The MicroBooNE Collaboration ††thanks<EMAIL_ADDRESS>
# First measurement of quasi-elastic $\Lambda$ baryon production in muon anti-
neutrino interactions in the MicroBooNE detector

P. Abratenko  Tufts University, Medford, MA, 02155, USA  D. Andrade Aldana
Illinois Institute of Technology (IIT), Chicago, IL 60616, 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  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  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  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  B. Bogart  University of
Michigan, Ann Arbor, MI, 48109, USA  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  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  SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, 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  Z. Djurcic
Argonne National Laboratory (ANL), Lemont, IL, 60439, 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  W. Foreman  Illinois Institute of Technology (IIT),
Chicago, IL 60616, 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  University of Oxford, Oxford OX1 3RH, 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  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  B. Irwin  University of Minnesota,
Minneapolis, MN, 55455, 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  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  Rutgers University,
Piscataway, NJ, 08854, 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  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  N. Martinez  Kansas State University (KSU),
Manhattan, KS, 66506, USA  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  K. Miller  University of Chicago, Chicago, IL,
60637, USA  J. Mills  Tufts University, Medford, MA, 02155, USA  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  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  N. Pallat  University of Minnesota, Minneapolis, MN,
55455, USA  V. Paolone  University of Pittsburgh, Pittsburgh, PA, 15260, USA
A. Papadopoulou  Argonne National Laboratory (ANL), Lemont, IL, 60439, USA
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  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  I. Pophale  Lancaster University, Lancaster LA1 4YW, United
Kingdom  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
Argonne National Laboratory (ANL), Lemont, IL, 60439, 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. 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  Tufts University, Medford, MA, 02155, USA  M. Ross-
Lonergan  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  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  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  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  J. Tyler
Kansas State University (KSU), Manhattan, KS, 66506, 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  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  L. E. Yates
Fermi National Accelerator Laboratory (FNAL), Batavia, IL 60510, 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

###### Abstract

We present the first measurement of the cross section of Cabibbo-suppressed
$\Lambda$ baryon production, using data collected with the MicroBooNE detector
when exposed to the neutrinos from the Main Injector beam at the Fermi
National Accelerator Laboratory. The data analyzed correspond to $2.2\times
10^{20}$ protons on target of neutrino mode running and $4.9\times 10^{20}$
protons on target of anti-neutrino mode running. An automated selection is
combined with hand scanning, with the former identifying five candidate
$\Lambda$ production events when the signal was unblinded, consistent with the
GENIE prediction of $5.3\pm 1.1$ events. Several scanners were employed,
selecting between three and five events, compared with a prediction from a
blinded Monte Carlo simulation study of $3.7\pm 1.0$ events. Restricting the
phase space to only include $\Lambda$ baryons that decay above MicroBooNE’s
detection thresholds, we obtain a flux averaged cross section of
$2.0^{+2.2}_{-1.7}\times 10^{-40}$ cm${}^{2}/$Ar, where statistical and
systematic uncertainties are combined.

In this letter we describe the measurement of the cross section for Cabibbo-
suppressed (direct) $\Lambda$-baryon production in a restricted phase space
using the MicroBooNE detector. The MicroBooNE detector MicroBooNE:2016pwy  is
a liquid argon time projection chamber (LArTPC) with several years of
accumulated data using the neutrinos produced by the Main Injector (NuMI) beam
MINERvA:2016iqn ; Adamson:2015dkw  at the Fermi National Accelerator
Laboratory. This enables studies of rare processes such as the direct
production of $\Lambda$ baryons in interactions between muon anti-neutrinos
and argon in the detector:

$\displaystyle\bar{\nu}_{\mu}+\textrm{Ar}\to\mu^{+}+\Lambda+X,$ (1)

where $X$ denotes additional final state particles with no strangeness. This
process is poorly constrained by existing measurements Ammosov:1986jn ;
Eichten:1972bb ; Erriquez1 ; Erriquez2 ; Brunner:1989kw ; Fanourakis:1980  and
is sensitive to the physics of the underlying neutrino interaction and nuclear
effects, including nucleon form factors and axial masses, hyperon-nucleus
potentials, and final state interactions Thorpe:2020tym ; Sobczyk:2019uej ;
Singh:2006xp . Such a process constitutes a potential source of background in
proton decay experiments, such as DUNE DUNE:2020fgq ; DUNE:2020ypp  and Hyper-
Kamiokande Hyper-Kamiokande:2018ofw . If the $\Lambda$ baryon undergoes a
secondary interaction with a nucleon, a kaon can be produced, mimicking the
$p\to K+\nu$ signal in these experiments. Additionally, this process is
exclusively the result of anti-neutrino interactions and therefore could be
used to constrain contamination from anti-neutrinos in a neutrino beam.

This letter describes the measurement of a restricted phase space cross
section for direct $\Lambda$ production using the MicroBooNE detector. To
maximize statistics, we combine data collected when the NuMI beam was
operating in its neutrino (forward horn current, FHC) and anti-neutrino
(reverse horn current, RHC) modes.

The selection searches for muon-anti-neutrino interactions with argon nuclei,
contained within the fiducial volume defined in Ref. MicroBooNE:2021zul , in
which a $\Lambda$ is produced through the strangeness-violating quasi-elastic
process and subsequently decays to a proton and negatively charged pion. This
decay produces a distinctive V shaped signature in the detector, an example of
which can be seen in Fig. 1.

Figure 1: A candidate $\bar{\nu}_{\mu}+\textrm{Ar}\to\mu^{+}+\Lambda$
interaction observed in MicroBooNE data. A cosmic ray is also reconstructed in
the event. The ionization is displayed by the color scale, with green/red
indicating weaker/stronger intensity. There is a region without active wires
partway along the muon track.

We employ the GENIE GENIE  event generator to simulate neutrino interactions
inside the MicroBooNE cryostat and surrounding material, in conjunction with
Geant 4 GEANT4:2002zbu  for particle propagation and secondary interactions,
followed by a simulation of the detector response to the interactions of those
particles. The event selection employs the Pandora multi-algorithm
reconstruction framework MicroBooNE:2017xvs  which identifies a reconstructed
neutrino vertex and the associated particles, which are classified as either
tracks or showers.

To isolate $\Lambda$ production events, we apply a number of criteria. Only
data collected using a trigger synchronized with the spills of the NuMI beam
are used to prevent any contamination from neutrinos produced by the Booster
Neutrino Beam MiniBooNE:2008hfu . A neutrino vertex must be reconstructed in
the fiducial volume defined in an earlier analysis MicroBooNE:2021zul  with at
least three associated tracks and no showers. Particle identification (PID)
scores MicroBooNE:2021ddy  are calculated for each track indicating whether
they are muon-like or proton-like, and the longest muon-like track is selected
as the muon candidate.

An array of boosted decision trees Hocker:2007ht  is employed to generate a
response score from several variables such as PID scores MicroBooNE:2021ddy
and the Pandora track/shower classification score VanDePontseele:2020tqz  to
select a pair of tracks consistent with the $\Lambda\to p+\pi^{-}$ decay. The
momenta of the proton and $\pi^{-}$ are estimated from the lengths and
directions of their respective tracks; the sum of these quantities gives the
momentum of the $\Lambda$ candidate. The reconstructed invariant mass $W$ and
angular deviation, defined as the angle between the line connecting the
primary vertex to the decay vertex and the momentum vector of the $\Lambda$
candidate, are calculated. Events with $1.09<W<1.19$ GeV and angular deviation
$<14^{\circ}$ are retained.

After deconvolution and noise removal MicroBooNE:2018swd ; MicroBooNE:2018swe
; MicroBooNE:2017qiu , the charge deposited on the wires of the detector can
be used to visualize the trajectories of particles produced in the
interaction. This is the information displayed in Fig. 1, in which the
green/red regions indicate nonzero activity. This is analyzed to determine if
the muon candidate and $\Lambda$ candidate form separate “islands” of
activity. This tests whether the $\Lambda$ candidate created a true secondary
vertex, a feature which discriminates $\Lambda$ production from background
processes with similar kinematics. The MicroBooNE detector records information
from three planes of parallel wires, one of which is oriented vertically while
the others are angled at $\pm 60^{\circ}$ from the vertical, providing
different views of the interaction. This test is performed separately using
information from each of the wire planes, enabling identification of the decay
vertex even when the orientation of the event makes this difficult when viewed
from one of the planes. The island finding algorithm is described in detail in
the supplemental material SupplementalMaterial .

After the automated event selection is complete, the background primarily
consists of other sources of $\Lambda$ baryons and hyperons, including other
quasi-elastic-like interactions (“direct”), deep inelastic scattering (DIS),
and resonant interactions (RES). A small number of background events produced
by secondary interactions of neutrons is predicted, in which charged particles
are liberated, most commonly $p\pi^{\pm}$ and $pp$ pairs, which can lead to a
similar V shape. The remainder is due to mis-reconstruction of events. Cosmic
rays and out-of-cryostat neutrino interactions (“dirt”) are included in the
simulation but none pass the selection. The numbers of events from each
category selected in the MC simulation are shown in Table 1. The final
efficiency of the automated selection is $6.8\%$.

A visual scan of event displays of the selected data is performed to remove
background selected due to reconstruction problems. To evaluate the background
rejection power and reliability of this technique, a blinded study with five
scanners was completed, using Monte Carlo (MC) simulated events that had
passed the automated selection. The mean selection rates of the five scanners
are calculated for the signal and each category of background, which
multiplied by the number of events of each type passing the automated
selection yields a new set of predictions. The signal and rates of each source
of background, before and after including the visual scanning, are compared in
Table 1. To maintain blindness in the final measurement, a separate set of MC
simulated events is mixed with the data from the signal region to conceal the
number of data events from the scanners. The visual scan reduces the final
selection efficiency to $6.1\%$.

As an additional test to confirm the validity of the visual scanning
procedure, an alternative analysis without hand scanning was performed. To
constrain the predicted background due to reconstruction problems, a sideband
is employed, created by inverting the cuts applied to the invariant mass and
angular deviation. The result of this alternative selection and constraint are
also used to calculate the cross section and yield a result consistent with
the one obtained when performing the visual scan, albeit with slightly poorer
sensitivity. This constraint method is described in the supplemental material
SupplementalMaterial .

Event Category | Selected MC | After Visual Scan
---|---|---
Signal | $2.5\pm 0.6$ | $2.3\pm 0.6$
Other $\Lambda$ | $0.7\pm 0.2$ | $0.5\pm 0.3$
Other hyperons | $1.0\pm 0.5$ | $0.7\pm 0.5$
Neutrons | $0.3\pm 0.1$ | $0.1\pm 0.1$
Mis-reconstruction | $0.9\pm 0.4$ | $0.1\pm 0.1$
Total Background | $2.8\pm 0.9$ | $1.4\pm 0.8$
Table 1: Events selected from Monte Carlo (MC) simulation using standard GENIE
model parameters, before and after the hand scanning selection efficiencies
are applied. Combined MC simulation statistical and systematic uncertainties
are shown.

Two sources of flux uncertainty are considered: the hadron production modeling
and the beamline geometry. The flux uncertainty in the predicted number of
signal events passing the event selection using the default simulation is
small (approximately 11%) due to the high neutrino energy threshold for
$\Lambda$ production. The uncertainties on the production rates for the
hadrons that subsequently decay into neutrinos dominate the flux uncertainty
in this energy region AliagaSoplin:2016shs . The uncertainty in the background
due to the flux is approximately 10%. The uncertainty in the total
$\bar{\nu}_{\mu}$ flux is around 23%.

To determine the uncertainties from the models used to derive the cross
sections for background neutrino interactions, we use the results of the fits
described in Ref. MicroBooNE:2021ccs , with 44 parameters varied in parallel
to produce 600 variations. In addition, we use predictions from 8 alternative
models to estimate uncertainties resulting from parameters that are difficult
to vary continuously. A 100% uncertainty is assumed for the background from
other CCQE-like hyperon production processes. The overall uncertainty due to
background neutrino interaction cross sections is around 35%.

Secondary interactions in the argon outside the nuclear remnant are described
by Geant 4 GEANT4:2002zbu ; we use the Geant4Reweight Calcutt:2021zck  package
to determine the uncertainties from the description of these reinteractions by
varying proton, charged pion, and $\Lambda$ baryon interaction cross sections.
We assume an uncertainty of $20\%$ on the proton and $\Lambda$ interaction
cross sections, while for the charged pions a pair of multi-target, multi-
channel fits are performed using external data to extract uncertainties on the
cross sections of individual interaction channels, as described in Ref.
Calcutt:2021zck . To include uncertainties on the neutron interaction cross
sections, a fit is performed to data from the CAPTAIN experiment
CAPTAIN:2019fxo , yielding an uncertainty of 26% on the total $n$-Ar cross
section. This uncertainty is included by re-scaling the rate of selected
events containing secondary interactions of neutrons by $\pm 26$%. The
resulting uncertainties in the predicted signal and background are 3% and 6%
respectively.

To assess the uncertainties on the modeling of the detector response, a set of
simulated neutrino interactions in MicroBooNE is fed into several alternative
detector models. These models vary the quantity of scintillation light
produced, the wire response MicroBooNE:2021roa ; MicroBooNE:2019efx , the
space charge MicroBooNE:2019koz ; MicroBooNE:2020kca , and the recombination
of argon ions. The simulated detector response from each of these models is
reconstructed and the $\Lambda$ selection criteria are applied. The
differences between the numbers of events selected using the standard detector
simulation and these alternative models are used to calculate a systematic
uncertainty. The uncertainties in the signal and background due to the
detector response model are 7% and 16% respectively.

The selection efficiencies and background acceptance rates of the five
individual scanners are treated as five sets of predictions, the spread of
which is used as an uncertainty. This is the largest source of uncertainty in
the background prediction, contributing a fractional uncertainty of
approximately 45%, while the uncertainty in the signal due to the visual
scanning is estimated to be 7%.

Lastly, MC simulation calculations of the selection efficiency show some non-
uniformity with respect to the shape $\Lambda$ baryon production cross
section. MC simulation events generated with the GENIE and NuWro generators
were analyzed, producing two separate estimates of the selection efficiency.
The difference between these two efficiency estimates, a relative change of
approximately 19%, was adopted as another uncertainty in the selection
efficiency. Variations in the model parameters, described in the supplemental
material SupplementalMaterial , were also studied but the resulting effects on
the efficiencies are smaller.

MicroBooNE is sensitive to protons and charged pions with momenta $>0.3$ GeV/c
and $>0.1$ GeV/c respectively, and the phase space of the measured cross
section is therefore restricted. The relation between the restricted phase
space cross section, $\sigma_{R}$ and the total cross section depends on the
momentum distribution of the $\Lambda$ baryons produced, and is described in
the supplemental material SupplementalMaterial . $\sigma_{R}$, is related to
the number of events observed in data, $N_{\textrm{obs}}$, by:

$\displaystyle\sigma_{R}=\frac{N_{\textrm{obs}}-B}{T\Phi\Gamma\epsilon},$ (2)

where $B$ is the predicted number of background events, $T$ the number of
argon nuclei in the fiducial volume, $\Phi$ the total muon anti-neutrino flux,
$\Gamma=0.64$ the branching fraction for the process $\Lambda\to p+\pi^{-}$
ParticleDataGroup:2020ssz , and $\epsilon$ the average selection efficiency.

To account for asymmetries in the statistical uncertainties on the data and MC
simulation, we employ a Bayesian procedure to calculate the full posterior
distribution on the extracted cross section. Bayesian posterior distributions
of the selection efficiency and background acceptance are estimated with the
TEfficiency class TEfficiency . The data statistical uncertainty is included
by applying Bayes’ theorem to the Poisson likelihood function, $P(N_{\rm
obs}|N)$:

$P(N|N_{\rm obs})=\frac{P(N_{\rm obs}|N)P(N)}{\int
P(N_{\textrm{obs}}|N)P(N)dN},$ (3)

from which we sample values of $N$. $P(N)$ is the Bayesian prior of $N$;
uniform priors are used for $N$, the background acceptance and selection
efficiency.

| $\epsilon$ | $\Phi$ | $B$
---|---|---|---
$\epsilon$ | 0.04572 | -0.00116 | 0.03237
$\Phi$ | -0.00116 | 0.05339 | 0.01887
$B$ | 0.03237 | 0.01887 | 0.33123
Table 2: Fractional covariance matrix between the uncertainties on the
selection efficiency $\epsilon$, the $\bar{\nu}_{\mu}$ flux $\Phi$, and the
predicted number of background events $B$. Figure 2: Posterior distribution
describing the extracted cross section compared with the MicroBooNE GENIE tune
MicroBooNE:2021ccs  and three predictions from the NuWro event generator. The
NuWro predictions include the effect of final state interactions, while GENIE
does not take them into account. The standard axial mass used by NuWro is
$1.03$ GeV.

Fig. 2 shows the Bayesian posterior probability distribution on the restricted
phase space cross section, which is extracted by repeatedly generating values
of $N$, $B$, and $\epsilon$ according to the Bayesian prior distributions
obtained above. Each time these values are generated, a value of $\sigma_{R}$
is calculated according to

$\displaystyle\sigma_{R}=\frac{N-(B+B_{0}\alpha_{B})}{T(\Phi+\Phi_{0}\alpha_{\Phi})\Gamma(\epsilon+\epsilon_{0}\alpha_{\epsilon})}.$
(4)

The fractional covariance matrix in Table 2 is combined with the central
values of $B$, $\Phi$, and $\epsilon$, to obtain their total covariance
matrix, which is used to construct a three dimensional Gaussian distribution
from which the systematic shifts, $\alpha_{B}$, $\alpha_{\Phi}$, and
$\alpha_{\epsilon}$, applied respectively to $B$, $\Phi$, and $\epsilon$ are
sampled. The uncertainties in $T$ and $\Gamma$ are assumed to be negligible.

After unblinding the data in the signal region, 5 events are selected by the
automated selection. The invariant masses of these events are compared with MC
simulation predictions in Fig. 3. The five hand scanners selected 3, 3, 4, 4,
and 5 events from the signal region. To extract the final cross section
posterior distribution, we sum the Bayesian posterior distributions
corresponding to observing those numbers of events and normalize the result to
1; the resulting distribution is shown in Fig. 2. The uncertainty in the cross
section is obtained by constructing a 68% credible interval from this
distribution. We obtain a cross section of $2.0^{+2.2}_{-1.7}\times 10^{-40}$
cm${}^{2}/$Ar (combining statistical and systematic uncertainties), a value
consistent with predictions from the GENIE GENIE  and NuWro Thorpe:2020tym
event generators. If we only apply the statistical fluctuations in Eq. 4, we
obtain uncertainties of ${}^{+2.0}_{-1.4}$, while if only the systematic
fluctuations are included, the uncertainties are ${}^{+1.2}_{-1.0}$,
indicating the statistics are the dominant source of uncertainty.

Figure 3: Selected MC simulation events and data, shown as a function of the
reconstructed invariant mass, when using the purely automated selection. Black
triangles indicate the locations of the selected data events. The mass of the
$\Lambda$ baryon is 1.115 GeV ParticleDataGroup:2020ssz . The hatched regions
indicate combined statistical and systematic uncertainties.

In summary, the first measurement of the rare channel of quasi-elastic-like
$\Lambda$ production in a LArTPC, using a mostly automated selection, has been
performed. As this is a rare channel, the dominant source of uncertainty is
data statistics. The adoption of a dedicated reconstruction algorithm for
secondary vertices may lead to some improvement in the selection efficiency,
but this will require significant development and is therefore beyond the
scope of this work. Data collected between 2017 and 2020 awaits analysis, with
which an approximately fourfold increase in signal events is expected.

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 UK
Research and Innovation (UKRI) Future Leaders Fellowship. 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. For the purpose of open
access, the authors have applied a Creative Commons Attribution (CC BY) public
copyright license to any Author Accepted Manuscript version arising from this
submission.

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