2021 053 01 April Neutral meson $R_{\rm pPb}$ up to high $p_{\mathrm{T}}$
ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

Neutral pion and $\eta$ meson production cross sections were measured up to
unprecedentedly high transverse momenta ($p_{\mathrm{T}}$) in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$. The mesons were reconstructed
via their two-photon decay channel in the rapidity interval $-1.3<y<0.3$ in
the ranges of $0.4<p_{\mathrm{T}}<200$ GeV/$c$ and $1.0<p_{\mathrm{T}}<50$
GeV/$c$, respectively. The respective nuclear modification factor
($R_{\mathrm{pPb}}$) is presented for $p_{\mathrm{T}}$ up to of 200 and 30
GeV/$c$, where the former was achieved extending the $\pi^{0}$ measurement in
pp collisions at $\sqrt{s}=8~{}\mathrm{TeV}$ using the merged cluster
technique. The values of $R_{\mathrm{pPb}}$ are below unity for
$p_{\mathrm{T}}<10$ GeV/$c$, while they are consistent with unity for
$p_{\mathrm{T}}>10$ GeV/$c$, leaving essentially no room for final state
energy loss. The new data provide strong constraints for nuclear parton
distribution and fragmentation functions over a broad kinematic range and are
compared to model predictions as well as previous results at
$\sqrt{s_{\mathrm{NN}}}=5.02~{}\mathrm{TeV}$.

##  1 Introduction

Measurements of identified hadron spectra in high-energy proton–proton (pp)
collisions are well suited to constrain perturbative predictions from Quantum
Chromodynamics (QCD) [1]. At large momentum transfer ($Q^{2}$) one relies in
these perturbative QCD (pQCD) calculations on the factorization of computable
short-range parton scattering processes such as quark–quark, quark–gluon and
gluon–gluon scatterings from long-range properties of QCD that need
experimental input. These non-perturbative properties are typically modeled by
parton distribution functions (PDFs), which describe the fractional-momentum
($x$) distributions of quarks and gluons within the proton, and fragmentation
functions (FFs), which describe the fractional-momentum ($z$) distribution of
quarks or gluons for hadrons of certain species.

In high-energy proton–nucleus (p–A) collisions, nuclear effects are expected
to significantly affect particle production, in particular at small $x$ [2].
Previous measurements of neutral pions and charged hadrons in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV at the LHC [3, 4, 5, 6] indeed revealed
distinct deviations from binary-scaled pp collisions, confirming earlier
results from deuteron–gold collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV at
RHIC [7, 8]. The modification at low $p_{\mathrm{T}}$ ($\sim$1 GeV/$c$), which
is commonly attributed to nuclear shadowing, can be parameterized by nuclear
parton distribution functions (nPDFs) [9, 10]. However, the high parton
densities reached at low $p_{\mathrm{T}}$ ($x$ as small as $\sim 5\cdot
10^{-4}$) makes the Color Glass Condensate (CGC) framework [11] applicable
which predicts strong particle suppression due to saturation of the parton
phase space in nuclei [12]. Recently, also parton energy loss in cold nuclear
matter was shown [13] to lead to suppressed particle yields at low
$p_{\mathrm{T}}$, while the previously observed collective effects in small
systems [14, 15, 16] also imply partonic rescatterings in hot nuclear matter
to play a role [17, 18].

In this letter, the nuclear modification of particle yields is quantified by

$R_{\mathrm{pPb}}=\frac{1}{A_{\mathrm{Pb}}}\frac{\mathrm{d}^{2}\sigma_{\mathrm{pPb}}}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\bigg{/}\frac{\mathrm{d}^{2}\sigma_{\mathrm{pp}}}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\,,$
(1)

where $A_{\mathrm{Pb}}=208$ is the nuclear mass number of lead and
$\mathrm{d}^{2}\sigma/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$ are the $\pi^{0}$
or $\eta$ meson cross sections measured in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=8.16$ TeV and in the corresponding pp reference system
at $\sqrt{s}=8~{}\mathrm{TeV}$. The new data constrain nPDFs and FFs over a
large range in $x$, and $Q^{2}$, including the centre-of-mass energy
dependence based on comparisons to lower-energy data [6].

##  2 Experimental setup

The neutral mesons were reconstructed via their two-photon decay channels
$\pi^{0}(\eta)\rightarrow\gamma\gamma$ using different reconstruction
techniques provided by the various subdetector systems of ALICE [19, 20].
Photons are either reconstructed using the Electromagnetic Calorimeter
(EMCal), the Photon Spectrometer (PHOS) or via the Photon Conversion Method
(PCM). The latter uses e+e- pairs from conversions, which are reconstructed
from tracks measured in the Inner Tracking System (ITS) [21] and the Time
Projection Chamber (TPC) [21] at $|\eta|<0.9$ inside a solenoidal magnetic
field of $B=0.5$ T. The EMCal [22, 23] is a lead-scintillator sampling
electromagnetic calorimeter at a radial distance of $4.28~{}\mathrm{m}$ from
the interaction point (IP) covering $\Delta\varphi=100^{\circ}$ in azimuth for
$|\eta|<0.7$ in pseudorapidity during the 2012 pp data taking period. During
the p–Pb data taking in 2016, additional modules [23] were available that
extended the coverage to $\Delta\varphi=107^{\circ}$ for $|\eta|<0.7$ and
added $\Delta\varphi=60^{\circ}$ opposite in azimuth for $0.22<|\eta|<0.7$.
The calorimeter provides an energy resolution of $\sigma_{E}/E=4.8\%/E\oplus
11.3\%/\sqrt{E}\oplus 1.7\%$, with $E$ in units of GeV. In its full
configuration, it consists of a total of 18240 cells of transverse size
$6\times 6$ cm2 each. The PHOS [24] is a lead tungstate electromagnetic
calorimeter with 12544 channels at a distance of $4.6~{}\mathrm{m}$ from the
IP, covering $\Delta\varphi=70^{\circ}$ and $|\eta|<0.12$. Its high light
yield combined with its cell size being only slightly larger than the Molière
radius of $2~{}\mathrm{cm}$ results in an energy resolution of
$\sigma_{E}/E=1.8\%/E\oplus 3.3\%/\sqrt{E}\oplus 1.1\%$.

##  3 Data samples and event selection

The p–Pb data at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ were recorded in
2016. Equal magnetic rigidity for proton and Pb beams in the LHC resulted in a
rapidity shift of $\Delta y_{\rm NN}=0.465$ in the direction of the proton
beam between the nucleon–nucleon centre-of-mass and the laboratory reference
system. The minimum bias (MB) event trigger required a coincidence at Level 0
(L0) of signals issued by the V0A and V0C detectors, which are two arrays of
32 scintillator tiles each covering full azimuth at $2.8<\textit{et al.}<5.1$
and $-3.7<\textit{et al.}<-1.7$, respectively [25]. Additional triggers at L0
required an energy deposit above $2$ GeV for EMCal and $4$ GeV for PHOS, in
$4\times 4$ adjacent cells in coincidence with the MB trigger. Based on the L0
preselection, further hardware Level 1 triggers were issued, two for the EMCal
with energy thresholds at 5.5 GeV and 8 GeV and one for the PHOS at 7 GeV. To
account for the yield enhancement of the event triggers, the trigger rejection
factors ($RF$) for the EMCal triggers were estimated through an error function
fit to the ratio of the cluster energy spectra in their plateau regions above
the respective trigger thresholds. A similar procedure was performed for the
PHOS triggers, where $RF$ is determined on the ratio of the corrected
$\pi^{0}$ meson spectra instead. The trigger rejection factors from these fits
are given in Table 1 for all event triggers. For the high threshold triggers,
$RF$ is obtained from the product $RF_{\mathrm{EMCal-L1low/MB}}\cdot
RF_{\mathrm{EMCal-L1high/low}}$ or $RF_{\mathrm{PHOS-L0/MB}}\cdot
RF_{\mathrm{PHOS-L1/L0}}$. Uncertainties on $RF$ are given as combined
statistical and systematic uncertainties where the latter part was determined
via variations of the low $E$ fit range. The integrated luminosities
($\mathscr{L_{\rm int}}$) of each trigger sample and for each reconstruction
method were calculated based on the MB cross section of
$\sigma_{\mathrm{MB}}=(2.09(2.10)\pm 0.04)$ b for the p–Pb (Pb–p) collisions
[26] and the respective $RF$ values as $\mathscr{L_{\rm int}}=RF\times
N_{\mathrm{events}}/\sigma_{\mathrm{MB}}$ and are listed in Table 1. For PCM-
EMC lower integrated lumiosities are reported due to the lack of TPC readout
in two thirds of the triggered data. The pp collision data set at a centre-of-
mass energy of $\sqrt{s}=8$ TeV used in this analysis was recorded in 2012 and
the respective integrated luminosities and $RF$ values are listed in Table 1.

Table 1: Trigger rejection factor $RF$ and total integrated luminosities based
on the individual samples for the different reconstruction methods and
triggers in pp collisions at $\sqrt{s}=8$ TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$. The uncertainty associated with
the determination of the MB cross section of 1.9% for p–Pb and 2.6% for pp is
not included. The value in brackets corresponds to the high luminosity minimum
bias data sample where TPC tracking is not available.

System/Trigger |  |  $\mathscr{L_{\rm int}}$ (nb-1) |
---|---|---|---
p–Pb | $RF$ | (m)EMC | PCM-EMC | PCM | PHOS
MB | - | $0.018(0.041)$ | $0.018$ | $0.022$ | $0.036$
EMCal L1 (low) | $288\pm 8$ | $0.206$ | $0.081$ | - | -
EMCal L1 (high) | $991\pm 29$ | $5.67$ | $1.42$ | - | -
PHOS L0 | $(1.66\pm 0.02)\cdot 10^{3}$ | - | - | - | $1.68$
PHOS L1 | $(1.55\pm 0.04)\cdot 10^{4}$ | - | - | - | $6.42$
pp |  |  |  |  |
MB | - | $1.94$ | $1.94$ | $2.17$ | $1.25$
EMCal/PHOS L0 | $64.6\pm 1.0$ | $39.4$ | $39.4$ | - | $136$
EMCal L1 | $(1.47\pm 0.06)\cdot 10^{4}$ | $606$ | $606$ | - | -

##  4 Analysis

Reconstructed tracks were used to determine the primary vertex of the
collision, which was required to be within 10 cm from the nominal IP position
along the beam direction. Pileup events ($\sim$1.5% in pp) containing multiple
collisions within a 300 ns window were rejected if more than one primary
vertex was reconstructed from SPD hits or if the number of SPD clusters was
not correlated with the number of track candidates. The photon and meson
reconstruction methods are analogous to those described in Refs. [27, 6]. To
achieve an optimal uncertainty cancellation on $R_{\mathrm{pPb}}$, the meson
analyses were performed simultaneously for the p–Pb and pp data sets using
identical methods and selections, where possible.

Photon reconstruction in the EMCal (PHOS) is based on grouping adjacent cells,
with energy deposits above $E_{\rm cell}^{\rm min}=100~{}(20)~{}\mathrm{MeV}$,
into clusters starting with a seed cell of $E_{\rm cell}^{\rm
seed}>500~{}(50)~{}\mathrm{MeV}$. The thresholds for PHOS are lower due to its
better energy resolution and finer granularity. Photon candidates in the EMCal
were required to have $|\eta_{\gamma}|<0.67$, a minimum of two cells in the
cluster ($N_{\rm cell}^{\rm cls}\geq 2$), and an elongation ($\sigma^{2}_{\rm
long}$ [28]) between $0.1$ and $0.5$. In PHOS, $|\eta_{\gamma}|<0.12$ was
required and the criteria $\sigma^{2}_{\rm long}>0.1$ and $N_{\rm cell}^{\rm
cls}\geq 3$ were only applied to clusters with $E>2~{}\mathrm{GeV}$. Hadron
and electron contamination of the photon clusters in the EMCal was removed if
an associated track was found with $E/p_{\rm track}<1.75$. The suppression of
false matches with the $E/p$ veto increased the photon efficiency by up to 50%
at high $p_{\mathrm{T}}$ with respect to previous measurements [27, 6].
Corrections for the non-linear energy response of the calorimeters were
applied to the cluster energy. For the EMCal the correction was obtained from
electron test beam data and from laboratory-based measurements of the low-gain
shapers in the front-end electronics. The correction is sizeable only at low
$E$ (6% at 1 GeV) and at high $E$ (14% at 200 GeV). It includes a residual
relative energy-and-position correction, which is applied on simulated EMCal
clusters to match the $\pi^{0}$ peak position in data. An improved description
of the EMCal cluster properties in simulations was achieved by introducing a
cross talk emulation within the same EMCal readout card as described in Ref.
[29]. The resulting agreement of the $\pi^{0}$ mass peak position is better
than 0.3% between data and simulation. For the PHOS, the energy non-linearity
was corrected by fixing the reconstructed $\pi^{0}$ mass to the nominal PDG
value [30].

Photon conversions were reconstructed by combining oppositely charged tracks,
originating from a common vertex up to a radius of $180$ cm, through a
secondary vertex finder. Only tracks with a TPC d$E$/d$x$ within $-3\sigma$
and $+4\sigma$ of the expected values for electrons were accepted, where
$\sigma$ is the d$E$/d$x$ resolution. Additionally, tracks with $p>0.4$
GeV/$c$ and d$E$/d$x$ up to $1\sigma$ above the expected value for pions were
rejected. For tracks with $p>3.5$ GeV/$c$, this was loosened to $0.5\sigma$.
The photon conversion selection criteria were further optimized with respect
to previous measurements [31, 27] to yield about 10% better efficiency at
similar purity.

An invariant mass ($m_{\gamma\gamma}$) technique was used for the
reconstruction of neutral pions and $\eta$ mesons. For this,
$m_{\gamma\gamma}$ was calculated for all possible combinations of photon
candidates per event taking either both photons reconstructed by the same
method (called PCM, EMC, and PHOS), or one photon reconstructed with PCM and
one with EMC (called PCM-EMC). The invariant mass distributions were
calculated in $p_{\mathrm{T}}$ intervals of the meson candidates (examples are
shown in Ref. [32]). For each interval, the combinatorial background, obtained
from event mixing, and residual correlated background were subtracted (see
Ref. [32]). The remaining distributions were then integrated in $\sim 3\sigma$
around the fitted mass peak position to determine the raw yields.

Figure 1: Shower shape distribution for the elongation
$\sigma_{\mathrm{long}}^{2}$ in PYTHIA 8 Monte Carlo simulations a) showing
the various contributions to the full cluster sample for a high
$p_{\mathrm{T}}$ example interval and b) compared to the
$\sigma_{\mathrm{long}}^{2}$ distribution in data in the same $p_{\mathrm{T}}$
interval.

Neutral pions with $p_{\mathrm{T}}>16$ GeV/$c$ were measured with the merged-
cluster (mEMC) method [31], which exploits single clusters in the EMCal that
result from overlapping energy deposits of both decay photons in the same
cluster due to the small opening angle for large pion momentum. The elongation
($\sigma^{2}_{\rm long}>0.27$) of clusters with $p_{\mathrm{T}}>16$ GeV/$c$
was used to discriminate between single-photon ($\sigma^{2}_{\rm long}\approx
0.25$) and merged-photon clusters. The $\sigma^{2}_{\rm long}$ distribution
was obtained in $p_{\mathrm{T}}$-intervals of the clusters and the integrated
counts above $0.27$ were used as raw $\pi^{0}$ candidate yields. An exemplary
$\sigma^{2}_{\rm long}$ distribution at high $p_{\mathrm{T}}$ is shown in Fig.
1a in simulation, broken up into the individual contributions to the full
cluster sample. Fig. 1b shows a comparison between the data and simulation
$\sigma^{2}_{\rm long}$ distributions, highlighting their good agreement
within uncertainties. The resulting $\pi^{0}$ purity is between 81–87%
decreasing with $p_{\mathrm{T}}$ in p–Pb and 83–89% in pp collisions. It was
determined via PYTHIA 8 [33] simulations with additional data-driven
corrections, which increase the relative fractions of prompt photons by 1–3%
and of $\eta$ mesons by 2%. POWHEG-Box [34, 35] simulations were used to
determine an additional purity correction for electrons from weak decays of up
to 3%.

Correction factors for reconstruction efficiency and kinematic acceptance (see
Ref. [32]) were obtained from simulations of the detector response with GEANT3
[36] using DPMJET [37] and PYTHIA 8 [33] as event generators. The correction
factors for secondary $\pi^{0}$ from long-lived strange hadron decays were
obtained from a particle-decay simulation based on measured spectra and are
dominated by contributions from ${\rm K_{S}^{0}}$ and $\Lambda$ decays [38,
27]. They amount to about 1–6% and decrease with $p_{\mathrm{T}}$. For the PCM
method, an additional correction for out-of-bunch pileup of 7 to 15%
decreasing with $p_{\mathrm{T}}$ was applied.

The spectra were normalized by the integrated luminosities of each trigger
sample and meson reconstruction method as listed in Table 1.

The systematic uncertainties on the $\pi^{0}$ ($\eta$) cross sections contain
contributions from the yield extraction of 1–10% (2–20%) depending on the
reconstruction method and $p_{\mathrm{T}}$. Further contributions from the
imperfect description of the selection variables in the simulation amount to
1–4% (1–6%), while the $p_{\mathrm{T}}$-independent material-budget
uncertainties are 4.5% per PCM photon, 2.8% per EMCal photon and 2% per PHOS
photon. Uncertainties arising from the out-of-bunch pileup determination reach
3–5% and global uncertainties on the trigger rejection factors are 2–3% [32].
For the mEMC analysis, the largest systematic uncertainty arises from the
shower overlaps in jets, which depend on the jet fragmentation and affect the
$\pi^{0}$ energy resolution in the EMCal. This uncertainty was estimated as
7–10%, obtained from varying the particle overlaps within clusters. The total
uncertainties on the $\pi^{0}$($\eta$) cross sections are between 5(8)% and
20(27)% and, due to uncertainty cancellations and correlations, between 7% and
24% on the $\eta/\pi^{0}$ ratio. For the $R_{\mathrm{pPb}}$, the
$p_{\mathrm{T}}$-independent uncertainties cancel as well as a fraction of the
remaining uncertainties resulting in a total uncertainty between 4(11)% and
25(32)%. A tabulated overview of the systematic uncertainty contributions for
selected $p_{\mathrm{T}}$-intervals is given in Table 2.

##  5 Results

Figure 2: Ratio of the neutral pion invariant differential cross sections to
the two-component model (TCM) fit of the combined spectrum for the different
reconstruction techniques PCM, PCM-EMC, EMC, PHOS and mEMC in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$. Statistical uncertainties are
given by the vertical error bars while systematic uncertainties are shown as
boxes. Table 2: Summary of relative systematic uncertainties in percent for
selected $p_{\mathrm{T}}$ intervals for the $\pi^{0}$ and $\eta$ meson cross
sections $\sigma_{\mathrm{p-Pb}}$ and nuclear modification factors
$R_{\mathrm{pPb}}$. The statistical uncertainties are given in addition to the
total systematic uncertainties for each bin. The combined statistical and
systematic uncertainties, obtained by applying the BLUE method [39, 40], are
also listed for all reconstruction methods available in the given
$p_{\mathrm{T}}$ bin, considering the uncertainty correlations for the
different methods. The uncertainty from the $\sigma_{\rm MB}$ determination of
1.9%, see Ref. [26], is independent of the reported measurements and is
separately indicated in the figures.

| source | $\sigma^{\pi^{0}}_{\mathrm{p-Pb}}$ | $R_{\mathrm{pPb}}^{\pi^{0}}$ | $\sigma^{\eta}_{\mathrm{p-Pb}}$ | $R_{\mathrm{pPb}}^{\eta}$ | $\eta/\pi^{0}_{\mathrm{p-Pb}}$
---|---|---|---|---|---|---
|  $p_{\mathrm{T}}$ (GeV/$c$) | 1.6 | 5.5 | 17 | 115 | 1.6 | 5.5 | 17 | 115 | 2.75 | 7 | 22.5 | 2.75 | 7 | 22.5 | 2.75 | 7 | 22.5
PCM | photon reco. | 10.7 | 9.1 | - | - | 0.7 | 1.5 | - | - | 9.5 | 10.5 | - | 2.0 | 3.0 | - | 2.7 | 4.6 | -
| meson reco. | 6.8 | 6.3 | - | - | 2.6 | 7.0 | - | - | 4.0 | 5.1 | - | 4.6 | 6.3 | - | 3.9 | 5.2 | -
| pileup | 5.5 | 3.3 | - | - | 5.9 | 6.3 | - | - | 4.9 | 4.1 | - | 6.1 | 6.1 | - | 2.6 | 1.9 | -
| stat. error | 2.2 | 6.7 | - | - | 3.0 | 9.2 | - | - | 12.0 | 25.9 | - | 18.7 | 37.3 | - | 12.9 | 25.9 | -
PCM- | PCM photon reco. | 4.7 | 5.5 | 5.0 | - | 1.3 | 3.5 | 3.3 | - | 7.5 | 7.3 | 8.1 | 5.0 | 5.5 | 6.2 | 6.0 | 4.5 | 7.8
EMC |  $\gamma$ cluster reco. | 3.5 | 3.8 | 4.4 | - | 1.8 | 2.1 | 3.8 | - | 4.8 | 5.1 | 6.5 | 2.9 | 3.3 | 9.6 | 3.6 | 3.8 | 5.0
| meson reco. | 2.4 | 1.0 | 1.5 | - | 2.9 | 2.3 | 2.2 | - | 3.3 | 4.7 | 14.4 | 5.5 | 5.4 | 8.3 | 3.7 | 6.3 | 14.4
| trigger and efficienc | 1.0 | 1.0 | 3.0 | - | 0.5 | 3.2 | 4.9 | - | 1.0 | 2.0 | 3.0 | 0.2 | 3.2 | 4.9 | 1.4 | 1.4 | 1.4
| stat. error | 2.2 | 3.7 | 3.6 | - | 2.6 | 5.7 | 5.3 | - | 14.2 | 11.4 | 16.4 | 0.0 | 0.0 | 0.0 | 14.1 | 14.0 | 12.5
EMC |  $\gamma$ cluster reco. | 7.2 | 5.9 | 7.1 | - | 4.8 | 2.7 | 4.3 | - | 9.5 | 8.5 | 9.5 | 7.0 | 6.6 | 8.2 | 7.3 | 6.9 | 8.6
| meson reco. | 3.5 | 4.1 | 7.3 | - | 5.1 | 4.7 | 7.0 | - | 23.7 | 7.3 | 3.0 | 29.4 | 8.3 | 4.8 | 23.9 | 7.9 | 8.6
| trigger and efficiency | 2.3 | 2.4 | 4.1 | - | 1.7 | 1.7 | 4.5 | - | 2.3 | 3.0 | 3.8 | 2.6 | 2.6 | 5.1 | 2.0 | 2.5 | 2.5
| stat. error | 3.1 | 2.0 | 4.2 | - | 4.4 | 3.1 | 5.3 | - | 20.8 | 7.9 | 6.9 | 23.9 | 15.4 | 27.8 | 20.9 | 8.1 | 12.5
PHOS |  $\gamma$ cluster reco. | 3.2 | 3.7 | 3.8 | - | 2.0 | 2.0 | 2.0 | - | 4.1 | 4.2 | 4.2 | - | - | - | 0.0 | 0.0 | 0.0
| meson reco. | 2.1 | 2.9 | 4.9 | - | 3.5 | 3.3 | 5.2 | - | 18.0 | 4.5 | 7.0 | - | - | - | 34.6 | 7.9 | 12.4
| trigger and efficiency | 2.8 | 2.8 | 3.4 | - | 7.4 | 7.4 | 14.6 | - | 1.6 | 2.5 | 2.5 | - | - | - | 1.0 | 1.0 | 1.0
| stat. error | 1.1 | 3.1 | 3.6 | - | 5.4 | 6.9 | 11.7 | - | 29.7 | 6.5 | 15.9 | - | - | - | 17.5 | 5.8 | 12.9
mEMC | meson PID | - | - | 5.4 | 5.8 | - | - | 2.3 | 3.6 | - | - | - | - | - | - | - | - | -
| cluster reco. | - | - | 8.3 | 9.5 | - | - | 1.0 | 1.0 | - | - | - | - | - | - | - | - | -
| trigger and efficiency | - | - | 4.1 | 4.1 | - | - | 3.8 | 3.8 | - | - | - | - | - | - | - | - | -
| stat. error | - | - | 2.4 | 5.7 | - | - | 2.7 | 10.8 | - | - | - | - | - | - | - | - | -
| combined sys. error | 3.6 | 3.9 | 4.9 | 11.9 | 2.7 | 2.9 | 2.9 | 5.4 | 5.6 | 5.3 | 6.1 | 5.9 | 6.8 | 11.5 | 8.6 | 4.5 | 8.2
| combined stat. error | 1.0 | 1.8 | 2.2 | 5.7 | 1.8 | 2.7 | 2.2 | 10.8 | 8.6 | 4.5 | 8.2 | 11.9 | 11.6 | 17.2 | 5.6 | 5.3 | 6.1

Figure 3: Neutral pion a) and $\eta$ meson d) cross sections for pp collisions
at $\sqrt{s}=8~{}\mathrm{TeV}$ and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ together with TCM fits, NLO
calculations [41, 42, 43] and PYTHIA 8 [33, 44] predictions using different
(n)PDFs [9, 10, 45]. Statistical uncertainties are shown as vertical bars; the
systematic uncertainties as boxes. The ratios of the $\pi^{0}$ spectra in p–Pb
and pp collisions to the TCM fits are shown in panel b) and c), respectively,
together with the ratios of the calculations to the fits; panel e) shows the
same for $\eta$ mesons in p–Pb collisions. In panel f) the $\eta/\pi^{0}$
ratios in pp and p–Pb collisions are compared to theory predictions. The
normalization uncertainty in the spectra ratio panels is indicated as a solid
gray box around unity.

The invariant differential cross sections and $R_{\mathrm{pPb}}$ measured by
each method are consistent within their uncertainties, as shown in Fig. 2. For
the calculation of $R_{\mathrm{pPb}}$ the spectra are shifted in the
$y$-direction, while for the cross sections they are shifted along the
$p_{\mathrm{T}}$-axis to account for the finite bin width [46]. They were
combined using the Best Linear Unbiased Estimate (BLUE) method [39, 40]
accounting for the partially correlated uncertainties. The resulting $\pi^{0}$
and $\eta$ invariant differential cross sections for p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ are shown in Fig. 3 together with
the $\pi^{0}$ cross section in pp collisions at $\sqrt{s}=8~{}\mathrm{TeV}$.
In both cases, the high $p_{\mathrm{T}}$ reach of $p_{\mathrm{T}}=200$ GeV/$c$
for the $\pi^{0}$ meson was enabled by the mEMC method, which allowed to
significantly extend the previous pp measurement beyond $35$ GeV/$c$ [27]. The
data is compared to a two-component model (TCM) fit [47], NLO calculations
[41, 42, 43], and PYTHIA 8 [33, 44] predictions using different nPDFs [9, 10,
45]. NLO calculations using the CT18 [48] PDF or nCTEQ15 [9] nPDF together
with DSS14 [41] or AESSS [42] fragmentation functions generally overestimate
the $\pi^{0}$ and $\eta$ spectra, while predicting a steeper falling spectrum
at high $p_{\mathrm{T}}$. Additional NLO calculations based on the more recent
NNFF1.0 [43] fragmentation functions are generally in good agreement with the
data but tend to underestimate the spectra at low $p_{\mathrm{T}}$. In Fig. 3
they are shown with factorization and renormalization scales varied from
$\mu=p_{\mathrm{T}}$ to $\mu=0.5p_{\mathrm{T}}$ and $2p_{\mathrm{T}}$ and
indicated by bands. PYTHIA 8 [33] calculations using EPPS16 [10] and nCTEQ15
[9] nPDFs describe the data, however without fully capturing the shape of the
$\pi^{0}$ spectra, in particular at low and intermediate $p_{\mathrm{T}}$, and
with a tendency to underestimate the $\eta$ spectra. For the $\eta/\pi^{0}$
ratio, presented in Fig. 3f, the differences in the shape and scale between
data and calculations approximately cancel. The ratio is rather well described
by the predictions and is consistent over the full $p_{\mathrm{T}}$ range
between both collision systems. For $p_{\mathrm{T}}>4$ GeV/$c$, the
$\eta/\pi^{0}$ ratio is $C^{\eta/\pi^{0}}_{\rm
pPb}=0.479\>\pm\>0.009(\mathrm{stat})\>\pm\>0.010(\mathrm{syst})$, consistent
with the previous measurement at a lower centre-of-mass energy [6] and with
$C^{\eta/\pi^{0}}_{\mathrm{pp}}=0.473\>\pm\>0.006(\mathrm{stat})\>\pm\>0.011(\mathrm{syst})$,
the reevaluated $\eta/\pi^{0}$ ratio in pp collisions at 8 TeV.

To provide the pp reference for the $R_{\mathrm{pPb}}$, the pp spectra
measured at $\sqrt{s}=8~{}\mathrm{TeV}$ were scaled to the p–Pb collision
energy and corrected for the rapidity difference, using the ratio of $\pi^{0}$
spectra generated with PYTHIA 8 Monash 2013 [44] for both kinematic regions,
leading to a 1–2% increase over the whole $p_{\mathrm{T}}$ range. The
resulting $R_{\mathrm{pPb}}$ at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$
is shown in Fig. 4a for both mesons together with theory predictions and in
Fig. 4b compared to data taken at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. In the
intermediate $p_{\mathrm{T}}$ region, the charged particle $R_{\mathrm{pPb}}$
exhibits an enhancement compared to the $\pi^{0}$ data, which is historically
attributed to the stronger Cronin effect for baryons [49, 50]. For
$p_{\mathrm{T}}>10$ GeV/$c$, no deviation from unity is observed within
uncertainties for both mesons, consistent with predictions and the ALICE
$\pi^{0}$ and h± measurements at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [6, 51], in
contrast to the moderate enhancement for charged hadrons seen by the CMS
experiment [5]. Fitting with a constant function resulted in $1.00\pm 0.01$
($0.96\pm 0.04$) with a $\chi^{2}/\mathrm{NDF}$ of 1.04 (0.45) for the
$\pi^{0}$ ($\eta$) meson. Based on the spectral slopes, the data disfavor a
more than 1% relative energy loss or an induced constant
$p_{\mathrm{T}}$-shift of more than 100 MeV from final-state effects in the
region between 10 and 20 GeV/$c$ for both mesons, consistent with the
calculations in Ref. [18].

Figure 4: a) $R_{\mathrm{pPb}}$ for $\pi^{0}$ and $\eta$ mesons in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ together with NLO
[10, 9], CGC [12] and FCEL [13] predictions. b) $R_{\mathrm{pPb}}$ for
$\pi^{0}$ at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ compared with
$\pi^{0}$ [6] and charged hadron measurements [51, 5] at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. c) Ratio of the $\pi^{0}$
$R_{\mathrm{pPb}}$ at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ to that at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV together with corresponding CGC and FCEL
model predictions. Statistical uncertainties are shown as vertical bars; the
systematic uncertainties as boxes. The overall normalization uncertainties are
indicated as solid boxes around unity and amount to 3.4% in a) and b), and to
6.2% in c).

For $p_{\mathrm{T}}<10$ GeV/$c$, a suppression of similar magnitude is
observed for both mesons within uncertainties. The suppression is described by
NLO calculations using EPPS16 [10] and nCETQ15 [9] nPDFs (the latter tends to
underpredict the data below 5 GeV/$c$), as well as by models using gluon
recombination as the CGC-based calculations [12] or parton energy loss in cold
nuclear matter in the framework of fully coherent energy loss (FCEL) [13].

The comparison of the $\pi^{0}$ $R_{\mathrm{pPb}}$ to the previous measurement
at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [6], as shown in Fig. 4c, is consistent
with unity within uncertainties, but the data hints at a stronger suppression
with increasing centre-of-mass energy. A stronger suppression could originate
from larger shadowing in the nPDFs, which due to the smaller $x$ probed at
8.16 TeV predict a ratio of about $0.98$ in the low $p_{\mathrm{T}}$ region,
or from the increasing relevance of gluon saturation, as indicated by the CGC
calculation [12]. The FCEL calculation predicts a negligible difference
between the two collision energies excluding coherent energy loss as the cause
of a stronger suppression. A constant fit for $p_{\mathrm{T}}<10$ GeV/$c$
yields a ratio of $0.93\pm 0.02_{\mathrm{tot}}\pm 0.06_{\mathrm{norm}}$, where
the normalization uncertainty is dominated by the interpolation of the
$\pi^{0}$ reference spectrum at 5.02 TeV.

##  6 Conclusion

In summary, cross sections for $\pi^{0}$ and $\eta$ mesons in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=8.16~{}\mathrm{TeV}$ were measured for
$0.4<p_{\mathrm{T}}<200$ GeV/$c$ and $1.0<p_{\mathrm{T}}<50$ GeV/$c$,
respectively, providing constraints for nuclear parton distributions and
fragmentation functions over an unprecedented kinematic range for light
mesons. By extending the reference $\pi^{0}$ measurement in pp collisions at
$\sqrt{s}=8~{}\mathrm{TeV}$ to the same $p_{\mathrm{T}}$ range using the mEMC
method, the $R_{\mathrm{pPb}}$ for $\pi^{0}$ was measured up to $200$ GeV/$c$.
The $R_{\mathrm{pPb}}$ is consistent with unity above 10 GeV/$c$, as expected
from calculations without parton energy loss, and strongly suppressed at low
$p_{\mathrm{T}}$, consistent with theory predictions that also include gluon
shadowing or saturation effects.

## Acknowledgments

We thank Werner Vogelsang for providing the pQCD calculations.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

## References

  * [1] N. Brambilla et al., “QCD and strongly coupled gauge theories: challenges and perspectives,” Eur. Phys. J. C 74 no. 10, (2014) 2981, arXiv:1404.3723 [hep-ph].
  * [2] C. Salgado et al., “Proton–nucleus collisions at the LHC: Scientific opportunities and requirements,” J. Phys. G 39 (2012) 015010, arXiv:1105.3919 [hep-ph].
  * [3] ALICE Collaboration, B. Abelev et al., “Transverse momentum dependence of inclusive primary charged-particle production in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV,” Eur. Phys. J. C 74 no. 9, (2014) 3054, arXiv:1405.2737 [nucl-ex].
  * [4] ATLAS Collaboration, G. Aad et al., “Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV p–Pb collisions measured by the ATLAS experiment,” Phys. Lett. B 763 (2016) 313–336, arXiv:1605.06436 [hep-ex].
  * [5] CMS Collaboration, V. Khachatryan et al., “Charged-particle nuclear modification factors in Pb–Pb and p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV,” JHEP 04 (2017) 039, arXiv:1611.01664 [nucl-ex].
  * [6] ALICE Collaboration, S. Acharya et al., “Neutral pion and $\eta$ meson production in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV,” Eur. Phys. J. C 78 no. 8, (2018) 624, arXiv:1801.07051 [nucl-ex].
  * [7] PHENIX Collaboration, S. Adler et al., “Absence of suppression in particle production at large transverse momentum in $\sqrt{s_{\mathrm{NN}}}=200$ GeV d–Au collisions,” Phys. Rev. Lett. 91 (2003) 072303, arXiv:nucl-ex/0306021.
  * [8] STAR Collaboration, J. Adams et al., “Evidence from d–Au measurements for final state suppression of high $p_{\mathrm{T}}$ hadrons in Au–Au collisions at RHIC,” Phys. Rev. Lett. 91 (2003) 072304, arXiv:nucl-ex/0306024.
  * [9] K. Kovarik et al., “nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework,” Phys. Rev. D 93 no. 8, (2016) 085037, arXiv:1509.00792 [hep-ph].
  * [10] K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, “EPPS16: Nuclear parton distributions with LHC data,” Eur. Phys. J. C 77 no. 3, (2017) 163, arXiv:1612.05741 [hep-ph].
  * [11] F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, “The Color Glass Condensate,” Ann. Rev. Nucl. Part. Sci. 60 (2010) 463–489, arXiv:1002.0333 [hep-ph].
  * [12] T. Lappi and H. Mäntysaari, “Single inclusive particle production at high energy from HERA data to proton–nucleus collisions,” Phys. Rev. D 88 (2013) 114020, arXiv:1309.6963 [hep-ph].
  * [13] F. Arleo, F. Cougoulic, and S. Peigné, “Fully coherent energy loss effects on light hadron production in pA collisions,” JHEP 09 (2020) 190, arXiv:2003.06337 [hep-ph].
  * [14] ALICE Collaboration, B. B. Abelev et al., “Multiparticle azimuthal correlations in p -Pb and Pb-Pb collisions at the CERN Large Hadron Collider,” Phys. Rev. C 90 no. 5, (2014) 054901, arXiv:1406.2474 [nucl-ex].
  * [15] CMS Collaboration, V. Khachatryan et al., “Evidence for Collective Multiparticle Correlations in p-Pb Collisions,” Phys. Rev. Lett. 115 no. 1, (2015) 012301, arXiv:1502.05382 [nucl-ex].
  * [16] CMS Collaboration, A. M. Sirunyan et al., “Observation of Correlated Azimuthal Anisotropy Fourier Harmonics in $pp$ and $p+Pb$ Collisions at the LHC,” Phys. Rev. Lett. 120 no. 9, (2018) 092301, arXiv:1709.09189 [nucl-ex].
  * [17] I. Vitev, “Non-Abelian energy loss in cold nuclear matter,” Phys. Rev. C 75 (2007) 064906, arXiv:hep-ph/0703002.
  * [18] A. Huss, A. Kurkela, A. Mazeliauskas, R. Paatelainen, W. van der Schee, and U. A. Wiedemann, “Predicting parton energy loss in small collision systems,” arXiv:2007.13758 [hep-ph].
  * [19] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002.
  * [20] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC,” Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [21] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking System with cosmic-ray tracks,” JINST 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].
  * [22] ALICE EMCal Collaboration, U. Abeysekara et al., “ALICE EMCal Physics Performance Report,” arXiv:1008.0413 [physics.ins-det].
  * [23] J. Allen et al., “ALICE DCal: An Addendum to the EMCal Technical Design Report Di-Jet and Hadron-Jet correlation measurements in ALICE,” CERN-LHCC-2010-011. ALICE-TDR-14-add-1. http://cds.cern.ch/record/1272952.
  * [24] ALICE Collaboration, G. Dellacasa et al., “ALICE technical design report of the photon spectrometer (PHOS),” CERN-LHCC-99-04. http://cds.cern.ch/record/381432.
  * [25] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO system,” JINST 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
  * [26] ALICE Collaboration, S. Acharya et al., “ALICE luminosity determination for p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV,” ALICE-PUBLIC-2018-002. https://cds.cern.ch/record/2314660.
  * [27] ALICE Collaboration, S. Acharya et al., “$\pi^{0}$ and $\eta$ meson production in proton–proton collisions at $\sqrt{s}=8$ TeV,” Eur. Phys. J. C 78 no. 3, (2018) 263, arXiv:1708.08745 [hep-ex].
  * [28] ALICE Collaboration, C. W. Fabjan et al., “ALICE: Physics performance report, volume II,” J. Phys. G 32 (2006) 1295–2040.
  * [29] ALICE Collaboration, S. Acharya et al., “Measurement of the inclusive isolated photon production cross section in pp collisions at $\sqrt{s}$ = 7 TeV,” Eur. Phys. J. C 79 no. 11, (2019) 896, arXiv:1906.01371 [nucl-ex].
  * [30] ALICE Collaboration, S. Acharya et al., “Calibration of the photon spectrometer PHOS of the ALICE experiment,” JINST 14 no. 05, (2019) P05025, arXiv:1902.06145 [physics.ins-det].
  * [31] ALICE Collaboration, S. Acharya et al., “Production of ${\pi^{0}}$ and $\eta$ mesons up to high transverse momentum in pp collisions at 2.76 TeV,” Eur. Phys. J. C 77 no. 5, (2017) 339, arXiv:1702.00917 [hep-ex].
  * [32] ALICE Collaboration, S. Acharya et al., “Supplemental material for “Nuclear modification factor of light neutral mesons up to high transverse momentum in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV",” CERN-EP-2021-053 (Aug, 2021) . https://cds.cern.ch/record/2759761.
  * [33] T. Sjostrand, S. Mrenna, and P. Z. Skands, “A brief introduction to PYTHIA 8.1,” Comput. Phys. Commun. 178 (2008) 852–867, arXiv:0710.3820 [hep-ph].
  * [34] S. Alioli, P. Nason, C. Oleari, and E. Re, “A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX,” JHEP 06 (2010) 043, arXiv:1002.2581 [hep-ph].
  * [35] S. Alioli, P. Nason, C. Oleari, and E. Re, “NLO vector-boson production matched with shower in POWHEG,” JHEP 07 (2008) 060, arXiv:0805.4802 [hep-ph].
  * [36] R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick, and L. Urban, “GEANT: Detector Description and Simulation Tool,” CERN-W5013. https://cds.cern.ch/record/1082634.
  * [37] S. Roesler, R. Engel, and J. Ranft, “The Monte Carlo event generator DPMJET-III,” in International Conference on Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications (MC 2000), pp. 1033–1038.  12, 2000.  arXiv:hep-ph/0012252.
  * [38] ALICE Collaboration, S. Acharya et al., “Direct photon production at low transverse momentum in proton-proton collisions at $\sqrt{s}=2.76$ and 8 TeV,” Phys. Rev. C 99 no. 2, (2019) 024912, arXiv:1803.09857 [nucl-ex].
  * [39] A. Valassi and R. Chierici, “Information and treatment of unknown correlations in the combination of measurements using the BLUE method,” Eur. Phys. J. C 74 (2014) 2717, arXiv:1307.4003 [physics.data-an].
  * [40] L. Lyons, D. Gibaut, and P. Clifford, “How to combine correlated estimates of a single physical quantity,” Nucl. Instrum. Meth. A 270 (1988) 110.
  * [41] D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto, and M. Stratmann, “Parton-to-pion fragmentation reloaded,” Phys. Rev. D91 no. 1, (2015) 014035, arXiv:1410.6027 [hep-ph].
  * [42] C. A. Aidala, F. Ellinghaus, R. Sassot, J. P. Seele, and M. Stratmann, “Global analysis of fragmentation functions for $\eta$ mesons,” Phys. Rev. D83 (2011) 034002, arXiv:1009.6145 [hep-ph].
  * [43] NNPDF Collaboration, V. Bertone, S. Carrazza, N. P. Hartland, E. R. Nocera, and J. Rojo, “A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties,” Eur. Phys. J. C 77 no. 8, (2017) 516, arXiv:1706.07049 [hep-ph].
  * [44] P. Skands, S. Carrazza, and J. Rojo, “Tuning PYTHIA 8.1: the Monash 2013 Tune,” Eur. Phys. J. C 74 no. 8, (2014) 3024, arXiv:1404.5630 [hep-ph].
  * [45] T.-J. Hou et al., “New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC,” Phys. Rev. D 103 no. 1, (2021) 014013, arXiv:1912.10053 [hep-ph].
  * [46] G. Lafferty and T. Wyatt, “Where to stick your data points: The treatment of measurements within wide bins,” Nucl. Instrum. Meth. A 355 (1995) 541–547.
  * [47] A. Bylinkin, N. S. Chernyavskaya, and A. A. Rostovtsev, “Predictions on the transverse momentum spectra for charged particle production at LHC-energies from a two component model,” Eur. Phys. J. C 75 no. 4, (2015) 166, arXiv:1501.05235 [hep-ph].
  * [48] M. Guzzi, P. Nadolsky, E. Berger, H.-L. Lai, F. Olness, and C. P. Yuan, “CT10 parton distributions and other developments in the global QCD analysis,” arXiv:1101.0561 [hep-ph].
  * [49] J. W. Cronin, H. J. Frisch, M. J. Shochet, J. P. Boymond, R. Mermod, P. A. Piroue, and R. L. Sumner, “Production of hadrons with large transverse momentum at 200, 300, and 400 GeV,” Phys. Rev. D 11 (1975) 3105–3123.
  * [50] A. H. Rezaeian and Z. Lu, “Cronin effect for protons and pions in high-energy pA collisions,” Nucl. Phys. A 826 (2009) 198–210, arXiv:0810.4942 [hep-ph].
  * [51] ALICE Collaboration, S. Acharya et al., “Transverse momentum spectra and nuclear modification factors of charged particles in pp, p–Pb and Pb–Pb collisions at the LHC,” JHEP 11 (2018) 013, arXiv:1802.09145 [nucl-ex].

##  Appendix A The ALICE Collaboration

S. Acharya142, D. Adamová97, A. Adler75, J. Adolfsson82, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed142, S. Ahmad16, S.U. Ahn77, I. Ahuja39,
Z. Akbar52, A. Akindinov94, M. Al-Turany109, S.N. Alam41, D. Aleksandrov90, B.
Alessandro60, H.M. Alfanda7, R. Alfaro Molina72, B. Ali16, Y. Ali14, A.
Alici26, N. Alizadehvandchali126, A. Alkin35, J. Alme21, T. Alt69, L.
Altenkamper21, I. Altsybeev114, M.N. Anaam7, C. Andrei49, D. Andreou92, A.
Andronic145, M. Angeletti35, V. Anguelov106, F. Antinori58, P. Antonioli55, C.
Anuj16, N. Apadula81, L. Aphecetche116, H. Appelshäuser69, S. Arcelli26, R.
Arnaldi60, I.C. Arsene20, M. Arslandok147,106, A. Augustinus35, R.
Averbeck109, S. Aziz79, M.D. Azmi16, A. Badalà57, Y.W. Baek42, X. Bai109, R.
Bailhache69, Y. Bailung51, R. Bala103, A. Balbino31, A. Baldisseri139, M.
Ball44, D. Banerjee4, R. Barbera27, L. Barioglio107,25, M. Barlou86, G.G.
Barnaföldi146, L.S. Barnby96, V. Barret136, C. Bartels129, K. Barth35, E.
Bartsch69, F. Baruffaldi28, N. Bastid136, S. Basu82, G. Batigne116, B.
Batyunya76, D. Bauri50, J.L. Bazo Alba113, I.G. Bearden91, C. Beattie147, I.
Belikov138, A.D.C. Bell Hechavarria145, F. Bellini26,35, R. Bellwied126, S.
Belokurova114, V. Belyaev95, G. Bencedi70, S. Beole25, A. Bercuci49, Y.
Berdnikov100, A. Berdnikova106, D. Berenyi146, L. Bergmann106, M.G. Besoiu68,
L. Betev35, P.P. Bhaduri142, A. Bhasin103, I.R. Bhat103, M.A. Bhat4, B.
Bhattacharjee43, P. Bhattacharya23, L. Bianchi25, N. Bianchi53, J. Bielčík38,
J. Bielčíková97, J. Biernat119, A. Bilandzic107, G. Biro146, S. Biswas4, J.T.
Blair120, D. Blau90, M.B. Blidaru109, C. Blume69, G. Boca29, F. Bock98, A.
Bogdanov95, S. Boi23, J. Bok62, L. Boldizsár146, A. Bolozdynya95, M.
Bombara39, P.M. Bond35, G. Bonomi141, H. Borel139, A. Borissov83, H. Bossi147,
E. Botta25, L. Bratrud69, P. Braun-Munzinger109, M. Bregant122, M. Broz38,
G.E. Bruno108,34, M.D. Buckland129, D. Budnikov110, H. Buesching69, S.
Bufalino31, O. Bugnon116, P. Buhler115, Z. Buthelezi73,133, J.B. Butt14, S.A.
Bysiak119, D. Caffarri92, M. Cai28,7, H. Caines147, A. Caliva109, E. Calvo
Villar113, J.M.M. Camacho121, R.S. Camacho46, P. Camerini24, F.D.M. Canedo122,
A.A. Capon115, F. Carnesecchi35,26, R. Caron139, J. Castillo Castellanos139,
E.A.R. Casula23, F. Catalano31, C. Ceballos Sanchez76, P. Chakraborty50, S.
Chandra142, S. Chapeland35, M. Chartier129, S. Chattopadhyay142, S.
Chattopadhyay111, A. Chauvin23, T.G. Chavez46, C. Cheshkov137, B. Cheynis137,
V. Chibante Barroso35, D.D. Chinellato123, S. Cho62, P. Chochula35, P.
Christakoglou92, C.H. Christensen91, P. Christiansen82, T. Chujo135, C.
Cicalo56, L. Cifarelli26, F. Cindolo55, M.R. Ciupek109, G. ClaiII,55, J.
CleymansI,125, F. Colamaria54, J.S. Colburn112, D. Colella108,54,34,146, A.
Collu81, M. Colocci35,26, M. ConcasIII,60, G. Conesa Balbastre80, Z. Conesa
del Valle79, G. Contin24, J.G. Contreras38, T.M. Cormier98, P. Cortese32, M.R.
Cosentino124, F. Costa35, S. Costanza29, P. Crochet136, E. Cuautle70, P. Cui7,
L. Cunqueiro98, A. Dainese58, F.P.A. Damas116,139, M.C. Danisch106, A. Danu68,
I. Das111, P. Das88, P. Das4, S. Das4, S. Dash50, S. De88, A. De Caro30, G. de
Cataldo54, L. De Cilladi25, J. de Cuveland40, A. De Falco23, D. De Gruttola30,
N. De Marco60, C. De Martin24, S. De Pasquale30, S. Deb51, H.F. Degenhardt122,
K.R. Deja143, L. Dello Stritto30, S. Delsanto25, W. Deng7, P. Dhankher19, D.
Di Bari34, A. Di Mauro35, R.A. Diaz8, T. Dietel125, Y. Ding137,7, R. Divià35,
D.U. Dixit19, Ø. Djuvsland21, U. Dmitrieva64, J. Do62, A. Dobrin68, B.
Dönigus69, O. Dordic20, A.K. Dubey142, A. Dubla109,92, S. Dudi102, M.
Dukhishyam88, P. Dupieux136, N. Dzalaiova13, T.M. Eder145, R.J. Ehlers98, V.N.
Eikeland21, D. Elia54, B. Erazmus116, F. Ercolessi26, F. Erhardt101, A.
Erokhin114, M.R. Ersdal21, B. Espagnon79, G. Eulisse35, D. Evans112, S.
Evdokimov93, L. Fabbietti107, M. Faggin28, J. Faivre80, F. Fan7, A. Fantoni53,
M. Fasel98, P. Fecchio31, A. Feliciello60, G. Feofilov114, A. Fernández
Téllez46, A. Ferrero139, A. Ferretti25, V.J.G. Feuillard106, J. Figiel119, S.
Filchagin110, D. Finogeev64, F.M. Fionda56,21, G. Fiorenza35,108, F. Flor126,
A.N. Flores120, S. Foertsch73, P. Foka109, S. Fokin90, E. Fragiacomo61, E.
Frajna146, U. Fuchs35, N. Funicello30, C. Furget80, A. Furs64, J.J.
Gaardhøje91, M. Gagliardi25, A.M. Gago113, A. Gal138, C.D. Galvan121, P.
Ganoti86, C. Garabatos109, J.R.A. Garcia46, E. Garcia-Solis10, K. Garg116, C.
Gargiulo35, A. Garibli89, K. Garner145, P. Gasik109, E.F. Gauger120, A.
Gautam128, M.B. Gay Ducati71, M. Germain116, J. Ghosh111, P. Ghosh142, S.K.
Ghosh4, M. Giacalone26, P. Gianotti53, P. Giubellino109,60, P. Giubilato28,
A.M.C. Glaenzer139, P. Glässel106, V. Gonzalez144, L.H. González-Trueba72, S.
Gorbunov40, L. Görlich119, S. Gotovac36, V. Grabski72, L.K. Graczykowski143,
L. Greiner81, A. Grelli63, C. Grigoras35, V. Grigoriev95, A. GrigoryanI,1, S.
Grigoryan76,1, O.S. Groettvik21, F. Grosa35,60, J.F. Grosse-Oetringhaus35, R.
Grosso109, G.G. Guardiano123, R. Guernane80, M. Guilbaud116, M. Guittiere116,
K. Gulbrandsen91, T. Gunji134, A. Gupta103, R. Gupta103, I.B. Guzman46, S.P.
Guzman46, L. Gyulai146, M.K. Habib109, C. Hadjidakis79, H. Hamagaki84, G.
Hamar146, M. Hamid7, R. Hannigan120, M.R. Haque143,88, A. Harlenderova109,
J.W. Harris147, A. Harton10, J.A. Hasenbichler35, H. Hassan98, D.
Hatzifotiadou55, P. Hauer44, L.B. Havener147, S. Hayashi134, S.T. Heckel107,
E. Hellbär69, H. Helstrup37, T. Herman38, E.G. Hernandez46, G. Herrera
Corral9, F. Herrmann145, K.F. Hetland37, H. Hillemanns35, C. Hills129, B.
Hippolyte138, B. Hofman63, B. Hohlweger92,107, J. Honermann145, G.H. Hong148,
D. Horak38, S. Hornung109, R. Hosokawa15, P. Hristov35, C. Huang79, C.
Hughes132, P. Huhn69, T.J. Humanic99, H. Hushnud111, L.A. Husova145, N.
Hussain43, D. Hutter40, J.P. Iddon35,129, R. Ilkaev110, H. Ilyas14, M.
Inaba135, G.M. Innocenti35, M. Ippolitov90, A. Isakov38,97, M.S. Islam111, M.
Ivanov109, V. Ivanov100, V. Izucheev93, B. Jacak81, N. Jacazio35, P.M.
Jacobs81, S. Jadlovska118, J. Jadlovsky118, S. Jaelani63, C. Jahnke123,122,
M.J. Jakubowska143, M.A. Janik143, T. Janson75, M. Jercic101, O. Jevons112, F.
Jonas98,145, P.G. Jones112, J.M. Jowett 35,109, J. Jung69, M. Jung69, A.
Junique35, A. Jusko112, J. Kaewjai117, P. Kalinak65, A. Kalweit35, V.
Kaplin95, S. Kar7, A. Karasu Uysal78, D. Karatovic101, O. Karavichev64, T.
Karavicheva64, P. Karczmarczyk143, E. Karpechev64, A. Kazantsev90, U.
Kebschull75, R. Keidel48, D.L.D. Keijdener63, M. Keil35, B. Ketzer44, Z.
Khabanova92, A.M. Khan7, S. Khan16, A. Khanzadeev100, Y. Kharlov93, A.
Khatun16, A. Khuntia119, B. Kileng37, B. Kim17,62, D. Kim148, D.J. Kim127,
E.J. Kim74, J. Kim148, J.S. Kim42, J. Kim106, J. Kim148, J. Kim74, M. Kim106,
S. Kim18, T. Kim148, S. Kirsch69, I. Kisel40, S. Kiselev94, A. Kisiel143, J.L.
Klay6, J. Klein35, S. Klein81, C. Klein-Bösing145, M. Kleiner69, T.
Klemenz107, A. Kluge35, A.G. Knospe126, C. Kobdaj117, M.K. Köhler106, T.
Kollegger109, A. Kondratyev76, N. Kondratyeva95, E. Kondratyuk93, J. Konig69,
S.A. Konigstorfer107, P.J. Konopka35,2, G. Kornakov143, S.D. Koryciak2, L.
Koska118, A. Kotliarov97, O. Kovalenko87, V. Kovalenko114, M. Kowalski119, I.
Králik65, A. Kravčáková39, L. Kreis109, M. Krivda112,65, F. Krizek97, K.
Krizkova Gajdosova38, M. Kroesen106, M. Krüger69, E. Kryshen100, M.
Krzewicki40, V. Kučera35, C. Kuhn138, P.G. Kuijer92, T. Kumaoka135, D.
Kumar142, L. Kumar102, N. Kumar102, S. Kundu35,88, P. Kurashvili87, A.
Kurepin64, A.B. Kurepin64, A. Kuryakin110, S. Kushpil97, J. Kvapil112, M.J.
Kweon62, J.Y. Kwon62, Y. Kwon148, S.L. La Pointe40, P. La Rocca27, Y.S. Lai81,
A. Lakrathok117, M. Lamanna35, R. Langoy131, K. Lapidus35, P. Larionov53, E.
Laudi35, L. Lautner35,107, R. Lavicka38, T. Lazareva114, R. Lea141,24, J.
Lee135, J. Lehrbach40, R.C. Lemmon96, I. León Monzón121, E.D. Lesser19, M.
Lettrich35,107, P. Lévai146, X. Li11, X.L. Li7, J. Lien131, R. Lietava112, B.
Lim17, S.H. Lim17, V. Lindenstruth40, A. Lindner49, C. Lippmann109, A. Liu19,
J. Liu129, I.M. Lofnes21, V. Loginov95, C. Loizides98, P. Loncar36, J.A.
Lopez106, X. Lopez136, E. López Torres8, J.R. Luhder145, M. Lunardon28, G.
Luparello61, Y.G. Ma41, A. Maevskaya64, M. Mager35, T. Mahmoud44, A. Maire138,
M. Malaev100, Q.W. Malik20, L. MalininaIV,76, D. Mal’Kevich94, N. Mallick51,
P. Malzacher109, G. Mandaglio33,57, V. Manko90, F. Manso136, V. Manzari54, Y.
Mao7, J. Mareš67, G.V. Margagliotti24, A. Margotti55, A. Marín109, C.
Markert120, M. Marquard69, N.A. Martin106, P. Martinengo35, J.L. Martinez126,
M.I. Martínez46, G. Martínez García116, S. Masciocchi109, M. Masera25, A.
Masoni56, L. Massacrier79, A. Mastroserio140,54, A.M. Mathis107, O.
Matonoha82, P.F.T. Matuoka122, A. Matyja119, C. Mayer119, A.L. Mazuecos35, F.
Mazzaschi25, M. Mazzilli35,54, M.A. Mazzoni59, J.E. Mdhluli133, A.F.
Mechler69, F. Meddi22, Y. Melikyan64, A. Menchaca-Rocha72, E. Meninno115,30,
A.S. Menon126, M. Meres13, S. Mhlanga125,73, Y. Miake135, L. Micheletti25,
L.C. Migliorin137, D.L. Mihaylov107, K. Mikhaylov76,94, A.N. Mishra146, D.
Miśkowiec109, A. Modak4, A.P. Mohanty63, B. Mohanty88, M. Mohisin Khan16, Z.
Moravcova91, C. Mordasini107, D.A. Moreira De Godoy145, L.A.P. Moreno46, I.
Morozov64, A. Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D.
Mühlheim145, S. Muhuri142, J.D. Mulligan81, A. Mulliri23, M.G. Munhoz122, R.H.
Munzer69, H. Murakami134, S. Murray125, L. Musa35, J. Musinsky65, C.J.
Myers126, J.W. Myrcha143, B. Naik50, R. Nair87, B.K. Nandi50, R. Nania55, E.
Nappi54, M.U. Naru14, A.F. Nassirpour82, A. Nath106, C. Nattrass132, A.
Neagu20, L. Nellen70, S.V. Nesbo37, G. Neskovic40, D. Nesterov114, B.S.
Nielsen91, S. Nikolaev90, S. Nikulin90, V. Nikulin100, F. Noferini55, S.
Noh12, P. Nomokonov76, J. Norman129, N. Novitzky135, P. Nowakowski143, A.
Nyanin90, J. Nystrand21, M. Ogino84, A. Ohlson82, V.A. Okorokov95, J.
Oleniacz143, A.C. Oliveira Da Silva132, M.H. Oliver147, A. Onnerstad127, C.
Oppedisano60, A. Ortiz Velasquez70, T. Osako47, A. Oskarsson82, J.
Otwinowski119, K. Oyama84, Y. Pachmayer106, S. Padhan50, D. Pagano141, G.
Paić70, A. Palasciano54, J. Pan144, S. Panebianco139, P. Pareek142, J. Park62,
J.E. Parkkila127, S.P. Pathak126, R.N. Patra103,35, B. Paul23, J. Pazzini141,
H. Pei7, T. Peitzmann63, X. Peng7, L.G. Pereira71, H. Pereira Da Costa139, D.
Peresunko90, G.M. Perez8, S. Perrin139, Y. Pestov5, V. Petráček38, M.
Petrovici49, R.P. Pezzi71, S. Piano61, M. Pikna13, P. Pillot116, O.
Pinazza55,35, L. Pinsky126, C. Pinto27, S. Pisano53, M. Płoskoń81, M.
Planinic101, F. Pliquett69, M.G. Poghosyan98, B. Polichtchouk93, S.
Politano31, N. Poljak101, A. Pop49, S. Porteboeuf-Houssais136, J. Porter81, V.
Pozdniakov76, S.K. Prasad4, R. Preghenella55, F. Prino60, C.A. Pruneau144, I.
Pshenichnov64, M. Puccio35, S. Qiu92, L. Quaglia25, R.E. Quishpe126, S.
Ragoni112, A. Rakotozafindrabe139, L. Ramello32, F. Rami138, S.A.R. Ramirez46,
A.G.T. Ramos34, R. Raniwala104, S. Raniwala104, S.S. Räsänen45, R. Rath51, I.
Ravasenga92, K.F. Read98,132, A.R. Redelbach40, K. RedlichV,87, A. Rehman21,
P. Reichelt69, F. Reidt35, H.A. Reme-ness37, R. Renfordt69, Z. Rescakova39, K.
Reygers106, A. Riabov100, V. Riabov100, T. Richert82,91, M. Richter20, W.
Riegler35, F. Riggi27, C. Ristea68, S.P. Rode51, M. Rodríguez Cahuantzi46, K.
Røed20, R. Rogalev93, E. Rogochaya76, T.S. Rogoschinski69, D. Rohr35, D.
Röhrich21, P.F. Rojas46, P.S. Rokita143, F. Ronchetti53, A. Rosano33,57, E.D.
Rosas70, A. Rossi58, A. Rotondi29, A. Roy51, P. Roy111, S. Roy50, N. Rubini26,
O.V. Rueda82, R. Rui24, B. Rumyantsev76, A. Rustamov89, E. Ryabinkin90, Y.
Ryabov100, A. Rybicki119, H. Rytkonen127, W. Rzesa143, O.A.M. Saarimaki45, R.
Sadek116, S. Sadovsky93, J. Saetre21, K. Šafařík38, S.K. Saha142, S. Saha88,
B. Sahoo50, P. Sahoo50, R. Sahoo51, S. Sahoo66, D. Sahu51, P.K. Sahu66, J.
Saini142, S. Sakai135, S. Sambyal103, V. SamsonovI,100,95, D. Sarkar144, N.
Sarkar142, P. Sarma43, V.M. Sarti107, M.H.P. Sas147, J. Schambach98,120, H.S.
Scheid69, C. Schiaua49, R. Schicker106, A. Schmah106, C. Schmidt109, H.R.
Schmidt105, M.O. Schmidt106, M. Schmidt105, N.V. Schmidt98,69, A.R.
Schmier132, R. Schotter138, J. Schukraft35, Y. Schutz138, K. Schwarz109, K.
Schweda109, G. Scioli26, E. Scomparin60, J.E. Seger15, Y. Sekiguchi134, D.
Sekihata134, I. Selyuzhenkov109,95, S. Senyukov138, J.J. Seo62, D.
Serebryakov64, L. Šerkšnytė107, A. Sevcenco68, T.J. Shaba73, A. Shabanov64, A.
Shabetai116, R. Shahoyan35, W. Shaikh111, A. Shangaraev93, A. Sharma102, H.
Sharma119, M. Sharma103, N. Sharma102, S. Sharma103, O. Sheibani126, K.
Shigaki47, M. Shimomura85, S. Shirinkin94, Q. Shou41, Y. Sibiriak90, S.
Siddhanta56, T. Siemiarczuk87, T.F. Silva122, D. Silvermyr82, G. Simonetti35,
B. Singh107, R. Singh88, R. Singh103, R. Singh51, V.K. Singh142, V.
Singhal142, T. Sinha111, B. Sitar13, M. Sitta32, T.B. Skaali20, G.
Skorodumovs106, M. Slupecki45, N. Smirnov147, R.J.M. Snellings63, C.
Soncco113, J. Song126, A. Songmoolnak117, F. Soramel28, S. Sorensen132, I.
Sputowska119, J. Stachel106, I. Stan68, P.J. Steffanic132, S.F.
Stiefelmaier106, D. Stocco116, I. Storehaug20, M.M. Storetvedt37, C.P.
Stylianidis92, A.A.P. Suaide122, T. Sugitate47, C. Suire79, M. Suljic35, R.
Sultanov94, M. Šumbera97, V. Sumberia103, S. Sumowidagdo52, S. Swain66, A.
Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi107, G. Taillepied136, J.
Takahashi123, G.J. Tambave21, S. Tang136,7, Z. Tang130, M. Tarhini116, M.G.
Tarzila49, A. Tauro35, G. Tejeda Muñoz46, A. Telesca35, L. Terlizzi25, C.
Terrevoli126, G. Tersimonov3, S. Thakur142, D. Thomas120, R. Tieulent137, A.
Tikhonov64, A.R. Timmins126, M. Tkacik118, A. Toia69, N. Topilskaya64, M.
Toppi53, F. Torales-Acosta19, S.R. Torres38, A. Trifiró33,57, S.
Tripathy55,70, T. Tripathy50, S. Trogolo35,28, G. Trombetta34, V. Trubnikov3,
W.H. Trzaska127, T.P. Trzcinski143, B.A. Trzeciak38, A. Tumkin110, R.
Turrisi58, T.S. Tveter20, K. Ullaland21, A. Uras137, M. Urioni141, G.L.
Usai23, M. Vala39, N. Valle29, S. Vallero60, N. van der Kolk63, L.V.R. van
Doremalen63, M. van Leeuwen92, P. Vande Vyvre35, D. Varga146, Z. Varga146, M.
Varga-Kofarago146, A. Vargas46, M. Vasileiou86, A. Vasiliev90, O. Vázquez
Doce107, V. Vechernin114, E. Vercellin25, S. Vergara Limón46, L. Vermunt63, R.
Vértesi146, M. Verweij63, L. Vickovic36, Z. Vilakazi133, O. Villalobos
Baillie112, G. Vino54, A. Vinogradov90, T. Virgili30, V. Vislavicius91, A.
Vodopyanov76, B. Volkel35, M.A. Völkl106, K. Voloshin94, S.A. Voloshin144, G.
Volpe34, B. von Haller35, I. Vorobyev107, D. Voscek118, J. Vrláková39, B.
Wagner21, C. Wang41, D. Wang41, M. Weber115, A. Wegrzynek35, S.C. Wenzel35,
J.P. Wessels145, J. Wiechula69, J. Wikne20, G. Wilk87, J. Wilkinson109, G.A.
Willems145, E. Willsher112, B. Windelband106, M. Winn139, W.E. Witt132, J.R.
Wright120, W. Wu41, Y. Wu130, R. Xu7, S. Yalcin78, Y. Yamaguchi47, K.
Yamakawa47, S. Yang21, S. Yano47,139, Z. Yin7, H. Yokoyama63, I.-K. Yoo17,
J.H. Yoon62, S. Yuan21, A. Yuncu106, V. Zaccolo24, A. Zaman14, C. Zampolli35,
H.J.C. Zanoli63, N. Zardoshti35, A. Zarochentsev114, P. Závada67, N.
Zaviyalov110, H. Zbroszczyk143, M. Zhalov100, S. Zhang41, X. Zhang7, Y.
Zhang130, V. Zherebchevskii114, Y. Zhi11, D. Zhou7, Y. Zhou91, J. Zhu7,109, A.
Zichichi26, G. Zinovjev3, N. Zurlo141

Affiliation Notes

I Deceased

II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy

III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy

IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

2 AGH University of Science and Technology, Cracow, Poland

3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

5 Budker Institute for Nuclear Physics, Novosibirsk, Russia

6 California Polytechnic State University, San Luis Obispo, California, United
States

7 Central China Normal University, Wuhan, China

8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico

10 Chicago State University, Chicago, Illinois, United States

11 China Institute of Atomic Energy, Beijing, China

12 Chungbuk National University, Cheongju, Republic of Korea

13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

14 COMSATS University Islamabad, Islamabad, Pakistan

15 Creighton University, Omaha, Nebraska, United States

16 Department of Physics, Aligarh Muslim University, Aligarh, India

17 Department of Physics, Pusan National University, Pusan, Republic of Korea

18 Department of Physics, Sejong University, Seoul, Republic of Korea

19 Department of Physics, University of California, Berkeley, California,
United States

20 Department of Physics, University of Oslo, Oslo, Norway

21 Department of Physics and Technology, University of Bergen, Bergen, Norway

22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

29 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia,
Italy

30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

34 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

35 European Organization for Nuclear Research (CERN), Geneva, Switzerland

36 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

37 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

38 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

39 Faculty of Science, P.J. Šafárik University, Košice, Slovakia

40 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

41 Fudan University, Shanghai, China

42 Gangneung-Wonju National University, Gangneung, Republic of Korea

43 Gauhati University, Department of Physics, Guwahati, India

44 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

45 Helsinki Institute of Physics (HIP), Helsinki, Finland

46 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

47 Hiroshima University, Hiroshima, Japan

48 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

49 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

50 Indian Institute of Technology Bombay (IIT), Mumbai, India

51 Indian Institute of Technology Indore, Indore, India

52 Indonesian Institute of Sciences, Jakarta, Indonesia

53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

54 INFN, Sezione di Bari, Bari, Italy

55 INFN, Sezione di Bologna, Bologna, Italy

56 INFN, Sezione di Cagliari, Cagliari, Italy

57 INFN, Sezione di Catania, Catania, Italy

58 INFN, Sezione di Padova, Padova, Italy

59 INFN, Sezione di Roma, Rome, Italy

60 INFN, Sezione di Torino, Turin, Italy

61 INFN, Sezione di Trieste, Trieste, Italy

62 Inha University, Incheon, Republic of Korea

63 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands

64 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

65 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

66 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

67 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

68 Institute of Space Science (ISS), Bucharest, Romania

69 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

70 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

71 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

72 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico

73 iThemba LABS, National Research Foundation, Somerset West, South Africa

74 Jeonbuk National University, Jeonju, Republic of Korea

75 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

76 Joint Institute for Nuclear Research (JINR), Dubna, Russia

77 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea

78 KTO Karatay University, Konya, Turkey

79 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

80 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France

81 Lawrence Berkeley National Laboratory, Berkeley, California, United States

82 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden

83 Moscow Institute for Physics and Technology, Moscow, Russia

84 Nagasaki Institute of Applied Science, Nagasaki, Japan

85 Nara Women’s University (NWU), Nara, Japan

86 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

87 National Centre for Nuclear Research, Warsaw, Poland

88 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India

89 National Nuclear Research Center, Baku, Azerbaijan

90 National Research Centre Kurchatov Institute, Moscow, Russia

91 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

92 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

93 NRC Kurchatov Institute IHEP, Protvino, Russia

94 NRC «Kurchatov»Institute - ITEP, Moscow, Russia

95 NRNU Moscow Engineering Physics Institute, Moscow, Russia

96 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

97 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

98 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

99 Ohio State University, Columbus, Ohio, United States

100 Petersburg Nuclear Physics Institute, Gatchina, Russia

101 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

102 Physics Department, Panjab University, Chandigarh, India

103 Physics Department, University of Jammu, Jammu, India

104 Physics Department, University of Rajasthan, Jaipur, India

105 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

106 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

107 Physik Department, Technische Universität München, Munich, Germany

108 Politecnico di Bari and Sezione INFN, Bari, Italy

109 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany

110 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

111 Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

112 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

113 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru

114 St. Petersburg State University, St. Petersburg, Russia

115 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

116 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France

117 Suranaree University of Technology, Nakhon Ratchasima, Thailand

118 Technical University of Košice, Košice, Slovakia

119 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland

120 The University of Texas at Austin, Austin, Texas, United States

121 Universidad Autónoma de Sinaloa, Culiacán, Mexico

122 Universidade de São Paulo (USP), São Paulo, Brazil

123 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

124 Universidade Federal do ABC, Santo Andre, Brazil

125 University of Cape Town, Cape Town, South Africa

126 University of Houston, Houston, Texas, United States

127 University of Jyväskylä, Jyväskylä, Finland

128 University of Kansas, Lawrence, Kansas, United States

129 University of Liverpool, Liverpool, United Kingdom

130 University of Science and Technology of China, Hefei, China

131 University of South-Eastern Norway, Tonsberg, Norway

132 University of Tennessee, Knoxville, Tennessee, United States

133 University of the Witwatersrand, Johannesburg, South Africa

134 University of Tokyo, Tokyo, Japan

135 University of Tsukuba, Tsukuba, Japan

136 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

137 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon
, Lyon, France

138 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France

139 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France

140 Università degli Studi di Foggia, Foggia, Italy

141 Università di Brescia, Brescia, Italy

142 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India

143 Warsaw University of Technology, Warsaw, Poland

144 Wayne State University, Detroit, Michigan, United States

145 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

146 Wigner Research Centre for Physics, Budapest, Hungary

147 Yale University, New Haven, Connecticut, United States

148 Yonsei University, Seoul, Republic of Korea


# Accessing United States Bulk Patent Data with patentpy and patentr

James Yu  BS
School of Medicine
Case Western Reserve University  Hayley Beltz, MS
Department of Astronomy
University of Michigan
Milind Y. Desai  MD  MBA
Department of Cardiovascular Medicine
Heart  Vascular & Thoracic Institute
Cleveland Clinic
Péter Érdi  PhD  DSc
Department of Physics
Center for Complex Systems Studies
Kalamazoo College
Jacob G. Scott, MD, DPhil
Translational Hematology & Oncology Research
Lerner Research Institute
Cleveland Clinic
Raoul R. Wadhwa, BA
Cleveland Clinic Lerner College of Medicine
Case Western Reserve University

###### Abstract

The United States Patent and Trademark Office (USPTO) provides publicly
accessible bulk data files containing information for all patents from 1976
onward. However, the format of these files changes over time and is memory-
inefficient, which can pose issues for individual researchers. Here, we
introduce the patentpy and patentr packages for the Python and R programming
languages. They allow users to programmatically fetch bulk data from the USPTO
website and access it locally in a cleaned, rectangular format. Research
depending on United States patent data would benefit from the use of patentpy
and patentr. We describe package implementation, quality control mechanisms,
and present use cases highlighting simple, yet effective, applications of this
software.

_Keywords_ patent $\cdot$ USPTO $\cdot$ Python $\cdot$ R $\cdot$ bulk data

## Introduction

The United States Patent and Trademark Office (USPTO) hosts bulk data files
for all patents published since 1976. This data holds interesting insights
into a large number of fields but is unfortunately difficult to access on
large scales. Files for each week can be hundreds of megabytes in size;
additionally, files from different years are sometimes formatted distinctly.
As a result of these challenges, potential users face a high barrier to entry
prior to taking advantage of the available data. The patentpy and patentr
packages simplify accessing USPTO data by providing programmatic interfaces
that return it in a single rectangular, tidy [1] format and significantly
reduce its storage size.

The patentpy package provides a Python interface with the functionality
implemented using a combination of Python and C++. The patentr package does
the same with an R interface. Since the two packages share functionality, they
also share a C++ code base, with each depending on existing XML libraries in
the respective language. Of note, Python and R both boast portability across
multiple operating systems, making the corresponding packages easily available
to a large number of users.

Currently, the most authoritative reference for patent analytics is the World
Intellectual Property Organization (WIPO) Manual. [2] According to the WIPO
Manual, multiple databases host patent data for exploration. These include The
Lens, Patentscope, espacenet, LATIPAT, EPO Open Patent Services, and Google
Patents, among others. Most of these web services provide user-friendly,
graphical point-and-click interfaces. While initially easier to use, the time
and effort scales proportionately to the number and complexity of searches
conducted. Thus, these services become cumbersome when attempting to access
large amount of patent data spanning over many years. In contrast, a
programmatic interface would require a higher initial investment, but
iteration would save significant additional effort for additional searches.
This is the specific niche that patentpy and patentr address.

To demonstrate the utility of these packages, we will collect an arbitrarily
selected set of patent data and conduct a preliminary analysis to answer four
research questions: (1) how many patents are issued weekly; (2) which IPC
classes grow fastest; (3) which IPC classes take longest to issue after
application submission; and (4) whether the time between application and
issuance changes over time. We hope these examples highlight that these
packages can be effectively combined with available software packages to
rapidly answer questions of interest. For the arbitrary dataset, we will
pretend that the first 8 weeks of a year have special significance, and that
we would like to focus our attention on these weeks for the first 5 years of
available patent data. Collecting this data takes a single line of code for
both packages using get_bulk_patent_data.

First, let us ask how many patents were issued weekly in the first 8 weeks of
each year. We process the data by extracting the year from each patent’s issue
date, aggregating and counting the number of patents issued each week, and
feeding the resulting data to a visualization library. A boxplot of the weekly
aggregated patent issue counts split by year results in Figure 1. We see that
roughly 1100-1400 patents were consistently granted in the first 8 weeks of
the year between 1976 and 1980, inclusive.

Figure 1: Distributions of number of patents issued weekly for the first 8
weeks between 1976 and 1980, inclusive.

Second, let us ask which classes of patents are growing the fastest. The USPTO
includes classifications based on the hierarchical International Patent
Classification (IPC) system. The USPTO reports the International Patent
Classification (IPC); this WIPO system hierarchically classifies patents
according to their relevant scientific discipline and is updated annually.
[37] From our dataset of patents from the first 8 weeks of each of 5 years, we
count the most commonly appearing classes and visualize the 10 most frequent
results in Figure 2. The C class corresponds to “Chemistry; Metallurgy”,
within which C07 corresponds to “Organic Chemistry”, within which C07D
corresponds to “Heterocyclic Compounds”; C07C corresponds to “Acyclic or
Carbocyclic Compounds”. Thus, the two fastest growing IPC classes in our
dataset were both related to the field of organic chemistry.

Third, we can continue our exploration of the IPC classes by asking whether
patents in different classes undergo reviews of different durations prior to
issuance. After a patent application is submitted, it must first be manually
approved and classified before being granted. We denote this time between
submission and issuance as the lag time. For the sake of simplicity, we filter
out patents that do not belong to one of the 10 classes shown in Figure 2. We
calculate the lag time between application and issuance, then visualize the
results as boxplots analogous to Figure 1. These results are shown in Figure
3. The lag time distribution for each of the 10 IPC classes is skewed right
with a median duration under 2 years.

Fourth, we can ask whether the lag time distribution changes across years. To
answer this question, we calculate the lag time between application and
issuance - this time without filtering out any patents from our collected
database - and visualize the results as boxplots (Figure 4). Here again, we
note that the distributions are skewed right with medians under 2 years.
However, we also note that the boxplot for 1980 is slightly shifted upward.
Following this forward may reveal a trend of increasing lag time as years
progress. Pursuing this research question remains an open question for
interested readers.

Figure 2: Number of patents issued in each International Patent Classification
(IPC) class. Only counts for the 10 most frequent classes are visualized. Only
patents issued in the first 8 weeks of the years between 1976 and 1980,
inclusive, are included.

## Implementation and architecture

The patentpy package was implemented in Python 3 and uses pybind11 to
incorporate C++. [3] The C++ code parses USPTO files with the TXT extension
and the lxml library parses USPTO XML files. [4] The data frame structure
provided by the pandas library encapsulates rectangular data returned to the
user. [5] The patentr package was implemented in R 4 and uses Rcpp to
incorporate C++. [6] The C++ code parses USPTO files with the TXT extension
and the xml2 libary parses USPTO XML files. [7] Tibbles form the core data
structure for patentr to store and return rectangular data to the user. Tibble
functionality depends on the tidyverse set of R packages. [8]

Both packages extract the same data for each patent and format it the same
way. Specifically, both return a rectangular data object with columns
representing a unique patent identifier (WKU), title, application date, issue
date, inventor(s), assignee(s), IPC class(es), reference(s), and claim(s).
Additionally, multiple values in the same column (e.g. multiple references),
are delimited by semi-colons in both programs, except for claims about the
patent’s novelty made by the preparer, for which text formatting is preserved.
Thus, when returned data from each package is saved as a comma-separated
values (CSV) file, outputs from both packages should be roughly equivalent.

The main entry point of the programmatic interface for each package is the
get_bulk_patent_data function, which downloads, parses, formats, and returns
USPTO bulk patent data based on the USPTO Green, Yellow, and Red books. [9]
Due to the portability of Python and R, both packages are available across
multiple operating systems and architectures. [10, 11]

Figure 3: Distributions for time between patent application date and issue
date, grouped by IPC class. Only patents issued in the first 8 weeks of the
years between 1976 and 1980, inclusive, were included.

## Quality control

Automated unit testing is implemented for patentpy, supported by Travis CI
continuous integration. Package functionality has been checked on the Windows,
Mac, Ubuntu, and Debian operating systems. Runtime errors are caught and
returned with appropriate error messages based on error type. Codecov
implements code coverage. Users can manually confirm package functionality by
locally running sample code provided in the README file or by downloading and
locally running test scripts, both of which are provided in patentpy’s code
repository.

Automated unit testing is implemented for patentr, supported by Travis CI and
AppVeyor CI continuous integration. Package functionality has been checked on
the Windows, Mac, Ubuntu, and Debian operating systems with regular checking
also completed by the Comprehensive R Archive Network (CRAN). Codecov
implements code coverage. The package is automatically checked with unit tests
upon installation from CRAN. Users can manually confirm package functionality
by locally running sample code provided in package documentation and the
repository README file or by locally running unit tests using the testthat
package. [18]

## Availability and dependencies

patentpy is available in the Python programming language (version $\geq 3.5$)
via the Python Package Index (PyPI) and patentr is available in the R
programming language (version $\geq 4.0$ via the Comprehensive R Archive
Network (CRAN); the source code of each package is publicly available at
https://github.com/JYProjs/patentpy and https://github.com/JYProjs/patentr,
respectively. patentpy depends on pandas (version $\geq 1.2$) and lxml
(version $\geq 4.6$). [4, 5] patentr depends on covr (version $\geq 3.5.1$),
dplyr (version $\geq 1.0.2$), knitr (version $\geq 1.33$), lubridate (version
$\geq 1.7.9$), magrittr (version $\geq 2.0$), progress (version $\geq 1.2.2$),
Rcpp (version $\geq 1.0.5$), readr (version $\geq 1.4.0$), rlang (version
$\geq 0.4.7$), rmarkdown (version $\geq 2.9$), testthat (version $\geq
3.0.4$), utils (version $\geq 4.0$), and xml2 (version $\geq 1.3.2$). [12, 8,
13, 14, 15, 6, 16, 17, 7]

## Reuse potential

Given the large amount of rich data available for patents and the significant
financial value that patents can hold, multiple research avenues have already
been pursued with tools analogous to patentpy and patentr. However, with their
introduction to the research literature, each individual project should no
longer require writing an entire base of code, saving time and resources. The
explored avenues of research range from studying international patent families
[19] and the network structure of patent citations [20] of to patent
protection for new forms of technology [21, 22, 23, 24] and management of
patent portfolios. [25, 26] Although USPTO bulk data files are identified by
patent publication date, the patentpy and patentr packages could be used for
data collection in any of the aforementioned research avenues.

Within the field of scientometrics, further analysis of co-citation networks
would be useful in the sub-field of bibliometrics. Studying innovation within
specific scientific fields over time and identifying crucial patents to the
development of new technologies would also be useful. In particular,
identifying prominent patent suites and oligopolies of corporate patent
assignees within scientific fields could result in illuminating research at
the intersection of scientometrics and economics. Outside of academia,
scientists in industry could use patent data to study innovation and guide
research development efforts based on evidence-based predictions. The
potential aforementioned pathways would all benefit from the use of either
patentpy or patentr for data collection purposes.

The presented packages are well complemented by available software for network
analysis, topological data analysis, and machine learning. As previously
mentioned, patent data can be structured as a citation network or a co-
citation network. These structures can then be analyzed with the existing
foundation of network and graph theory to gain insight into the evolution of
the patent network over time and the change in dynamic metrics on the patent
network. The igraph package implements this functionality and would work well
with patentpy and patentr in a single pipeline. [27] Topological data analysis
is a growing field, with an increasing number of applications of the Mapper
algorithm [33] and persistent homology [34] appearing in the scientific
literature. Analyzing the topology of patent networks could be completed well
with packages like scikit-tda in Python and TDAstats in R. [28, 29]

Machine learning pipelines have the ability to incorporate network analytics
and topological features; even without these, machine learning has high
potential use with patent data. Supervised learning and natural language
processing can be combined to automate classification of patents based on
title, references, and claim text. Reinforcement learning can be combined with
ranking algorithms to measure the importance of a patent over time. [35, 36]
Even unsupervised learning can be applied to find patent clusters across IPC
classes and identify potential relationships between otherwise unrelated
patents. The scikit-learn package in Python and the caret and tidymodels
packages in R would be candidate packages to perform such analyses on data
acquired via the packages introduced in this report. [30, 31, 32] Useful
extensions and improvements to patentpy and patentr would include the addition
of a shared interface to coordinate pipelines across the aforementioned
packages, depending on the technique used to answer a research question.

Contributions to patentpy and patentr are welcome and can be made via the code
repository for each package. Contributors can open pull requests to
incorporate additions or changes. Issues can also be opened to make feature
requests and identify bugs. The authors of this report bear responsibility for
maintaining patentpy and patentr, and we welcome community involvement.
Support mechanisms include continuous integration with the Travis and AppVeyor
tools to validate package function over time, particularly as the programming
languages and software dependencies evolve.

Figure 4: Distributions for time between patent application date and issue
date, grouped by issue year. Only patents issued in the first 8 weeks of the
years between 1976 and 1980, inclusive, were included.

## Acknowledgements

This project was supported by the NIH R37 grant CA244613. The authors declare
that they have no competing interests.

## References

  * [1] Wickham, H 2014 Tidy Data. Journal of Statistical Software 59(10): 1-23. DOI: https://doi.org/10.18637/jss.v059.i10.
  * [2] Oldham, P, Kitsara I 2016 The WIPO Manual on Open Source Patent Analytics. https://wipo-analytics.github.io.
  * [3] Jakob, W, Rhinelander, J, Moldovan, D 2017 pybind11 - Seamless Operability Between C++ and Python. https://github.com/pybind/pybind11.
  * [4] Behnel, S, Faassen, M, Bicking, I 2005 lxml: XML and HTML with Python. https://github.com/lxml/lxml.
  * [5] McKinney, W 2010 Data structures for statistical computing in python. Proceedings of the 9th Python in Science Conference 445: 51. DOI:
https://doi.org/10.25080/Majora-92bf1922-00a.

  * [6] Eddelbuettel, D, François, R 2011 Rcpp: Seamless R and C++ Integration. Journal of Statistical Software 40(8): 1. DOI: https://doi.org/10.18637/jss.v040.i08.
  * [7] Wickham, H, Hester, J, Ooms, J 2020 xml2: Parse XML. Comprehensive R Archive Network. https://CRAN.R-project.org/package=xml2.
  * [8] Wickham, H, Averick, M, Bryan, J, et al 2019 Welcome to the tidyverse. Journal of Open Source Software 4(43): 1686. DOI: https://doi.org/10.21105/joss.01686.
  * [9] XML Resources | USPTO 2021 https://www.uspto.gov/learning-and-resources/xml-resources.
  * [10] Python Core Team 2015 Python: A Dynamic, Open Source Programming Language. Python Software Foundation https://www.python.org.
  * [11] R Core Team 2014 R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing http://www.R-project.org.
  * [12] Hester, J 2020 covr: Test Coverage for Packages. Comprehensive R Archive Network. https://CRAN.R-project.org/package=covr.
  * [13] Xie, Y 2015 Dynamic Documents with R and knitr, 2nd ed. Chapman and Hall/CRC.
  * [14] Bache, S M, Wickham, H 2020 magrittr: A Forward-Pipe Operator for R. Comprehensive R Archive Network. https://CRAN.R-project.org/package=magrittr.
  * [15] Csardi, G, FitzJohn, R 2020 progress: Terminal Progress Bars. Comprehensive R Archive Network. https://CRAN.R-project.org/package=progress.
  * [16] Henry, L, Wickham, H 2021 rlang: Functions for Base Types and Core R and ‘Tidyverse’ Features. Comprehensive R Archive Network. https://CRAN.R-project.org/package=rlang.
  * [17] Xie, Y, Allaire, J J, Grolemund, G 2018 R Markdown: The Definitive Guide. Chapman and Hall/CRC. URL: https://bookdown.org/yihui/rmarkdown.
  * [18] Wickham, H 2011 testthat: Get Started with Testing. R Journal 3: 5. DOI: https://doi.org/10.32614/RJ-2011-002.
  * [19] Dechezleprêtre, A, Ménière, Y, Mohnen, M 2017 International Patent Families: From Application Strategies to Statistical Indicators. Scientometrics 111(1): 793. DOI: https://doi.org/10.1007/s11192-017-2311-4.
  * [20] Bruck, P, Réthy, I, Szente, J, Tobochnik, J, Érdi, P 2016 Recognition of Emerging Technology Trends: Class-selective Study of Citations in the U.S. Patent Citation Network. Scientometrics 107: 1465. DOI: https://doi.org/10.1007/s11192-016-1899-0.
  * [21] Sherkow, J S 2017 Patent Protection for Microbial Technologies. FEMS Microbiol Lett 364(20). DOI: https://doi.org/10.1093/femsle/fnx205.
  * [22] Singh, R, Brumlik, C, Vaidya, M, Choudhury, A 2020 A Patent Review on Nanotechnology-based Nose-to-Brain Drug Delivery. Recent Pat Nanotechnol 14(3): 174. DOI: https://doi.org/10.2174/1872210514666200508121050.
  * [23] Lahrtz, F 2015 How to Successfully Patent Therapeutic Antibodies. J Biomol Screen 20(4): 484. DOI: https://doi.org/10.1177/1087057114567457.
  * [24] Krauß, J, Kuttenkeuler, D 2021 When to File for a Patent? The Scientist’s Perspective. N Biotechnol 60: 124. DOI: https://doi.org/10.1016/j.nbt.2020.10.006.
  * [25] Conegundes de Jesus, C K, Salerno, M S 2018 Patent Portfolio Management: Literature Review and a Proposed Model. Expert Opin Ther Pat 28(6): 505. DOI: https://doi.org/10.1080/13543776.2018.1472238.
  * [26] Weingarten, M D, Cyr, S K 2019 Securing and Maintaining a Strong Patent Portfolio for Pharmaceuticals. ACS Med Chem Lett 10(6): 838. DOI:
https://doi.org/10.1021/acsmedchemlett.9b00201.

  * [27] Csardi, G, Nepusz, T 2006 The igraph Software Package for Complex Network Research. InterJournal Complex Systems: 1695.
  * [28] Saul, N, Tralie, C 2019 Scikit-TDA: Topological Data Analysis for Python. DOI: https://doi.org/10.5281/zenodo.2533369.
  * [29] Wadhwa, R R, Williamson, D F K, Dhawan A, Scott J G 2018 TDAstats: R Pipeline for Computing Persistent Homology in Topological Data Analysis. Journal of Open Source Software 3(28): 860. DOI: https://doi.org/10.21105/joss.00860.
  * [30] Pedregosa, F, Varoquaux, G, Gramfort, A, et al 2011 Scikit-learn: Machine Learning in Python. Journal of Machine Learning 12: 2825.
  * [31] Kuhn, M 2021 caret: Classification and Regression Training. Comprehensive R Archive Network. https://CRAN.R-project.org/package=caret.
  * [32] Kuhn, M, Wickham, H 2020 Tidymodels: A Collection of Packages for Modeling and Machine Learning Using tidyverse Principles. Comprehensive R Archive Network. https://CRAN.R-project.org/package=tidymodels.
  * [33] Singh, G, Memoli, F, Carlsson, G 2007 Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. Eurographics Symposium on Point-Based Graphics. DOI: https://doi.org/10.2312/SPBG/SPBG07/091-100.
  * [34] Carlsson, G 2009 Topology and data. Bulletin of the American Mathematical Society 46: 255-308. DOI: https://doi.org/10.1090/S0273-0979-09-01249-X.
  * [35] Beltz, H, Fulop, A, Wadhwa, R R, Erdi, P 2017 From Ranking and Clustering of Evolving Networks to Patent Citation Analysis. 2017 International Joint Conference on Neural Networks: 1388-1394. DOI: https://doi.org/10.1109/IJCNN.2017.7966015.
  * [36] Beltz, H, Rutledge, T, Wadhwa, R R, Bruck, P, Tobochnik J, Fulop A, Fenyvesi, G, Erdi, P 2019 Ranking Algorithms: Application for Patent Citation Network. In: Information Quality in Information Fusion and Decision Making: 519-538.
  * [37] International Patent Classification (IPC). World Intellectual Property Organization. https://www.wipo.int/classifications/ipc/en.