# Investigation of the MicroBooNE neutrino cross sections on Argon

M. Martini  IPSA-DRII, 63 boulevard de Brandebourg, 94200 Ivry-sur-Seine,
France  Sorbonne Université, Université Paris Diderot, CNRS/IN2P3, Laboratoire
de Physique Nucléaire et de Hautes Energies (LPNHE), Paris, France  M. Ericson
Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822,
F-69622, Villeurbanne, France  Theory division, CERN, CH-12111 Geneva  G.
Chanfray  Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR
5822, F-69622, Villeurbanne, France

###### Abstract

Experimental data of charged current inclusive neutrino cross sections on
argon as a function of different variables have recently appeared. We have
compared them to our theoretical approach. Overall we find an agreement in
spite of a tendency of underestimation in some specific regions. A new aspect
is the availability of data in terms of the energy transfer to the nucleus,
which allows a better separation of the different reaction mechanisms. We
explain the deterioration of agreement in specific kinematical conditions by
the absence in our model of two-pion production and other inelastic channels,
more important for MicroBooNE than for T2K.

##  I Introduction

In order to increase the number of interactions, neutrino experiments at
intermediate energies use complex nuclei as detectors. Following the MiniBooNE
measurement Aguilar-Arevalo et al. (2010) of charged current quasielastic-like
(CCQE-like) cross section, a large number of data has been collected, mainly
on carbon (the target nucleus of MiniBooNE, MINERvA, T2K and NOvA
experiments), but also on oxygen and iron. For a review see for example Refs.
Katori and Martini (2018); Alvarez-Ruso et al. (2018).

Another important nucleus is argon. Argon detectors are used in the context of
the short-baseline Fermilab neutrino program Machado et al. (2019) aimed at
the investigation of the possible existence of a sterile neutrino, a topic
recently revived by new MicroBooNE measurements Abratenko et al. (2022a, b,
c). Argon nucleus will also be used in DUNE, one of the next-generation long-
baseline neutrino oscillation experiments Branca et al. (2021). Recently,
after the pioneering measurements by ArgoNeuT Anderson et al. (2012), four
muon neutrino differential cross sections on argon have been published by the
MicroBooNE collaboration: two inclusive measurements Abratenko et al. (2019);
Abratenko et al. (2022d) that include all charged-current events in which one
muon is detected and two semi-inclusive ones, characterized by the detection
of zero pion, one muon and one proton Abratenko et al. (2020a) and by the
detection of zero pion, one muon and any number of protons Abratenko et al.
(2020b), respectively called CC0$\pi$1p and CC0$\pi$Np. These results refer to
flux-integrated cross sections. The flux involved is the Booster Neutrino Beam
(BNB), published in Ref. Abratenko et al. (2019) for the MicroBooNE
experiment. Its normalized behavior is very similar to the previous MiniBooNE
one Aguilar-Arevalo et al. (2009).

The aim of the present paper is to confront the predictions of our approach on
neutrino interactions with nuclei with the MicroBooNE experimental data on
argon, focusing on the inclusive ones. Other theoretical evaluations of
neutrino cross sections on argon have been performed Meucci et al. (2013);
Gallmeister et al. (2016); Van Dessel et al. (2018); Akbar et al. (2017); Van
Dessel et al. (2019); Nikolakopoulos et al. (2021); Barbaro et al. (2021);
Franco-Patino et al. (2021); Butkevich (2022); Abratenko et al. (2022e);
Gonzalez-Rosa et al. (2022).

##  II Our theoretical model

Our theoretical model has been described in detail in Ref. Martini et al.
(2009). It is based on nuclear response functions treated in the random phase
approximation (RPA) on top of a local Fermi gas calculation. It includes the
quasielastic cross section, the multinucleon emission and the coherent and
incoherent single pion production. In our works Martini et al. (2009, 2010) we
explained the debated MiniBooNE quasielastic-like cross section on carbon
Aguilar-Arevalo et al. (2010) by stressing the crucial role of the
multinucleon (also called 2p-2h or np-nh) excitations contribution which
sizeably increases the genuine quasielastic cross section. We have made in
Ref. Martini et al. (2011) an improvement of our original description of the
quasielastic channel with the introduction of relativistic corrections. Our
model has successfully reproduced several muon-neutrino flux-integrated double
differential cross sections: the MiniBooNE CCQE-like neutrino Martini et al.
(2011) and antineutrino Martini and Ericson (2013) ones, as well as their
combination Ericson and Martini (2015), the MiniBooNE CC1$\pi^{+}$ and the T2K
CC inclusive Martini and Ericson (2014), the T2K CC0$\pi$ for neutrinos Abe et
al. (2016) as well as for antineutrinos and their combination Abe et al.
(2020). Single differential electron-neutrino T2K CC inclusive cross sections
have been successfully reproduced as well Martini et al. (2016). The agreement
of our predictions with several neutrino flux-integrated differential cross
section data was, in some kinematical conditions (forward lepton scattering
angle, low $Q^{2}$), the result of a delicate balance between the quenching of
the quasielastic due to RPA effects and the multinucleon enhancement. In this
context, it is important to remind that the amount of RPA effects is model
dependent. When the starting point of the calculation is the local Fermi gas,
as in our case, these effects can lead to large reduction of the quasielastic
cross sections. On the contrary, when a proper nucleus ground state is
considered, i.e. when mean field potential and/or realistic spectral function
are used, RPA effects are smaller Pandey et al. (2015); Nieves and Sobczyk
(2017). Despite the differences on the treatment of the nucleus ground state,
and consequently on the amount of RPA effects, the results obtained for the
quasielastic cross section are globally in agreement each others when RPA
and/or spectral function effects are taken into account. This is shown in Ref.
Nieves and Sobczyk (2017) where the interplay between these two nuclear
effects is analyzed in large details. The correspondence between the response
function and the spectral function approaches is discussed also by us in Ref.
Chanfray et al. (2021), where we have shown that the amount of nucleon
correlations of our approach is compatible with the one obtained via ab-initio
calculations.

All the studies mentioned above concerned the 12C cross sections. In the
present article we want to confront our theory to recent inclusive MicroBooNE
data Abratenko et al. (2019); Abratenko et al. (2022d) which refer to 40Ar.
This nucleus has a different number of protons (18) and neutrons (22). In
order to keep the description close to our previous one on 12C, we perform the
calculations of nuclear responses, based on local density approximation, by
approximating both the proton and the neutron density profiles of 40Ar by the
proton density profile of 40Ca111footnotetext: The impact of 40Ar Fermi
momentum asymmetry for protons and neutrons on the quasielastic responses per
nucleon has been investigated by Barbaro et al. Barbaro et al. (2018) who find
small effects. It may justify our approximation to calculate the responses per
nucleon for the symmetric 40Ca.. For the quasielastic cross section of 40Ar,
we rescale the 40Ca results according to the real number of active nucleons,
i.e the quasielastic 40Ca results are multiplied by $\frac{22}{20}$. For one
pion production we do not consider a possible rescaling effect which is less
important since both protons and neutrons are active in this channel.
Concerning the 2p-2h excitations, for the quasi-deuteronic contribution, which
is the dominant term and goes as the product of the proton and neutron
densities, $\rho_{p}\rho_{n}$, the difference between argon and calcium
represents only a $1\%$ correction. This is due to the fact that the excess of
neutrons in argon with respect to calcium is equal to the deficit of protons.
For the np-nh sector, in our approach we include the nucleon-nucleon (NN)
short-range correlations, the $\Delta$-MEC contribution and the NN
correlations-MEC interference, that we denote N$\Delta$ interference. In this
work we calculate the $\Delta$-MEC contribution directly for 40Ca. Instead for
the NN and N$\Delta$ interference parts, assuming a linear $A$-dependence, we
simply rescale our previous parametrization for 12C (the so called “new” in
Ref.Martini et al. (2009)) by a factor $\frac{40}{12}$. For the NN
contributions this assumption is reasonable, as discussed in Ref. Mosel and
Gallmeister (2016), even if it deviates by about 20% from the full results
obtained in Ref. Mosel and Gallmeister (2016) which take into account nuclear
surface corrections: a ratio of about 4.2 for the presence of short-range
pairs in 40Ar vs. 12C is predicted in Ref. Mosel and Gallmeister (2016), while
$40/12=3.\bar{3}$.

Beyond the inclusive measurements Abratenko et al. (2019); Abratenko et al.
(2022d), the MicroBooNE collaboration also published two semi-inclusive
$\nu_{\mu}$ cross sections: one with one muon, no pion and one single proton
in the final state Abratenko et al. (2020a), commonly referred as CC0$\pi$1p
cross section, and another with one muon, zero pion and at least one proton in
the final state Abratenko et al. (2020b), called CC0$\pi$Np cross section.
Beyond the differences in the final states, the two measurements also differ
on the restrictions applied to the muon and proton phase-space. In the case of
CC0$\pi$1p, the proton kinematic constraints are $0.3<p_{p}<1.0$ GeV/c and
$\cos\theta_{p}>0.15$. The proton kinematic constraints in the CC0$\pi$Np
measurement are less stringent: $0.3<p_{p}<1.2$ GeV/c. Since our formalism is
based on inclusive response functions, which are built by integrating on the
nucleonic kinematical variables and depend only on the transferred energy
$\omega$ and on the norm of the momentum transfer $|\vec{q}|$, we cannot
constrain the kinematics of outgoing protons. Furthermore in our formalism we
do not include final state interactions (FSI) for the proton neither pion
absorption due to pion FSI. For these reasons our inclusive theoretical
predictions cannot be directly compared with the semi-inclusive measurements
and here we focus only on inclusive cross sections. The extension of our
formalism to semi-inclusive processes requires further theoretical
developments.

##  III Results on charged current inclusive cross sections

###  III.1 MicroBooNE and T2K double differential cross sections

In the charged current interaction inclusive measurement only the charged
lepton is detected and all reaction mechanisms (quasielastic, nuclear
resonances, multinucleon excitations, one- and multi-pion production, deep
inelastic scattering) can contribute to this process. Since all channels are
included, the inclusive measurements present two advantages with respect to
exclusive channels measurements. Firstly they are not affected by the
necessity to subtract the background which comes from the open channels other
than the channel in consideration. Second they accumulate more rapidly enough
statistics of events to allow more detailed cross sections evaluations. Indeed
the first MicroBooNE published cross section is the inclusive one Abratenko et
al. (2019) and concerns double differential cross sections. While instead the
subsequent exclusive results, CC0$\pi$1p Abratenko et al. (2020a) and
CC0$\pi$Np Abratenko et al. (2020b), refer to single differential cross
sections.

Figure 1: MicroBooNE and T2K normalized $\nu_{\mu}$ fluxes.

Notice that in the flux-integrated inclusive cross section, the relative
weight of the different mechanisms depend on the energy profile of the
neutrino beam as different channels peak in different neutrino energy regions.
In our present evaluation of the MicroBooNE flux-integrated double
differential cross section we assume that the quasielastic, the multinucleon
emission and the single pion production (coherent and incoherent) are the only
open channels. With this assumption we have successfully reproduced Martini
and Ericson (2014) the data of the T2K experiment whose neutrino flux peaks in
the same region as the MicroBooNE one, but has a different energy profile, as
shown in Fig. 1.

Figure 2: T2K flux-integrated $\nu_{\mu}$ CC inclusive double differential
cross section per nucleon of carbon as a function of the muon momentum
$p_{\mu}$ calculated in average for different cosine intervals of muon
scattering angle $\theta$. The experimental T2K polystyrene data are taken
from Ref. Abe et al. (2018). The different contributions to the inclusive
cross sections obtained in our approach are shown.

Before we turn to the inclusive MicroBooNE cross section on argon, we
investigate further the inclusive cross section per nucleon of carbon by
considering more recent inclusive T2K data on polystyrene Abe et al. (2018).
They are characterized by an increased angular acceptance and higher
statistics as compared to the previous ones of Ref. Abe et al. (2013) that we
used as a test of our approach in Ref. Martini and Ericson (2014). The larger
precision of these recent data allows a more stringent test of our model. In
Fig. 2 we compare our calculations with these data. Since the results are
given per nucleon, the difference between our theoretical calculation on
carbon and the experimental measurement, which involves carbon (86.1%),
hydrogen (7.4%) and oxygen (3.7%), can be ignored. The agreement is remarkable
in nearly all the bins. Some deviation appears in the forward direction for
$p_{\mu}>1.5$ GeV/c. A similar discrepancy appears in the comparison between
the data and the Monte Carlo simulations performed by T2K.

Figure 3: MicroBooNE flux-integrated $\nu_{\mu}$ CC inclusive double
differential cross section on argon per nucleon as a function of the muon
momentum $p_{\mu}$ calculated in average for different cosine intervals of
muon scattering angle $\theta$. The experimental MicroBooNE data are taken
from Ref. Abratenko et al. (2019). The different contributions to the
inclusive cross sections obtained in our model are shown.

We now turn to the MicroBooNE experiment. In Fig.3 we confront our
calculations with these data. We plot separately the different contributions
to the inclusive cross section: the quasielastic, the multinucleon emission
(np-nh) and the one pion production (coherent and incoherent). The overall
agreement is reasonable, though not as good as in the 12C T2K case: a
disagreement shows up for low $p_{\mu}$. The SuSA calculation of Ref. Barbaro
et al. (2021) displays a similar trend. The same features appear in the recent
SuSAv2 results Gonzalez-Rosa et al. (2022) which incorporate inelastic
contributions beyond Delta excitations, absent in our case.

###  III.2 MicroBooNE energy dependent cross sections

At this stage it is interesting to analyze new MicroBooNE data on inclusive
cross section Abratenko et al. (2022d) which may help to elucidate the reason
of the disagreement at low $p_{\mu}$. The new measured quantities are the
total cross section as a function of the neutrino energy $\sigma(E_{\nu})$,
the flux integrated differential cross section as a function of the muon
energy $\frac{d\sigma}{dE_{\mu}}$, and the flux integrated differential cross
section as a function of the transferred energy $\frac{d\sigma}{d\omega}$.
This is the first measurement of this type, after the MINERvA one Rodrigues et
al. (2016) at larger neutrino energies. We remind that, since the neutrino
beams are not monochromatic, all the neutrino cross sections that are not
expressed in terms of the measured lepton kinematics variables are affected by
the energy reconstruction problem Martini et al. (2012, 2013); Nieves et al.
(2012); Lalakulich et al. (2012); Ankowski and Mariani (2017). This is the
case of $\sigma(E_{\nu})$ and $\frac{d\sigma}{d\omega}$. In Ref.Abratenko et
al. (2022d) the experimental results have been presented for the first time as
a function of true neutrino energy $E_{\nu}$ and transferred energy $\omega$.
This has been made possible by a new procedure (based on the comparison
between the data and the Monte Carlo predictions constrained on the lepton
kinematics) allowing the mapping between the true $E_{\nu}$ and $\omega$ on
one hand, and the reconstructed neutrino energy $E_{\nu}^{\textrm{rec}}$ and
hadronic energy $E_{\textrm{had}}^{\textrm{rec}}$ on the other hand. This new
way to present the experimental results allows us to compare the data with our
theoretical results as a function of the true $E_{\nu}$ and $\omega$.

Figure 4: Charged current inclusive $\nu_{\mu}$ cross section on argon per
nucleon as a function of the neutrino energy. The experimental MicroBooNE data
are taken from Ref. Abratenko et al. (2022d). The genuine quasielastic, the
np-nh contributions, the coherent and incoherent 1$\pi$ production as well as
the sum of these channels calculated in our RPA model are shown. The genuine
quasielastic and the total cross section are shown also when the RPA is
switched off.

Concerning the total cross section as a function of the true neutrino energy
$\sigma(E_{\nu})$, we plot in Fig.4 the experimental inclusive result compared
to our evaluation, with and without RPA effects, for the sum of all the
channels included in our model (QE, np-nh, coherent and incoherent $1\pi$
production). Even if the published experimental results extend up to
$E_{\nu}=2.6$ GeV, in Fig.4 we stop our comparison at $E_{\nu}=1.2$ GeV. The
reason is that, as written in Ref.Martini et al. (2009), our numerical
calculations of the nuclear responses, and consequently of the cross sections,
extend only up to the transferred energy $\omega=1$ GeV. In the total cross
section, such the one of Fig.4, the $\omega>1$ GeV responses start to
contribute for $E_{\nu}=1.2$ GeV. For the same reason, our theoretical curves
of the flux-integrated $\frac{d\sigma}{d\omega}$ shown in Fig.6 stop at
$\omega=1$ GeV. On the contrary, this cut in the transferred energy is not a
problem for the flux integrated $\frac{d^{2}\sigma}{dp_{\mu}~{}d\cos\theta}$
and $\frac{d\sigma}{dE_{\mu}}$ (shown in Figs. 3 and 5 respectively) for any
$p_{\mu}$ or $E_{\mu}$ values, first since the $\omega>1$ GeV contributions
are largely subdominant (almost negligible) in the kinematical conditions of
the experimental results discussed here, second because an
interpolation/extrapolation procedure to go from our initial input, the
$\frac{d^{2}\sigma}{d\omega~{}d\cos\theta}$ at different fixed neutrino
energies, to the flux-integrated $\frac{d^{2}\sigma}{dE_{\mu}~{}d\cos\theta}$
allows us to include these $\omega>1$ GeV contributions. Returning to the
total cross section as a function of the neutrino energy shown in Fig.4, the
agreement is good up to $E_{\nu}\simeq 0.7$ GeV. This is not the case of other
models, such as GENIE v3 Alvarez-Ruso et al. (2021), MicroBooNE MC Abratenko
et al. (2022e), NEUT Hayato and Pickering (2021) and NuWro Golan et al. (2012)
which underestimate the data, with the exception of GiBUU Buss et al. (2012),
as shown in Ref. Abratenko et al. (2022d). Beyond $E_{\nu}\simeq 0.7$ GeV our
evaluation as well underestimates the data. A similar deviation between the
data and our evaluation occurred for 12C cross section Martini and Ericson
(2014) measured by SciBooNE Nakajima et al. (2011). This is due to inelastic
channels missing in our description such as $2\pi$ production.

Figure 5: Charged current inclusive MicroBooNE $\nu_{\mu}$ flux-integrated
single differential cross section on argon per nucleon as a function of the
muon energy $E_{\mu}$. Left panel: the genuine quasielastic, the np-nh
contributions, the coherent and incoherent 1$\pi$ production as well as the
sum of these channels calculated in our RPA model are shown. Right panel: our
total RPA predictions averaged on different bins calculated before (dotted
line) and after (continuous line) the additional MicroBooNE smearing explained
in the text. The experimental MicroBooNE data and the additional smearing
matrix are taken from Ref. Abratenko et al. (2022d)

A lack of strength is also visible in the flux integrated single differential
cross section $\frac{d\sigma}{dE_{\mu}}$ plotted as a function of the muon
energy $E_{\mu}$ in Fig.5. It appears in the same muon kinematical region as
the one of the double differential cross section shown in Fig. 3. For
$\frac{d\sigma}{dE_{\mu}}$ also the already mentioned models used in Ref.
Abratenko et al. (2022d) lead to an underestimation of the data. For a more
quantitative comparison of our predictions with data and other models, we
apply to our theoretical calculations the additional smearing needed for the
comparison with the MicroBooNE data, as discussed and provided in the
supplemental material of Ref. Abratenko et al. (2022d) via smearing matrices.
This smearing is a result of the regularization in the data unfolding
procedure. The results we obtain by applying this additional smearing are
shown in the right panel of Fig.5 which displays the smeared
$\frac{d\sigma}{dE_{\mu}}$ cross section. The effect of the smearing is small.
This will not be the case for the $\frac{d\sigma}{d\omega}$ cross section
discussed later. Beyond the additional smearing matrices, the MicroBooNE
collaboration also published the covariance matrices of their cross section
measurements. It allows to perform the $\chi^{2}$ test statistic via the
covariance matrix formalism. We have calculated the $\chi^{2}/\textrm{ndf}$ of
our model for the $\frac{d\sigma}{dE_{\mu}}$ cross section and we obtained
$\chi^{2}/\textrm{ndf}=27.9/11$, a value larger than the one of GiBUU,
$\chi^{2}/\textrm{ndf}$=16.7/11, the model which better predicts these data.
However our $\chi^{2}/\textrm{ndf}$ is lower than the one of GENIEv3
($\chi^{2}/\textrm{ndf}$=32.4/11).

Figure 6: Charged current inclusive MicroBooNE $\nu_{\mu}$ flux-integrated
single differential cross section on argon per nucleon as a function of the
transferred energy $\omega$. The experimental MicroBooNE data are taken from
Ref. Abratenko et al. (2022d). The genuine quasielastic, the np-nh
contributions, the coherent and incoherent 1$\pi$ production as well as the
sum of these channels calculated in our RPA model are shown. The genuine
quasielastic and the total cross section are shown also when the RPA is
switched off.

Figure 7: Charged current inclusive MicroBooNE $\nu_{\mu}$ flux-integrated
single differential cross section on argon per nucleon as a function of the
transferred energy $\omega$ calculated in our model with (left panel) and
without (right panel) RPA effects before (dotted lines) and after (continuous
lines) the additional MicroBooNE smearing. The experimental MicroBooNE data
and the additional smearing matrix are taken from Ref. Abratenko et al.
(2022d).  Figure 8: Charged current quasielastic, multinucleon, coherent and
incoherent 1$\pi$ production contributions to the MicroBooNE $\nu_{\mu}$ flux-
integrated single differential cross section on argon per nucleon as a
function of the transferred energy $\omega$ calculated in our RPA model
(dotted line) and by employing the additional MicroBooNE smearing (continuous
line).

In figure 5, which displays the differential cross section in terms of muon
variables, the different reactions channels are entangled. The flux integrated
differential cross section $\frac{d\sigma}{d\omega}$ as a function of the
transferred energy $\omega$ allows instead a better separation of the
different channel contributions, such as quasielastic, np-nh, 1$\pi$
production, which peak at different $\omega$ values. The comparison between
the MicroBooNE data and our predictions for this cross section is shown in
Fig.6. At low energy transfer the cross section is dominated by the
quasielastic channel which is quenched by RPA effects in our theoretical
calculations. A lack of strength shows up for $0.2<\omega<0.6$ GeV but the
additional smearing should be applied to our curves before drawing any
conclusions. This is done in Fig.7 for the sum of all the channels we take
into account, with and without RPA effects. The first observation is that the
impact of this smearing is larger for this $\frac{d\sigma}{d\omega}$ cross
section than for the $\frac{d\sigma}{dE_{\mu}}$ one shown in Fig.5. The
smearing produces a redistribution of the strength which is more important
when the cross section is peaked, such as the quasielastic or the pion
production, as illustrated also in Fig. 8. Furthermore this smearing reduces
the difference between the results with and without RPA. By using the
uncertainty covariance matrix delivered by MicroBooNE for this
$\frac{d\sigma}{d\omega}$ cross section as well, we calculate
$\chi^{2}/\textrm{ndf}=17.2/8$ for our model including RPA effects. This
result is comparable to the one of GiBUU, $\chi^{2}/\textrm{ndf}=17.0/8$, the
model which better reproduces the data as compared to the other Monte Carlo
predictions, characterized by a larger $\chi^{2}/\textrm{ndf}$, up to
$\chi^{2}/\textrm{ndf}=33.8/8$ for MicroBooNE MC. A possible reason for our
better agreement with data as compared to the predictions of GENIEv3,
MicroBooNE MC, NEUT and NuWro is that these models implement a multinucleon
contribution deduced for the evaluation of Nieves et al. Nieves et al. (2011)
which is smaller than our by about a factor 2 Morfin et al. (2012); Katori and
Martini (2018); Abe et al. (2016). Ignoring RPA effects, our $\chi^{2}$
decreases to $\chi^{2}/\textrm{ndf}=13.4/8$. This is a consequence of the
displacement of the QE strength from $\omega<0.2$ GeV to larger transferred
energies due to the additional smearing, which partially compensates our
underestimation of data for $\omega>0.2$ GeV. This underestimation which, even
if less pronounced that in the other Monte Carlo predictions except GiBUU,
remains even after the additional smearing, seems to start at $\omega\simeq
2m_{\pi}$. It may signal the absence in our description of $2\pi$ production
and other inelastic channels. This absence could also explain the
underestimation of the inclusive MicroBooNE double differential cross section
at low $p_{\mu}$, already pointed for Fig.3. One wonders why this
underestimation does not appear in the T2K inclusive data shown in Fig.2. The
reason is possibly due to the difference between the T2K and MicroBooNE
neutrino energy profiles, the second one having a significant high energy
contribution, absent for T2K, see Fig.1.

##  IV Conclusions

We have analyzed in this work the recent MicroBooNE data of neutrino cross
sections on argon. We have considered the charged current inclusive
measurements: the total cross section as a function of the neutrino energy and
three flux integrated quantities, the double differential cross section as a
function of the muon momentum and scattering angle, the single differential
ones as a function of the muon energy and of the energy $\omega$ transferred
to the nucleus. We have compared them to our theoretical approach. Overall we
find an agreement with the data, in spite of a tendency of underestimation in
some specific regions. The availability of covariant matrices for some
experimental results allows quantitative comparisons between different models.
Our model is particularly efficient in the case of the
$\frac{d\sigma}{d\omega}$ data, a new type of measurement recently available.
These data allow a better separation of the different reaction channels, even
after the additional smearing needed for comparing models and data. Our
analysis shows that the low $\omega$ region is dominated by the quasielastic.
At larger $\omega$ a lack of agreement shows up: our predictions underestimate
the data. The two pions production and other inelastic contributions which are
not taken into account in our description are the natural candidates to
explain this underestimation. These channels are more relevant for MicroBooNE
than for T2K, due to the different energy profiles of these neutrino beams.

## Acknowledgement

We acknowledge the IPSA students B. Chaillié, V. Demoly and Q. Jacquet for the
interest on this work in its early stage. We thank M. B. Barbaro, V. Belocchi,
A. De Pace, T. Ericson, J. M. Franco-Patino, C. Giganti and W. Gu for
interesting discussions. One of us (M. M.) acknowledges the support of the
CERN Neutrino Platform and the hospitality of the CERN theory department,
where part of this work was done.

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