The MicroBooNE Collaboration ††thanks<EMAIL_ADDRESS>
#  Measurement of neutral current single $\pi^{0}$ production on argon with
the MicroBooNE detector

P. Abratenko  Tufts University, Medford, MA, 02155, USA  J. Anthony
University of Cambridge, Cambridge CB3 0HE, United Kingdom  L. Arellano  The
University of Manchester, Manchester M13 9PL, United Kingdom  J. Asaadi
University of Texas, Arlington, TX, 76019, USA  A. Ashkenazi  Tel Aviv
University, Tel Aviv, Israel, 69978  S. Balasubramanian  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  B. Baller  Fermi
National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  C. Barnes
University of Michigan, Ann Arbor, MI, 48109, USA  G. Barr  University of
Oxford, Oxford OX1 3RH, United Kingdom  J. Barrow  Massachusetts Institute of
Technology (MIT), Cambridge, MA, 02139, USA  Tel Aviv University, Tel Aviv,
Israel, 69978  V. Basque  Fermi National Accelerator Laboratory (FNAL),
Batavia, IL 60510, USA  L. Bathe-Peters  Harvard University, Cambridge, MA
02138, USA  O. Benevides Rodrigues  Syracuse University, Syracuse, NY, 13244,
USA  S. Berkman  Fermi National Accelerator Laboratory (FNAL), Batavia, IL
60510, USA  A. Bhanderi  The University of Manchester, Manchester M13 9PL,
United Kingdom  A. Bhat  Syracuse University, Syracuse, NY, 13244, USA  M.
Bhattacharya  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510,
USA  M. Bishai  Brookhaven National Laboratory (BNL), Upton, NY, 11973, USA
A. Blake  Lancaster University, Lancaster LA1 4YW, United Kingdom  T. Bolton
Kansas State University (KSU), Manhattan, KS, 66506, USA  J. Y. Book  Harvard
University, Cambridge, MA 02138, USA  L. Camilleri  Columbia University, New
York, NY, 10027, USA  D. Caratelli  University of California, Santa Barbara,
CA, 93106, USA  Fermi National Accelerator Laboratory (FNAL), Batavia, IL
60510, USA  I. Caro Terrazas  Colorado State University, Fort Collins, CO,
80523, USA  F. Cavanna  Fermi National Accelerator Laboratory (FNAL), Batavia,
IL 60510, USA  G. Cerati  Fermi National Accelerator Laboratory (FNAL),
Batavia, IL 60510, USA  Y. Chen  Universität Bern, Bern CH-3012, Switzerland
SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA  D. Cianci
Columbia University, New York, NY, 10027, USA  J. M. Conrad  Massachusetts
Institute of Technology (MIT), Cambridge, MA, 02139, USA  M. Convery  SLAC
National Accelerator Laboratory, Menlo Park, CA, 94025, USA  L. Cooper-
Troendle  Wright Laboratory, Department of Physics, Yale University, New
Haven, CT, 06520, USA  J. I. Crespo-Anadón  Centro de Investigaciones
Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid E-28040, Spain
M. Del Tutto  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510,
USA  S. R. Dennis  University of Cambridge, Cambridge CB3 0HE, United Kingdom
P. Detje  University of Cambridge, Cambridge CB3 0HE, United Kingdom  A.
Devitt  Lancaster University, Lancaster LA1 4YW, United Kingdom  R. Diurba
Universität Bern, Bern CH-3012, Switzerland  University of Minnesota,
Minneapolis, MN, 55455, USA  R. Dorrill  Illinois Institute of Technology
(IIT), Chicago, IL 60616, USA  K. Duffy  University of Oxford, Oxford OX1 3RH,
United Kingdom  S. Dytman  University of Pittsburgh, Pittsburgh, PA, 15260,
USA  B. Eberly  University of Southern Maine, Portland, ME, 04104, USA  A.
Ereditato  Universität Bern, Bern CH-3012, Switzerland  J. J. Evans  The
University of Manchester, Manchester M13 9PL, United Kingdom  R. Fine  Los
Alamos National Laboratory (LANL), Los Alamos, NM, 87545, USA  O. G. Finnerud
The University of Manchester, Manchester M13 9PL, United Kingdom  G. A.
Fiorentini Aguirre  South Dakota School of Mines and Technology (SDSMT), Rapid
City, SD, 57701, USA  R. S. Fitzpatrick  University of Michigan, Ann Arbor,
MI, 48109, USA  B. T. Fleming  Wright Laboratory, Department of Physics, Yale
University, New Haven, CT, 06520, USA  N. Foppiani  Harvard University,
Cambridge, MA 02138, USA  D. Franco  Wright Laboratory, Department of Physics,
Yale University, New Haven, CT, 06520, USA  A. P. Furmanski  University of
Minnesota, Minneapolis, MN, 55455, USA  D. Garcia-Gamez  Universidad de
Granada, Granada E-18071, Spain  S. Gardiner  Fermi National Accelerator
Laboratory (FNAL), Batavia, IL 60510, USA  G. Ge  Columbia University, New
York, NY, 10027, USA  S. Gollapinni  University of Tennessee, Knoxville, TN,
37996, USA  Los Alamos National Laboratory (LANL), Los Alamos, NM, 87545, USA
O. Goodwin  The University of Manchester, Manchester M13 9PL, United Kingdom
E. Gramellini  Fermi National Accelerator Laboratory (FNAL), Batavia, IL
60510, USA  P. Green  The University of Manchester, Manchester M13 9PL, United
Kingdom  H. Greenlee  Fermi National Accelerator Laboratory (FNAL), Batavia,
IL 60510, USA  W. Gu  Brookhaven National Laboratory (BNL), Upton, NY, 11973,
USA  R. Guenette  Harvard University, Cambridge, MA 02138, USA  The University
of Manchester, Manchester M13 9PL, United Kingdom  P. Guzowski  The University
of Manchester, Manchester M13 9PL, United Kingdom  L. Hagaman  Wright
Laboratory, Department of Physics, Yale University, New Haven, CT, 06520, USA
O. Hen  Massachusetts Institute of Technology (MIT), Cambridge, MA, 02139, USA
R. Hicks  Los Alamos National Laboratory (LANL), Los Alamos, NM, 87545, USA
C. Hilgenberg  University of Minnesota, Minneapolis, MN, 55455, USA  G. A.
Horton-Smith  Kansas State University (KSU), Manhattan, KS, 66506, USA  R.
Itay  SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA  C.
James  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA
X. Ji  Brookhaven National Laboratory (BNL), Upton, NY, 11973, USA  L. Jiang
Center for Neutrino Physics, Virginia Tech, Blacksburg, VA, 24061, USA  J. H.
Jo  Wright Laboratory, Department of Physics, Yale University, New Haven, CT,
06520, USA  R. A. Johnson  University of Cincinnati, Cincinnati, OH, 45221,
USA  Y.-J. Jwa  Columbia University, New York, NY, 10027, USA  D. Kalra
Columbia University, New York, NY, 10027, USA  N. Kamp  Massachusetts
Institute of Technology (MIT), Cambridge, MA, 02139, USA  N. Kaneshige
University of California, Santa Barbara, CA, 93106, USA  G. Karagiorgi
Columbia University, New York, NY, 10027, USA  W. Ketchum  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  M. Kirby  Fermi
National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  T. Kobilarcik
Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  I.
Kreslo  Universität Bern, Bern CH-3012, Switzerland  M. B. Leibovitch
University of California, Santa Barbara, CA, 93106, USA  I. Lepetic  Rutgers
University, Piscataway, NJ, 08854, USA  J.-Y. Li  University of Edinburgh,
Edinburgh EH9 3FD, United Kingdom  K. Li  Wright Laboratory, Department of
Physics, Yale University, New Haven, CT, 06520, USA  Y. Li  Brookhaven
National Laboratory (BNL), Upton, NY, 11973, USA  K. Lin  Los Alamos National
Laboratory (LANL), Los Alamos, NM, 87545, USA  B. R. Littlejohn  Illinois
Institute of Technology (IIT), Chicago, IL 60616, USA  W. C. Louis  Los Alamos
National Laboratory (LANL), Los Alamos, NM, 87545, USA  X. Luo  University of
California, Santa Barbara, CA, 93106, USA  K. Manivannan  Syracuse University,
Syracuse, NY, 13244, USA  C. Mariani  Center for Neutrino Physics, Virginia
Tech, Blacksburg, VA, 24061, USA  D. Marsden  The University of Manchester,
Manchester M13 9PL, United Kingdom  J. Marshall  University of Warwick,
Coventry CV4 7AL, United Kingdom  D. A. Martinez Caicedo  South Dakota School
of Mines and Technology (SDSMT), Rapid City, SD, 57701, USA  K. Mason  Tufts
University, Medford, MA, 02155, USA  A. Mastbaum  Rutgers University,
Piscataway, NJ, 08854, USA  N. McConkey  The University of Manchester,
Manchester M13 9PL, United Kingdom  V. Meddage  Kansas State University (KSU),
Manhattan, KS, 66506, USA  T. Mettler  Universität Bern, Bern CH-3012,
Switzerland  K. Miller  University of Chicago, Chicago, IL, 60637, USA  J.
Mills  Tufts University, Medford, MA, 02155, USA  K. Mistry  The University of
Manchester, Manchester M13 9PL, United Kingdom  A. Mogan  Colorado State
University, Fort Collins, CO, 80523, USA  T. Mohayai  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  M. Mooney  Colorado
State University, Fort Collins, CO, 80523, USA  A. F. Moor  University of
Cambridge, Cambridge CB3 0HE, United Kingdom  C. D. Moore  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  L. Mora Lepin  The
University of Manchester, Manchester M13 9PL, United Kingdom  J. Mousseau
University of Michigan, Ann Arbor, MI, 48109, USA  S. Mulleriababu
Universität Bern, Bern CH-3012, Switzerland  D. Naples  University of
Pittsburgh, Pittsburgh, PA, 15260, USA  A. Navrer-Agasson  The University of
Manchester, Manchester M13 9PL, United Kingdom  N. Nayak  Brookhaven National
Laboratory (BNL), Upton, NY, 11973, USA  M. Nebot-Guinot  University of
Edinburgh, Edinburgh EH9 3FD, United Kingdom  R. K. Neely  Kansas State
University (KSU), Manhattan, KS, 66506, USA  D. A. Newmark  Los Alamos
National Laboratory (LANL), Los Alamos, NM, 87545, USA  J. Nowak  Lancaster
University, Lancaster LA1 4YW, United Kingdom  M. Nunes  Syracuse University,
Syracuse, NY, 13244, USA  N. Oza  Los Alamos National Laboratory (LANL), Los
Alamos, NM, 87545, USA  O. Palamara  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  V. Paolone  University of Pittsburgh,
Pittsburgh, PA, 15260, USA  A. Papadopoulou  Massachusetts Institute of
Technology (MIT), Cambridge, MA, 02139, USA  V. Papavassiliou  New Mexico
State University (NMSU), Las Cruces, NM, 88003, USA  H. B. Parkinson
University of Edinburgh, Edinburgh EH9 3FD, United Kingdom  S. F. Pate  New
Mexico State University (NMSU), Las Cruces, NM, 88003, USA  N. Patel
Lancaster University, Lancaster LA1 4YW, United Kingdom  A. Paudel  Kansas
State University (KSU), Manhattan, KS, 66506, USA  Z. Pavlovic  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  E. Piasetzky  Tel Aviv
University, Tel Aviv, Israel, 69978  I. D. Ponce-Pinto  Wright Laboratory,
Department of Physics, Yale University, New Haven, CT, 06520, USA  S. Prince
Harvard University, Cambridge, MA 02138, USA  X. Qian  Brookhaven National
Laboratory (BNL), Upton, NY, 11973, USA  J. L. Raaf  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  V. Radeka  Brookhaven
National Laboratory (BNL), Upton, NY, 11973, USA  A. Rafique  Kansas State
University (KSU), Manhattan, KS, 66506, USA  M. Reggiani-Guzzo  The University
of Manchester, Manchester M13 9PL, United Kingdom  L. Ren  New Mexico State
University (NMSU), Las Cruces, NM, 88003, USA  L. C. J. Rice  University of
Pittsburgh, Pittsburgh, PA, 15260, USA  L. Rochester  SLAC National
Accelerator Laboratory, Menlo Park, CA, 94025, USA  J. Rodriguez Rondon  South
Dakota School of Mines and Technology (SDSMT), Rapid City, SD, 57701, USA  M.
Rosenberg  University of Pittsburgh, Pittsburgh, PA, 15260, USA  M. Ross-
Lonergan  Columbia University, New York, NY, 10027, USA  Los Alamos National
Laboratory (LANL), Los Alamos, NM, 87545, USA  C. Rudolf von Rohr  Universität
Bern, Bern CH-3012, Switzerland  G. Scanavini  Wright Laboratory, Department
of Physics, Yale University, New Haven, CT, 06520, USA  D. W. Schmitz
University of Chicago, Chicago, IL, 60637, USA  A. Schukraft  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  W. Seligman  Columbia
University, New York, NY, 10027, USA  M. H. Shaevitz  Columbia University, New
York, NY, 10027, USA  R. Sharankova  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  J. Shi  University of Cambridge, Cambridge CB3
0HE, United Kingdom  J. Sinclair  Universität Bern, Bern CH-3012, Switzerland
A. Smith  University of Cambridge, Cambridge CB3 0HE, United Kingdom  E. L.
Snider  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA
M. Soderberg  Syracuse University, Syracuse, NY, 13244, USA  S. Söldner-
Rembold  The University of Manchester, Manchester M13 9PL, United Kingdom  P.
Spentzouris  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510,
USA  J. Spitz  University of Michigan, Ann Arbor, MI, 48109, USA  M. Stancari
Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  J. St.
John  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  T.
Strauss  Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, USA
K. Sutton  Columbia University, New York, NY, 10027, USA  S. Sword-Fehlberg
New Mexico State University (NMSU), Las Cruces, NM, 88003, USA  A. M. Szelc
University of Edinburgh, Edinburgh EH9 3FD, United Kingdom  W. Tang
University of Tennessee, Knoxville, TN, 37996, USA  N. Taniuchi  University of
Cambridge, Cambridge CB3 0HE, United Kingdom  K. Terao  SLAC National
Accelerator Laboratory, Menlo Park, CA, 94025, USA  C. Thorpe  Lancaster
University, Lancaster LA1 4YW, United Kingdom  D. Torbunov  Brookhaven
National Laboratory (BNL), Upton, NY, 11973, USA  D. Totani  University of
California, Santa Barbara, CA, 93106, USA  M. Toups  Fermi National
Accelerator Laboratory (FNAL), Batavia, IL 60510, USA  Y.-T. Tsai  SLAC
National Accelerator Laboratory, Menlo Park, CA, 94025, USA  M. A. Uchida
University of Cambridge, Cambridge CB3 0HE, United Kingdom  T. Usher  SLAC
National Accelerator Laboratory, Menlo Park, CA, 94025, USA  B. Viren
Brookhaven National Laboratory (BNL), Upton, NY, 11973, USA  M. Weber
Universität Bern, Bern CH-3012, Switzerland  H. Wei  Brookhaven National
Laboratory (BNL), Upton, NY, 11973, USA  Louisiana State University, Baton
Rouge, LA, 70803, USA  A. J. White  Wright Laboratory, Department of Physics,
Yale University, New Haven, CT, 06520, USA  Z. Williams  University of Texas,
Arlington, TX, 76019, USA  S. Wolbers  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  T. Wongjirad  Tufts University, Medford, MA,
02155, USA  M. Wospakrik  Fermi National Accelerator Laboratory (FNAL),
Batavia, IL 60510, USA  K. Wresilo  University of Cambridge, Cambridge CB3
0HE, United Kingdom  N. Wright  Massachusetts Institute of Technology (MIT),
Cambridge, MA, 02139, USA  W. Wu  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  E. Yandel  University of California, Santa
Barbara, CA, 93106, USA  T. Yang  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  G. Yarbrough  University of Tennessee,
Knoxville, TN, 37996, USA  L. E. Yates  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  Massachusetts Institute of Technology (MIT),
Cambridge, MA, 02139, USA  H. W. Yu  Brookhaven National Laboratory (BNL),
Upton, NY, 11973, USA  G. P. Zeller  Fermi National Accelerator Laboratory
(FNAL), Batavia, IL 60510, USA  J. Zennamo  Fermi National Accelerator
Laboratory (FNAL), Batavia, IL 60510, USA  C. Zhang  Brookhaven National
Laboratory (BNL), Upton, NY, 11973, USA

(August 28, 2024)

###### Abstract

We report the first measurement of $\pi^{0}$ production in neutral current
(NC) interactions on argon with average neutrino energy of $\lesssim 1$ GeV.
We use data from the MicroBooNE detector’s 85-tonne active volume liquid argon
time projection chamber situated in Fermilab’s Booster Neutrino Beam and
exposed to $5.89\times 10^{20}$ protons on target for this measurement.
Measurements of NC $\pi^{0}$ events are reported for two exclusive event
topologies without charged pions. Those include a topology with two photons
from the decay of the $\pi^{0}$ and one proton and a topology with two photons
and zero protons. Flux-averaged cross-sections for each exclusive topology and
for their semi-inclusive combination are extracted (efficiency-correcting for
two-plus proton final states), and the results are compared to predictions
from the genie, neut, and NuWro neutrino event generators. We measure cross
sections of $1.243\pm 0.185$ (syst) $\pm 0.076$ (stat), $0.444\pm 0.098\pm
0.047$, and $0.624\pm 0.131\pm 0.075$ $[10^{-38}\textrm{cm}^{2}/\textrm{Ar}]$
for the semi-inclusive NC$\pi^{0}$, exclusive NC$\pi^{0}$+1p, and exclusive
NC$\pi^{0}$+0p processes, respectively.

##  I Introduction

Neutrino-nucleus cross-sections have been the subject of intense study both
experimentally and within the theory community in recent years due to their
role in interpreting neutrino oscillation measurements and searches for other
rare processes in neutrino scattering [1]. While neutrino oscillation
experiments primarily rely on measuring the rate of charged current (CC)
interactions, it is also important that we build a solid understanding of
inclusive and exclusive neutral current (NC) neutrino interactions.

NC neutrino interactions are of particular importance to $\nu_{e}$ and
$\bar{\nu}_{e}$ measurements in the energy range of a few hundred MeV. This is
especially true for detectors that cannot perfectly differentiate between
photon- and electron-induced electromagnetic showers, and therefore where NC
$\pi^{0}$ production followed by the subsequent decay
$\pi^{0}\rightarrow\gamma\gamma$ can be misidentified as $\nu_{e}$ or
$\bar{\nu}_{e}$ CC scattering. Misidentification of photons as electrons
complicates the interpretation of $\nu_{e}$ appearance measurements aiming to
measure subtle signals. These include sterile neutrino oscillation searches
with the upcoming Short Baseline Neutrino (SBN) experimental program [2] and
CP violation measurements and mass hierarchy determination with the future
Deep Underground Neutrino Experiment (DUNE) [3].

Furthermore, NC $\pi^{0}$ events can contribute as background to searches for
rare neutrino scattering processes such as NC $\Delta$ resonance production
followed by $\Delta$ radiative decay, or NC coherent single-photon production
at energies below 1 GeV [4]. This is primarily a consequence of the limited
geometric acceptance of some detectors, whereby one of the photons from a
$\pi^{0}$ decay can escape the active volume of the detector. Depending on a
detector’s ability to resolve electromagnetic shower substructure, NC
$\pi^{0}$ events can further contribute as background to searches for new
physics beyond the Standard Model (BSM), such as $e^{+}e^{-}$ production
predicted by a number of BSM models [5, 6, 7, 8, 9].

Finally, NC measurements themselves can provide a unique channel for probing
new physics. For example, searches for non-unitarity in the three-neutrino
paradigm or searches for active to sterile neutrino oscillations are possible
via NC rate disappearance measurements [10, 11]. Such searches can provide
complementary information to non-unitarity or light sterile neutrino
oscillation parameters otherwise accessible only through CC measurements.

Using a liquid argon time projection chamber (LArTPC) as its active detector,
MicroBooNE [12] shares the same technology and neutrino target nucleus as the
upcoming SBN and future DUNE experiments. MicroBooNE’s 85 metric ton active
volume LArTPC is situated 468.5 m away from the proton beam target in the
muon-neutrino-dominated Booster Neutrino Beam (BNB) at Fermilab [13] which is
also used by SBN. The resulting neutrino beam has a mean energy $\langle
E_{\nu}\rangle=0.8$ GeV and is composed of $93.7\%\leavevmode\nobreak\
\nu_{\mu}$, $5.8\%\leavevmode\nobreak\ \bar{\nu}_{\mu}$, and
$0.5\%\leavevmode\nobreak\ \nu_{e}/\bar{\nu}_{e}$. MicroBooNE’s cross-section
measurements on argon are therefore timely and directly relevant to these
future (SBN and DUNE) programs.

We present the first measurement of neutrino-induced NC single-$\pi^{0}$
($1\pi^{0}$) production on argon with a mean neutrino energy in the 1 GeV
regime, which is also the highest-statistics measurement of this interaction
channel on argon to date. This measurement is relevant to the physics programs
of experiments that operate in the few-GeV regime (SBN [2], DUNE [3], NO$\nu$A
[14, 15], T2K [16], and Hyper-K [17]), especially those which share argon as a
target material. Additionally, this measurement has been used to provide an
indirect constraint to the rate of NC $1\pi^{0}$ backgrounds in MicroBooNE’s
recent search for a single-photon excess [4]. The only previous results for NC
$1\pi^{0}$ scattering on argon are from the ArgoNeuT collaboration using the
NuMI beam which has a much higher mean neutrino beam energy of 9.6 GeV for
$\nu_{\mu}$ and of 3.6 GeV for $\overline{\nu}_{\mu}$ [18].

The interaction final states that are measured in this analysis are defined as

$\displaystyle\nu+\mathcal{A}\rightarrow\nu+\mathcal{A^{\prime}}+\pi^{0}+X,$
(1)

where $\mathcal{A}$ represents the struck (argon) nucleus,
$\mathcal{A^{\prime}}$ represents the residual nucleus, and $X$ represents
exactly one or zero protons plus any number of neutrons, but no other hadrons
or leptons. The protons are identifiable in the MicroBooNE LArTPC by their
distinct ionizing tracks while the $\pi^{0}$ is identifiable through the
presence of two distinct electromagnetic showers, one for each photon from the
$\pi^{0}\rightarrow\gamma\gamma$ decay, with kinematic properties such that
they reconstruct to approximately the $\pi^{0}$ invariant mass.

These one proton and zero proton samples are used first to perform a rate
validation check and subsequently in three distinct cross-section
measurements. By leveraging the capability of LArTPCs to detect and identify
protons we perform the world’s first exclusive NC$\pi^{0}$+0p and
NC$\pi^{0}$+1p cross-section extractions and additionally measure the cross-
section for NC$\pi^{0}$ interactions semi-inclusively using both the one
proton and zero proton samples combined. Each of these cross-section
extractions utilizes a distinct signal definition. The signal definitions for
the two exclusive measurements place a threshold on true proton kinetic energy
of greater than 50 MeV, while the semi-inclusive measurement allows for any
number of protons. The signal definitions for all three measurements also
require that there are no other hadrons or leptons in the final state (as
noted above). MeV-scale photons, which may arise from nuclear de-excitation
processes within the struck nucleus, are allowed in the final state. Finally,
the signal definitions allow for interactions of all flavors of neutrinos that
are present: $\nu_{\mu}$, $\bar{\nu}_{\mu}$, $\nu_{e}$, and $\bar{\nu}_{e}$.

These definitions are comparable to other historical NC $\pi^{0}$ measurements
which typically require one and only one $\pi^{0}$ meson and little hadronic
activity in the detector [19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. This
differs from the more inclusive approach of the ArgoNeuT experiment motivated
both by its higher energy beam as well as the need to mitigate the low
statistics of its data sample [18]. Making use of the MicroBooNE LArTPC’s
power in examining hadronic final state multiplicities and kinematic
properties with high resolution, the flux-averaged cross-sections extracted in
this analysis extend our understanding of this important interaction channel.
The exclusive cross-sections reported provide new information useful for the
tuning of NC $1\pi^{0}$ production and nuclear final state interactions in
neutrino-argon scattering models, while the semi-inclusive cross-section
enables a direct comparison to the MiniBooNE measurement of NC $\pi^{0}$
production.

##  II Analysis Overview

This measurement uses data corresponding to a BNB exposure of $5.89\times
10^{20}$ protons on target (POT), collected during the period 2016–2018 and
referred to as “Runs 1–3” in many of the subsequent figures. Neutrino-argon
interactions are simulated using a custom tune [29] of the genie neutrino
event generator v3.0.6 [30, 31] (based on model set G18_10a_02_11a) adopted by
the MicroBooNE Collaboration. This tune specifically targets CC quasi-elastic
(QE) and CC multi-nucleon interaction models and overall has very little
direct effect on this NC-focused analysis. genie v3 uses the Berger-Sehgal
[32, 33] model for resonant production of $\pi^{0}$ and includes improved
agreement with an expanded data set for the $A$-dependence of final state
interactions (FSI), updated form factors [34], updated diagrams for pion
production processes [33, 35, 36], and a new tune to neutrino-proton and
neutrino-deuterium cross-section data [31]. The MicroBooNE Monte Carlo (MC)
prediction further makes use of geant4 v4_10_3_03c [37] for particle
propagation and re-interactions within the detector and a custom detector
response model all implemented within the LArSoft framework [38].

The MicroBooNE data and MC reconstruction chain begins by reading out and
processing the ionization charge signals detected on the 8,192 wires that make
up the three anode planes of the MicroBooNE LArTPC. The procedure includes
noise removal [39] and signal processing as described in [40] and [41].
Localized regions of interest referred to as “hits” are then identified and
fit to Gaussian pulses. The collection of these hits and their characteristics
such as readout time, wire channel number, and integrated charge are then used
as input to the Pandora pattern recognition framework for further processing
[42]. The Pandora framework clusters and matches hits across three 2D
projected views of the MicroBooNE active TPC volume to form 3D reconstructed
objects. These objects are then classified as track-like or shower-like based
on a multivariate classifier score and aggregated into candidate neutrino
interactions. Pandora also reconstructs a candidate neutrino interaction
vertex based on the position and orientation of the reconstructed tracks and
showers which represents the most likely position of the neutrino interaction.

Being a surface detector, MicroBooNE is subject to a constant stream of high-
energy cosmic rays impinging on the detector that substantially outnumber the
neutrino interactions and form the largest background to candidate neutrino
interactions. To incorporate the effect of cosmic-ray contamination in the
simulation, cosmic ray data recorded in situ at MicroBooNE, when the beam is
not present, are used as overlays (at the wire signal waveform level) to
simulated neutrino interactions. During the 2.3 ms that it takes to “drift”
ionization charge associated with neutrino interaction final states across the
maximum 2.56 m drift distance, $\mathcal{O}(10)$ cosmic rays are expected to
enter the detector. In order to reduce this cosmic-ray contamination,
scintillation light recorded by the MicroBooNE photo-detector system is
matched to candidate neutrino interactions during reconstruction and is also
required to occur in time with the 1.6 $\mu$s long BNB neutrino spill.

To select a high-purity sample of BNB neutrino NC $1\pi^{0}$ interactions, a
series of topological, pre-selection, and boosted decision tree (BDT)-based
selections are applied. This results in two mutually exclusive final selection
topologies: $2\gamma 1p$, which targets two photons and one proton in the
final state, and $2\gamma 0p$, which targets two photons and zero protons in
the final state. The different selection stages are described below, along
with the details of the systematic uncertainty evaluation.

###  II.1 Topological Selection and Pre-Selection

The event selection begins with topology-based criteria for candidate neutrino
interactions identified by Pandora and targets two mutually exclusive
topological definitions: (a) two showers and one track ($2\gamma 1p$), and (b)
two showers and zero tracks ($2\gamma 0p$). The two showers correspond to the
photons expected from $\pi^{0}$ decay. The presence of a track corresponds to
a reconstructed proton exiting the nucleus while the zero-track case suggests
either a low-energy proton that is not reconstructed or no charged hadrons at
all exiting the nucleus.

Once events with the desired signal topologies are identified, a series of
loose “pre-selection” requirements is applied to reduce obvious backgrounds or
mis-reconstructed events. These pre-selection requirements include shower
energy thresholds of 30 MeV for the leading shower and 20 MeV for the
subleading shower in both topologies. The pre-selection also requires that the
reconstructed neutrino interaction point be contained in a fiducial volume,
defined as at least 5 cm away from any TPC wall, in order to help reduce the
number of selected events with tracks that exit the detector. For the
2$\gamma$1p topology, the non-zero conversion distance of photons is
explicitly used by requiring that each shower has a reconstructed start point
of at least 1 cm from the reconstructed neutrino interaction vertex. Typically
the reconstructed neutrino interaction vertex is identified as the start of
the reconstructed proton candidate track. In order to remove a very small
number of poorly reconstructed events in which the candidate track is not
consistent with the hypothesis of originating from the candidate neutrino
interaction vertex, a requirement is placed to ensure the track start point is
always within 10 cm of the reconstructed neutrino interaction vertex. The
efficiency of selecting NC $1\pi^{0}$ \+ 0 (1)p events using these pre-
selection requirements is 21.5% (19.9%). Note that the efficiency of the 1p
selection is lower because of the additional requirements placed on the track
reconstruction.

###  II.2 Boosted Decision Tree-Based Selection

After applying the pre-selection requirements, the remaining signal and
background are further differentiated and separated using two tailored BDTs
trained on simulation. The gradient boosting algorithm XGBoost [43] is used to
train each of the BDTs. They take as input various reconstructed kinematic,
geometric, and calorimetric variables both for the signal (defined as an NC
interaction with identically one $\pi^{0}$ in the final state) and for the
background interactions. Because the two tailored BDTs target different
topologies, notably including one track in the case of $2\gamma 1p$ and zero
tracks in the case of $2\gamma 0p$, the signal definitions used for the two
BDTs are slightly different. NC $\pi^{0}$ events with exactly one proton with
true kinetic energy above 20 MeV are used as the training signal for the
$2\gamma 1p$ BDT while NC $\pi^{0}$ events with no protons with true kinetic
energy above 20 MeV are used as the training signal for the $2\gamma 0p$ BDT.
We note that the 20 MeV threshold used in the BDT training is lower than the
50 MeV proton kinetic energy threshold used later during cross-section
extraction, as during training we are aiming to push the threshold as low as
possible. Each BDT is trained on ten reconstructed variables. Due to the
existence of a proton candidate track in the $2\gamma 1p$ sample, these ten
variables differ for each BDT. They are listed below.

Variables used in both $\bm{2\gamma 1p}$ and $\bm{2\gamma 0p}$ BDTs:

  * •

Leading and subleading shower impact parameters: The perpendicular distance
between the back-projection of the reconstructed shower and the candidate
neutrino interaction point which is a metric of how well each shower “points”
back to the reconstructed neutrino interaction point.

  * •

Leading and subleading shower conversion distances: Defined as the distance
between the reconstructed start of the shower and reconstructed neutrino
interaction point.

  * •

Reconstructed energy of the leading shower.

Variables used in only the $\bm{2\gamma 1p}$ BDT:

  * •

Reconstructed track length.

  * •

Reconstructed track vertical angle: Defined as the arctangent of the track
direction in the vertical plane with respect to the beam axis.

  * •

Distance from track end to TPC wall: Calculated as the shortest distance to
the closest TPC wall.

  * •

Reconstructed mean energy deposition per unit length ($dE/dx$) of the track.

  * •

Ratio of $dE/dx$ of the first half of track to that of the second half of the
track: A metric for identifying stopping proton tracks that contain a Bragg
peak.

Variables used in only the $\bm{2\gamma 0p}$ BDT:

  * •

Reconstructed energy of the subleading shower.

  * •

Leading and subleading shower geometric length per unit energy: The ratio of
each shower’s geometric length to its reconstructed energy. The geometric
length is an estimate of the 3D extent of the electromagnetic shower.

  * •

Pandora “neutrino score”: A multivariate classifier in the Pandora
reconstruction suite which scores all reconstructed neutrino candidates based
on their geometric and kinematic features as to how likely a candidate is due
to a neutrino interaction or cosmic in origin.

  * •

Reconstructed leading shower vertical angle: Direction in the vertical plane
with respect to the beam axis.

By construction, BDT scores lie on the interval of [0, 1]. After training, the
resulting BDT score distributions, tested on a statistically independent
simulation and data set, are shown in Fig. 1. The simulation and data points
agree across the full range of BDT classifier score within systematic and
statistical uncertainties (the definition of these systematic uncertainties is
described in detail in Sec. II.3). The bimodal distribution of the $2\gamma
1p$ BDT response indicates greater separation power between signal and
background compared to that for $2\gamma 0p$ because the addition of the
reconstructed track gives access to an entirely separate handle on background
rejection. For this and subsequent MC simulation comparisons to data, the
simulation predictions are broken down into the following eight categories,
based on genie truth-level information:

  * •

NC 1$\pi^{0}$: All neutral current interactions that produce one exiting
$\pi^{0}$ regardless of incoming neutrino flavor. This is our targeted signal
selection, and it is further split into two sub-categories, “NC 1$\pi^{0}$
Coherent” and “NC 1$\pi^{0}$ Non-Coherent” contributions, based on their
interaction types. Non-Coherent scattering occurs when a neutrino interacts
with a nucleon inside the argon nucleus, potentially knocking out one or more
nucleons. In coherent scattering the neutrino interacts with the nucleus as a
whole, leaving it in its ground state. This interactions occurs with low
momentum-transfer, and as such the resulting $\pi^{0}$ tends to be very
forward relative to the incoming neutrino beam.

  * •

NC $\Delta\rightarrow N\gamma$: Leading Standard Model source of NC single-
photon production below 1 GeV originating from radiative decay of the
$\Delta(1232)$ baryon.

  * •

CC $\nu_{\mu}1\pi^{0}$: All $\nu_{\mu}$ CC interactions that have one true
exiting $\pi^{0}$.

  * •

CC $\nu_{e}/\overline{\nu}_{e}$ Intrinsic: All CC $\nu_{e}$ or
$\overline{\nu}_{e}$ interactions regardless of whether or not a $\pi^{0}$ was
emitted.

  * •

BNB Other: All remaining BNB neutrino interactions that take place in the
active TPC volume of MicroBooNE and are not covered by the above five
categories, such as multiple $\pi^{0}$ events and $\eta$ meson decay. See
section II.6 for more details.

  * •

Dirt (Outside TPC): All BNB neutrino interactions that take place outside the
MicroBooNE active TPC but have final states that enter and interact inside the
active TPC detector. This can originate from scattering off liquid argon in
the cryostat vessel outside the active TPC volume or from interactions in the
concrete and “dirt” surrounding the cryostat itself.

  * •

Cosmic Data: Coincident cosmic ray interactions that take place during a BNB
spill but without any true neutrino interaction present.

The final NC $1\pi^{0}$-enriched samples are selected by placing a requirement
on the BDT score distribution that maximizes the product of NC $1\pi^{0}$
signal efficiency and purity. This corresponds to a threshold on the BDT
scores of $>0.854$ and $>0.950$ for $2\gamma 1p$ and $2\gamma 0p$,
respectively. The final distributions are provided and discussed in Sec. II.5.

(a) $2\gamma 1p$

(b) $2\gamma 0p$

Figure 1: The BDT classifier score for (a) $2\gamma 1p$ and (b) $2\gamma 0p$
targeted selections. Higher scores indicate more NC $1\pi^{0}$ signal-like
events, and lower scores indicate more background-like events. The red
vertical lines indicate the threshold positions, keeping all events to the
right, for the final selections.

###  II.3 Systematic Uncertainty Evaluation

Systematic uncertainties on the MC simulation prediction include contributions
from uncertainties in the neutrino flux, the cross-section modeling, hadron
re-interactions, detector effects, and the effect of finite statistics used in
the background predictions (both simulations and cosmic ray data).

The flux systematic uncertainties incorporate hadron production uncertainties
where the Booster proton beam hits the beryllium target, uncertainties on pion
and nucleon scattering in the target and surrounding aluminum magnetic
focusing horn of the BNB, and mismodeling of the horn current. Following [44],
these are implemented by reweighting the flux prediction according to neutrino
type, parentage, and energy, and studying the propagated effects on the final
event distributions.

The cross-section uncertainties incorporate modeling uncertainties on the
genie prediction [29, 30, 31], evaluated by genie reweighting tools. The
default genie uncertainties on NC resonant production arising from NC resonant
vector and axial mass parameters of $m_{V}=0.840\pm 0.084$ GeV and
$m_{A}=1.120\pm 0.224$ GeV, respectively, were assumed. genie uses an
effective cascade empirical model for hadronic final-state interactions,
called _hA2018_ , which allows for reweighting to estimate the effect on final
distributions. For more information on cross-section uncertainties in
MicroBooNE, please see [29].

The hadron-argon reinteraction uncertainties are associated with the
propagation of hadrons through the detector, as modeled in geant4 [37]. Both
charged pions and proton reinteractions during propagation were considered and
their impact estimated using the geant4reweight tool [45].

The detector modeling and response uncertainties are evaluated using
MicroBooNE’s novel data-driven technique for assessing and propagating LArTPC
detector-related systematic uncertainties [46]. This approach uses in situ
measurements of distortions in the TPC wire readout waveform signals – caused
by detector effects such as electron diffusion, electron drift lifetime,
electric field, and the electronics response – to parameterize these effects
at the TPC wire level. This provides a detector model-agnostic way to study
and evaluate their effects on the high level variables and, subsequently, the
final event distributions. Additional detector systematics corresponding to
variations in the charge recombination model, the scintillation light yield,
and space charge effects [47, 48] are separately evaluated and also included.

###  II.4 Shower Energy Calibration

Electromagnetic shower reconstruction in LArTPCs is known to be a lossy
process primarily due to mis-clustering and thresholding effects. Current
reconstruction algorithms often miss small, low-energy hits in an
electromagnetic shower when clustering objects, and some of the hits that are
reconstructed may fall below the energy threshold. On average, these effects
are expected to yield shower energy losses of approximately 20% [49]. This can
be seen in Fig. 2, which shows true and reconstructed shower energy for a
dedicated high statistics sample of simulated true NC 1$\pi^{0}$ events, where
the reconstructed shower energy falls systematically below the true shower
energy in simulation. By performing a linear fit to the most probable values
of reconstructed shower energy in bins of true shower energy, shown as the
pink straight line in Fig. 2, a correction factor is extracted which brings
the reconstructed values closer to expectation. This fit results in an energy
correction that is applied to all reconstructed showers,

$E_{\textrm{corr}}=(1.21\pm 0.03)E_{\textrm{reco}}+(9.88\pm 4.86)\
\textrm{MeV},$ (2)

and represents a correction of approximately 20%, as expected.

Figure 2: Reconstructed shower energy vs. true shower energy for a dedicated
high statistics sample of simulated true NC $1\pi^{0}$ events. Only showers
with a reconstructed energy of at least $20$ MeV are considered.

###  II.5 Final Selected Spectra

(a) $\pi^{0}$ momentum dependence

(b) Proton kinetic energy dependence

Figure 3: (a) Efficiencies of the final $2\gamma 1p$, $2\gamma 0p$ and
combined $2\gamma(0+1)p$ selections as a function of true $\pi^{0}$ momentum.
(b) Efficiencies as a function true leading exiting proton kinetic energy for
all NC1$\pi^{0}$ events that are reconstructed as either $1p$ or $0p$. Events
in which there are no exiting protons are included in the first bin. As can be
seen, a threshold of $\approx$ 50 MeV proton kinetic energy is where events
start to shift between the $2\gamma 0p$ and $2\gamma 1p$ selections which was
subsequently chosen as the signal definition for $0p$ and $1p$ signal events.

After applying the BDT requirements, 1130 selected data events remain with 634
and 496 falling into the $2\gamma 1p$ and $2\gamma 0p$ selections,
respectively. For the $2\gamma 1p$ selection, the BDT score requirement
efficiency is 85.6% and the purity is 63.5% while for the $2\gamma 0p$
selection, the efficiency and purity are 58.8% and 52.9%, respectively. The
$2\gamma 1p$ and $2\gamma 0p$ BDT selection efficiencies and purities are both
calculated relative to their signal definition, with proton multiplicity
counted with a kinetic energy threshold of 50 MeV. The efficiencies at each
stage of the analysis are provided in Table 1, and the total efficiency for
each selection is shown as a function of (a) true $\pi^{0}$ momentum and (b)
true proton kinetic energy in Fig. 3. Overall, the $1p$ selection is more
efficient and of higher signal purity relative to the $0p$ selection due to
the existence of a reconstructed particle track which greatly helps to tag the
neutrino interaction point and reject backgrounds. This track information,
particularly track calorimetry, provides an additional handle on the neutrino
interaction mode; a proton-like track is highly indicative of an NC $1\pi^{0}$
interaction whereas CC interactions generally have a muon track in the final
state.

(a) $2\gamma 1p$

(b) $2\gamma 0p$

Figure 4: The reconstructed diphoton invariant mass for both the (a) $2\gamma 1p$ and (b) $2\gamma 0p$ final selected data. The result of fitting a Gaussian plus linear function to the data is shown in cyan. Table 1: NC $1\pi^{0}$ efficiencies for the $2\gamma 1p$ and $2\gamma 0p$ selections. The topological and combined efficiencies are evaluated relative to the defined exclusive $2\gamma 1p$ and $2\gamma 0p$ signal definitions, inside the active TPC. The pre-selection and BDT selection efficiencies are evaluated relative to their respective preceding selection stage. The final efficiencies are the combined total efficiency for each selection. Selection Stage |  $2\gamma 1p$ eff. |  $2\gamma 0p$ eff.
---|---|---
Topological | 62.5% | 47.4%
Pre-selection | 19.9% | 21.5%
BDT Selection | 85.6% | 58.8%
Final Efficiencies | 10.7% | 6.0%

The resulting distributions as a function of the reconstructed two-photon
invariant mass are shown in Fig. 4. The invariant mass is reconstructed from
the energy and direction of the two photon candidate showers as

$M_{\gamma\gamma}^{2}=2E_{\gamma 1}E_{\gamma 2}(1-\cos\theta_{\gamma\gamma}),$
(3)

where $\cos\theta_{\gamma\gamma}$ is the opening angle between the two
showers. For the $2\gamma 1p$ case where a track has been identified as a
candidate proton, the directions of the showers and thus the opening angle
between them are calculated by constructing the direction between the
candidate neutrino interaction point and the shower start point. For the
$2\gamma 0p$ selection, however, no such candidate track exists. Instead, the
shower direction and opening angle are entirely estimated from the geometric
shape of the showers themselves.

A Gaussian-plus-linear fit is performed to each observed distribution in data
to extract the reconstructed $\pi^{0}$ invariant mass while taking into
account the non-$\pi^{0}$ background contamination. For the $2\gamma 1p$ event
sample, this fit gives a Gaussian mean of 138.9$\pm$2.1 MeV/$c^{2}$ with a
width of 31.7$\pm$2.4 MeV/$c^{2}$. For the $2\gamma 0p$ event sample, the
corresponding fit gives a Gaussian mean of 143.3$\pm$3.2 MeV/$c^{2}$ with a
width of 47.9$\pm$4.9 MeV/$c^{2}$. As a goodness-of-fit test, the resulting
$\chi^{2}$ per degree of freedom is 1.20 and 1.45 for the $2\gamma 1p$ and
$2\gamma 0p$ fits, respectively. These both show agreement with the expected
invariant mass of the $\pi^{0}$ of $134.9770\pm 0.0005$ MeV/$c^{2}$ [50]
giving confidence and validation of the calorimetric energy reconstruction of
the showers. Additional distributions showing the reconstructed $\pi^{0}$
momentum as well as the reconstructed angle of the outgoing $\pi^{0}$ with
respect to the incoming neutrino beam are provided in Fig. 5.

(a) $2\gamma 1p$: Reconstructed $\pi^{0}$ momentum

(b) $2\gamma 0p$: Reconstructed $\pi^{0}$ momentum

(c) $2\gamma 1p$: Reconstructed cosine of $\pi^{0}$ angle

(d) $2\gamma 0p$: Reconstructed cosine of $\pi^{0}$ angle

Figure 5: The reconstructed $\pi^{0}$ momentum ((a) and (b)) and reconstructed
$\pi^{0}$ angle with respect to the neutrino beam ((c) and (d)) for both the
$2\gamma 1p$ ((a) and (c)) and $2\gamma 0p$ ((b) and (d)) final selected data.
The prediction shows agreement with the observed data within assigned
uncertainties for the ranges shown, although a systematic deficit is observed
in the total event rates as is discussed in Sec. III.

Two additional reconstructed distributions of interest are highlighted. First,
the reconstructed cosine of the center-of-mass (CM) decay angle is shown in
Fig. 6. This is defined as the angle between the lab-frame $\pi^{0}$ momentum
direction and the decay axis of the two daughter photons in the CM frame,

$\cos\theta_{\text{CM}}=\frac{|E_{\gamma 1}-E_{\gamma 2}|}{|p_{\pi^{0}}|}.$
(4)

This quantity should be an isotropic flat distribution for true
$\pi^{0}\rightarrow\gamma\gamma$ signal events, and any deviation from this
can highlight regions of inefficiency in reconstruction or selection. As can
be seen in Fig. 6, for both $2\gamma 1p$ and $2\gamma 0p$ selections, the
distributions taper off at high $\cos\theta_{\text{CM}}$ which corresponds to
increasingly asymmetric $\pi^{0}$ decays. When reconstructing asymmetric
$\pi^{0}$ decay events, it is more likely that the subleading photon shower is
missed due to its low energy. Note, however, that the observed data show the
same trend as the simulation within uncertainty.

Figure 7 additionally highlights the reconstructed photon conversion distance
for all showers in the final $2\gamma 1p$ selection. Well-reconstructed
showers with conversion distances as far as 100 cm from the candidate neutrino
interaction are observed. This helps validate the assumption that the
reconstructed showers are indeed likely to be true photons as
$\mathcal{O}$(100) MeV photons are expected to have a mean free path in argon
of $\approx 20$ cm. Note that, as the $2\gamma 0p$ selection does not have any
visible hadronic activity for tagging the interaction point, the corresponding
conversion distance is significantly harder to estimate.

(a) $2\gamma 1p$

(b) $2\gamma 0p$

Figure 6: The reconstructed cosine of the center-of-mass angle for the (a)
$2\gamma 1p$ and (b) $2\gamma 0p$ final selected data. Figure 7: The
reconstructed conversion distance of both photons in the $2\gamma 1p$ final
selection. There are well-reconstructed showers with conversion distances as
far as 100 cm from the candidate neutrino interaction.

Finally, Fig. 8 shows two example event displays of selected events in data
for both the $2\gamma 1p$ and $2\gamma 0p$ topologies. Each event shows two
well-reconstructed showers pointing back to a common interaction point with
properties consistent with those being photons from a $\pi^{0}$ decay.

(a) $2\gamma 1p$

(b) $2\gamma 0p$

Figure 8: Event displays of candidate NC $1\pi^{0}$ events found in the
MicroBooNE data using (a) the $2\gamma 1p$ selection and (b) the $2\gamma 0p$
selection, on the MicroBooNE TPC collection plane. The horizontal axis here
corresponds to the increasing wires, with an associated distance in cm. The
vertical axis represents the TPC drift time. The aspect ratio of this plot is
set such that the length scale shown for the horizontal axis is the same for
the vertical axis.

###  II.6 Background Discussion and Validation

In order to validate the background modelling in this analysis we developed a
background rich sideband selection by inverting the BDT score cuts shown in
Fig. 1. This gives us a high statistics sample of “CC$1\pi^{0}$” and “BNB
Other” background categories with which to compare to data. In addition to
inverting the BDT score an additional cosmic rejection cut, where we require
the Pandora neutrino score to be $>0.5$, is applied to provide a higher purity
of the backgrounds we wish to study. These distributions are shown in Fig.
9(a) and 9(b) for $2\gamma 1p$ and $2\gamma 0p$ respectively. This is
particularly useful for $2\gamma 1p$ inverted selection as the resulting
spectrum is rich in CC$1\pi^{0}$ for higher reconstructed $\pi^{0}$ momenta,
and richer in “BNB Other” at low momenta. For the $2\gamma 0p$ background rich
sample there is still a significant amount of rejected NC $\pi^{0}$ signal
events, but the enhanced backgrounds still provide additional validation. The
data is observed to be in good agreement with the prediction, within assigned
uncertainties, with a $\chi^{2}/\text{ndof}$ of $24.61/20$ and $17.49/22$ for
$2\gamma 1p$ and $2\gamma 0p$ respectively. This gives us confidence that the
backgrounds and uncertainties are sufficiently modelled for a cross-section
extraction to proceed.

We can also break down the “BNB Other” category further in order to improve
our understanding of this important background. We find that approximately
$75\%$ of “BNB Other” events contain true photons reconstructed, and in case
of $2\gamma 1p$ 84% have true protons reconstructed. This indicates that
despite being a background category the BDT’s are indeed selecting events with
a very high purity of true photons and protons, as is the target of the
selection. The approximate breakdown of “BNB Other” after applying the BDT
cuts is found to be

  * •

$\approx 25\%$ are events in which multiple $\pi^{0}$ are exiting the nucleus
but only 1 $\pi^{0}$ is reconstructed correctly,

  * •

$\approx 25\%$ are events in which no $\pi^{0}$ exits the nucleus but due to
baryon or charged pion re-scattering in the argon, a $\pi^{0}$ is subsequently
created and reconstructed,

  * •

$\approx 25\%$ are events in which there is no $\pi^{0}$ and a NC proton is
reconstructed as the track with cosmic contamination resulting in a $2\gamma$
event mimicking a $\pi^{0}$,

  * •

$\approx 20\%$ are events containing a NC $\eta\rightarrow\gamma\gamma$ decay
event. These are generally rejected due to them having higher energies, but a
small number are selected as they are topologically identical to the
$\pi^{0}\rightarrow\gamma\gamma$ decay signal,

  * •

$\approx 5\%$ Miscellaneous other reconstruction failures, representing less
than 1% of total background events.

In the case of CC$1\pi^{0}$ we see a similar situation, with 97.3% (98.1%) of
$2\gamma 1p$ ($2\gamma 0p$) background events having at least 1 shower matched
to a true $\pi^{0}$ and with 78% of tracks in the $2\gamma 1p$ sample being
correctly matched to a proton. As such, the vast majority of these events have
the correct target particle content, but rather the muon itself is missed.
This primarily occurs when the muon is incorrectly clustered into a photon
electro-magnetic shower due to close proximity, or when the muon is correctly
reconstructed but is mis-identified as a cosmic muon, with the associated
$\pi^{0}$ then being reconstructed as an isolated neutrino event.

(a) $2\gamma 1p$ background validation sample

(b) $2\gamma 0p$ background validation sample

Figure 9: Background rich sidebands for validation created by inverting the
BDT selection cuts, for (a) $2\gamma 1p$ and (b) $2\gamma 0p$ samples. We
observe good agreement between the data and prediction, within the assigned
uncertainties giving us confidence in the background modelling.

##  III NC $\pi^{0}$ Rate Validation

NC $1\pi^{0}$ events contribute as a dominant background to NC single-photon
production measurements carried out or planned by MicroBooNE such as searches
for NC $\Delta$ radiative decay [4], NC coherent single-photon production, or
more rare $e^{+}e^{-}$ pair production motivated in BSM theories. In addition
to using these selected events as a calibration sample for understanding and
validating shower reconstruction performance, they are also used to validate
the observed overall rate of this process as currently modeled with genie.
Assuming genie provides a sufficient description of the observed data, this
sample can and has been used to provide an in situ constraint on NC $1\pi^{0}$
mis-identified backgrounds, e.g. as in [4]. Alternatively, these measurements
can be used to increase our understanding of our current NC $\pi^{0}$
modelling and potentially motivate genie tuning.

As shown in Fig. 5, both the $2\gamma 1p$ and the $2\gamma 0p$ selections see
an overall deficit in data relative to the MC prediction. This is more
pronounced in the $2\gamma 1p$ selection where the ratio of the number of
selected data events to the number of selected simulated events is 0.79. As it
is also known that the genie branching fraction of coherent NC $1\pi^{0}$
production on argon is significantly lower than expectation extrapolated from
MiniBooNE’s $\pi^{0}$ measurement on mineral oil [23], the possibility of a
correction to genie predictions on both non-coherent and coherent NC
$1\pi^{0}$ production is explicitly examined. The MC predictions are fitted to
data allowing both coherent and non-coherent NC $1\pi^{0}$ rates to vary. Both
normalization-only and normalization plus shape variations to the coherent and
non-coherent rates are explored; all yield similar conclusions. This section
describes the normalization plus shape variation fit in detail.

The normalization plus shape variation fit is performed as a function of
reconstructed $\pi^{0}$ momentum for both 2$\gamma 1p$ and $2\gamma 0p$
selections, using [0, 0.075, 0.15, 0.225, 0.3, 0.375, 0.45, 0.525, 0.6, 0.675,
and 0.9] GeV/c bin limits. In the fit, MC predicted coherent NC $1\pi^{0}$
events are scaled by a normalization factor $N_{coh}$, and MC predicted non-
coherent NC $1\pi^{0}$ events are scaled on an event-by-event basis depending
on their corresponding true $\pi^{0}$ momentum according to
$(a+b|\vec{p}^{\leavevmode\nobreak\ true}_{\pi^{0}}|)$, where the true
$\pi^{0}$ momentum is given in [GeV/c]. This linear scaling as a function of
$\pi^{0}$ momentum was chosen because it was the simplest implementation that
was consistent with the observed data-to-MC deficit, as observed in Fig. 5(a).

At each set of fitting parameters ($N_{coh}$, $a$, $b$), a $\chi^{2}$ is
evaluated between the scaled prediction for this parameter set and the
observed data using the Combined-Neyman-Pearson $\chi^{2}$ [51]. The
$\chi^{2}$ calculation makes use of a covariance matrix including statistical
and systematic uncertainties and correlations corresponding to the scaled
prediction. Flux, cross section, detector and geant4 systematic uncertainties
are included in the fit including bin-to-bin systematic correlations. As the
goal of the fit is to extract the normalization and scaling parameters of the
coherent and non-coherent NC $1\pi^{0}$ rates, the cross-section normalization
uncertainties of coherent and non-coherent NC $1\pi^{0}$ are not included.
Note that the cross-section normalization uncertainties of coherent and non-
coherent NC $1\pi^{0}$ are only removed for the purposes of this fit and not
for the cross section extraction described in the following section.

The data-extracted best-fit parameters correspond to $a=0.98$ and $b=-1.0$
[c/GeV] for the scaling parameters of the non-coherent NC $1\pi^{0}$ events,
and $N_{coh}=2.6$ for the NC coherent $\pi^{0}$ normalization factor with no
enhancement, $N_{coh}=1$, being allowed within the $1\sigma$ error bands. This
best-fit gives a $\chi^{2}$ per degree of freedom ($dof$) of 8.46/17. The
$\chi^{2}/dof$ at the genie central value (CV) prediction is 13.74/20 yielding
a $\Delta\chi^{2}$ between the genie CV and the best-fit point of 5.28 for 3
$dof$. Although the goodness-of-fit $\chi^{2}/dof$ values for both scenarios
are acceptable due to the generally large uncertainties, the momentum-
dependent shift is preferred over the genie CV at the 1.43$\sigma$ level. The
1D marginalized $\Delta\chi^{2}$ distributions in Fig. 10 also confirm that
the genie CV prediction agrees with data within uncertainty. The data and MC
comparisons of the reconstructed $\pi^{0}$ momentum distributions scaled to
the best-fit parameters are provided in Fig. 11 and, compared to those
corresponding to the genie CV, show better agreement with data after the fit.

Figure 10: The distribution of marginalized $\Delta\chi^{2}$, as a function of
flat normalization factor for (a) coherent NC 1$\pi^{0}$ momentum-independent
scaling factor, (b) non-coherent NC 1$\pi^{0}$ momentum-independent scaling
factor, and (c) coefficient of momentum-dependent scaling factor for NC non-
coherent 1$\pi^{0}$, marginalized over the other two parameters. The red
arrows indicate parameter values expected for the genie central value
prediction. The 1$\sigma$, 90% and 99% C.L. lines are based on the assumption
that the distribution follows a $\chi^{2}$ distribution with 1 degree of
freedom.

(a) $2\gamma 1p$

(b) $2\gamma 0p$

Figure 11: The data-MC comparison for (a) $2\gamma 1p$ and (b) $2\gamma 0p$
selections, as a function of reconstructed $\pi^{0}$ momentum. Monte Carlo
predictions at the central value and at the best-fit point
($\text{N}_{coh}=2.6$, $a=0.98$, $b=-1.0$ [c/GeV]) are both shown, with
prediction and corresponding systematic error evaluated at the genie central
value in salmon, and at the best-fit in blue. Note that the systematic
uncertainties on the plot include MC intrinsic statistical error and all the
systematic errors (flux, cross-section and detector), with the exception of
cross section normalization uncertainties on coherent and non-coherent NC
1$\pi^{0}$.

While the data suggest that genie may over-estimate NC $1\pi^{0}$ production,
the results demonstrate that the genie prediction of NC $1\pi^{0}$s is
accurate within uncertainty. This validates the approach of using the measured
NC $1\pi^{0}$ event rate as a powerful in situ constraint of genie-predicted
NC $1\pi^{0}$ backgrounds as in [4]. We stress that while this result
motivates a momentum dependent shift in how we model our NC $\pi^{0}$ events,
we do not apply this change to our modeling, relying instead on the fact that
the assigned uncertainty covers the observed discrepancy. Future work will
investigate further the possibility of tuning genie with results such as these
to obtain better model predictions. On the other hand, it is natural to
extract a data-driven NC 1$\pi^{0}$ cross-section on argon using these
selections, and compare to a number of neutrino event generators, including
genie. This is described below.

##  IV Inclusive and Exclusive NC 1$\pi^{0}$ Cross-Sections on Argon

###  IV.1 Methodology

The prescription for calculating the cross section is provided in Eq. (5)
where the components are defined as follows: $N^{\text{obs}}_{NC1\pi^{0}}$,
$N_{\text{cosmic}}$, and $N_{\text{bkg}}$ denote the number of selected data
events, the number of background events arising from cosmic rays traversing
the detector, and the number of expected beam-correlated background events,
respectively; $\epsilon_{NC1\pi^{0}}$ denotes the efficiency of selecting
NC1$\pi^{0}$ events; $\Phi$ denotes the integrated flux; and
$N_{\text{targets}}$ denotes the number of argon atoms in the fiducial volume
of the analysis.

$\sigma_{NC1\pi^{0}}=\frac{N^{\text{obs}}_{NC1\pi^{0}}-N_{\text{cosmic}}-N_{\text{bkg}}}{\epsilon_{NC1\pi^{0}}\Phi
N_{\text{targets}}}.$ (5)

This calculation is performed independently using each of the 2$\gamma 1p$ and
2$\gamma 0p$ selections to measure an exclusive cross section. These
measurements are denoted as the NC$\pi^{0}$+1p and NC$\pi^{0}$+0p cross
sections, respectively; in each case one or zero protons is explicitly
required in the signal definition (described in detail below). Additionally,
the calculation is performed using the combined 2$\gamma(0+1)p$ selection to
measure a semi-inclusive cross section, NC$\pi^{0}$, with no requirement on
the number of protons in the signal definition. Note that this semi-inclusive
measurement is efficiency-corrected to include 2+ proton final states that are
not included in the final selected events (11% of the total number of NC
$\pi^{0}$ interactions, per GENIE). As noted in Section II.3, the simulation
is run multiple times to encompass the effect of varying underlying sources of
systematic uncertainty. The calculation of each cross section is performed
separately in each of these systematic “universes” to guarantee that all
correlations between components of the cross section are handled correctly.
This is done using tools from the MINERvA Analysis Toolkit [52].

Both selections, as well as their combination, correspond to approximately,
but not identically, the same POT, provided in Table 2 (due to differences in
the computational processing of the two samples). To extract the semi-
inclusive cross section from the combined 2$\gamma(0+1)p$ selection, the
relevant 2$\gamma 0p$ distributions are scaled down by the ratio between the
POT of the 2$\gamma 1p$ data sample (smaller POT) and the POT of the 2$\gamma
0p$ data sample and then are added to the 2$\gamma 1p$ distributions. This
operation is performed for $N^{\text{obs}}_{NC1\pi^{0}}$, $N_{\text{cosmic}}$,
$N_{bkg}$, and the numerator of the efficiency.

$N^{\text{obs}}_{NC1\pi^{0}}$ and $N_{\text{cosmic}}$ are measured in data and
therefore there is no systematic uncertainty attributed to them. These values
are reported in Table 2. $N_{bkg}$ is extracted from the simulation, and we
note that many of the key backgrounds in this analysis are shared with
MicroBooNE’s search for NC $\Delta$ radiative decay [4]. The dominant
contributions to the uncertainty on the background event rate for each
analysis are from FSI related to inelastic nucleon scattering, pion and
nucleon absorption, and pion charge-exchange. The axial and vector mass
parameters, $m_{A}$ and $m_{V}$, respectively, in the charged current resonant
form factors are also sources of significant uncertainties; this is consistent
with expectation because of the large background due to charged-current
interactions in which a $\pi^{0}$ is produced.

The efficiency of the selection is constructed using as the numerator the
number of signal events passing all reconstruction cuts and analysis BDTs in
simulation and as the denominator the total number of signal events preceding
the application of any cuts or analysis BDTs. The difference in signal
definition between the semi-inclusive measurement and each of the two
exclusive measurements is contained in the efficiency denominator. The
exclusive measurements and the semi-inclusive measurement each use a distinct
efficiency denominator, reflecting the total number of simulated events truly
satisfying the corresponding signal definition. In each of the exclusive
measurements, the signal definition is taken to be NC1$\pi^{0}$ with exactly
zero or one final-state proton with a kinetic energy above 50 MeV. In the
semi-inclusive measurement, the signal definition is taken to be NC1$\pi^{0}$,
notably allowing for any number of protons in the final state. The efficiency
for each analysis is reported in Table 2.

The integrated flux is calculated separately for all four neutrino species
($\nu_{\mu}$, $\bar{\nu}_{\mu}$, $\nu_{e}$, $\bar{\nu}_{e}$), and the sum of
these integrated fluxes is used to normalize each cross section measurement.
This choice was made because of the inability to identify the species of the
incident neutrino based on the neutral current final state. The integrated
flux is varied within each flux systematic “universe”, and the correlations
between each varied flux and the corresponding variations in the predicted
background and efficiency are taken into account when extracting the cross
sections.

The number of argon atoms used is calculated as $N_{\text{targets}}=\rho
VN_{A}/M_{Ar}$, where $V=5.64\times 10^{7}\text{cm}^{3}$ is the fiducial
volume of the analysis, $\rho=1.3954$ g/cm3 is the density of argon at the
temperature in the cryostat, and $M_{Ar}=39.948$ g/mol is the molar mass of
argon. A 1% uncertainty is assigned to the number of targets to reflect
variation in the argon density through temperature and pressure fluctuations.

Table 2: Summary table of all inputs to the cross section calculation, reported as $\sigma\pm\text{sys}\pm\text{stat}$ uncertainty. Note that while the individual errors on the components are given here, the full uncertainty on the cross section is calculated properly assuming full correlations. | NC$\pi^{0}$ (semi-inclusive) | NC$\pi^{0}+1p$ (exclusive) | NC$\pi^{0}+0p$ (exclusive)
---|---|---|---
Samples Used |  $2\gamma(0+1)p$ Selection |  $2\gamma 1p$ Selection |  $2\gamma 0p$ Selection
N${}_{\text{targets}}$ [$10^{30}$ Ar atoms] | 1.187 $\pm$ 0.119 $\pm$ 0.00
Flux [$10^{-10}$ $\nu$/POT/cm2] | 7.876 $\pm$ 0.902 $\pm$ 0.00
POT of sample [$10^{20}$ POT] | 5.84 $\pm$ 0.12 $\pm$ 0.00 | 5.84 $\pm$ 0.12 $\pm$ 0.0 | 5.89 $\pm$ 0.12 $\pm$ 0.00
Efficiency | 0.089 $\pm$ 0.003 $\pm$ 0.001 | 0.107 $\pm$ 0.006 $\pm$ 0.002 | 0.060 $\pm$ 0.003 $\pm$ 0.001
Selected data [evts] | 1125.9 $\pm$ 0.0 $\pm$ 33.5 | 634.0 $\pm$ 0.0 $\pm$ 25.2 | 496.0 $\pm$ 0.0 $\pm$ 22.3
Cosmic data [evts] | 177.0 $\pm$ 0.0 $\pm$ 8.9 | 96.1 $\pm$ 0.0 $\pm$ 6.5 | 81.5 $\pm$ 0.0 $\pm$ 6.1
Background [evts] | 345.8 $\pm$ 51.1 $\pm$ 9.0 | 279.6 $\pm$ 43.5 $\pm$ 7.2 | 208.3 $\pm$ 33.5 $\pm$ 7.0
Background-subtracted rate [evts] | 603.2 $\pm$ 51.1 $\pm$ 35.8 | 258.3 $\pm$ 43.5 $\pm$ 27.0 | 206.1 $\pm$ 33.5 $\pm$ 24.1
$\sigma_{NC1\pi^{0}}$ [$10^{-38}$cm2/Ar] | 1.243 $\pm$ 0.185 $\pm$ 0.076 | 0.444 $\pm$ 0.098 $\pm$ 0.047 | 0.624 $\pm$ 0.131 $\pm$ 0.075

###  IV.2 Results and Interpretation

The calculation of each cross section from its components follows from Eq. (5)
and is summarized in Table 2. The resulting cross sections are shown in Fig.
12, compared to the simulated cross sections from several neutrino event
generators including genie, NuWro [53], and neut [54]. NEUT and GENIE both use
the Berger-Sehgal model as their foundation for modeling pion production in
the $\Delta(1232)$ resonance region, while NuWro implements a custom model
optimized for the $\Delta$ resonance peak region. The complete details of the
models used in each generator are discussed at length in Ref. [55]. The genie
curve shown is generated using the MicroBooNE cross-section “tune” [29], which
does not modify the genie v3.0.6 central value prediction (because the tune
did not adjust the NC interaction model), but does define the uncertainty on
the prediction. The error bars on the data points include systematic error
associated with the modeling of background events that enters into the cross-
sections via background subtraction as well as error associated with the
modeling of the signal events that enters into the cross-sections via
efficiency correction. The shaded band around the GENIE central value
prediction shows the error associated with the prediction of the signal cross
section.

We observe a consistent deficit in data compared to genie for the combined
semi-inclusive measurement and for each of the individual NC$\pi^{0}$+1p and
NC$\pi^{0}$+0p exclusive measurements. Overall, the neut predictions most
closely match the reported measurements across semi-inclusive and exclusive
final states. Additionally we note that while NuWro is generally consistent
with the other generators in its semi-inclusive and exclusive 1p predictions,
its exclusive 0p prediction is higher compared to neut and genie predictions.
The extracted semi-inclusive NC$\pi^{0}$ cross section is 1.24 $\pm$ 0.19
(syst) $\pm$ 0.08 (stat) [$10^{-38}$cm2/Ar] which is 26% lower than the genie
prediction of 1.68 [$10^{-38}$cm2/Ar]. We calculate a $\chi^{2}$ test
statistic comparing our data measurement with full uncertainties to the CV of
each model prediction for both exclusive NC$\pi^{0}$+0p and NC$\pi^{0}$+1p
cross sections simultaneously (i.e. two degrees of freedom). The resulting
values are 7.6, 7.7, 2.4, and 5.1 for comparisons against genie v3, genie v2,
neut, and NuWro, respectively.

The corresponding breakdown of uncertainty for each of the measurement
channels is shown in Fig. 13. In all cases the flux, genie, and statistical
uncertainties are dominant. The dominant contributions to the genie
uncertainties enter into the cross section via the background subtraction and,
as noted above, arise from the modeling of final-state interactions and the
axial and vector mass parameters governing CC resonant pion production.

Figure 12: Measured semi-inclusive NC$\pi^{0}$, exclusive NC$\pi^{0}$+1p, and
exclusive NC$\pi^{0}$+0p cross sections, each compared to the corresponding
genie v3 (G18_10a_02_11) cross section and its uncertainty (shaded red bands)
as well as other contemporary neutrino generators. Inner error bars on data
points are statistical only; outer are statistical and systematic, summed in
quadrature. Figure 13: Error budget for the semi-inclusive NC$\pi^{0}$,
exclusive NC$\pi^{0}$+1p, and exclusive NC$\pi^{0}$+0p cross section
measurements.

To further understand this measurement, it is instructive to compare it to
previous experimental measurements of NC$\pi^{0}$ production. We compare our
measurement to that performed by MiniBooNE which operated in the same beamline
as MicroBooNE but which utilized a different detector material (mineral oil,
CH2) as the neutrino scattering target. In MiniBooNE’s NC $\pi^{0}$ analysis,
they measured NC interactions wherein only one $\pi^{0}$ and no additional
mesons exited the target nucleus (no requirement on the number or identity of
outgoing nucleons was made). A final flux-averaged cross section of 4.76 $\pm$
0.76 $\pm$ 0.05 [$10^{-40}$cm2/nucleon] was reported [25]. We can compare this
result to our semi-inclusive result by comparing each to the same neutrino
generator. This is shown in Fig. 14 where we compare both to the default GENIE
v3.0.6 on argon and mineral oil respectively. We observe that while this
result on argon lies slightly below the expected central value, both our
result and MiniBooNE’s agree with GENIE v3.0.6 within assigned uncertainties.

Figure 14: Comparison of this semi-inclusive result on argon (left) as well as
that from MiniBooNE on mineral oil CH2 (right), to the same GENIE v3.0.6.
While the published MiniBooNE result was originally compared to a prediction
made using the NUANCE v3 generator [56], we have instead generated a
prediction using GENIE to aid in a comparison between the two experimental
results. MiniBooNE’s statistical uncertainty is small and only the systematic
error bar is visible. Shaded error bands show GENIE uncertainty only.

##  V Summary

In summary, we report the highest statistics measurement to date of neutrino
neutral current single pion production on argon, including the first exclusive
measurements of this process ever made in argon. These cross sections are
measured using the MicroBooNE detector exposed to the Fermilab Booster
Neutrino Beamline, which has $\langle E_{\nu}\rangle<1$ GeV. As presented
within this paper, kinematic distributions of the $\pi^{0}$ momentum and angle
relative to the beam direction provide some sensitivity to contributions to
this process from coherent and non-coherent pion production and suggest that,
given the currently analyzed MicroBooNE data statistics, the nominal genie
neutrino event generator used for MicroBooNE Monte Carlo modeling describes
the observed distributions within uncertainties. This has provided an
important validation check justifying the use of this sample as a powerful
constraint for backgrounds to single-photon searches in MicroBooNE, e.g. in
[4].

Using a total of 1,130 observed NC $\pi^{0}$ events, a flux-averaged cross
section has been extracted for neutrinos with a mean energy of 804 MeV and has
been found to correspond to $1.243\pm 0.185$ (syst) $\pm 0.076$ (stat),
$0.444\pm 0.098\pm 0.047$, and $0.624\pm 0.131\pm 0.075$
$[10^{-38}\textrm{cm}^{2}/\textrm{Ar}]$ for the semi-inclusive NC$\pi^{0}$,
exclusive NC$\pi^{0}$+1p, and exclusive NC$\pi^{0}$+0p processes compared to
$1.678$, $0.722$, and $0.774$ $[10^{-38}\textrm{cm}^{2}/\textrm{Ar}]$ in the
default genie prediction used by MicroBooNE. Comparison to other generators
including neut and NuWro show reasonable agreement with the neut predictions
found to be slightly more consistent with the MicroBooNE data-extracted cross-
section for all three exclusive and semi-inclusive processes.

###### Acknowledgements.

This document was prepared by the MicroBooNE collaboration using the resources
of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of
Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi
Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359.
MicroBooNE is supported by the following: the U.S. Department of Energy,
Office of Science, Offices of High Energy Physics and Nuclear Physics; the
U.S. National Science Foundation; the Swiss National Science Foundation; the
Science and Technology Facilities Council (STFC), part of the United Kingdom
Research and Innovation; the Royal Society (United Kingdom); and The European
Union’s Horizon 2020 Marie Sklodowska-Curie Actions. Additional support for
the laser calibration system and cosmic ray tagger was provided by the Albert
Einstein Center for Fundamental Physics, Bern, Switzerland. We also
acknowledge the contributions of technical and scientific staff to the design,
construction, and operation of the MicroBooNE detector as well as the
contributions of past collaborators to the development of MicroBooNE analyses,
without whom this work would not have been possible.

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