# Study of pion production in $\nu_{\mu}$ interactions on 40Ar in DUNE using
GENIE and NuWro event generators

H.R. Sharma1111E-mail<EMAIL_ADDRESS>Srishti Nagu2222E-mail:
<EMAIL_ADDRESS>Jyotsna Singh2333E-mail<EMAIL_ADDRESS>,
R.B. Singh2444E-mail<EMAIL_ADDRESS>, Baba Potukuchi1555E-mail:
<EMAIL_ADDRESS>Department of Physics, University of Jammu, Jammu,
India1 Department of Physics, Lucknow University, Lucknow, India2

###### Abstract

The study of pion production and the effects of final state interactions (FSI)
are important for data analysis in all neutrino experiments. For energies at
which current neutrino experiments are being operated, a significant
contribution to pion production is made by resonance production process. After
its production, if a pion is absorbed in the nuclear matter, the event may
become indistinguishable from quasi-elastic scattering process and acts as a
background. The estimation of this background is very essential for
oscillation experiments and requires good theoretical models for both pion
production at primary vertex and after FSI. Due to FSI, the number of final
state pions is significantly different from the number produced at primary
vertex. As the neutrino detectors can observe only the final state particles,
the correct information about the particles produced at the primary vertex is
overshadowed by FSI. To overcome this difficulty, a good knowledge of FSI is
required which may be provided by theoretical models incorporated in Monte
Carlo (MC) neutrino event generators. They provide theoretical predictions of
neutrino interactions for different experiments and serve as a bridge between
theoretical models and experimental measurements. In this work, we will
present simulated events for two different MC generators - GENIE and NuWro,
for pion production in $\nu_{\mu}$CC interactions on 40Ar target in DUNE
experimental set up. A brief outline of theoretical models used by generators
is presented. The results of pion production are presented in the form of
tables showing the occupancy of primary and final state pion topologies with
100$\%$ detector resolution and with kinetic energy detector threshold cuts.
We observe that NuWro (v-19.02.2) is more transparent (less responsive) to
absorption and charge exchange processes as compared to GENIE (v-3.00.06),
pions are more likely to be absorbed than created during their intranuclear
transport and there is need to improve detector technology to improve the
detector threshold for better results.

##  I Introduction

Driven by new experiments and modern detector technology, neutrino physics is
entering a precision era and this requires an improved theoretical and
phenomenological description of neutrino interactions. Neutrinos rarely
interact with matter and can travel long distances without any interactions.
The neutrino properties are still not entirely understood and this makes its
research a challenge for both theoretical and experimental points of view.
Electroweak theory of Standard Model (SM) describes the neutrino interactions.
In its earlier formulation, SM assumed the neutrino to be massless particle
and and so the mass-mixing was not expected unlike quarks. The mass mixing
would also be possible in lepton sector if neutrino had mass and a neutrino
produced in a specific flavour could be later seen as neutrino of another
flavour, the phenomenon called neutrino oscillations. No fundamental principle
in physics requires neutrino to be massless. The strength of mass mixing in
leptonic sector is defined by Pontecorvo-Maki-Nakagawa-Sakata (PMNS)
matrixGiganti:2017fhf . PMNS can be expressed by three mixing angles
($\theta_{12}$, $\theta_{23}$, $\theta_{13}$) and CP phase factor
($\delta_{cp}$). Apart from these mass mixing parameters, the probability for
neutrino oscillation depends on actual neutrino masses (or on the difference
of their squares) i.e. $\Delta m^{2}_{21}$ = $m^{2}_{2}$ \- $m^{2}_{1}$;
$\Delta m^{2}_{32}$ = $m^{2}_{3}$ \- $m^{2}_{2}$; $\Delta m^{2}_{31}$ =
$\Delta m^{2}_{32}$ \+ $\Delta m^{2}_{21}$.

For current and future neutrino experiments, understanding of charged current
(CC) neutrino-nucleus interactions in few GeV energy region is very important.
But the study of these interactions in this energy region is complicated and
requires many intermediate steps, such as understanding the neutrino-nucleus
cross-sections, description of nuclear models, modelling of hadronization and
intranuclear hadron transport and nuclear effects. For this we require a
canonical Monte Carlo generator which may take into consideration all these
steps. There are a number of Monte Carlo generators dedicated to the
description of neutrino interactions like ANIS Gazizov:2004va , GENIE
Andreopoulos:2015wxa , NuWro (Golan:2012wx, ; Sobczyk:2008zz, ), GiBUU
(Buss:2011mx, ; Gibuu, ), MARLEY Gardiner:2021qfr , FLUKA Battistoni:2009zzb ,
NEUT Hayato  and Nuance Casper:2002sd . All these generators are based on
similar assumptions. The primary neutrino interactions and final state
interactions are considered separately in each generator.

In this work, GENIE and NuWro generators are taken into consideration for
simulation work of pion production in neutrino-nucleus interactions. Pions
form an important background MicroBooNE:2021sne  in many oscillation
experiments and are also theoretically challenging due to processes they
undergo in FSI Naaz:2018amr . For both GENIE and NuWro, DUNE flux has been
used for interactions on 40Ar target. For each generator only the charged
current (CC) interactions were considered. The processes enabled were quasi-
elastic (QE) scattering, resonance (RES) production, deep-inelastic scattering
(DIS), coherent (COH) pion production. The data generated was then analysed
for various pion topologies before and after final state interactions
(secondary interactions). It is crucial for the presently running experiments
like T2K T2K:2019bcf  and NOvA NOvA:2019cyt  and the future long-baseline
neutrino-oscillation experiments like DUNE (DUNE:2020lwj, ; DUNE:2020ypp, ;
DUNE:2021cuw, ) and Hyper-KamioKande Hyper-Kamiokande:2018ofw  to clearly
understand neutrino-nucleus interactions.

The DUNE (Deep Underground Neutrino Experiment) is a worldwide effort to
construct a long-baseline neutrino oscillation experiment at Fermi National
Accelerator Laboratory (FNAL) USA. It has a Near Detector (ND) located 575 m
from the neutrino source and 60 m underground DUNE:2020jqi  on the Fermilab
site in Illinois and a Far Detector (FD) located approximately 1.5 km
underground at a distance of nearly 1300 km from Fermilab at Sanford
Underground Research facility (SURF) in South Dakota, USA. The primary
scientific goals of this extremely advanced detector are to carry out a
comprehensive program of neutrino oscillation measurements using $\nu_{\mu}$
and $\overline{\nu}_{\mu}$ beams from Fermilab and constraining the CP
violation phase in leptonic sector. As the distance between FD and ND is about
1300 km, it will provide a baseline facility of length 1300 km to study matter
effect. Both ND and FD will use Ar target material to observe the neutrino
spectrum that will help to overcome various systematic uncertainties. ND will
observe unoscillated neutrino spectrum and FD will observe oscillated neutrino
spectrum. ND and FD at DUNE will have different dimensions and technology. The
DUNE Near Detector has three primary detector components and two of those
components have capability to move off the beam axis: 1) A 50 ton LArTPC (ND-
LAr) constructed using ArgonCube with pixellated read out 2) The ND-GAr
detector (also sometimes called the multipurpose detector, or MPD) that
consists of high pressure gaseous argon TPC surrounded by an electromagnetic
calorimeter (Ecal) in a 0.5 T magnetic field 3) An on-axis beam monitor called
System for on-Axis Neutrino Detection (SAND) that monitors the flux of
neutrinos. It consists of an inner tracker surrounded by an Ecal inside a
large solenoidal magnet. In current scenario, two options are being explored
for the inner tracker, one based on a combination of plastic scintillator
cubes with TPCs and other based on straw-tubes.

The capacity of ND-LAr and ND-GAr to move to take data in positions off the
beam axis is reffered to as DUNE-PRISM (DUNE Precision Reaction Independent
Spectrum Measurement). The DUNE FD consists of four similar LArTPCs, each
LArTPC will have fiducial mass of at least 40 kt. Each LArTPC detector will be
installed in a cryostat with internal dimensions 15.1 m (w) $\times$ 14 m (h)
$\times$ 62 m (l) with a total LAr mass of about 17.5 kt. Excellent tracking
and calorimetry performance will be provided by LArTPC which makes it an ideal
choice for the DUNE-FD.

Accelerator generated beams are used in many long baseline neutrino
oscillation experimentsNagu:2019uco . As these neutrino beams are not mono
energetic, reconstruction of neutrino energy is required and for that complete
information of final state particles is necessary. The identification of
primary state particles in the presence of nuclear effects is a difficult task
since the particles produced in the primary neutrino-nucleus vertex and the
particles captured by the detector can be different because of FSI. This means
energy reconstruction of neutrinos from final state particles needs careful
examination. Neutrino experiments use heavy nuclear targets for large event
statistics (which reduces statistical errors) but the use of heavy targets
gives boost to nuclear effects thereby shifting the attention to systematic
errors. The current knowledge of nuclear effects is still insufficient to have
clear understanding of systematic errorsNaaz:2018amr . It must be emphasized
that success of any neutrino experiment depends on successful understanding,
quantifying and reducing of systematic errors coming from modelling neutrino-
nucleus interactions.

In our simulation, the DUNE neutrino flux flux:link  in the energy range
0.125-19.875 GeV on ${}^{40}Ar$ nuclei was used. The neutrino flux used in our
simulation work is shown in Fig. 1. It covers the energy spectrum from about
hundred MeV to tens of GeV and peaks around 2.5 GeV. The Neutrino at Main
Injector (NuMI) beamline facility at Fermilab provides an intense, high
purity, wide-band neutrino beam with an initial power of 1.2 MW (will be
further upgraded to 2.4 MW) for which 1.1$\times$1021 protons are expected per
year from the accelerator. The primary beam of protons coming from the main
injector accelerator in the energy range 60-120 GeV is made to smash on the
graphite target which results in the production of pions and kaons. These
mesons will be further focussed toward a 200 m long decay pipe with the help
of magnetic horns where they will decay into neutrinos and leptons. The
neutrino and anti-neutrino beams can be separately ejected by changing the
polarity of focussing magnets.

This paper is organised into following sections: Section-II contains
description of pion production in neutrino-nucleus interactions. In this
section QE, RES, DIS and COH processes are discussed in detail. An outline of
GENIE and NuWro MC generators with various models used by them is given in
Section-III. Results of simulation are given in Section-IV followed by summary
and conclusions in Section-V.

Figure 1: DUNE flux as a function of neutrino energy used in our work.

##  II Pion Production in neutrino-nucleus interactions

The simplest description of neutrino-nucleus interactions is built upon two
attributes: a characterization of neutrino-nucleus scattering and a model for
nucleons in the nucleus. The modelling of neutrino-nucleus interactions is
complex as it requires linking together many different pieces of theory. We
will focus on neutrino-nucleus interactions in the nuclear environment. The
description of hadronization process and final state interaction models are
often specific to a particular generator.
In its simplest and most common approach (called impulse approximation
approach), neutrino-nucleus scattering is treated as the incoherent sum of
scattering from free nucleons in the nucleus. But practically, nucleons in the
nucleus are not independent particles but bound states and more complex
nuclear dynamics are involved in calculating the cross-section. The total
cross-section of neutrino-nucleus charged-current scattering has the form
Kuzmin:2005bm :

$\sigma^{tot}_{\nu N}=\sigma^{QE}_{\nu N}+\sigma^{1\pi}_{\nu
N}+\sigma^{2\pi}_{\nu N}+........+\sigma^{1K}_{\nu N}+......+\sigma^{DIS}_{\nu
N}$ (1)

Here $\nu$ represents neutrino, N is nucleon, $\sigma^{tot}_{\nu N}$ is sum
total of all cross sections, $\sigma^{QE}_{\nu N}$ is cross section for QE
scattering, $\sigma^{1\pi}_{\nu N}$ is cross section for single pion
production and so on.

Neutrinos interact weakly with matter by the exchange of $W^{\pm}$ and $Z^{0}$
bosons. At low neutrino energies, QE scattering process is favoured. With the
increase in neutrino energy RES and then DIS processes become predominant
(Fig. 2). DUNE flux peaks around 2.5 GeV and at this energy RES and DIS cross-
sections have almost similar magnitudes. This is a problem experimentally, as
in a detector, RES events can have signatures indistinguishable to DIS events.
Thus, it is hard to measure each process separately.

In QE scattering target nucleon remains a single nucleon in the final state
and only changes its charge in CC weak interactions. In this scattering no
pions are produced directly, but can be produced through final state
interactions. Inside the nuclear environment, hadrons can be scattered
elastically or inelastically, can be absorbed or charged exchanged and can
even produce more pions. Thus, it is expected that a small number of events
with no pions in primary state may produce pions in the final state. For
$\nu_{\mu}$ beam, the CC QE scattering reaction is written as:

$\nu_{\mu}+n\longrightarrow\mu^{-}+p$ (2)

Here $\nu_{\mu}$ is muon neutrino, n is neutron, $\mu^{-}$ is muon and p is
proton.

Figure 2: Neutrino-nucleus cross-sections on ${}^{40}Ar$ target for QE, RES
and DIS processes, measured using NuWro (left) and GENIE (right) generators.

Fig. 3 (left) shows how pions are produced in QE scattering process and how a
pion can be absorbed (right) inside the nucleus Andreopoulos:2015wxa  during
its intranuclear transport. Although the dominant processes that produce pions
directly are DIS, RES and COH. These processes are shown in Fig. 4
Antonello:2009ca .

Figure 3: Pion production in QE scattering (left) and absorption in RES
scattering (right) Andreopoulos:2015wxa  Figure 4: Pion production via various
processesAntonello:2009ca

In RES scattering, pions are produced from resonances. In RES production
process, a neutrino excites the target nucleon to a resonance state. The
produced resonance state quickly decays into a nucleon and a single pion
state. The dominant contribution from this process comes from $\Delta$ (1232)
resonance state, although production of higher resonance states is also
possible. The CC RES scattering processes are illustrated as under (for
$\nu_{\mu}$ beam):

$\nu_{\mu}+p\longrightarrow\mu^{-}+\Delta^{++};\Delta^{++}\longrightarrow
p+\pi^{+}$ (3)

$\nu_{\mu}+n\longrightarrow\mu^{-}+\Delta^{+};\Delta^{+}\longrightarrow
n+\pi^{+}$ (4)

$\nu_{\mu}+n\longrightarrow\mu^{-}+\Delta^{+};\Delta^{+}\longrightarrow
p+\pi^{0}$ (5)

If a pion produced in a RES process gets absorbed in the nucleus then it
becomes difficult to identify whether this process is a RES process. Thus the
resulting event gives the impression of a different process and is called a
fake event. In a particular interaction channel, pure events are those in
which particles detected by the detector are the same as were produced at the
primary vertex.

In DIS, a high energy neutrino penetrates deep inside the nucleon and scatters
off a quark in the nucleon via exchange of W and Z bosons producing a lepton
and a hadronic system in the final state. For CC $\nu_{\mu}$ interaction, the
process looks like:

$\nu_{\mu}+N\longrightarrow\mu^{-}+n\pi^{\pm}+X$ (6)

Where N is a nucleon (proton or neutron), n is a number and X is any set of
final nucleons.

Neutrinos can also interact with the whole nucleus coherently producing pions
(coherent (COH) pion production). For CC $\nu_{\mu}$ interaction, the process
can be written as:

$\nu_{\mu}+A\longrightarrow\mu^{-}+A^{\prime}+m^{+}$ (7)

Where A is the nucleus in initial state, $A^{\prime}$ is the nucleus in final
state and $m^{+}$ = $\pi^{+}$, $k^{+}$, $\rho^{+}$ …….

The common approach with Monte Carlo generators is to use the Relativistic
Fermi Gas (RFG) model Smith2  modified by Bodek and Ritchi to describe the
nuclear environment. In the model, fermi motion of individual nucleons is
taken into account but its implementation often differs for different neutrino
generators. The importance of considering Pauli blocking Benhar:2006nr ,
impulse approximation Frullani:1984nn  and use of spectral functions Benhar
is also taken into account for better description. The description of
hadronisation and the propagation of secondary particles to come out of the
nucleus is also necessary. The simulation must cover the description of both
re-scattering and absorption effects and for this modelling of final state
interactions is required.

##  III GENIE and NuWro Monte Carlo Generators

Neutrino event generators are the simulation tools which are used in the study
of neutrino physics and these generators can be optimized using experimental
data gathered from some previous experiments. Generators work as a bridge
between experimental and theoretical frameworks. The two neutrino event
generators used in this work are GENIE (Generates Events for Neutrino
Interaction Experiments) and NuWro (developed by Wroclaw University). In our
simulation studies, we have used version 3.00.06 of GENIE and version 19.02.2
of NuWro which are the latest stable releases. GENIE is a universal neutrino
event generator, developed by international collaboration and written in C++.
It is a modern and most sophisticated platform for simulating neutrino events
and is developed by taking into consideration ongoing neutrino oscillation
experiments. It simulates neutrino interactions for all neutrino flavours and
all targets over energy range from few MeV to several hundred GeV. This
generator has already been used by experiments like MINOS Evans:2013pka ,
MINERvAMINERvA:2004gta , T2KT2K:2019bcf  , MicroBooNEMicroBooNE:2007ivj ,
NOvANOvA:2019cyt  and AgroNEUTSoderberg:2009qt . NuWro is more theory
oriented, developed by Wroclaw University and written in C++. It is simple but
complete package for generating neutrino-nucleus interactions. NuWro clearly
specifies incoming (in), primary state (out) and final state (post) particles
of an interaction. In this generator simulation parameters can be fixed in a
plane text file (params.txt) and it gives output in a root file. For
scattering off free nucleon, NuWro can simulate events for neutrino energies
from threshold to TeV. In NuWro, a beam can be set manually or can be loaded
from ROOT format file, there are choices for description of target nucleus
including Fermi gas and spectral functions, there are various parametrizations
of nuclear form factors and there is a detector geometry module. Many quantum
effects like formation zone and Pauli blocking are included. This makes NuWro
a good tool for the use in neutrino experiments. Recently it has been
successfully used by experiments like T2K and MINERvA.

###  III.1 GENIE

The physics models used in GENIE can be easily understood by classifying them
into three categories: cross-section models, hadronization models and nuclear
physics models. For cross-sections, charged-current quasi-elastic scattering
is described using Llewellyn-Smith model LlewellynSmith:1971uhs  using latest
BBBA07 form factors Bodek:2007wz . Rein-Sehgal modelRein:1980wg  has been used
for the production of baryon resonances. For DIS interactions, Bodek and Yang
model Bodek:2002ps , with modification at low $Q^{2}$, is used. Rein-Sehgal
model with an updated PCAC formula Dieter  is used for coherent pion
production interactions. The hadronization process employs default AGKY model
GENIE:2021wox . It includes a phenomenological description of low invariant
mass region using Koba-Nielson-Olsen (KNO) scalingKoba:1972ng , while at
higher masses it gradually switches over to the PYTHIA/JETSET model, the
transition being gradual and continuous. To take into consideration the effect
of nuclear environment, implementation of Fermi Gas model with modification by
Bodek and Ritchie, is used to include nucleon-nucleon correlations. The
factors like Pauli blocking and differences between free nucleon and nuclear
structure functions is also taken into consideration. The INTRANUCLEAR/hA
model is used to handle intranuclear hadron transport.

###  III.2 NuWro

In NuWro, QE events are simulated using Llewellyn-Smith model with latest
BBBA05 form factors Bradford:2006yz . In RES, only $\Delta$(1232) contribution
is based on Rein-Sehgal model and for rest of resonances, Adler-Rarita-
Schwinger modelGraczyk:2009qm  has been used. Rein-Sehgal model is used for
simulating coherent pion production interactions. This Rein-Sehgal modelLalit
is different from that used in RES processes. The RES region is defined by a
cut on invariant mass as W$<$ 1.4 GeV. NuWro uses Quark-Parton model
Sjostrand:2006za  to describe DIS events. The DIS contribution is turned on
when W$>$1.6 GeV. In the region 1.4 GeV$<$W$<$1.6 GeV, RES contribution is
linearly turned off as the DIS contribution is turned on. NuWro uses its own
hadronization model together with Bodek-Yang model. The effects of nuclear
environment are taken into consideration using Relativistic Fermi Gas (RFG)
model.

##  IV Results

For both GENIE and NuWro, we have generated 2 Million similar sets of events
using DUNE flux. The number of pions produced in both primary and final states
were obtained on event by event basis for each generator. These simulated
results are presented in the form of tables which show topologies of pion
produced in primary and final states. A primary state contains topology of
that pions which are produced in the primary neutrino-nucleus interactions. A
final state contains topology of that pions which are produced after any of
the secondary interactions (like intra-nuclear scattering or absorption) may
have taken place. For fair comparison of generators, a description of models
used by the generators and physics choices has already been given.

| Primary Hadronic States
---|---
Final states | $0\pi$ | $\pi^{0}$ | $\pi^{+}$ | $\pi^{-}$ | $2\pi^{0}$ | $2\pi^{+}$ | $2\pi^{-}$ | $\pi^{0}\pi^{+}$ | $\pi^{0}\pi^{-}$ | $\pi^{+}\pi^{-}$ | $\geq 3\pi$ | total
$0\pi$ | 407305 | 44000 | 132839 | 580 | 343 | 900 | 0 | 2763 | 45 | 710 | 727 | 590212
$\pi^{0}$ | 4751 | 151844 | 78184 | 449 | 4747 | 945 | 0 | 15006 | 122 | 645 | 3021 | 259744
$\pi^{+}$ | 7238 | 13618 | 424563 | 482 | 141 | 6715 | 0 | 14061 | 11 | 4520 | 3227 | 474576
$\pi^{-}$ | 1361 | 13113 | 5557 | 1787 | 178 | 22 | 0 | 801 | 120 | 4502 | 1458 | 28899
$2\pi^{0}$ | 45 | 6167 | 12943 | 136 | 14478 | 395 | 0 | 7310 | 71 | 358 | 5805 | 47708
$2\pi^{+}$ | 32 | 729 | 6223 | 30 | 22 | 17805 | 0 | 3191 | 01 | 238 | 4836 | 33108
$2\pi^{-}$ | 0 | 180 | 43 | 08 | 31 | 01 | 0 | 07 | 32 | 26 | 257 | 585
$\pi^{0}\pi^{+}$ | 228 | 11314 | 22979 | 314 | 1251 | 3664 | 0 | 79596 | 41 | 2462 | 10997 | 132846
$\pi^{0}\pi^{-}$ | 26 | 6021 | 3469 | 283 | 1369 | 25 | 0 | 928 | 467 | 2370 | 3827 | 18785
$\pi^{+}\pi^{-}$ | 160 | 19693 | 61491 | 1490 | 572 | 929 | 0 | 7018 | 59 | 30890 | 9646 | 131948
$\geq 3\pi$ | 794 | 11554 | 16293 | 2845 | 5724 | 6810 | 01 | 30554 | 1907 | 14505 | 190602 | 281589
total | 421970 | 278233 | 764584 | 8404 | 28856 | 38212 | 01 | 161235 | 2876 | 61226 | 234403 | 2000000
Table 1: Occupancy of primary and final state hadronic systems for 2 Million events in GENIE(v3.00.06) using DUNE flux on 40Ar target for $\nu_{\mu}$-nucleus CC interactions, without applying detector cuts. Different topological groups for primary and final state systems were made on the basis of number of pions produced event wise. | Primary Hadronic States
---|---
Final states | $0\pi$ | $\pi^{0}$ | $\pi^{+}$ | $\pi^{-}$ | $2\pi^{0}$ | $2\pi^{+}$ | $2\pi^{-}$ | $\pi^{0}\pi^{+}$ | $\pi^{0}\pi^{-}$ | $\pi^{+}\pi^{-}$ | $\geq 3\pi$ | total
$0\pi$ | 433572 | 31896 | 105429 | 1293 | 258 | 315 | 0 | 2898 | 17 | 1388 | 155 | 577221
$\pi^{0}$ | 6241 | 165238 | 28650 | 318 | 3433 | 166 | 0 | 21266 | 285 | 905 | 1434 | 227936
$\pi^{+}$ | 9768 | 7182 | 405364 | 49 | 144 | 3478 | 0 | 20052 | 03 | 10336 | 1121 | 457497
$\pi^{-}$ | 4342 | 8160 | 6090 | 13807 | 165 | 37 | 01 | 957 | 223 | 10592 | 787 | 45161
$2\pi^{0}$ | 884 | 3522 | 1818 | 09 | 14327 | 30 | 0 | 6834 | 74 | 226 | 5305 | 33029
$2\pi^{+}$ | 119 | 248 | 4596 | 0 | 18 | 12374 | 0 | 4170 | 0 | 638 | 2803 | 24966
$2\pi^{-}$ | 69 | 245 | 214 | 55 | 17 | 02 | 13 | 95 | 54 | 655 | 304 | 1723
$\pi^{0}\pi^{+}$ | 615 | 3864 | 8448 | 04 | 745 | 978 | 0 | 163227 | 16 | 3545 | 10181 | 191623
$\pi^{0}\pi^{-}$ | 436 | 2772 | 1524 | 117 | 847 | 21 | 0 | 1859 | 2970 | 3563 | 6081 | 20190
$\pi^{+}\pi^{-}$ | 651 | 2351 | 9279 | 167 | 71 | 275 | 0 | 5945 | 45 | 94266 | 9794 | 122844
$\geq 3\pi$ | 423 | 3120 | 5697 | 73 | 1522 | 1106 | 01 | 17519 | 263 | 9403 | 258684 | 297810
total | 457120 | 228598 | 577108 | 15892 | 21547 | 18782 | 15 | 244822 | 3950 | 135517 | 296649 | 2000000
Table 2: Occupancy of primary and final state hadronic systems for 2 Million
events in NuWro(v19.02.2) using DUNE flux on 40Ar target for
$\nu_{\mu}$-nucleus CC interactions, without applying detector cuts. Different
topological groups for primary and final state systems were made on the basis
of number of pions produced event wise.

For GENIE, the results of simulation for 2 Million events using default values
of axial masses: $M_{A}^{QE}$ =0.99 GeV/$c^{2}$, $M_{A}^{RES}$ =1.12
GeV/$c^{2}$, $M_{A}^{COH}$ =1.00 GeV/$c^{2}$, are shown in Table. 1. The table
shows the occupancy of primary and final state topologies. A comparison plot
for primary and final state pions is shown in Fig. 5 (left panel).

For NuWro, the results of simulation for 2 Million events using values of
axial masses: $M_{A}^{QE}$ =0.99 GeV/$c^{2}$, $M_{A}^{\pi}$ =0.94 GeV/$c^{2}$,
$M_{A}^{COH}$ =1.00 GeV/$c^{2}$ and NuWro’s intranuclear cascade model, are
shown in Table 2. A comparison plot for primary and final state pions is shown
in Fig. 5 (right panel).

From Table 1 (GENIE) and Table 2 (NuWro), it is clear that for two generators,
in many cases, there are some large differences in both primary and final
state topologies (i.e. the number of pions observed in primary and final
states). The differences can also be observed from Fig. 5, wherein plots for
number of pions observed on event by event basis, in primary and final states
have been shown for each generator. In many cases, these differences are above
statistical fluctuations. For example, number of $\pi^{+}$ observed in the
final state corresponding to $\pi^{0}$ in the primary state is 13618 for GENIE
while the corresponding number for NuWro is 7182, the difference is more than
47 $\%$. The number of $\pi^{0}$ observed in the final state corresponding to
$\pi^{+}$ in the primary state is 78184 for GENIE while the corresponding
number is 28650 for NuWro, the difference is even larger. The number of
$\pi^{-}$ observed in the final state corresponding to $\pi^{-}$ in the
primary state is 1787 for GENIE while the corresponding number is 13807 for
NuWro. These differences are attributed to the fact that DUNE flux peaks
around 2.5 GeV and in this energy region QE, RES and DIS processes all
contribute significantly towards total cross-section. Although the models used
to describe these processes separately are often common to a generator, still
there are many differences in the way in which a particular generator takes
into consideration the merging of the relative contributions in this energy
region. This effect in combination with other input parameters can lead to
observed differences from the same set of models.

Another observation from the two tables is that both the generators have
larger number of zero pion (0$\pi$) topologies in the final states than in the
primary states. This shows that pions are more likely to be absorbed than
created during their intranuclear transport. Generally, QE processes give rise
to topologies with 0$\pi$ in the primary and final states while RES and DIS
processes are likely to result in events with pions in the primary and final
states. Also both the generators have almost similar 0$\pi$ topologies. The
differences may arise due to the difference in the values of form-factor
parameters and nuclear models used in each generator.

Using Tables 1 and 2, percentage of events without pion $(0\pi)$, with exactly
one pion (1$\pi$) and with more than one pion ($>$1$\pi$) is shown in Table 3.
It is observed that single pion production (1$\pi$) is favoured in GENIE while
multiple pion production is more in case of NuWro.

Pions | GENIE | NuWro
---|---|---
$0\pi$ | 21.1$\%$ (29.5$\%$) | 22.9$\%$ (28.9$\%$)
$1\pi^{0}$ | 13.9$\%$ (13$\%$) | 11.4$\%$ (11.4$\%$)
$1\pi^{+}$ | 38.2$\%$ (23.7$\%$) | 28.9$\%$ (22.9$\%$)
$1\pi^{-}$ | 0.4$\%$ (1.4$\%$) | 0.8$\%$ (2.3$\%$)
$1\pi$ | 52.6$\%$ (38.2$\%$) | 41.1$\%$ (36.5$\%$)
$>$1$\pi$ | 26.3$\%$ (32.3$\%$) | 36.1$\%$ (34.6$\%$)
Table 3: Percentage of events without pion (0$\pi$), with exactly one pion (1$\pi$) and with more than one pion ($>$1$\pi$), at primary vertex. Values in brackets refer to results after final state interactions. Process | GENIE | NuWro
---|---|---
$\pi^{0}\longrightarrow\pi^{0}$ | 54.6$\%$ | 72.3$\%$
$\pi^{+}\longrightarrow\pi^{+}$ | 55.5$\%$ | 70.2$\%$
$\pi^{0}\longrightarrow 0\pi^{\prime}s$ | 15.8$\%$ | 14$\%$
$\pi^{+}\longrightarrow 0\pi^{\prime}s$ | 17.4$\%$ | 18.3$\%$
$\pi^{0}\longrightarrow\pi^{+}$ | 4.9$\%$ | 3.1$\%$
$\pi^{0}\longrightarrow\pi^{-}$ | 4.7$\%$ | 3.6$\%$
$\pi^{+}\longrightarrow\pi^{0}$ | 10.2$\%$ | 5$\%$
Table 4: Rate of events with single pion or no pion in the final state if
there was single pion in the primary state, without applying detector cuts.
Figure 5: Figure showing number of pions produced on event by event basis in
primary and final states for GENIE (left panel) and NuWro (right panel)
generators without applying detector cuts. Black lines represent primary
states and red lines represent final states in both the panels. Figure 6:
Figure showing number of pions produced on event by event basis in primary and
final states for GENIE (left panel) and NuWro (right panel) generators with KE
detector threshold cuts. Black lines represent primary states and red lines
represent final states in both the panels.

Tables 1 and 2 contain important information about final state interactions.
To extract this information, we have compiled a summary table (Table 4). The
summary table shows directly the topology changing effect due to intranuclear
hadron transport. In this table, we show for each generator, out of all events
with a given primary state topology, the fraction of those which have both the
primary and final state topologies. The first two rows show the transparency
of the nucleus. These rows give us the percentage of events with a single pion
in the primary state that will still have the single pion in the final state.
We observe that it is more likely that the pion created in the primary vertex
will not re-interact. The next rows show the fraction of pions absorbed and
the remaining three rows show the effect due to charge exchange. It is clear
that current version of NuWro (v19.02.2) has high transparency than current
version of GENIE (v3.00.06). This may be due to response of a generator to
absorption and charge exchange processes (NuWro could have too little and
GENIE could have too much). Taking into consideration the complex nature of
final state interactions, one can say that the agreement is still good despite
these differences. The analysed MC generators give quite a similar results. As
single pion events form the main background in neutrino oscillation
experiments, the analysis done may be quite useful.

CC1$\pi^{+}$ to CCQE cross-section ratio can be calculated from the
corresponding numbers in our simulation for both the generators. Table 5 shows
comparison of ratio for two generators. For primary hadronic sates, GENIE
ratio is higher than that of NuWro which shows that GENIE has higher cross-
section for single $\pi^{+}$ production. The corresponding ratio for MiniBooNE
data rescaled for isoscalar target and corrected for FSI’s is (1.318$\pm$
0.247) for neutrino energy of (2.1 $\pm$ 0.3) GeVMiniBooNE:2009koj . Also
percentage change in ratio due to FSI is 56 for GENIE and 39 for NuWro which
indicates that GENIE shows more effects of FSI on $\pi^{+}$ than NuWro.

Generator |  $1\pi^{+}/0\pi$ ( Primary state total) |  $1\pi^{+}/0\pi$ ( Final state total) | Percentage change after FSI
---|---|---|---
GENIE | 1.8 | 0.8 | 56
NuWro | 1.3 | 0.8 | 39
Table 5: The ratio 1$\pi^{+}/0\pi$ for GENIE (v3.00.06) and NuWro (v19.02.2)
using DUNE flux and 40Ar target

The analysis done and results shown up to now were with 100 percent detector
resolution (no detector cuts applied). We will now show the results with
detector cuts on kinetic energy (KE) thresholds taken from DUNE CDR
DUNE:2016ymp ; DUNE:2016rla ; DUNE:2015lol ). The KE thresholds used in our
analysis are summarized in Table 6. These thresholds are applied to the
outgoing pions and only pions with KE above these thresholds will be
identified in the final state. The results of simulation for different
topologies of pions observed in the primary state and final states, with KE
detector threshold cuts, are shown in Tables 7 and 8. Again there are
differences in both primary and final state topologies more or less similar to
differences observed in Tables 1 and 2. The differences can also be observed
from Fig. 6 where number of pions observed in primary and final states are
plotted on event by event basis.

Particle type | KE detection threshold
---|---
$e^{\pm}$, $\mu^{\pm}$, $\gamma$ | 30MeV
$\pi^{\pm}$ | 100MeV
p, n, other | 50MeV
Table 6: Detection thresholds for various final state particles at DUNE

If a pion has KE below the detector threshold, the pion is not identified in
the final state. Thus, in a final state with single pion topology, if the KE
of the pion is below the detector threshold, the pion will not be detected in
the final state and the event becomes a fake event for 0$\pi$ topology thereby
increasing its number. This is clear from Tables 1, 2, 7 and 8 that both the
generators have fairly larger number of events (entries) in final state for
0$\pi$ topology when KE threshold cuts have been applied than without such
cuts. For GENIE, the total number of 0$\pi$ events in the final state without
detector cuts (Table 1) is 590212 and with detector cuts the number is 766776
(Table 7) while for NuWro the corresponding numbers are 577221 (Table 2) and
746450 (Table 8) respectively. The change is about 23$\%$ in for both the
generators. On the other hand, in an event with multiple pions in the final
state, if one pion has KE below the detector threshold, that pion will not be
identified and the topology of final state changes thereby increasing the
number of events for the resulting topology state. Using Tables 7 and 8,
percentage of events in final state without pion $(0\pi)$, with exactly one
pion (1$\pi$) and with more than one pion ($>$1$\pi$), with detector cuts, is
shown in Table 9. For comparison, the corresponding results without applying
detector cuts are also given in the same table (i.e. Table 9). Thus, it is
clear that detector thresholds can give significant changes in pion topologies
in the final state and should be taken into account for correct analysis of
pions produced at the primary vertex.

| Primary Hadronic States
---|---
Final states | $0\pi$ | $\pi^{0}$ | $\pi^{+}$ | $\pi^{-}$ | $2\pi^{0}$ | $2\pi^{+}$ | $2\pi^{-}$ | $\pi^{0}\pi^{+}$ | $\pi^{0}\pi^{-}$ | $\pi^{+}\pi^{-}$ | $\geq 3\pi$ | total
$0\pi$ | 412822 | 80693 | 247916 | 1472 | 1060 | 3365 | 0 | 9361 | 197 | 2189 | 7701 | 766776
$\pi^{0}$ | 2898 | 135349 | 66084 | 519 | 9203 | 1398 | 0 | 28002 | 177 | 1085 | 13053 | 257768
$\pi^{+}$ | 4218 | 16922 | 371771 | 791 | 444 | 12399 | 0 | 27860 | 27 | 9658 | 12145 | 456235
$\pi^{-}$ | 891 | 15670 | 19761 | 1757 | 493 | 436 | 0 | 2550 | 163 | 9631 | 6086 | 57438
$2\pi^{0}$ | 38 | 3696 | 5373 | 98 | 11178 | 266 | 0 | 5337 | 67 | 320 | 12437 | 38810
$2\pi^{+}$ | 34 | 632 | 3379 | 89 | 61 | 12840 | 0 | 3210 | 07 | 820 | 8806 | 29878
$2\pi^{-}$ | 04 | 199 | 431 | 34 | 63 | 24 | 0 | 183 | 22 | 475 | 990 | 2425
$\pi^{0}\pi^{+}$ | 242 | 6301 | 11874 | 253 | 1365 | 2557 | 0 | 59936 | 94 | 2118 | 19201 | 103941
$\pi^{0}\pi^{-}$ | 42 | 3123 | 2441 | 206 | 1346 | 153 | 0 | 2220 | 375 | 2032 | 8017 | 19955
$\pi^{+}\pi^{-}$ | 141 | 8662 | 28289 | 1011 | 563 | 1305 | 01 | 6528 | 65 | 24269 | 18040 | 88874
$\geq 3\pi$ | 640 | 6986 | 7265 | 2174 | 3080 | 3469 | 0 | 16048 | 1682 | 8629 | 127927 | 177900
total | 421970 | 278233 | 764584 | 8404 | 28856 | 38212 | 01 | 161235 | 2876 | 61226 | 234403 | 2000000
Table 7: Occupancy of primary and final state hadronic systems for 2 Million events in GENIE(v3.00.06) using DUNE flux on 40Ar target for $\nu_{\mu}$-nucleus CC interactions with KE threshold detector cuts. Different topological groups for primary and final state systems were made on the basis of number of pions produced event wise. | Primary Hadronic States
---|---
Final states | $0\pi$ | $\pi^{0}$ | $\pi^{+}$ | $\pi^{-}$ | $2\pi^{0}$ | $2\pi^{+}$ | $2\pi^{-}$ | $\pi^{0}\pi^{+}$ | $\pi^{0}\pi^{-}$ | $\pi^{+}\pi^{-}$ | $\geq 3\pi$ | total
$0\pi$ | 446462 | 66167 | 193147 | 7180 | 1828 | 1751 | 01 | 16182 | 216 | 8463 | 5053 | 746450
$\pi^{0}$ | 3327 | 145671 | 20119 | 161 | 7584 | 252 | 0 | 42866 | 1303 | 1679 | 11212 | 234474
$\pi^{+}$ | 4487 | 5327 | 347435 | 50 | 199 | 6777 | 0 | 42241 | 22 | 23051 | 8966 | 438555
$\pi^{-}$ | 2129 | 5714 | 4835 | 8336 | 217 | 74 | 04 | 1605 | 435 | 22155 | 5525 | 51029
$2\pi^{0}$ | 221 | 1519 | 751 | 04 | 10210 | 15 | 0 | 4642 | 44 | 170 | 9744 | 27320
$2\pi^{+}$ | 20 | 112 | 1781 | 0 | 09 | 8775 | 0 | 2690 | 0 | 598 | 6839 | 20824
$2\pi^{-}$ | 15 | 80 | 71 | 24 | 09 | 0 | 10 | 66 | 32 | 576 | 592 | 1475
$\pi^{0}\pi^{+}$ | 144 | 1486 | 3160 | 01 | 443 | 592 | 0 | 123904 | 15 | 2374 | 24910 | 157031
$\pi^{0}\pi^{-}$ | 114 | 995 | 530 | 51 | 516 | 13 | 0 | 1419 | 1767 | 2317 | 13086 | 20808
$\pi^{+}\pi^{-}$ | 155 | 747 | 3536 | 68 | 42 | 199 | 0 | 3584 | 36 | 70881 | 22185 | 101433
$\geq 3\pi$ | 46 | 780 | 1443 | 17 | 490 | 334 | 0 | 5621 | 80 | 3253 | 188537 | 200601
total | 457120 | 228598 | 577108 | 15892 | 21547 | 18782 | 15 | 244822 | 3950 | 135517 | 296649 | 2000000
Table 8: Occupancy of primary and final state hadronic systems for 2 Million events in NuWro(v19.02.2) using DUNE flux on 40Ar target for $\nu_{\mu}$-nucleus CC interactions with KE detector threshold cuts. Different topological groups for primary and final state systems were made on the basis of number of pions produced event wise. | With Detector Cuts | Without Detector Cuts
---|---|---
Pions | GENIE | NuWro | GENIE | NuWro
$0\pi$ | 38.3$\%$ | 37.3$\%$ | 29.5$\%$ | 28.9$\%$
$1\pi^{0}$ | 12.9$\%$ | 11.7$\%$ | 13$\%$ | 11.4$\%$
$1\pi^{+}$ | 22.8$\%$ | 21.9$\%$ | 23.7$\%$ | 22.9$\%$
$1\pi^{-}$ | 2.9$\%$ | 2.6$\%$ | 1.4$\%$ | 2.3$\%$
$1\pi$ | 38.6$\%$ | 36.2$\%$ | 38.2$\%$ | 36.5$\%$
$>$1$\pi$ | 23.1$\%$ | 26.5$\%$ | 32.3$\%$ | 34.6$\%$
Table 9: Percentage of events in final state without pion (0$\pi$), with exactly one pion (1$\pi$) and with more than one pion ($>$1$\pi$), with KE detector threshold cuts. The results obtained without applying these cuts are also given for comparison. | With Detector Cuts | Without Detector Cuts
---|---|---
Process | GENIE | NuWro | GENIE | NuWro
$\pi^{0}\longrightarrow\pi^{0}$ | 48.6$\%$ | 63.7$\%$ | 54.6$\%$ | 72$.3\%$
$\pi^{+}\longrightarrow\pi^{+}$ | 48.6$\%$ | 60.2$\%$ | 55.5$\%$ | 70.2$\%$
$\pi^{0}\longrightarrow 0\pi^{\prime}s$ | 29$\%$ | 28.9$\%$ | 15.8$\%$ | 14$\%$
$\pi^{+}\longrightarrow 0\pi^{\prime}s$ | 32.4$\%$ | 33.5$\%$ | 17.4$\%$ | 18.3$\%$
$\pi^{0}\longrightarrow\pi^{+}$ | 6.1$\%$ | 2.3$\%$ | 4.9$\%$ | 3.1$\%$
$\pi^{0}\longrightarrow\pi^{-}$ | 5.6$\%$ | 2.5$\%$ | 4.7$\%$ | 3.6$\%$
$\pi^{+}\longrightarrow\pi^{0}$ | 8.6$\%$ | 3.5$\%$ | 10.2$\%$ | 5$\%$
Table 10: Rate of events with single pion or no pion in the final state if
there was single pion in the primary state with KE detector threshold cuts.
The results obtained without applying these detector cuts are also shown for
comparison.

The summary of results obtained from Tables 7 and 8 is shown in Table 10. It
is clear from Tables 4 and 10 that applied threshold cuts have shown certain
differences for all processes and appreciable differences for some of the
processes. In the process, $\pi^{0}$ $\longrightarrow$ $\pi^{0}$, the
percentage of event rate has been reduced from 55 (without detector cuts) to
49.1 (with detector cuts) in GENIE and from 71.5 (with detector cuts) to 62.8
(without detector cuts) in NuWro. Similar trend is followed in the process
$\pi^{+}$ $\longrightarrow$ $\pi^{+}$. Third and fourth rows show that
percentage of pion absorbed is more in the presence of KE detector threshold
cuts which is obvious as pions with KE less than detector threshold energy are
not taken in the final state and this decreases the percentage of final state
pions which in a sense is equivalent to a pion absorbed and not reaching the
final state thereby increasing the percentage of pion absorbed. The last three
rows show the effect of charge exchange where there is not much difference for
the processes with and without detector threshold cuts. As is clear from Table
10, the two generators are following similar trends for results with and
without detector threshold cuts. The results are also shown in Fig. 6 where
plots for number of pions observed on event by event basis in primary and
final states, with KE detector threshold cuts, have been shown for each
generator. It is clear that single pion events which come from RES scattering
are least effected by KE detector threshold cuts.

##  V Summary and Conclusions

In the present work, we report an extensive analysis of effect of final state
interactions on pion production for $\nu_{\mu}$-nucleus interactions on 40Ar
target. The results are obtained for 100$\%$ detector resolution and then
compared with the results obtained after applying KE detector threshold cuts.
The latest versions of GENIE and NuWro generators were used as simulation
tools. We have shown in Tables 1 and 2 that two generators, despite having
similar sets of models, can give some differences in results of pion
production both in primary and final states. This may be due to differences in
the implementation of models and other input parameters used in two
generators.
Both the generators show almost similar effects of final state interactions on
pions during their intranuclear transport after being produced at primary
vertex. This is clear from Table 3. It is clear from Fig. 5 that final state
interactions create a difference between pions observed in the detector (final
state pions) and pions produced at the primary vertex (primary state pions).
Tables 1 and 2 also make it clear that both the generators have larger number
of 0$\pi$ topologies in the final state than initial state leading to the
conclusion that pions are more likely to be absorbed than created during their
intranuclear transport.
We have also explained the topology changing effect during intranuclear hadron
transport, using summary table (Table 4). The effect is more for GENIE than
NuWro which shows that current version of NuWro shows high transparency than
the current version of GENIE.
CC1$\pi^{+}$ to CCQE cross-section ratio is calculated from the corresponding
numbers in our simulation for both the generators. Table 5, shows that GENIE
has a higher cross-section for single $\pi^{+}$ production than NuWro at the
primary vertex. Also percentage change in ratio after FSI is higher for GENIE
than NuWro. On the whole, taking into consideration the complex nature of FSI,
two generators are giving quite a similar results.
Finally, we applied KE threshold cuts on the outgoing particles which are to
be detected by the detector. Significant differences are observed on the final
state particles with the application of detector threshold cuts. This can be
seen from Table 10 and Figs. 5 and 6. Thus detector threshold are to be taken
into account to get correct information about the particles produced in
neutrino interactions and there is need to improve the detector technology to
improve the detector threshold for better results.

Our results indicate that for a neutrino oscillation experiment like DUNE, the
best strategy should be to have authentic accuracy of nuclear models used in
neutrino event generators applied for simulation and for that a canonical
neutrino event generator is required. As it is critical to understand nuclear
effects, a clear understanding of hadronic physics of neutrino-nucleus
interactions is required. The detector thresholds are to be minimized by using
advanced detector technology.

In future, more neutrino event generators would be used to compare the
results. Also 2p2h events (also called meson exchange(MEC) events) which have
signatures indistinguishable from QE events and act as background for QE
events, would be taken into consideration in our future simulation work.

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