of running with $Q^{2}$ of the strong coupling $\alpS(m_{\cPZ})$ are
listed. In these tunes, we use the Schuler-Sjöstrand diffraction model [44]
and also include the simulation of CD processes. The number of degrees of
freedom for tunes CP1 and CP2 is 63.  pythia8 parameter CP1 CP2 PDF Set
NNPDF3.1 LO NNPDF3.1 LO $\alpS(m_{\cPZ})$ 0.130 0.130
SpaceShower:rapidityOrder off off MultipartonInteractions:EcmRef [] 7000 7000
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ value/order 0.1365/LO 0.130/LO
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ value/order 0.1365/LO 0.130/LO
$\alpS^{\mathrm{MPI}}(m_{\cPZ})$ value/order 0.130/LO 0.130/LO
$\alpS^{\mathrm{ME}}(m_{\cPZ})$ value/order 0.130/LO 0.130/LO
MultipartonInteractions:pT0Ref [] 2.4 2.3 MultipartonInteractions:ecmPow 0.15
0.14 MultipartonInteractions:coreRadius 0.54 0.38
MultipartonInteractions:coreFraction 0.68 0.33 ColorReconnection:range 2.63
2.32 $\chi^{2}$/dof 0.89 0.54

CMS pythia8 NLO-PDF tune CP3 and NNLO-PDF tunes CP4 and CP5. Both the values
at $Q=m_{\cPZ}$ and the order of running with $Q^{2}$ of the strong coupling
$\alpS$ are listed. In these tunes, we use the Schuler-Sjöstrand diffraction
model [44] and also include the simulation of CD processes. The number of
degrees of freedom for tunes CP3, CP4, and CP5 is 63.  pythia8 parameter CP3
CP4 CP5 PDF Set NNPDF3.1 NLO NNPDF3.1 NNLO NNPDF3.1 NNLO $\alpS(m_{\cPZ})$
0.118 0.118 0.118 SpaceShower:rapidityOrder off off on
MultipartonInteractions:EcmRef [] 7000 7000 7000
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ value/order 0.118/NLO 0.118/NLO 0.118/NLO
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ value/order 0.118/NLO 0.118/NLO 0.118/NLO
$\alpS^{\mathrm{MPI}}(m_{\cPZ})$ value/order 0.118/NLO 0.118/NLO 0.118/NLO
$\alpS^{\mathrm{ME}}(m_{\cPZ})$ value/order 0.118/NLO 0.118/NLO 0.118/NLO
MultipartonInteractions:pT0Ref [] 1.52 1.48 1.41
MultipartonInteractions:ecmPow 0.02 0.02 0.03
MultipartonInteractions:coreRadius 0.54 0.60 0.76
MultipartonInteractions:coreFraction 0.39 0.30 0.63 ColorReconnection:range
4.73 5.61 5.18 $\chi^{2}$/dof 0.76 0.80 1.04

Figure 4:  The transMIN (upper left) charged-particle and (upper right)
charged $\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-
particle and (lower right) charged $\pt^{\text{sum}}$ densities, as a function
of the transverse momentum of the leading charged particle,
$\pt^{\text{max}}$, from the CMS $\sqrt{s}=13\TeV$ analysis [16]. Charged
hadrons are measured with $\pt>0.5\GeV$ in $\abs{\eta}<2.0$. The transMIN
densities are more sensitive to the MPI, whereas the transMAX densities are
more sensitive to ISR and FSR. The data are compared with the CMS pythia8 LO-
PDF tunes CP1 and CP2. The ratios of the simulations to the data (MC/Data) are
also shown, where the shaded band indicates the total experimental uncertainty
in the data. Vertical lines drawn on the data points refer to the total
uncertainty in the data. Vertical lines drawn on the MC points refer to the
statistical uncertainty in the predictions. Horizontal bars indicate the
associated bin width.

Figure 5: The transMIN (upper left) charged-particle and (upper right) charged
$\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-particle
and (lower right) charged $\pt^{\text{sum}}$ densities, as a function of the
transverse momentum of the leading charged particle, $\pt^{\text{max}}$, from
the CMS $\sqrt{s}=13\TeV$ analysis [16]. Charged hadrons are measured with
$\pt>0.5\GeV$ in $\abs{\eta}<2.0$. The data are compared with the CMS pythia8
(N)NLO-PDF tunes CP3, CP4, and CP5. The ratios of simulations to the data
(MC/Data) are also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 6: The transMIN (upper left) charged-particle and (upper right) charged
$\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-particle
and (lower right) charged $\pt^{\text{sum}}$ densities, as a function of the
transverse momentum of the leading charged particle, $\pt^{\text{max}}$, from
the CMS $\sqrt{s}=7\TeV$ analysis [10]. Charged hadrons are measured with
$\pt>0.5\GeV$ in $\abs{\eta}<0.8$. The data are compared with the CMS pythia8
LO-PDF tunes CP1 and CP2. The ratios of simulations to the data (MC/Data) are
also shown, where the shaded band indicates the total experimental uncertainty
in the data. Vertical lines drawn on the data points refer to the total
uncertainty in the data. Vertical lines drawn on the MC points refer to the
statistical uncertainty in the predictions. Horizontal bars indicate the
associated bin width.

Figure 7: The transMIN (upper left) charged-particle and (upper right) charged
$\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-particle
and (lower right) charged $\pt^{\text{sum}}$ densities, as a function of the
transverse momentum of the leading charged particle, $\pt^{\text{max}}$, from
the CMS $\sqrt{s}=7\TeV$ analysis [10]. Charged hadrons are measured with
$\pt>0.5\GeV$ in $\abs{\eta}<0.8$. The data are compared with the CMS pythia8
(N)NLO-PDF tunes CP3, CP4, and CP5. The ratios of simulations to the data
(MC/Data) are also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 8: The transMIN (upper left) charged-particle and (upper right) charged
$\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-particle
and (lower right) charged $\pt^{\text{sum}}$ densities, as a function of the
transverse momentum of the leading charged particle, $\pt^{\text{max}}$, from
the CDF $\sqrt{s}=1.96\TeV$ analysis [9]. Charged hadrons are measured with
$\pt>0.5\GeV$ in $\abs{\eta}<0.8$. The data are compared with the CMS pythia8
LO-PDF tunes CP1 and CP2. The ratios of simulations to the data (MC/Data) are
also shown, where the shaded band indicates the total experimental uncertainty
in the data. Vertical lines drawn on the data points refer to the total
uncertainty in the data. Vertical lines drawn on the MC points refer to the
statistical uncertainty in the predictions. Horizontal bars indicate the
associated bin width.

Figure 9: The transMIN (upper left) charged-particle and (upper right) charged
$\pt^{\text{sum}}$ densities and the transMAX (lower left) charged-particle
and (lower right) charged $\pt^{\text{sum}}$ densities, as a function of the
transverse momentum of the leading charged particle, $\pt^{\text{max}}$, from
the CDF $\sqrt{s}=1.96\TeV$ analysis [9]. Charged hadrons are measured with
$\pt>0.5\GeV$ in $\abs{\eta}<0.8$. The data are compared with the CMS pythia8
(N)NLO-PDF tunes CP3, CP4, and CP5. The ratios of simulations to the data
(MC/Data) are also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 10: The pseudorapidity distribution of charged hadrons measured in
$\abs{\eta}<2$ for an inclusive selection in inelastic proton-proton
collisions, with zero magnetic field strength (B = 0 T), from the CMS
$\sqrt{s}=13\TeV$ analysis [18]. The data are compared with (left) the CMS
pythia8 LO-PDF tunes CP1 and CP2, and with (right) the CMS pythia8 NLO-PDF
tune CP3 and the CMS pythia8 NNLO-PDF tunes CP4 and CP5. The ratios of
simulations to the data (MC/Data) are also shown, where the shaded band
indicates the total experimental uncertainty in the data. Vertical lines drawn
on the data points refer to the total uncertainty in the data. Vertical lines
drawn on the MC points refer to the statistical uncertainty in the
predictions. Horizontal bars indicate the associated bin width.

The contribution from CR also changes among the different tunes and depends on
the choice of PDF and its order. In particular, the amount of CR is also
affected by the shape of the PDFs at small fractional momenta $x$.

Parameters related to the overlap matter distribution function differ between
the different tunes. They are strongly correlated with the other UE parameters
governing the MPI and CR contributions. In general, for a given value of the
matter fraction (coreFraction), MPI contributions increase for decreasing
values of the core radius (coreRadius). The inclusion of the rapidity ordering
for ISR in tune CP5 impacts the UE observables by reducing the number of
charged particles, and needs to be compensated by a larger amount of MPI
contributions.

The $\chi^{2}$ per degree of freedom (dof) listed in Tables 0.5 and 0.5 refers
to the quantity $\chi^{2}(p)$ in Eq. (1), divided by dof in the fit. The
eigentunes (Appendix A) correspond to the tunes in which the changes in the
$\chi^{2}$ ($\Delta\chi^{2}$) of the fit relative to the best fit value equals
the $\chi^{2}$ value obtained in the tune, ,
$\Delta\chi^{2}_{\text{min}}=\chi^{2}$. Such a variation of the $\chi^{2}$
produces a tune whose uncertainty bands are roughly the same as the
uncertainties in the fitted data points. This is the main motivation why this
choice of variation was considered. For all tunes in Tables 0.5 and 0.5, the
fit quality is good, with $\chi^{2}$/dof values very close to 1.

Figures 4–7 show comparisons of the UE observables measured at various
collision energies to predictions from the new tunes. Figures 4 and 5 compare
the charged-particle and $\pt^{\text{sum}}$ densities measured at
$\sqrt{s}=13\TeV$ by the CMS experiment [16] in the transMIN and transMAX
regions to predictions from the LO-PDF-based tunes and the higher-order-PDF-
based tunes. Figures 6 and 7 compare the charged-particle and
$\pt^{\text{sum}}$ densities measured at $\sqrt{s}=7\TeV$ by the CMS
experiment [10] in the transMIN and transMAX regions to predictions from the
LO-PDF-based tunes and the higher-order-PDF-based tunes. In Figs. 8 and 9
similar comparisons are shown for the observables measured at
$\sqrt{s}=1.96\TeV$ by the CDF experiment [9] in the transMIN and transMAX
regions. All predictions reproduce well the UE observables at $\sqrt{s}=1.96$,
7, and 13. Predictions from LO tunes are slightly better than the higher-order
tunes in describing the energy dependence of the considered UE measurements.

In the region of small $\pt^{\text{max}}$ values ($\pt^{\text{max}}<3\GeV$),
where contributions from diffractive processes are relevant, the predictions
do not always reproduce the measurements and exhibit discrepancies up to 20%.
Predictions from all of the new tunes cannot reproduce the UE data measured at
$\sqrt{s}=300$ and 900 [9].

Figure 10 shows the charged-particle multiplicity as a function of
pseudorapidity for charged particles in $\abs{\eta}<2$ measured by the CMS
experiment at $\sqrt{s}=13\TeV$ [18] in MB events. These events were recorded
with no magnetic field, so all particles irrespective of their are measured.
Data are compared with the predictions of the new pythia8 tunes. All of them
are able to reproduce the measurement at the same level of agreement,
independently of the PDF used for the UE simulation. We could not find any MB
or UE observable where the level of agreement between data and predictions
from the different tunes is significantly different.

##  0.6 Validation of the new pythia8 tunes

In this section, comparisons of the predictions obtained with the new tunes to
various experimental measurements performed by the CMS experiment are
provided. Unless otherwise stated, the comparisons are made at
$\sqrt{s}=13\TeV$. We compare the CMS UE tunes with MB and UE data measured at
central and forward pseudorapidities that are not used in the fits. We examine
how well multijet, Drell–Yan, and top quark observables are predicted by MC
simulations using higher-order ME generators merged with pythia8 with the
various new tunes.

###  0.6.1 Comparisons using event-shape observables

In this subsection, predictions of the new tunes are compared to event-shape
observables measured at LEP, in electron-positron collisions. These
observables are particularly sensitive to the value of
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$. Given the leptonic initial state, there is
no effect coming from the values of the MPI, color reconnection, and ISR
parameters.

When predictions with 8 are used, an optimal value of
$\alpS^{\mathrm{FSR}}(m_{\cPZ})\sim 0.13$ is found, which best describes these
observables, independent of the PDF used for the modeling of the PS evolution.

Figures 11 and 12 display the oblateness ($O$), sphericity ($S$), thrust
($T$), and thrust major ($T_{\text{major}}$), measured in
$\Pep\Pem\rightarrow\PZ\PGg^{*}\rightarrow\PQq\PAQq$ final states at
$\sqrt{s}=91.2$ by the ALEPH experiment [45]. These observables measure the
topology of the event. An isotropic event would have a value of $T$ close to
0.5, while values of $T$ close to 1 correspond to 2-jet events.

Predictions obtained with mg5_amc with up to 4 partons in the final state, and
interfaced with the UE from the tune CUETP8M1 and the new 8 tunes CP2, CP3,
and CP5 are considered (Figure 11). Predictions using the tune CP2 do not
describe the event-shape observables very well, with discrepancies with the
data up to 30% in the $T$ and $T_{\text{major}}$. In particular, tune CP2
predicts too many isotropical events. A similar description is obtained for
predictions of mg5_amc\+ 8 with the tune CUETP8M1. A better agreement in the
event-shape variables is observed for predictions using tune CP3 and CP5. A
correct description of event-shape observables strongly depends on the value
of the FSR strong coupling. The observations above indicate that when merged
configurations are considered, , mg5_amc \+ pythia8, where partons at higher
multiplicities in the final state are simulated at the ME level, the
description of event-shape observables degrades. A value of
$\alpS^{\mathrm{FSR}}(m_{\cPZ})\sim 0.13$ generally overestimates the number
of final-state partons, while a lower $\alpS^{\mathrm{FSR}}(m_{\cPZ})\sim
0.12$ performs better.

At large values of $T$, where the hadronization effects become relevant, we
observe a large difference between predictions from tunes using a small
$\alpS^{\mathrm{FSR}}$ (CP3 and CP5) and tunes using a large
$\alpS^{\mathrm{FSR}}$ (CP2 and CUETP8M1). These differences may be due to the
interplay between the value of the strong coupling and the hadronization.
Analyses particularly sensitive to hadronization should carefully evaluate the
corresponding systematic uncertainties. In some cases retuning hadronization
parameters may be desired.

We also compared mg5_amc\+ 8 with CP5, and CP5 with CMW rescaling [46] (Figure
12). Apart from $T$, for all shape variables considered, CP5 without CMW
rescaling describes the data better.

Figure 11: The normalized cross sections as a function of event-shape
variables, oblateness (upper left), sphericity (upper right), thrust (lower
left), and thrust major (lower right) from the ALEPH $\sqrt{s}=91.2\GeV$
analysis [45], compared with the predictions by mg5_amc \+ pythia8 with –MLM
merging, for tunes CP2, CP3, and CP5. The ratio of the simulations to the data
(MC/Data) is also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 12: The normalized cross sections as a function of event-shape
variables, oblateness (upper left), sphericity (upper right), thrust (lower
left), and thrust major (lower right) from the ALEPH $\sqrt{s}=91.2\GeV$
analysis [45], compared with the predictions by mg5_amc \+ pythia8 with –MLM
merging, for tune CP5, CP5 with CMW rescaling, CP5 FSR up, and CP5 FSR down.
The ratio of the simulations to the data (MC/Data) is also shown, where the
shaded band indicates the total experimental uncertainty in the data. Vertical
lines drawn on the data points refer to the total uncertainty in the data.
Vertical lines drawn on the MC points refer to the statistical uncertainty in
the predictions. Horizontal bars indicate the associated bin width.

###  0.6.2 Comparisons using MB and other UE observables

In this subsection, predictions of the new tunes are compared to the
observables measured in MB collisions that are sensitive to contributions from
soft emissions and MPI. Figure 13 shows the charged-particle multiplicity as a
function of pseudorapidity [24] in NSD-enhanced and SD-enhanced event samples.
The details of the selections can be found in Ref. [24]. These observables are
sensitive to SD, CD, and DD dissociation. It is observed that predictions from
all of the tunes are similar to each other and describe well the measurements
for both considered selections. This shows that the number of charged
particles produced in diffractive processes and inelastic collisions is
simultaneously described by the new CMS tunes. Figure 13 also demonstrates
that tunes based on NNPDF3.1 PDF sets at orders higher than LO adequately
describe the MB data.

Figure 14 shows the UE observables, , charged-particle multiplicity and
$\pt^{\text{sum}}$ densities [16], as a function of the of the leading jet
reconstructed using just charged particles. The observables shown in Fig. 14
are from events selected without requiring any NSD- or SD-enhanced selections.
The CMS UE tunes describe well UE-sensitive data measured using the leading
charged-particle jet for ${}^{\text{jet}}>10\GeV$. Tunes based on NLO or NNLO
PDF sets, , CP3, CP4, and CP5, describe the region at lower ${}^{\text{jet}}$
better than CP1 and CP2, which are based on LO PDF sets. Predictions obtained
with CP1 and CP2 underestimate the UE observables by about $\approx$15–20%.
Predictions obtained with CP3, CP4, and CP5 describe the UE in events
characterized using the leading charged particle, as well as those
characterized by the leading charged-particle jet, quite well.

Predictions for observables measured in the forward region are compared with
data and shown in Figs. 15 and 16. The energy flow, defined as the average
energy per event [47], as a function of $\eta$ with the Hadron Forward (HF)
calorimeter [48] covering $3.15<\abs{\eta}<5.20$ and the CASTOR calorimeter
[48] covering $-6.6<\eta<-5.2$, is well reproduced by all tunes. A different
level of agreement is achieved for predictions from the new CMS tunes for the
spectrum of the total energy E measured in the CASTOR calorimeter at
$\sqrt{s}=13\TeV$ [49], displayed in Fig. 16. In particular, the tunes based
on LO PDF sets reproduce the energy spectrum well at large values
($\text{E}>2000\GeV$), but have differences of up to 40% at low values
($\text{E}<800\GeV$). The tunes using higher-order PDF sets are closer to the
data at low energy values, with differences up to 20%, but tend to
overestimate the energy at large values. This dissimilar behaviour is driven
by the different pT0Ref values of the tunes. The fiducial inelastic cross
sections [50], when two different selections are applied in the forward
region, are not well reproduced by any of the new tunes or by CUETP8M1, with
differences up to 10%. This might be because of the Schüler–Sjöstrand [44]
diffraction model used in the simulation, which might have a suboptimal
description of the low-mass diffractive components. A better description might
be provided by tunes using the Donnachie–Landshoff [51] or minimum-bias
Rockefeller [52] diffractive models.

Figure 13: The pseudorapidity distribution ($\pt>0.5\GeV$, $\abs{\eta}<2.4$)
for (left) the NSD-enhanced and (right) the SD-enhanced event selection of
charged particles in inelastic proton-proton collisions, from the CMS
$\sqrt{s}=13\TeV$ analysis [24]. The data are compared with the CMS pythia8
LO-PDF tunes CP1 and CP2, the CMS pythia8 NLO-PDF tune CP3, and the CMS
pythia8 NNLO-PDF tunes CP4 and CP5. The ratio of the simulations to the data
(MC/Data) is also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 14: The transMIN charged-particle multiplicity (left column) and sum
densities (right column) for particles with $\pt>0.5\GeV$ in $\abs{\eta}<2.0$
as a function of the transverse momentum of the leading charged-particle jet,
$\pt^{\text{jet}}$, from the CMS $\sqrt{s}=13\TeV$ analysis [16]. The upper-
row plots show the LO tunes, while the lower-row plots show the higher-order
tunes. The ratio of the simulations to the data (MC/Data) is also shown, where
the shaded band indicates the total experimental uncertainty in the data.
Vertical lines drawn on the data points refer to the total uncertainty in the
data. Vertical lines drawn on the MC points refer to the statistical
uncertainty in the predictions. Horizontal bars indicate the associated bin
width.

Figure 15: The energy flow measured in an inclusive selection as a function of
pseudorapidity, from the CMS $\sqrt{s}=13\TeV$ analysis [47]. The data are
compared with (left) the CMS pythia8 LO-PDF tunes CP1 and CP2, and with
(right) the CMS pythia8 NLO-PDF tune CP3 and the CMS pythia8 NNLO-PDF tunes
CP4 and CP5. The ratio of the simulations to the data (MC/Data) is also shown,
where the shaded band indicates the total experimental uncertainty in the
data. Vertical lines drawn on the data points refer to the total uncertainty
in the data. Vertical lines drawn on the MC points refer to the statistical
uncertainty in the predictions. Horizontal bars indicate the associated bin
width.

Figure 16: The total energy spectrum measured in the pseudorapidity interval
$-6.6<\eta<-5.2$, from the CMS $\sqrt{s}=13\TeV$ analysis [49]. The data are
compared with (left) the CMS pythia8 LO-PDF tunes CP1 and CP2, and with
(right) the CMS pythia8 NLO-PDF tune CP3 and the CMS pythia8 NNLO-PDF tunes
CP4 and CP5. The ratio of the simulations to the data (MC/Data) is also shown,
where the shaded band indicates the total experimental uncertainty in the
data. Vertical lines drawn on the data points refer to the total uncertainty
in the data. Vertical lines drawn on the MC points refer to the statistical
uncertainty in the predictions. Horizontal bars indicate the associated bin
width.

###  0.6.3 Comparisons using observables in multijet final states

In this subsection, we present comparisons of observables measured in multijet
final states. For these studies, the NLO dijet MEs implemented in the event
generator merged with the pythia8 simulation of the PS and UE are used. The
merging between the ME calculations and the pythia8 UE simulation is performed
using the shower-veto procedure, which rejects showers if their transverse
momentum is greater than the minimal of all final-state partons simulated in
the ME (parameter ${}^{\text{hard}}=2\GeV$ [53]). Variables in multijet
events, such as jet transverse momenta or azimuthal dijet correlations, are
expected to be less affected by MPI contributions, since jets at high ($>$100)
mainly originate from the hard scattering or additional hard emissions, which
are simulated in the calculation by the ME formalism. However, the MPI
contribution still has some impact because it adds an average energy offset to
the event, which is then included in the jet reconstruction [54, 55]. The
predictions reproduce well inclusive jet cross sections as a function of jet
at both central and forward jet rapidities, irrespective of the cone size (0.4
or 0.7) used for the jet clustering algorithm [56].

Figure 17: The azimuthal difference $\Delta\phi_{1,2}$ between the leading two
jets with $\abs{\eta}<2.4$ in dijet events with leading-jet transverse
momentum in the range (left) $200<\pt^{\text{lead}}<300\GeV$ and (right)
$300<\pt^{\text{lead}}<400\GeV$, from the CMS $\sqrt{s}=13\TeV$ analysis [57].
The jets are reconstructed using the anti-jet finding algorithm [58, 59] with
a distance parameter of 0.4. The data are compared with predictions of the NLO
dijet ME calculation from , interfaced to the pythia8 tunes CUETP8M1, CP2,
CP4, and CP5. Tunes CP1 and CP3 are not shown in the plot but present a
similar behavior as tunes CP2 and CP4. The ratios of simulations to the data
(MC/Data) are also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Figure 17 shows the normalized cross section [57] as a function of the
azimuthal difference $\Delta\phi_{1,2}$ between the two leading jets for two
different selections on the leading jet : $200<\pt<300\GeV$ and
$300<\pt<400\GeV$. The results indicate that UE tunes based on an NLO
evaluation of $\alpS(m_{\cPZ})$ describe the data better than UE tunes based
on LO evolution. In particular, the better agreement is driven by the lower
value of $\alpS^{\mathrm{ISR}}(m_{\cPZ})$. In fact, predictions obtained with
merged with pythia8 with the CUETP8M1 or CP2 tune exhibit a strong jet
decorrelation, due to a large contribution from emissions simulated from the
PS, and they overestimate the cross sections at small and medium
$\Delta\phi_{1,2}$ values ($\Delta\phi_{1,2}<2.4$). The PS component is
reduced by the lower value of $\alpS(m_{\cPZ})$, which increases the degree of
correlation between the selected jets, resulting in a better description of
the data by predictions of the CP4 and CP5 tunes. A similar outcome was also
observed for an analogous measurement performed at the D0 experiment at
$\sqrt{s}=1.96\TeV$ [60]. In general, predictions obtained from + pythia8 tend
to differ from the data at low and intermediate $\Delta\phi_{1,2}$ values
($\Delta\phi_{1,2}<2.7$) by 10–40%.

###  0.6.4 Comparisons using observables sensitive to double-parton scattering

In this subsection, we present comparisons of predictions of the new tunes to
DPS-sensitive observables measured by the CMS experiment at $\sqrt{s}=7\TeV$
in final states with four jets (4j) [61], and with two jets originating from
bottom quarks ( jets) [62] and two other jets (2b2j) [63].

The topology in the transverse plane of the physics objects measured in the
final state is sensitive to contributions from DPS. In particular, the 4j
analysis performed by the CMS experiment requires two jets at high (hard jets)
and two jets at low (soft jets); the 2b2j measurement selects two jets
originating from quarks and two other jets (light-flavor jets). Both of them
measured the $\Delta$S observable, defined as:

$\Delta
S=\arccos\left(\frac{\vec{p}_{\text{T,1}}\cdot\vec{p}_{\text{T,2}}}{\abs{\vec{p}_{\text{T,1}}}\abs{\vec{p}_{\text{T,2}}}}\right),\\\
$ (2)

where $\vec{p}_{\mathrm{T,1}}$ refers to the momentum of the hard-jet or
bottom jet pair system and $\vec{p}_{\mathrm{T,2}}$ to that of the soft-jet or
light-flavor jet pair system. This variable relates the production planes of
the hard (bottom) jet and soft- (light-flavor) jet pairs. Details of the event
selection and of the specific analyses can be found in Refs. [61] and [63].

Assuming that the two hard scatterings occurring within the same collision are
completely independent of each other, the DPS cross section for a given
process can be expressed through the inclusive partonic cross sections of the
two single scatterings and an effective cross section, $\sigma_{\text{eff}}$.
In a geometrical approach, this cross section is related to the transverse
size of the proton and to the total inelastic proton-proton ($\Pp\Pp$) cross
section [64, 65]. When no correlations among the partons inside the proton are
present, $\sigma_{\text{eff}}$ is similar to the inelastic $\Pp\Pp$ cross
section. In this simple factorized approach, one expects $\sigma_{\text{eff}}$
to be independent of the partonic final states of the two hard processes
occurring within the same collision. In pythia8, the value of
$\sigma_{\text{eff}}$ is calculated by dividing the ND cross section by the
so-called “enhancement factor”, which depends on the parameters of the overlap
matter distribution function and on pT0Ref [40]. For central $\Pp\Pp$
collisions, the enhancement factor tends to be large, translating to a lower
value of $\sigma_{\text{eff}}$ and a larger DPS contribution. For peripheral
interactions, enhancement factors are small, giving large values of
$\sigma_{\text{eff}}$ and a small DPS contribution.

Table 0.6.4 shows the values of $\sigma_{\text{eff}}$ published by the CMS
Collaboration for the 4j and the 2b2j measurements. A previous study [5]
concluded that observables sensitive to semi-hard MPI and those sensitive to
DPS cannot be described by a single set of parameters. Table 0.6.4 displays
the $\sigma_{\text{eff}}$ values obtained from the new CMS UE tunes. The
central values of $\sigma_{\text{eff}}$ are consistent among the new tunes and
are slightly larger than the values of the DPS-based tunes [5].

Figure 18 shows the comparisons of predictions obtained from pythia8 with
tunes CUETP8M1, CP2, CP4, and CP5 to the DPS observables measured in the 4j
and 2b2j final states. Predictions from the CP2 tune based on a LO PDF set
describe the central values better than the CP4 and CP5 tunes based on an NNLO
PDF set or the old tune CUETP8M1. This is due to the different pT0Ref value
used by CP2, CP4, and CP5, which determines the amount of simulated MPI. The
value of the pT0Ref parameter is driven by the distribution of the gluon
distribution function at low $x$, which is very different in LO and NNLO PDF
sets. Additionally, predictions obtained with CP4 describe the DPS-sensitive
observables better than CP5. This is due to the different rapidity ordering
used for the PS emissions in the two tunes. By removing the rapidity ordering
for the PS emissions (CP4), the simulation produces more radiation and
decreases the correlation between the selected jet pairs compared to CP5. This
reduced jet correlation tends to mimic a DPS event by producing low values of
$\Delta$S. We have checked that the observables sensitive to color coherence,
which were measured by the CMS experiment at $\sqrt{s}=7\TeV$ [66], are well
described by predictions from both CP4 and CP5 tunes, despite the difference
in the rapidity ordering of the PS simulation between the two tunes.

Values of $\sigma_{\text{eff}}$ at $\sqrt{s}=7\TeV$ published by the CMS
Collaboration for the four-jet final states, obtained by fitting predictions
of the pythia8 MC event generator to DPS-sensitive measured observables.
Final state Generator $\sigma_{\text{eff}}$ [mb] ($\sqrt{s}=7\TeV$) 4j pythia8
19.0${}^{+4.7}_{-3.0}$ [5] 2b2j pythia8 23.2${}^{+3.3}_{-2.5}$ [67]

Values of $\sigma_{\text{eff}}$ at $\sqrt{s}=7$ and 13obtained with the new
CMS UE tunes.  $\sqrt{s}=7\TeV$ $\sqrt{s}=13\TeV$ $\sigma_{\text{eff}}$ [mb]
$\sigma_{\text{eff}}$ [mb] CP1 26.3${}^{+1.0}_{-1.7}$ 27.8${}^{+1.1}_{-1.4}$
CP2 24.7${}^{+1.0}_{-1.6}$ 26.0${}^{+1.0}_{-1.3}$ CP3 24.1${}^{+1.0}_{-1.5}$
25.2${}^{+1.0}_{-1.3}$ CP4 23.9${}^{+1.0}_{-1.5}$ 25.3${}^{+1.1}_{-1.4}$ CP5
24.0${}^{+1.0}_{-1.6}$ 25.3${}^{+1.0}_{-1.3}$

Figure 18: The correlation observable $\Delta$S measured in 4j (left) and 2b2j
(right) production, compared to predictions of pythia8 tunes CUETP8M1, CP2,
CP4, and CP5, from the CMS $\sqrt{s}=7\TeV$ analyses [61, 63]. Tunes CP1 and
CP3 are not shown in the plot but show a similar behaviour as, respectively,
tunes CP2 and CP4. The ratios of simulations to the data (MC/Data) are also
shown, where the shaded band indicates the total experimental uncertainty in
the data. Vertical lines drawn on the data points refer to the total
uncertainty in the data. Vertical lines drawn on the MC points refer to the
statistical uncertainty in the predictions. Horizontal bars indicate the
associated bin width.

###  0.6.5 Comparisons using observables in top quark production

In the following, we investigate how the new pythia8 tunes describe the CMS
data when different ME generators, namely and mg5_amc, are employed. Both ME
configurations use the NNPDF3.1 NNLO PDF with $\alpS(m_{\cPZ})=0.118$ and
assume a top quark mass ($m_{\PQt}$) value of 172.5.

In the configuration, the ME heavy quark production mode [68, 39, 36] is used.
In this configuration, simulates inclusive production at NLO, where the first
additional jet is computed at LO, while mg5_amc performs the calculation with
up to 2 additional jets at NLO, with a third jet simulated at LO. The
generator scales the real emission cross section by a damping function that
controls the ME-PS merging and that regulates the high- radiation. The damping
variable used in the simulation is set to 1.379 times $m_{\PQt}$, a value
derived from data at $\sqrt{s}=8\TeV$ in the dilepton channel using a similar
ME calculation and assuming the CP5 tune. The factorization and
renormalization scales are assumed equal to the transverse mass of the top
quark, $\mT^{\PQt}=\sqrt{\smash[b]{m_{\PQt}^{2}+\pt^{2}}}$. The minimum for
the emission of light quarks in is 0.8. The pThard parameter is set to 0 and
the hardness criterion, defined by the pTdef option, is set to 1. The merging
scale in mg5_amc is set to 40, and the threshold applied to regulate multijet
MEs in the mg5_amc FxFx merging procedure, is 20.

Distributions [69] in the lepton+jets channel are compared to predictions from
different tunes using various settings, namely, + pythia8, and mg5_amc+pythia8
with FxFx merging [38], referred to as mg5_amc [FxFx] hereafter, with the
CUETP8M1, CP2, CP4, and CP5 tunes. Figure 19 (upper panel) displays the
normalized cross section in bins of of the top quark decaying leptonically
($\PQt_{\ell}$), in data and simulation. For all tunes, + pythia8 predictions
have deviations below 10% with respect to the central values of the data. The
central values of predictions from mg5_amc [FxFx] and data agree within
$\approx$10% for $\pt(\PQt_{\ell})<400\GeV$ and within $\approx$20% for higher
.

Figure 19 (middle panel) shows the normalized cross section in bins of $m$()
in data and simulation. Predictions from and mg5_amc [FxFx] with the new tunes
describe the central values of the data reasonably well. Normalized cross
sections in bins of number of additional jets in data and simulation in the
lepton+jets channel at $\sqrt{s}=13\TeV$ are shown in Fig. 19 (lower panel).
The cross sections are compared with the predictions of and of mg5_amc [FxFx].
The central values predicted by + pythia8 are in good agreement with data when
CP5 tune is used. The value of $\alpS^{\mathrm{ISR}}(m_{\cPZ})$ in combination
with the rapidity ordering for ISR in the pythia8 simulation affects the
additional jet distribution in events. Predictions obtained from + pythia8
overestimate the data when a high value of
$\alpS^{\mathrm{ISR}}(m_{\cPZ})\approx 0.13$ is used (CUETP8M1 and CP2 tunes)
irrespective of rapidity ordering for ISR. It is observed that even when
$\alpS^{\mathrm{ISR}}(m_{\cPZ})=0.118$ is used, predictions from the CP4 tune
overshoot the data at high jet multiplicities. A much better agreement of
central values is obtained only when rapidity ordering for ISR is switched on
in the pythia8 simulation and $\alpS^{\mathrm{ISR}}(m_{\cPZ})=0.118$ is used
as in the CP5 tune. Predictions from mg5_amc [FxFx]+pythia8 with CUETP8M1,
CP2, CP4, and CP5 tunes describe the central values of the data reasonably
well.

Figure 19: The normalized cross section in the lepton+jets channel, as a
function of the transverse momentum of the top quark for leptonically decaying
top quarks ($t_{\ell}$) (upper), the invariant mass of the system, $m$()
(middle), and in bins of number of additional jets (lower) from CMS
$\sqrt{s}=13\TeV$ analysis [69]. The data are compared with the predictions of
(left) and mg5_amc [FxFx] (right). In both cases, the PS simulation is done
with the pythia8 tunes CUETP8M1, CP2, CP4, or CP5. Tunes CP1 and CP3 are not
shown in the plot but present a similar behaviour as, respectively, tunes CP2
and CP4. The ratios of simulations to the data (MC/Data) are also shown, where
the shaded band indicates the total experimental uncertainty in the data.
Vertical lines drawn on the data points refer to the total uncertainty in the
data. Vertical lines drawn on the MC points refer to the statistical
uncertainty in the predictions. Horizontal bars indicate the associated bin
width.

Comparisons are also made using jet substructure observables in events in the
lepton+jets channel using measurements by CMS at $\sqrt{s}=13\TeV$ [70].
Figure 20 displays the comparisons using the distribution of the angle between
two groomed subjets, $\Delta R_{g}$, which is found to be the most sensitive
to $\alpS^{\mathrm{FSR}}(m_{\cPZ})$ [70]. The data are compared to simulations
with the tunes CUETP8M1, CP2, CP4, and CP5, as well as CP5 FSR up
($\alpS^{\mathrm{FSR}}(m_{\cPZ})=0.122$), CP5 FSR down
($\alpS^{\mathrm{FSR}}(m_{\cPZ})=0.115$), and CP5 with CMW rescaling. It is
observed that tunes with higher $\alpS^{\mathrm{FSR}}(m_{\cPZ})$ (CUETP8M1,
CP2, and CP5 FSR up) describe the data better. Tune CP5 with CMW rescaling
resolves the discrepancy of CP5 at high $\Delta R_{g}$, but worsens the
description at $\Delta R_{g}\sim 0.27$ compared to CP5. It should be noted
that a fit to the $\Delta R_{g}$ distribution using a b-enriched sample yields
$\alpS^{\mathrm{FSR}}(m_{\cPZ})=0.130^{+0.016}_{-0.020}$ [70] without CMW
rescaling, while a fit to the distirubtion of the UE observable
$\overline{\pt}$ measured in events yields
$\alpS^{\mathrm{FSR}}(m_{\cPZ})=0.120\pm 0.006$ [22]. Therefore, in events, UE
and jet substructure observables prefer different central
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ values, but they are compatible within
uncertainties.

Figure 20: Comparison with the measurement [70] of the angle between two
groomed subjets, $\Delta R_{g}$ in events predicted by + pythia8 for the
different tunes. The data are compared to tunes CUETP8M1, CP2, CP4, and CP5
(left). Tunes CP1 and CP3 are not displayed but they present a similar
behavior as tunes CP2 and CP4, respectively. The data are also compared to
CP5, CP5 FSR up, CP5 FSR down, and CP5 with CMW rescaling (right). The ratios
of simulations to the data (MC/Data) are also shown, where the shaded band
indicates the total experimental uncertainty in data. Vertical lines drawn on
the data points refer to the total uncertainty in the data. Horizontal bars
indicate the associated bin width.

###  0.6.6 Comparisons using observables in and boson production

In this subsection, we present a validation of the new CMS UE tunes for
observables measured in events with a or boson in the final state at
$\sqrt{s}=13\TeV$. For the comparisons, we use predictions obtained with
mg5_amc $+$ pythia8 at LO using the –MLM merging scheme, and at NLO using the
FxFx merging scheme. The –MLM merging scale is set to 19, while for FxFx the
corresponding scale is set to 30. In both cases the MEs include the final
states with 0, 1, 2, and 3 partons, and up to 2 partons are calculated at NLO
precision in the FxFx case. To ease the comparison of the different tunes, the
same PDF, NNPDF3.1 NNLO, and $\alpS(m_{\cPZ})=0.118$ are used for the ME
calculation independently of the tune.

First, UE observables [21] in Drell–Yan events in an invariant mass window of
81–101around the boson peak for muonic decays are studied. The charged-
particle density and transverse momentum sum are measured as a function of the
boson in the three regions introduced in Section 0.6.2: toward, away, and
transverse. The regions are defined with respect to the boson direction. The
measurements are compared with FxFx predictions obtained with the CUETP8M1,
CP2, CP4, and CP5 tunes in Fig. 21. The measurements are, in general, well-
described by all tunes.

Figure 21: The charged-particle multiplicity (left) and $\pt^{\text{sum}}$
(right) in the toward (upper), transverse (middle), and away (lower) regions
measured as a function of the boson in Drell–Yan events at $\sqrt{s}=13\TeV$
[21], and compared with the predictions obtained by an inclusive NLO ME
calculated by mg5_amc, interfaced to the UE simulation of pythia8 with the
CUETP8M1, CP2, CP4, and CP5 tunes. Tunes CP1 and CP3 are not shown in the plot
but present a similar behaviour as, respectively, tunes CP2 and CP4. The
ratios of simulations to the data (MC/Data) are also shown, where the shaded
band indicates the total experimental uncertainty of the data. Vertical lines
drawn on the data points refer to the total uncertainty in the data. Vertical
lines drawn on the MC points refer to the statistical uncertainty in the
predictions. Horizontal bars indicate the associated bin width.

The description of the cross section as a function of the jet multiplicity is
also investigated in +jets [71] and +jets [72] final states. The +jets
measurement is restricted to the phase space where the two leptons have
$\pt>20\GeV$ and $\abs{y}<2.4$ and the dilepton mass lies in a $\pm 20\GeV$
window around 91. The momenta of the photons inside a cone of
$\Delta\text{R}<0.1$ are added to the lepton momentum in order to partly
recover the energy lost by FSR. Jets are clustered using the anti-algorithm
with $R=0.4$ and must satisfy the criteria $\pt>30\GeV$ and $\abs{y}<2.4$. The
distance between the selected leptons and the leading jet $\Delta
R(\ell,\mathrm{j})$ must be greater than 0.4. For the +jets measurement, the
phase space is restricted by a transverse mass requirement, $\mT>50\GeV$, and
by requirements on the muon, $\pt>25\GeV$ and $\abs{y}<2.4$. In the +jets
measurements the same clustering algorithm, the FSR recovery prescription
described above, and the lepton jet separation requirement are applied.

The comparisons of the jet multiplicities to various predictions are shown in
Fig. 22. The measurement of the cross section inclusive in the number of jets,
$N$, is not available for the +jets analysis and the lower plots start at
$N=1$. The –MLM predictions of the jet multiplicity have little sensitivity to
the UE and PS tunes, so all the tunes provide a good description this
observable, with a slightly better agreement observed for the CP2 tune. In the
case of the FxFx sample, the CP5 tune predicts fewer events with a jet
multiplicity of more than four with respect to the measurement. The deficit
increases for increasing jet multiplicities. The CUETP8M1 tune shows a similar
behaviour, though.

Figure 22: Comparison with the measurement [71, 72] of the inclusive jet
multiplicity in +jets (upper) and +jets (lower) events predicted by mg5_amc \+
pythia8 with –MLM merging (left) and FxFx merging (right) for the different
tunes. Tunes CP1 and CP3 are not shown in the plot but present a similar
behaviour as, respectively, tunes CP2 and CP4. The ratios of simulations to
the data (MC/Data) are also shown, where the shaded band indicates the total
experimental uncertainty in the data. Vertical lines drawn on the data points
refer to the total uncertainty in the data. Vertical lines drawn on the MC
points refer to the statistical uncertainty in the predictions. Horizontal
bars indicate the associated bin width.

Predictions using the new CMS UE tunes are also compared with the $\pt$
balance between the boson and the jets with $\pt>30\GeV$ and $\abs{y}<2.4$
using the variable
${}^{\text{bal}}=\lvert\ptvec(\cPZ)+\sum_{\text{jets}}\ptvec(\mathrm{j}_{i})\rvert$
[71]. This variable is sensitive to PS and UE. The comparison is shown in Fig.
23 for events with at least one jet. Differences between the tunes are
significant only in the region below $\approx$20\. The discrepancy in this
region for the FxFx samples indicates that the distribution peaks at lower
values for CP4 and CP5 than in data.

Figure 23: Comparison with the measurement [71] of the balance predicted by
mg5_amc \+ pythia8 with –MLM merging (left) and FxFx merging (right) for the
different tunes for events with at least one jet. Tunes CP1 and CP3 are not
shown in the plot but they present a similar behaviour as tunes CP2 and CP4,
respectively. The ratios of simulations to the data (MC/Data) are also shown,
where the shaded band indicates the total experimental uncertainty in the
data. Vertical lines drawn on the data points refer to the total uncertainty
in the data. Vertical lines drawn on the MC points refer to the statistical
uncertainty in the predictions. Horizontal bars indicate the associated bin
width.

Results of Ref. [71] are also used to validate the description of the
transverse momentum of the weak vector boson in $\cPZ$ \+ $\geq 1$ jet events.
The comparison is shown in Fig. 24. The new tunes provide similar descriptions
for this distribution. Predictions using –MLM achieve a poor agreement with
the data, independently of the UE tune, with respect to FxFx, which is able to
describe the transverse momentum of the boson at $\pt>10\GeV$. The region
below 10is poorly described for both FxFx and –MLM and the new tunes, but is
well-described by predictions using the CUETP8M1 tune.

Figure 24: Comparison with the measurement [71] of the (Z) predicted by
mg5_amc \+ pythia8 with –MLM merging (left) and FxFx merging (right) for the
different tunes. Tunes CP1 and CP3 are not shown in the plot but they present
a similar behaviour as tunes CP2 and CP4, respectively. The ratios of
simulations to the data (MC/Data) are also shown, where the shaded band
indicates the total experimental uncertainty in data. Vertical lines drawn on
the data points refer to the total uncertainty in the data. Vertical lines
drawn on the MC points refer to the statistical uncertainty in the
predictions. Horizontal bars indicate the associated bin width.

To summarize the study of weak vector boson production, the CP2, CP4, and CP5
tunes provide similar descriptions of the UE observables with a reasonable
agreement with the data. In general, the CP2 tune performs better in
describing variables such as ${}^{\text{bal}}$ and (Z). For the jet
multiplicity, the CP2 and CP4 tunes are equally good in describing the
measurement, whereas CP5 tends to undershoot the PS dominated region with at
least five jets with a significance of 3.5 standard deviations.

##  0.7 Summary and conclusions

A new set of tunes for the underlying-event (UE) simulation in the pythia8
event generator is obtained by fitting various measurements sensitive to soft
and semihard multipartonic interactions at different collision energies. To
derive these tunes, the leading order (LO), next-to-leading order (NLO), or
next-to-next-to-leading order (NNLO) versions of the NNPDF3.1 parton
distribution function (PDF) set for the simulation of the underlying-event
components are used. In these tunes, the values of the strong coupling,
$\alpS(m_{\cPZ})$, used for the simulation of hard scattering, initial- and
final-state radiation, and multiple-parton interactions are chosen consistent
with the order of the PDF used. In the LO NNPDF3.1 set,
$\alpS(m_{\cPZ})=0.130$, whereas for the NLO and NNLO NNPDF3.1 sets,
$\alpS(m_{\cPZ})=0.118$. In general, the combination of contributions from
multiple-parton interactions and parton-shower emissions is crucial to give a
good description of variables measured in soft-collision events. The infrared
threshold is relatively independent of center-of-mass energy when using NLO or
NNLO PDF sets. Irrespective of the specific PDF used, predictions from the new
tunes reproduce well the UE measurements at center-of-mass energies
$\sqrt{s}=1.96$ and 7. A significant improvement in the description of UE
measurements at 13is observed with respect to predictions from old tunes that
were extracted using data at lower collision energies. For the first time,
predictions based on higher-order PDF sets are shown to give a reliable
description of minimum-bias (MB) and UE measurements, with a similar level of
agreement as predictions from tunes using LO PDF sets.

Predictions of the new tunes agree well with the data for MB observables
measured at pseudorapidities in the central ($\abs{\eta}<2.4$) and forward
($3.2<\abs{\eta}<4.7$) regions. The new CMS tunes simultaneously describe the
number of charged particles produced in diffractive processes and MB
collisions. Neither the new CMS tunes nor the CUETP8M1 tune describe the very
forward region ($-6.6<\eta<-5.2$) well.

Measurements sensitive to double-parton scattering contributions are
reproduced better by predictions using the LO PDF set in the UE simulation,
without rapidity ordering of the initial-state shower.

The UE simulation provided by the new tunes can be interfaced to higher-order
and multileg matrix element generators, such as and mg5_amc, without degrading
the good description of UE observables. Such predictions also reproduce well
observables measured in multijet final states, Drell–Yan, and top quark
production processes. The central values of the normalized cross section in
bins of the number of additional jets predicted by +pythia8 overestimate the
data when a high value of $\alpS^{\mathrm{ISR}}(m_{\cPZ})\gtrsim 0.130$ is
used (CMS pythia8 CP1 and CP2 tunes). Even when
$\alpS^{\mathrm{ISR}}(m_{\cPZ})=0.118$ is used, the CP4 tune overestimates the
data at high jet multiplicities. This is cured by the rapidity ordering of the
initial-state shower (CP5 tune). Measurements of azimuthal dijet correlations
are also better described when a value of
$\alpS^{\mathrm{ISR}}(m_{\cPZ})=0.118$ is used in predictions obtained with
merged with pythia8.

Comparisons with LEP event-shape observables and the distribution of the angle
between two groomed subjets ($\Delta R_{g}$) in events at the LHC show that in
ME-PS merged configurations CMW rescaling is disfavored. It is also found that
$\Delta R_{g}$ is better described by tunes with
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ higher than $\sim$0.120 while LEP event-shape
observables and UE event observables in events prefer a central value
$\sim$0.120 [22].

All of the new CMS tunes are supplied with their eigentunes, which can also be
used to determine the uncertainties associated with the theoretical
predictions. We show that predictions using the new tunes based on PDFs
determined at LO, NLO, and NNLO agree reasonably well with the measurements,
and that the new tunes can also be applied to LO and NLO calculations merged
with parton showers, multiple-parton interactions, and hadronization.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centres and personnel of the Worldwide LHC Computing Grid for
delivering so effectively the computing infrastructure essential to our
analyses. Finally, we acknowledge the enduring support for the construction
and operation of the LHC and the CMS detector provided by the following
funding agencies: the Austrian Federal Ministry of Education, Science and
Research and the Austrian Science Fund; the Belgian Fonds de la Recherche
Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding
Agencies (CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP); the Bulgarian Ministry of
Education and Science; CERN; the Chinese Academy of Sciences, Ministry of
Science and Technology, and National Natural Science Foundation of China; the
Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science,
Education and Sport, and the Croatian Science Foundation; the Research
Promotion Foundation, Cyprus; the Secretariat for Higher Education, Science,
Technology and Innovation, Ecuador; the Ministry of Education and Research,
Estonian Research Council via IUT23-4, IUT23-6 and PRG445 and European
Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry
of Education and Culture, and Helsinki Institute of Physics; the Institut
National de Physique Nucléaire et de Physique des Particules / CNRS, and
Commissariat à l’Énergie Atomique et aux Énergies Alternatives / CEA, France;
the Bundesministerium für Bildung und Forschung, Deutsche
Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher
Forschungszentren, Germany; the General Secretariat for Research and
Technology, Greece; the National Research, Development and Innovation Fund,
Hungary; the Department of Atomic Energy and the Department of Science and
Technology, India; the Institute for Studies in Theoretical Physics and
Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di
Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and
National Research Foundation (NRF), Republic of Korea; the Ministry of
Education and Science of the Republic of Latvia; the Lithuanian Academy of
Sciences; the Ministry of Education, and University of Malaya (Malaysia); the
Ministry of Science of Montenegro; the Mexican Funding Agencies (BUAP,
CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI); the Ministry of Business,
Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission;
the Ministry of Science and Higher Education and the National Science Centre,
Poland; the Fundação para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the
Ministry of Education and Science of the Russian Federation, the Federal
Agency of Atomic Energy of the Russian Federation, Russian Academy of
Sciences, the Russian Foundation for Basic Research, and the National Research
Center “Kurchatov Institute”; the Ministry of Education, Science and
Technological Development of Serbia; the Secretaría de Estado de
Investigación, Desarrollo e Innovación, Programa Consolider-Ingenio 2010, Plan
Estatal de Investigación Científica y Técnica y de Innovación 2013–2016, Plan
de Ciencia, Tecnología e Innovación 2013–2017 del Principado de Asturias, and
Fondo Europeo de Desarrollo Regional, Spain; the Ministry of Science,
Technology and Research, Sri Lanka; the Swiss Funding Agencies (ETH Board, ETH
Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and
Technology, Taipei; the Thailand Center of Excellence in Physics, the
Institute for the Promotion of Teaching Science and Technology of Thailand,
Special Task Force for Activating Research and the National Science and
Technology Development Agency of Thailand; the Scientific and Technical
Research Council of Turkey, and Turkish Atomic Energy Authority; the National
Academy of Sciences of Ukraine, and State Fund for Fundamental Researches,
Ukraine; the Science and Technology Facilities Council, UK; the US Department
of Energy, and the US National Science Foundation. Individuals have received
support from the Marie-Curie programme and the European Research Council and
Horizon 2020 Grant, contract Nos. 675440 and 765710 (European Union); the
Leventis Foundation; the A.P. Sloan Foundation; the Alexander von Humboldt
Foundation; the Belgian Federal Science Policy Office; the Fonds pour la
Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-
Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-
Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science –
EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology
Commission, No. Z181100004218003; the Ministry of Education, Youth and Sports
(MEYS) of the Czech Republic; the Lendület (“Momentum”) Programme and the
János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the
New National Excellence Program ÚNKP, the NKFIA research grants 123842,
123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the
Council of Scientific and Industrial Research, India; the HOMING PLUS
programme of the Foundation for Polish Science, cofinanced from European
Union, Regional Development Fund, the Mobility Plus programme of the Ministry
of Science and Higher Education, the National Science Center (Poland),
contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543,
2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406;
the National Priorities Research Program by Qatar National Research Fund; the
Programa de Excelencia María de Maeztu, and the Programa Severo Ochoa del
Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-
ESF, and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral
Fellowship, Chulalongkorn University, and the Chulalongkorn Academic into Its
2nd Century Project Advancement Project (Thailand); the Welch Foundation,
contract C-1845; and the Weston Havens Foundation (USA).

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##  .8 Tables of tune uncertainties

This section provides the values of the parameters corresponding to the
uncertainties when the new CMS pythia8 tunes are used. The tune uncertainty is
obtained by extracting the eigentunes, which are defined by a change in the
$\chi^{2}$ of the fit that equals the absolute $\chi^{2}$ value obtained in
the tune. The eigentunes refer to the variations of the tunes along each of
the maximally independent directions in the parameter space, obtained by using
the covariance matrix in the region of the best tune. The number of directions
defined in the parameter space equals the number of free parameters $n$ used
in the fit and results into 2$n$ parameter variations, , eigentunes. These
variations represent a good set of systematic uncertainties in the given tune.

The estimations of the tune uncertainties, which have 2$n$ parameter
variations, , 10 for the new CMS pythia8 tunes, are very time consuming in
analyses, since for each variation separate samples must be produced.
Therefore, a lower number of variations is preferred. Hence, two variations,
one “up” and one “down”, are defined. For the definition of the two
variations, predictions using the parameters of the eigentunes are implemented
for the UE observables at $\sqrt{s}=13\TeV$ and their differences with respect
to the central predictions are added in quadrature. This procedure is applied
in each bin and tune uncertainties are estimated without any correlation
across the different bins. Positive differences between central predictions
and tune variations define the upper edge of the bin-by-bin uncertainty, while
negative differences define the lower edge of the bin-by-bin uncertainty. By
following the same approach used for the extraction of the central values of
the new CMS pythia8 tunes, the upper edge is fitted to obtain the “up
variation”, while the “down variation” is obtained by fitting the lower edge.
The parameters of the up- and down-variations are listed in Table .8 for the
tunes using LO PDF sets, and in Table .8 for the tunes using (N)NLO PDF sets.
We checked that for a wide range of MB and UE observables at $\sqrt{s}=13\TeV$
predictions from up- and down-variations, obtained by including the full set
of eigenvalues, reproduce well the upper and the lower edge of the
predictions. Hence, tune uncertainties estimated by evaluating predictions of
up- and down-variations represent a reliable way of estimating the systematic
uncertainties in the tunes. The correlation matrix for the fit of the CP5 tune
is displayed in Table .8. It is retrieved by evaluating the correlation of the
parameter variations obtained in the eigentunes.

Parameters of the “up-” and “down-”variation eigentunes for the pythia8 CP1,
and CP2 tunes.  pythia8 Parameter CP1 CP1 CP2 CP2 Up Down Up Down
MultipartonInteractions:pT0Ref [] 2.30 2.40 2.34 2.33
MultipartonInteractions:ecmPow 0.15 0.15 0.14 0.14
MultipartonInteractions:coreFraction 0.51 0.39 0.51 0.23
MultipartonInteractions:coreRadius 0.58 0.60 0.41 0.34
ColourReconnection:range 8.31 8.50 1.46 2.56

Parameters of the “up-” and “down-”variation eigentunes for the pythia8 CP3,
CP4, and CP5 tunes.  pythia8 Parameter CP3 CP3 CP4 CP4 CP5 CP5 Up Down Up Down
Up Down MultipartonInteractions:pT0Ref [] 1.48 1.54 1.48 1.54 1.41 1.46
MultipartonInteractions:ecmPow 0.02 0.02 0.02 0.02 0.03 0.03
MultipartonInteractions:coreFraction 0.35 0.25 0.36 0.33 0.43 0.73
MultipartonInteractions:coreRadius 0.49 0.35 0.58 0.57 0.67 0.69
ColourReconnection:range 8.15 3.96 7.93 6.88 4.88 4.69

The correlation matrix, retrieved when extracting the CP5 tune. This is
obtained by evaluating the correlation values of the parameter variations
obtained in the eigentunes.  pT0Ref ecmPow coreFraction coreRadius range
pT0Ref 1.00 -0.21 -0.19 -0.19 0.15 ecmPow -0.21 1.00 0.30 0.69 -0.21
coreFraction -0.19 0.30 1.00 0.32 -0.64 coreRadius -0.19 0.69 0.32 1.00 -0.52
range 0.15 -0.21 -0.64 -0.52 1.00

Variations of the values of the ISR and FSR are also studied, in order to
check the consistency of the selected $\alpS^{\mathrm{ISR}}(m_{\cPZ})$ and
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ values selected for the tunes and to estimate
the allowed range of $\alpS^{\mathrm{ISR}}(m_{\cPZ})$ and
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ values in the PS using the CP5 tune. Starting
from tune CP5, the value of $\alpS^{\mathrm{ISR}}(m_{\cPZ})$ is fitted to UE
observables measured by CMS at $\sqrt{s}=13\TeV$. The same procedure is
repeated when $\alpS^{\mathrm{FSR}}(m_{\cPZ})$ is fitted. The parameters
obtained from the fits are shown in Table .8, along with the up and down
variation.

“Up” and “Down” ISR and FSR variations for CP5 when
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ or $\alpS^{\mathrm{FSR}}(m_{\cPZ})$ is
treated as a free parameter.  pythia8 Parameter Central Up Down $\chi^{2}$/dof
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ value 0.121 0.128 0.114 0.75
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ value 0.119 0.122 0.115 0.78

Figure 25 shows the predictions of the CP5 tune, with the corresponding
variation bands relative to the UE parameters, and the
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ and $\alpS^{\mathrm{FSR}}(m_{\cPZ})$ values
for the charged-particle and $\pt^{\text{sum}}$ densities at $\sqrt{s}=13\TeV$
in the transMIN region.

Figure 25: The variations allowed by the CP5 tune when
$\alpS^{\mathrm{ISR}}(m_{\cPZ})$ (blue band) and
$\alpS^{\mathrm{FSR}}(m_{\cPZ})$ (red band) are left free in the fit for
charged-particle (left) and charged $\pt^{\text{sum}}$ (right) density in the
transMIN region at $\sqrt{s}=13\TeV$. Vertical lines drawn on the data points
refer to the total uncertainty in the data. The grey band represents the total
UE uncertainty for the tune CP5. Horizontal bars indicate the associated bin
width.

##  .9 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan, A. Tumasyan Institut für Hochenergiephysik, Wien, Austria
W. Adam, F. Ambrogi, E. Asilar, T. Bergauer, J. Brandstetter, M. Dragicevic,
J. Erö, A. Escalante Del Valle, M. Flechl, R. Frühwirth1, V.M. Ghete, J.
Hrubec, M. Jeitler1, N. Krammer, I. Krätschmer, D. Liko, T. Madlener, I.
Mikulec, N. Rad, H. Rohringer, J. Schieck1, R. Schöfbeck, M. Spanring, D.
Spitzbart, W. Waltenberger, J. Wittmann, C.-E. Wulz1, M. Zarucki Institute for
Nuclear Problems, Minsk, Belarus
V. Chekhovsky, V. Mossolov, J. Suarez Gonzalez Universiteit Antwerpen,
Antwerpen, Belgium
E.A. De Wolf, D. Di Croce, X. Janssen, J. Lauwers, M. Pieters, H. Van
Haevermaet, P. Van Mechelen, N. Van Remortel Vrije Universiteit Brussel,
Brussel, Belgium
S. Abu Zeid, F. Blekman, J. D’Hondt, J. De Clercq, K. Deroover, G. Flouris, D.
Lontkovskyi, S. Lowette, I. Marchesini, S. Moortgat, L. Moreels, Q. Python, K.
Skovpen, S. Tavernier, W. Van Doninck, P. Van Mulders, I. Van Parijs
Université Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, H. Brun, B. Clerbaux, G. De Lentdecker, H. Delannoy, B.
Dorney, G. Fasanella, L. Favart, R. Goldouzian, A. Grebenyuk, A.K. Kalsi, T.
Lenzi, J. Luetic, N. Postiau, E. Starling, L. Thomas, C. Vander Velde, P.
Vanlaer, D. Vannerom, Q. Wang Ghent University, Ghent, Belgium
T. Cornelis, D. Dobur, A. Fagot, M. Gul, I. Khvastunov2, D. Poyraz, C. Roskas,
D. Trocino, M. Tytgat, W. Verbeke, B. Vermassen, M. Vit, N. Zaganidis
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
H. Bakhshiansohi, O. Bondu, S. Brochet, G. Bruno, C. Caputo, P. David, C.
Delaere, M. Delcourt, A. Giammanco, G. Krintiras, V. Lemaitre, A. Magitteri,
K. Piotrzkowski, A. Saggio, M. Vidal Marono, P. Vischia, S. Wertz, J. Zobec
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
F.L. Alves, G.A. Alves, M. Correa Martins Junior, G. Correia Silva, C. Hensel,
A. Moraes, M.E. Pol, P. Rebello Teles Universidade do Estado do Rio de
Janeiro, Rio de Janeiro, Brazil
E. Belchior Batista Das Chagas, W. Carvalho, J. Chinellato3, E. Coelho, E.M.
Da Costa, G.G. Da Silveira4, D. De Jesus Damiao, C. De Oliveira Martins, S.
Fonseca De Souza, H. Malbouisson, D. Matos Figueiredo, M. Melo De Almeida, C.
Mora Herrera, L. Mundim, H. Nogima, W.L. Prado Da Silva, L.J. Sanchez Rosas,
A. Santoro, A. Sznajder, M. Thiel, E.J. Tonelli Manganote3, F. Torres Da Silva
De Araujo, A. Vilela Pereira Universidade Estadual Paulista a, Universidade
Federal do ABC b, São Paulo, Brazil
S. Ahujaa, C.A. Bernardesa, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M.
Gregoresb, P.G. Mercadanteb, S.F. Novaesa, SandraS. Padulaa Institute for
Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia,
Bulgaria
A. Aleksandrov, R. Hadjiiska, P. Iaydjiev, A. Marinov, M. Misheva, M. Rodozov,
M. Shopova, G. Sultanov University of Sofia, Sofia, Bulgaria
A. Dimitrov, L. Litov, B. Pavlov, P. Petkov Beihang University, Beijing, China
W. Fang5, X. Gao5, L. Yuan Institute of High Energy Physics, Beijing, China
M. Ahmad, J.G. Bian, G.M. Chen, H.S. Chen, M. Chen, Y. Chen, C.H. Jiang, D.
Leggat, H. Liao, Z. Liu, S.M. Shaheen6, A. Spiezia, J. Tao, Z. Wang, E.
Yazgan, H. Zhang, S. Zhang6, J. Zhao State Key Laboratory of Nuclear Physics
and Technology, Peking University, Beijing, China
Y. Ban, G. Chen, A. Levin, J. Li, L. Li, Q. Li, Y. Mao, S.J. Qian, D. Wang
Tsinghua University, Beijing, China
Y. Wang Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C.A. Carrillo Montoya, L.F. Chaparro Sierra, C. Florez,
C.F. González Hernández, M.A. Segura Delgado University of Split, Faculty of
Electrical Engineering, Mechanical Engineering and Naval Architecture, Split,
Croatia
B. Courbon, N. Godinovic, D. Lelas, I. Puljak, T. Sculac University of Split,
Faculty of Science, Split, Croatia
Z. Antunovic, M. Kovac Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, K. Kadija, B. Mesic, M. Roguljic, A. Starodumov7,
T. Susa University of Cyprus, Nicosia, Cyprus
M.W. Ather, A. Attikis, M. Kolosova, G. Mavromanolakis, J. Mousa, C. Nicolaou,
F. Ptochos, P.A. Razis, H. Rykaczewski Charles University, Prague, Czech
Republic
M. Finger8, M. Finger Jr.8 Escuela Politecnica Nacional, Quito, Ecuador
E. Ayala Universidad San Francisco de Quito, Quito, Ecuador
E. Carrera Jarrin Academy of Scientific Research and Technology of the Arab
Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
A. Mahrous9, Y. Mohammed10, E. Salama11,12 National Institute of Chemical
Physics and Biophysics, Tallinn, Estonia
S. Bhowmik, A. Carvalho Antunes De Oliveira, R.K. Dewanjee, K. Ehataht, M.
Kadastik, M. Raidal, C. Veelken Department of Physics, University of Helsinki,
Helsinki, Finland
P. Eerola, H. Kirschenmann, J. Pekkanen, M. Voutilainen Helsinki Institute of
Physics, Helsinki, Finland
J. Havukainen, J.K. Heikkilä, T. Järvinen, V. Karimäki, R. Kinnunen, T.
Lampén, K. Lassila-Perini, S. Laurila, S. Lehti, T. Lindén, P. Luukka, T.
Mäenpää, H. Siikonen, E. Tuominen, J. Tuominiemi Lappeenranta University of
Technology, Lappeenranta, Finland
T. Tuuva IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
M. Besancon, F. Couderc, M. Dejardin, D. Denegri, J.L. Faure, F. Ferri, S.
Ganjour, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry, C. Leloup,
E. Locci, J. Malcles, G. Negro, J. Rander, A. Rosowsky, M.Ö. Sahin, M. Titov
Laboratoire Leprince-Ringuet, Ecole polytechnique, CNRS/IN2P3, Université
Paris-Saclay, Palaiseau, France
A. Abdulsalam13, C. Amendola, I. Antropov, F. Beaudette, P. Busson, C.
Charlot, R. Granier de Cassagnac, I. Kucher, A. Lobanov, J. Martin Blanco, C.
Martin Perez, M. Nguyen, C. Ochando, G. Ortona, P. Paganini, J. Rembser, R.
Salerno, J.B. Sauvan, Y. Sirois, A.G. Stahl Leiton, A. Zabi, A. Zghiche
Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
J.-L. Agram14, J. Andrea, D. Bloch, J.-M. Brom, E.C. Chabert, V. Cherepanov,
C. Collard, E. Conte14, J.-C. Fontaine14, D. Gelé, U. Goerlach, M. Jansová,
A.-C. Le Bihan, N. Tonon, P. Van Hove Centre de Calcul de l’Institut National
de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne,
France
S. Gadrat Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3,
Institut de Physique Nucléaire de Lyon, Villeurbanne, France
S. Beauceron, C. Bernet, G. Boudoul, N. Chanon, R. Chierici, D. Contardo, P.
Depasse, H. El Mamouni, J. Fay, L. Finco, S. Gascon, M. Gouzevitch, G.
Grenier, B. Ille, F. Lagarde, I.B. Laktineh, H. Lattaud, M. Lethuillier, L.
Mirabito, S. Perries, A. Popov15, V. Sordini, G. Touquet, M. Vander Donckt, S.
Viret Georgian Technical University, Tbilisi, Georgia
T. Toriashvili16 Tbilisi State University, Tbilisi, Georgia
Z. Tsamalaidze8 RWTH Aachen University, I. Physikalisches Institut, Aachen,
Germany
C. Autermann, L. Feld, M.K. Kiesel, K. Klein, M. Lipinski, M. Preuten, M.P.
Rauch, C. Schomakers, J. Schulz, M. Teroerde, B. Wittmer RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany
A. Albert, D. Duchardt, M. Erdmann, S. Erdweg, T. Esch, R. Fischer, S. Ghosh,
A. Güth, T. Hebbeker, C. Heidemann, K. Hoepfner, H. Keller, L. Mastrolorenzo,
M. Merschmeyer, A. Meyer, P. Millet, S. Mukherjee, T. Pook, M. Radziej, H.
Reithler, M. Rieger, A. Schmidt, D. Teyssier, S. Thüer RWTH Aachen University,
III. Physikalisches Institut B, Aachen, Germany
G. Flügge, O. Hlushchenko, T. Kress, T. Müller, A. Nehrkorn, A. Nowack, C.
Pistone, O. Pooth, D. Roy, H. Sert, A. Stahl17 Deutsches Elektronen-
Synchrotron, Hamburg, Germany
M. Aldaya Martin, T. Arndt, C. Asawatangtrakuldee, I. Babounikau, K.
Beernaert, O. Behnke, U. Behrens, A. Bermúdez Martínez, D. Bertsche, A.A. Bin
Anuar, K. Borras18, V. Botta, A. Campbell, P. Connor, C. Contreras-Campana, V.
Danilov, A. De Wit, M.M. Defranchis, C. Diez Pardos, D. Domínguez Damiani, G.
Eckerlin, T. Eichhorn, A. Elwood, E. Eren, E. Gallo19, A. Geiser, J.M. Grados
Luyando, A. Grohsjean, M. Guthoff, M. Haranko, A. Harb, H. Jung, M. Kasemann,
J. Keaveney, C. Kleinwort, J. Knolle, D. Krücker, W. Lange, A. Lelek, T. Lenz,
J. Leonard, K. Lipka, W. Lohmann20, R. Mankel, I.-A. Melzer-Pellmann, A.B.
Meyer, M. Meyer, M. Missiroli, J. Mnich, V. Myronenko, S.K. Pflitsch, D.
Pitzl, A. Raspereza, P. Saxena, P. Schütze, C. Schwanenberger, R. Shevchenko,
A. Singh, H. Tholen, O. Turkot, A. Vagnerini, M. Van De Klundert, G.P. Van
Onsem, R. Walsh, Y. Wen, K. Wichmann, C. Wissing, O. Zenaiev University of
Hamburg, Hamburg, Germany
R. Aggleton, S. Bein, L. Benato, A. Benecke, V. Blobel, T. Dreyer, A.
Ebrahimi, E. Garutti, D. Gonzalez, P. Gunnellini, J. Haller, A. Hinzmann, A.
Karavdina, G. Kasieczka, R. Klanner, R. Kogler, N. Kovalchuk, S. Kurz, V.
Kutzner, J. Lange, D. Marconi, J. Multhaup, M. Niedziela, C.E.N. Niemeyer, D.
Nowatschin, A. Perieanu, A. Reimers, O. Rieger, C. Scharf, P. Schleper, S.
Schumann, J. Schwandt, J. Sonneveld, H. Stadie, G. Steinbrück, F.M. Stober, M.
Stöver, B. Vormwald, I. Zoi Karlsruher Institut fuer Technologie, Karlsruhe,
Germany
M. Akbiyik, C. Barth, M. Baselga, S. Baur, E. Butz, R. Caspart, T. Chwalek, F.
Colombo, W. De Boer, A. Dierlamm, K. El Morabit, N. Faltermann, B. Freund, M.
Giffels, M.A. Harrendorf, F. Hartmann17, S.M. Heindl, U. Husemann, I.
Katkov15, S. Kudella, S. Mitra, M.U. Mozer, Th. Müller, M. Musich, M. Plagge,
G. Quast, K. Rabbertz, M. Schröder, I. Shvetsov, H.J. Simonis, R. Ulrich, S.
Wayand, M. Weber, T. Weiler, C. Wöhrmann, R. Wolf Institute of Nuclear and
Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Anagnostou, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas, G. Paspalaki
National and Kapodistrian University of Athens, Athens, Greece
A. Agapitos, G. Karathanasis, P. Kontaxakis, A. Panagiotou, I. Papavergou, N.
Saoulidou, E. Tziaferi, K. Vellidis National Technical University of Athens,
Athens, Greece
K. Kousouris, I. Papakrivopoulos, G. Tsipolitis University of Ioánnina,
Ioánnina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, S. Mallios, N.
Manthos, I. Papadopoulos, E. Paradas, J. Strologas, F.A. Triantis, D.
Tsitsonis MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
M. Bartók21, M. Csanad, N. Filipovic, P. Major, M.I. Nagy, G. Pasztor, O.
Surányi, G.I. Veres Wigner Research Centre for Physics, Budapest, Hungary
G. Bencze, C. Hajdu, D. Horvath22, Á. Hunyadi, F. Sikler, T.Á. Vámi, V.
Veszpremi, G. Vesztergombi${}^{\textrm{\textdagger}}$ Institute of Nuclear
Research ATOMKI, Debrecen, Hungary
N. Beni, S. Czellar, J. Karancsi21, A. Makovec, J. Molnar, Z. Szillasi
Institute of Physics, University of Debrecen, Debrecen, Hungary
P. Raics, Z.L. Trocsanyi, B. Ujvari Indian Institute of Science (IISc),
Bangalore, India
S. Choudhury, J.R. Komaragiri, P.C. Tiwari National Institute of Science
Education and Research, HBNI, Bhubaneswar, India
S. Bahinipati24, C. Kar, P. Mal, K. Mandal, A. Nayak25, S. Roy Chowdhury, D.K.
Sahoo24, S.K. Swain Panjab University, Chandigarh, India
S. Bansal, S.B. Beri, V. Bhatnagar, S. Chauhan, R. Chawla, N. Dhingra, S.K.
Gill, R. Gupta, A. Kaur, M. Kaur, P. Kumari, M. Lohan, M. Meena, A. Mehta, K.
Sandeep, S. Sharma, J.B. Singh, A.K. Virdi, G. Walia University of Delhi,
Delhi, India
A. Bhardwaj, B.C. Choudhary, R.B. Garg, M. Gola, S. Keshri, Ashok Kumar, S.
Malhotra, M. Naimuddin, P. Priyanka, K. Ranjan, Aashaq Shah, R. Sharma Saha
Institute of Nuclear Physics, HBNI, Kolkata, India
R. Bhardwaj26, M. Bharti26, R. Bhattacharya, S. Bhattacharya, U. Bhawandeep26,
D. Bhowmik, S. Dey, S. Dutt26, S. Dutta, S. Ghosh, K. Mondal, S. Nandan, A.
Purohit, P.K. Rout, A. Roy, G. Saha, S. Sarkar, M. Sharan, B. Singh26, S.
Thakur26 Indian Institute of Technology Madras, Madras, India
P.K. Behera, A. Muhammad Bhabha Atomic Research Centre, Mumbai, India
R. Chudasama, D. Dutta, V. Jha, V. Kumar, D.K. Mishra, P.K. Netrakanti, L.M.
Pant, P. Shukla, P. Suggisetti Tata Institute of Fundamental Research-A,
Mumbai, India
T. Aziz, M.A. Bhat, S. Dugad, G.B. Mohanty, N. Sur, RavindraKumar Verma Tata
Institute of Fundamental Research-B, Mumbai, India
S. Banerjee, S. Bhattacharya, S. Chatterjee, P. Das, M. Guchait, Sa. Jain, S.
Karmakar, S. Kumar, M. Maity27, G. Majumder, K. Mazumdar, N. Sahoo, T.
Sarkar27 Indian Institute of Science Education and Research (IISER), Pune,
India
S. Chauhan, S. Dube, V. Hegde, A. Kapoor, K. Kothekar, S. Pandey, A. Rane, A.
Rastogi, S. Sharma Institute for Research in Fundamental Sciences (IPM),
Tehran, Iran
S. Chenarani28, E. Eskandari Tadavani, S.M. Etesami28, M. Khakzad, M.
Mohammadi Najafabadi, M. Naseri, F. Rezaei Hosseinabadi, B. Safarzadeh29, M.
Zeinali University College Dublin, Dublin, Ireland
M. Felcini, M. Grunewald INFN Sezione di Bari a, Università di Bari b,
Politecnico di Bari c, Bari, Italy
M. Abbresciaa,b, C. Calabriaa,b, A. Colaleoa, D. Creanzaa,c, L. Cristellaa,b,
N. De Filippisa,c, M. De Palmaa,b, A. Di Florioa,b, F. Erricoa,b, L. Fiorea,
A. Gelmia,b, G. Iasellia,c, M. Incea,b, S. Lezkia,b, G. Maggia,c, M. Maggia,
G. Minielloa,b, S. Mya,b, S. Nuzzoa,b, A. Pompilia,b, G. Pugliesea,c, R.
Radognaa, A. Ranieria, G. Selvaggia,b, A. Sharmaa, L. Silvestrisa, R.
Vendittia, P. Verwilligena INFN Sezione di Bologna a, Università di Bologna b,
Bologna, Italy
G. Abbiendia, C. Battilanaa,b, D. Bonacorsia,b, L. Borgonovia,b, S. Braibant-
Giacomellia,b, R. Campaninia,b, P. Capiluppia,b, A. Castroa,b, F.R. Cavalloa,
S.S. Chhibraa,b, G. Codispotia,b, M. Cuffiania,b, G.M. Dallavallea, F.
Fabbria, A. Fanfania,b, E. Fontanesi, P. Giacomellia, C. Grandia, L.
Guiduccia,b, F. Iemmia,b, S. Lo Meoa,30, S. Marcellinia, G. Masettia, A.
Montanaria, F.L. Navarriaa,b, A. Perrottaa, F. Primaveraa,b, A.M. Rossia,b, T.
Rovellia,b, G.P. Sirolia,b, N. Tosia INFN Sezione di Catania a, Università di
Catania b, Catania, Italy
S. Albergoa,b, A. Di Mattiaa, R. Potenzaa,b, A. Tricomia,b, C. Tuvea,b INFN
Sezione di Firenze a, Università di Firenze b, Firenze, Italy
G. Barbaglia, K. Chatterjeea,b, V. Ciullia,b, C. Civininia, R.
D’Alessandroa,b, E. Focardia,b, G. Latino, P. Lenzia,b, M. Meschinia, S.
Paolettia, L. Russoa,31, G. Sguazzonia, D. Stroma, L. Viliania INFN Laboratori
Nazionali di Frascati, Frascati, Italy
L. Benussi, S. Bianco, F. Fabbri, D. Piccolo INFN Sezione di Genova a,
Università di Genova b, Genova, Italy
F. Ferroa, R. Mulargiaa,b, E. Robuttia, S. Tosia,b INFN Sezione di Milano-
Bicocca a, Università di Milano-Bicocca b, Milano, Italy
A. Benagliaa, A. Beschib, F. Brivioa,b, V. Cirioloa,b,17, S. Di Guidaa,b,17,
M.E. Dinardoa,b, S. Fiorendia,b, S. Gennaia, A. Ghezzia,b, P. Govonia,b, M.
Malbertia,b, S. Malvezzia, D. Menascea, F. Monti, L. Moronia, M. Paganonia,b,
D. Pedrinia, S. Ragazzia,b, T. Tabarelli de Fatisa,b, D. Zuoloa,b INFN Sezione
di Napoli a, Università di Napoli ’Federico II’ b, Napoli, Italy, Università
della Basilicata c, Potenza, Italy, Università G. Marconi d, Roma, Italy
S. Buontempoa, N. Cavalloa,c, A. De Iorioa,b, A. Di Crescenzoa,b, F.
Fabozzia,c, F. Fiengaa, G. Galatia, A.O.M. Iorioa,b, L. Listaa, S.
Meolaa,d,17, P. Paoluccia,17, C. Sciaccaa,b, E. Voevodinaa,b INFN Sezione di
Padova a, Università di Padova b, Padova, Italy, Università di Trento c,
Trento, Italy
P. Azzia, N. Bacchettaa, D. Biselloa,b, A. Bolettia,b, A. Bragagnolo, R.
Carlina,b, P. Checchiaa, M. Dall’Ossoa,b, P. De Castro Manzanoa, T. Dorigoa,
U. Dossellia, F. Gasparinia,b, U. Gasparinia,b, A. Gozzelinoa, S.Y. Hoh, S.
Lacapraraa, P. Lujan, M. Margonia,b, A.T. Meneguzzoa,b, J. Pazzinia,b, M.
Presillab, P. Ronchesea,b, R. Rossina,b, F. Simonettoa,b, A. Tiko, E.
Torassaa, M. Tosia,b, M. Zanettia,b, P. Zottoa,b, G. Zumerlea,b INFN Sezione
di Pavia a, Università di Pavia b, Pavia, Italy
A. Braghieria, A. Magnania, P. Montagnaa,b, S.P. Rattia,b, V. Rea, M.
Ressegottia,b, C. Riccardia,b, P. Salvinia, I. Vaia,b, P. Vituloa,b INFN
Sezione di Perugia a, Università di Perugia b, Perugia, Italy
M. Biasinia,b, G.M. Bileia, C. Cecchia,b, D. Ciangottinia,b, L. Fanòa,b, P.
Laricciaa,b, R. Leonardia,b, E. Manonia, G. Mantovania,b, V. Mariania,b, M.
Menichellia, A. Rossia,b, A. Santocchiaa,b, D. Spigaa INFN Sezione di Pisa a,
Università di Pisa b, Scuola Normale Superiore di Pisa c, Pisa, Italy
K. Androsova, P. Azzurria, G. Bagliesia, L. Bianchinia, T. Boccalia, L.
Borrello, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa, G. Fedia, F. Fioria,c,
L. Gianninia,c, A. Giassia, M.T. Grippoa, F. Ligabuea,c, E. Mancaa,c, G.
Mandorlia,c, A. Messineoa,b, F. Pallaa, A. Rizzia,b, G. Rolandi32, P.
Spagnoloa, R. Tenchinia, G. Tonellia,b, A. Venturia, P.G. Verdinia INFN
Sezione di Roma a, Sapienza Università di Roma b, Rome, Italy
L. Baronea,b, F. Cavallaria, M. Cipriania,b, D. Del Rea,b, E. Di Marcoa,b, M.
Diemoza, S. Gellia,b, E. Longoa,b, B. Marzocchia,b, P. Meridiania, G.
Organtinia,b, F. Pandolfia, R. Paramattia,b, F. Preiatoa,b, S. Rahatloua,b, C.
Rovellia, F. Santanastasioa,b INFN Sezione di Torino a, Università di Torino
b, Torino, Italy, Università del Piemonte Orientale c, Novara, Italy
N. Amapanea,b, R. Arcidiaconoa,c, S. Argiroa,b, M. Arneodoa,c, N. Bartosika,
R. Bellana,b, C. Biinoa, A. Cappatia,b, N. Cartigliaa, F. Cennaa,b, S.
Comettia, M. Costaa,b, R. Covarellia,b, N. Demariaa, B. Kiania,b, C.
Mariottia, S. Masellia, E. Migliorea,b, V. Monacoa,b, E. Monteila,b, M.
Montenoa, M.M. Obertinoa,b, L. Pachera,b, N. Pastronea, M. Pelliccionia, G.L.
Pinna Angionia,b, A. Romeroa,b, M. Ruspaa,c, R. Sacchia,b, R. Salvaticoa,b, K.
Shchelinaa,b, V. Solaa, A. Solanoa,b, D. Soldia,b, A. Staianoa INFN Sezione di
Trieste a, Università di Trieste b, Trieste, Italy
S. Belfortea, V. Candelisea,b, M. Casarsaa, F. Cossuttia, A. Da Rolda,b, G.
Della Riccaa,b, F. Vazzolera,b, A. Zanettia Kyungpook National University,
Daegu, Korea
D.H. Kim, G.N. Kim, M.S. Kim, J. Lee, S. Lee, S.W. Lee, C.S. Moon, Y.D. Oh,
S.I. Pak, S. Sekmen, D.C. Son, Y.C. Yang Chonnam National University,
Institute for Universe and Elementary Particles, Kwangju, Korea
H. Kim, D.H. Moon, G. Oh Hanyang University, Seoul, Korea
B. Francois, J. Goh33, T.J. Kim Korea University, Seoul, Korea
S. Cho, S. Choi, Y. Go, D. Gyun, S. Ha, B. Hong, Y. Jo, K. Lee, K.S. Lee, S.
Lee, J. Lim, S.K. Park, Y. Roh Sejong University, Seoul, Korea
H.S. Kim Seoul National University, Seoul, Korea
J. Almond, J. Kim, J.S. Kim, H. Lee, K. Lee, K. Nam, S.B. Oh, B.C. Radburn-
Smith, S.h. Seo, U.K. Yang, H.D. Yoo, G.B. Yu University of Seoul, Seoul,
Korea
D. Jeon, H. Kim, J.H. Kim, J.S.H. Lee, I.C. Park Sungkyunkwan University,
Suwon, Korea
Y. Choi, C. Hwang, J. Lee, I. Yu Vilnius University, Vilnius, Lithuania
V. Dudenas, A. Juodagalvis, J. Vaitkus National Centre for Particle Physics,
Universiti Malaya, Kuala Lumpur, Malaysia
Z.A. Ibrahim, M.A.B. Md Ali34, F. Mohamad Idris35, W.A.T. Wan Abdullah, M.N.
Yusli, Z. Zolkapli Universidad de Sonora (UNISON), Hermosillo, Mexico
J.F. Benitez, A. Castaneda Hernandez, J.A. Murillo Quijada Centro de
Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
H. Castilla-Valdez, E. De La Cruz-Burelo, M.C. Duran-Osuna, I. Heredia-De La
Cruz36, R. Lopez-Fernandez, J. Mejia Guisao, R.I. Rabadan-Trejo, M. Ramirez-
Garcia, G. Ramirez-Sanchez, R. Reyes-Almanza, A. Sanchez-Hernandez Universidad
Iberoamericana, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera, F. Vazquez Valencia Benemerita
Universidad Autonoma de Puebla, Puebla, Mexico
J. Eysermans, I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada Universidad
Autónoma de San Luis Potosí, San Luis Potosí, Mexico
A. Morelos Pineda University of Auckland, Auckland, New Zealand
D. Krofcheck University of Canterbury, Christchurch, New Zealand
S. Bheesette, P.H. Butler National Centre for Physics, Quaid-I-Azam
University, Islamabad, Pakistan
A. Ahmad, M. Ahmad, M.I. Asghar, Q. Hassan, H.R. Hoorani, W.A. Khan, A.
Saddique, M.A. Shah, M. Shoaib, M. Waqas National Centre for Nuclear Research,
Swierk, Poland
H. Bialkowska, M. Bluj, B. Boimska, T. Frueboes, M. Górski, M. Kazana, M.
Szleper, P. Traczyk, P. Zalewski Institute of Experimental Physics, Faculty of
Physics, University of Warsaw, Warsaw, Poland