1

52. Neutrino Cross Section Measurements

52. Neutrino Cross Section Measurements
Revised August 2023 by G.P. Zeller (FNAL).
Neutrino cross sections are an essential ingredient in all neutrino experiments. Interest in
neutrino scattering has increased due to the need for such information in the interpretation ofneutrino oscillation data [1, 2] and given that uncertainties in neutrino-nucleus scattering remain adominate source of systematic uncertainty in many neutrino oscillation measurements. Historically,neutrino scattering results on both charged current (CC) and neutral current (NC) channels havebeen collected over many decades using a variety of targets, analysis techniques, and detector
technologies. With the advent of intense neutrino sources constructed for neutrino oscillation
investigations, experiments are now remeasuring such interaction cross sections with a renewed
appreciation for nuclear effects1 and the need for more precise neutrino flux estimations [3, 4].
This work summarizes accelerator-based neutrino cross section measurements performed in the∼ 0.1 − 300 GeV range with an emphasis on inclusive, quasi-elastic, and pion production processes,
areas where we have the most experimental input at present (Table 52.1). For a more comprehensive
discussion of neutrino cross sections, including neutrino-electron elastic scattering and lower energy
neutrino measurements, the reader is directed to a review of this subject [5]. Here, we survey existing
experimental data on neutrino interactions and do not attempt to provide a census of the associatedtheoretical calculations [6], which are both critical and plentiful. Companion electron-nucleus
scattering data [7] are additionally playing an increased role in neutrino interaction predictions
through such efforts as the e4ν collaboration [8].
Table 52.1: List of beam properties, targets, and run durations for modern accelerator-based neutrino experiments studying neutrino scattering.
hEν i, hEν ineutrinorun
Experiment
beam
(GeV)
target(s)periodArgoNeuTν, ν
4.3, 3.6
Ar2009 – 2010
FASERν
ν, ν> 200
W, emulsion 2021 –ICARUS (at CNGS) ν
20
Ar2010 – 2012
ICARUS (at FNAL)
ν
0.8
Ar
2021 –
K2K
ν
1.3
CH, H2 O 2003 – 2004
MicroBooNEν
0.8
Ar
2015 – 2020
MINERvAν, ν 3.5 (LE), He, C, CH, 2009 – 2019
5.5 (ME) H2 O, Fe, Pb
MiniBooNEν, ν0.8, 0.7
CH22002 – 2019
MINOS
ν, ν
3.5, 6.1
Fe2004 – 2016
NINJA
ν, ν
0.6, 0.6 Fe, emulsion 2015 –NOMADν, ν 23.4, 19.7
C1995 – 1998
NOvA
ν, ν
2.0, 2.0
CH22010 –
SBND
ν
0.8
Ar
2024 –
0.8, 0.7
CH
2007 – 2008
SciBooNE
ν, ν
T2K
ν, ν
0.6, 0.6 CH, H2 O, Fe 2010 –1
Nuclear effects refer to kinematic and final state effects which impact neutrino scattering off nuclei. Such effects
can be significant and are particularly relevant given that modern neutrino experiments make use of nuclear targets
to increase their event yields.

S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
31st May, 2024 10:17am

52. Neutrino Cross Section Measurements2

52.1 Inclusive Scattering

σCC / Eν (10-38

cm2 / GeV)Over the years, many experiments have measured the total inclusive charged current crosssection for neutrino (νµ N → µ− X) and antineutrino (ν µ N → µ+ X) scattering covering a broad
range of neutrino energies. As can be seen in Fig. 52.1, which shows this data over decades oftime and energy, the inclusive cross section approaches a linear dependence on neutrino energy.
This behavior is expected for point-like scattering of neutrinos from quarks, an assumption which
breaks down at lower energies. Modern measurements of such inclusive neutrino scattering crosssections and their target nuclei are summarized in Table 52.2. The reader is also referred to a recent
review of the status of measurements and calculations in the shallow and deep inelastic scattering
regions [9].
MicroBooNE, PRL 128, 151801 (2022)
MicroBooNE, PRL 123, 131801 (2019)
NINJA, PTEP 3, 033C01 (2021)
T2K, PRD 98,1.6012004 (2018)
T2K, PRD 96, 052001 (2017)
MINERvA, PRD 95, 072009 (2017)
T2K, PRD 93,1.4
072002 (2016)
T2K (CH), PRD 90, 052010 (2014)
ArgoNeuT, PRD 89, 112003 (2014)
ArgoNeuT, PRL 108, 161802 (2012)
1.283, 012005 (2011)
SciBooNE, PRD
MINOS, PRD 81, 072002 (2010)

1.6
1.4
1.2
1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

NOMAD, PLB 660, 19 (2008)
NuTeV, PRD 74, 012008 (2006)
CCFR (1997 Seligman Thesis)
IHEP-JINR, ZP C70, 39 (1996)
CDHS, ZP C35, 443 (1987)
BNL, PRD 25, 617 (1982)
GGM-SPS, PL 104B, 235 (1981)
ANL, PRD 19, 2521 (1979)
BEBC, ZP C2, 187 (1979)
GGM-PS, PL 84B (1979)
IHEP-ITEP, SJNP 30, 527 (1979)
SKAT, PL 81B, 255 (1979)

νµ N → µ - X

νµ N → µ + X

0

1

10

100

150

200

250

300

350

Eν (GeV)Figure 52.1: Measurements of per nucleon νµ and ν µ CC inclusive scattering cross sections divided
by neutrino energy as a function of neutrino energy. Note the transition between logarithmic andlinear scales occurring at 100 GeV. Neutrino cross sections are typically twice as large as theircorresponding antineutrino counterparts, although this difference can be larger at lower energies.
NC cross sections (not shown) are generally smaller compared to their CC counterparts.
To provide a more complete picture, differential cross sections for such inclusive scattering processes have also been reported. These include historical measurements on iron from NuTeV [10] andmodern measurements on a variety of nuclear targets from ArgoNeuT [11,12], MicroBooNE [13,14],
MINERvA [15–18], NINJA [19, 20], NOvA [21], and T2K [22, 23]. More recently, MINERvA has
provided measurements in terms of longitudinal and transverse muon momenta [16, 17], MicroBooNE has measured the first triple differential cross sections in argon [24], and T2K has provided
the first measurement of the antineutrino inclusive cross section at low energy [25] (Fig. 52.1).
At high energy, the inclusive cross section is dominated by deep inelastic scattering (DIS).
Several neutrino experiments have measured DIS cross sections for specific targets and final states,for example, MINERvA has measured ratios of neutrino DIS cross sections on a variety of nuclear
31st May, 2024

52. Neutrino Cross Section Measurements

3targets including lead, iron, and carbon [26, 27]. Other experiments have measured opposite-sign
dimuon production, the most recent being from CHORUS [28], NOMAD [29], and NuTeV [30].
Multiple efforts are also now underway to measure inclusive neutrino scattering cross sections at
significantly higher neutrino energies, including at the LHC in FASERν [31] and using atmospheric
neutrinos in IceCube [32].
Table 52.2: Published measurements of muon neutrino and antineutrino
CC inclusive cross sections from modern accelerator-based neutrino experiments.
experiment measurementtargetArgoNeuTνµ [11, 12], ν µ [12]Ar
MicroBooNE νµ [13, 24, 33]
Ar
MINERνAνµ [15–18, 26, 27, 34], ν µ [34], ν µ /νµ [35] C, CH, Fe, Pb
MINOSνµ [36], ν µ [36]Fe
NINJA
νµ [19, 20], ν µ [19]
H2 O, FeNOMAD
νµ [37]CNOvA
νµ [21]
CH2
SciBooNEνµ [38]CHT2K
νµ [22, 23, 39–41], ν µ /νµ [25]CH, H2 O, FeAt lower neutrino energies, the inclusive cross section is an additionally complex combinationof quasi-elastic scattering and pion production processes, two areas we discuss next.

52.2 Quasi-elastic scattering
Quasi-elastic (QE) scattering is the dominant neutrino interaction for neutrino energies less than
∼ 1 GeV and represents a large fraction of the signal samples in many neutrino oscillation experiments, which is why this process has received considerable attention in recent years. Historically,neutrino (antineutrino) quasi-elastic scattering refers to the process, νµ n → µ− p (ν µ p → µ+ n),
where a charged lepton and single nucleon are ejected in the elastic interaction of a neutrino (orantineutrino) with a nucleon in the target material. This is the final state one would strictly observe, for example, in scattering off of a free nucleon target. There were many early measurementsof neutrino QE scattering that span back to the 1970’s [5]. In many of these initial measurements,
bubble chamber experiments employed light targets (hydrogen or deuterium) and required both
the detection of the final state muon and single nucleon2 ; thus the final state was clear and elastic
kinematic conditions could be verified. The situation is more complicated, of course, for heavier
nuclear targets used in modern neutrino experiments. In this case, nuclear effects can impact thesize and shape of the cross section as well as the final state composition, kinematics, and topology.
Due to intranuclear hadron rescattering and the effects of correlations between target nucleons,
additional particles may be ejected in the final state; hence, a QE interaction on a nuclear target
does not necessarily imply the ejection of a lepton and a single nucleon. One therefore needs totake care in defining what one means by neutrino QE scattering when scattering off targets heavier
than hydrogen or deuterium. Because of this, modern experiments tend to instead report crosssections for processes involving pionless (e.g., nucleon-only) final states, often referred to as CC
0π or QE-like reactions in recent literature. Such measurements are summarized in Table 52.3.
Many modern experiments have also recently opted to report QE-like cross sections as a functionof observed final state particle kinematics. Such measurements can be more difficult to directly2

In the case of deuterium, many experiments additionally observed the spectator proton.

31st May, 2024

52. Neutrino Cross Section Measurements

4compare between experiments but have the advantage of being much less model-dependent andprovide more stringent tests of the theory than historical cross sections as a function of derived
quantities such as neutrino energy (Eν ) or 4-momentum transfer (Q2 ). More recently, new thoughthas been given to the means for directly comparing experimental measurements produced in theseless model-dependent forms [42].
Table 52.3: Published modern measurements of muon neutrino QE andNC elastic scattering cross sections with pionless final states.
experiment
ArgoNeuT

measurement
2p [43]targetAr

K2K

MA [44]

H2 O
2

dσ dσ
dσ
dσ
σ
MicroBooNE dp[45, 46], dδαdT dδp[47, 48],µ dpp d cos θµ d cos θp
T

Ar

d2 σ

dδpT x dδpT y [47], 2p [49], Λ [50]MINERνA

d2 σ
dσ
dσ
dσ dσ
dpT dp|| [51–55], dδpT x dδpT y [56], dpn dδαT [57],
d2 σ
dσ
dσ
2
[58, 59], 1p [60], dEavail
dq3 [61], dQ2 [62], FA (Q ) [63]dQ2

CH,Fe,Pb

MiniBooNE

d2 σ
dTµ dθµ [64, 65], MA [66], NC [67, 68]

CH2

MINOS

MA [69]Fe

NINJA

2p [70]Fe

NOMAD

MA , σ(Eν ) [71]CSuper-K

NC [72]

H2 O

T2K

d2 σ
dTµ dθµ [73–78], σ(Eν ) [79], MA [80], NC [81],dσdσdδpT dδαT [82], O/C [76]CH,H2 O

The topic of neutrino QE scattering began drawing considerable attention following the first double differential cross section measurements of this process that revealed a significantly larger crosssection than originally anticipated, predominantly in the backwards muon scattering region [64,65].
Such an enhancement was observed many years prior in transverse electron-nucleus scattering [83]and was attributed to the presence of correlations between nucleons in the target nucleus. As
a result, the impact of such nuclear effects on neutrino QE scattering has recently become thesubject of intense experimental and theoretical scrutiny with implications on event rates, nucleon
emission, neutrino energy reconstruction, and neutrino versus antineutrino cross sections. The
reader is referred to reviews of the situation in [6, 84, 85]. To help drive further progress in understanding the underlying nuclear contributions, pionless (e.g., nucleon-only) cross sections have beenreported for the first time in the form of double-differential distributions by MiniBooNE [64, 65],
MINERvA [51–55, 61], and T2K [73–78]. Such double-differential cross sections in terms of final
state particle kinematics reduce the model-dependence of the reported data, provide the most ro31st May, 2024

552. Neutrino Cross Section Measurementsbust measurements available, and allow a more rigorous two-dimensional test of the underlying
nuclear theory. MicroBooNE, MINERvA, and T2K have been especially prolific in recent years inprobing this interaction process (Table 52.3). Neutrino experiments have also launched dedicatedstudies of the hadronic side of these interactions, including ArgoNeuT [43,86], MicroBooNE [45,46],
MINERvA [60, 87], and T2K [82]. MINERvA has been the first modern experiment to measureneutron emission in antineutrino interactions [88] and has simultaneously measured neutrino QE
cross sections on a variety of nuclear targets ranging from carbon to lead [55]. ArgoNeuT [43],MicroBooNE [49], and NINJA [70] have explored two-proton final states. T2K has probed ratiosof oxygen to carbon [76, 89], asymmetries between neutrino and antineutrino scattering [77], andsimultaneous measurements both on and off axis to the neutrino beam [78]. In addition, the exploration of transverse kinematic variables and momentum imbalances in pionless neutrino scatteringis allowing better constraints on the various nuclear contributions to the cross section. Such scrutiny
includes important evaluations from MicroBooNE [47, 48], MINERvA [51, 52, 56, 57] and T2K [82].
With the MiniBooNE results having first revealed these additional complexities in neutrino-nucleus
QE scattering, measurements from multiple neutrino experiments, on multiple targets, and using
a variety of kinematic information have been crucial in gaining a better handle on the underlying
nuclear physics impacting neutrino-nucleus interactions. What we once thought was “simple” QE
scattering is in fact not so simple.
Equally important, neutrino experiments such as MINERvA have revisited the extraction of theaxial form factor from light target data using modern higher statistics data sets [63]. In addition tosuch charged current investigations, measurements of the neutral current counterpart of this channel
have also been performed. The most recent NC elastic scattering cross section measurements
include those from BNL E734 [90], MiniBooNE [67, 68], Super-K [72], and T2K [81]. A numberof measurements of the Cabibbo-suppressed antineutrino QE hyperon production cross section
have additionally been reported [91, 92], most recently by MicroBooNE [50]. As an exciting new
addition, there have also been the first observations of the very challenging-to-detect coherent elastic
neutrino-nucleus scattering (CEνNS) process now in multiple nuclei by COHERENT [93, 93, 94].

52.3 Pion Production
In addition to such elastic scattering processes, neutrinos can also inelastically scatter producing
a nucleon excited state (∆, N ∗ ). Such baryonic resonances quickly decay, most often to a nucleon
and single-pion final state. Historically, experiments have measured various exclusive final states
associated with these reactions, the majority of which have been on hydrogen and deuterium targets[5]. There have been several recent re-analyses of this data to better understand the consistency
between data sets [95], nucleon form factors [96], and non-resonant contributions [97]. Also, modern
measurements of neutrino-induced pion production have since been performed on a variety of
nuclear targets (Table 52.4).
In addition to resonance production processes, neutrinos can also coherently scatter off of theentire nucleus and produce a distinctly forward-scattered single pion final state. Both CC (νµ A →µ− A π + , ν µ A → µ+ A π − ) and NC (νµ A → νµ Aπ 0 , ν µ A → ν µ Aπ 0 ) processes are possible inthis case. Even though the level of coherent pion production is small compared to their resonant
counterpart, observations exist across a broad energy range and on multiple nuclear targets [135].
More recently, several modern neutrino experiments have either measured or set limits on coherent
pion production cross sections including ArgoNeuT [98], K2K [102], MINERvA [109, 111, 113],
MiniBooNE [123], MINOS [124], NOMAD [125], NOvA [126], SciBooNE [128, 130], and T2K [102].
As with inclusive and quasi-elastic scattering, a new appreciation for the significance of nuclear
effects has also surfaced in pion production physics, again due to the use of heavy nuclear targets
in modern neutrino experiments. Many experiments have been careful to report cross sections for
31st May, 2024

652. Neutrino Cross Section Measurements
Table 52.4: Summary of modern measurements of NC and CC scatteringcross sections involving a single pion or multiple pions in the final state.
experimentπ±
π0targetArgoNeuT
CC [98, 99]
NC [100]
Ar
K2K
CC [101, 102]
CC [103], NC [104]CH, H2 O
MicroBooNE–
CC [105], NC [106]Ar
MINERνA
CC [107–114] CC [108, 115–117], NC [118] C, CH, H2 O, Fe, Pb
MiniBooNE CC [119, 120]
CC [121], NC [122, 123]
CH2
MINOS
–
NC [124]Fe
NOMAD–
NC [125]
C
NOvA–
NC [126, 127]C
SciBooNE
CC [128]
NC [129, 130]
CH
T2K
CC [131–134]–
CH, H2 O

various detected final states, thereby not correcting for large and uncertain nuclear effects (e.g.,pion rescattering, charge exchange, and absorption) which can introduce significant sources of
uncertainty and model dependence. Providing the most comprehensive survey of neutrino singlepion production to date, MiniBooNE has published a total of 16 single- and double-differential crosssections for both the final state muon (in the case of CC scattering) and pions in these interactions;thus, providing the first measurements of such final state kinematic distributions [119–122]. At
similar neutrino energies, T2K has provided new data [131] including the first measurement of theAdler angles in neutrino-nucleus scattering [133] and the first exploration of transverse kinematic
imbalances in pion production processes [134]. MINERvA has produced a similar accompanimentof measurements at higher neutrino energies [108, 110, 112, 116] and uniquely on multiple nuclear
targets [114]. Importantly, MINERvA has been working towards an improved nuclear model [117]that can potentially describe all of the pion reaction channels simultaneously, an issue that many
experiments have struggled with up until now [108]. ArgoNeuT [99, 100] and MicroBooNE [105,106] have since been adding new information on single pion production in argon. Regardlessof the interaction channel or target material, differential cross section measurements in terms ofobserved final state particle kinematics are preferred for their reduced model dependence and for the
additional kinematic information they provide. Such a new direction has been the focus of modern
measurements as opposed to the reporting of more model-dependent, historical cross sections as
a function of Eν or Q2 . Together with similar results for other interaction channels, a better
understanding and modeling of nuclear effects will be possible moving forward. MINERvA [136]has already taken a large step in this direction by explicitly tuning the physics in existing neutrino
event generators to best fit the experimental data on pion production.
It should be noted that baryonic resonances can also decay to multi-pion, other mesonic (K, η,ρ, etc.), and even photon final states. Experimental results for these channels are typically sparse or
non-existent. More recently, MicroBooNE has produced the first measurement of neutrino-induced
η production on argon [137]. Photon production processes can comprise an important backgroundfor νµ → νe appearance searches in some detectors and thus have become the focus of recent
experimental investigations, most notably in NOMAD [138] and T2K [139, 140]. There have also
been several recent measurements of kaon final states produced in neutrino NC and CC scatteringin MINERvA [141–143] that are providing needed background constraints for certain nucleon decay
searches.
31st May, 2024

52. Neutrino Cross Section Measurements

752.4 Electron Neutrino Scattering
The aforementioned cross section measurements are all for either muon neutrino or muon antineutrino scattering. With the production of predominantly muon neutrino beams for neutrino
oscillation studies, the availability of electron neutrino scattering data is by construction limited.
However, for the first time, measurements of electron neutrino scattering cross sections are being
produced by a variety of modern neutrino experiments (Table 52.5). Such measurements are important as they verify our assumptions about lepton universality and validate the use of muon neutrino
data to constrain electron neutrino interaction predictions. For lower energy and historical electron
neutrino cross section measurements, the reader is directed to reference [5].
Table 52.5: Published measurements of electron neutrino and antineutrino cross sections from modern accelerator-based neutrino experiments.
experiment CC inclusive QE-like π production target
ArgoNeuT[144]
Ar
COHERENT[145]
I
MicroBooNE [146, 147]
[148]
Ar
MINERνA
[149]
CH
NOvA
[150]
CH2
T2K
[151–153]
CH, H2 O

52.5 Outlook
Neutrino experiments continue to produce critical neutrino scattering measurements on nuclei
as they accumulate increased statistics and pursue new ways of reporting their measurements.
Analysis of a broad energy range of data from MINERvA is providing some of the most detailed
analysis of nuclear effects in neutrino interactions by examining multiple nuclei in a single experiment. Data from ArgoNeuT, MicroBooNE, ICARUS and soon also SBND are probing deeper
into complex neutrino final states using the superior capabilities of liquid argon time projection
chambers, while the T2K and NOvA near detectors continue to collect high statistics samples inintense neutrino beams. Together with dedicated discussions between experiments on how best toreport neutrino cross section measurements [154] and with accompanying work being advanced bytheorists to further improve nuclear model calculations [6], we are starting to significantly advanceour understanding of neutrino-nucleus scattering.

52.6 Acknowledgments
The author thanks Anne Schukraft (Fermilab) for help in preparing the plots and content of
this review.
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