Testing CCQE and 2p2h models in the NEUT neutrino interaction generator with published datasets from the MiniBooNE and MINERvA experiments

1.6 MB·

by  C. Wilkinson

Testing CCQE and 2p2h models in the NEUT neutrino interaction generator with
published datasets from the MiniBooNE and MINERνA experiments
C. Wilkinson,1,2,∗ R. Terri,3,† C. Andreopoulos,4,5 A. Bercellie,6 C. Bronner,7 S. Cartwright,2 P. de Perio,8,‡
J. Dobson,9,§ K. Duffy,10 A.P. Furmanski,11,¶ L. Haegel,12 Y. Hayato,13,14 A. Kaboth,15,4 K. Mahn,16
K.S. McFarland,6 J. Nowak,17 A. Redij,1 P. Rodrigues,6 F.Sánchez,18 J.D. Schwehr,19 P. Sinclair,9 J.T. Sobczyk,20
P. Stamoulis,21 P. Stowell,2 R. Tacik,22,23 L. Thompson,2 S. Tobayama,24 M.O. Wascko,9 and J. Żmuda20
1University of Bern, Albert Einstein Center for Fundamental Physics,
Laboratory for High Energy Physics (LHEP), Bern, Switzerland
2University of Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom
3Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom
4STFC, Rutherford Appleton Laboratory, Harwell Oxford,
and Daresbury Laboratory, Warrington, United Kingdom
5University of Liverpool, Department of Physics, Liverpool, United Kingdom
6 6University of Rochester, Department of Physics and Astronomy, Rochester, New York, USA
1 7Kavli Institute for the Physics and Mathematics of the Universe (WPI),
0
The University of Tokyo Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan
2 8University of Toronto, Department of Physics, Toronto, Ontario, Canada

n 9Imperial College London, Department of Physics, London, United Kingdom
a 10Oxford University, Department of Physics, Oxford, United Kingdom
J 11University of Warwick, Department of Physics, Coventry, United Kingdom
1 12University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
2 13Kavli Institute for the Physics and Mathematics of the Universe (WPI),
Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan

] 14University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
x
15Royal Holloway University of London, Department of Physics, Surrey, United Kingdom
e
16Michigan State University, Department of Physics and Astronomy, East Lansing, Michigan, U.S.A.
-
p 17Lancaster University, Physics Department, Lancaster, United Kingdom
e 18Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of
h Science and Technology, Campus UAB, Bellaterra (Barcelona) Spain
[ 19Colorado State University, Department of Physics, Fort Collins, Colorado, U.S.A.

20Wrocław University, Faculty of Physics and Astronomy, Wrocław, Poland
1
21IFIC (CSIC & University of Valencia), Valencia, Spain
v
2 22University of Regina, Department of Physics, Regina, Saskatchewan, Canada
9 23TRIUMF, Vancouver, British Columbia, Canada
5 24University of British Columbia, Department of Physics and Astronomy, Vancouver, British Columbia, Canada
5 (Dated: January 22, 2016)
0
The MiniBooNE large axial mass anomaly has prompted a great deal of theoretical work on
.
1 sophisticated Charged Current Quasi-Elastic (CCQE) neutrino interaction models in recent years.
0 AsthedominantinteractionmodeatT2Kenergies,andthesignalprocessinoscillationanalyses,it
6 is important for the T2K experiment to include realistic CCQE cross section uncertainties in T2K
1 analyses. To this end, T2K’s Neutrino Interaction Working Group has implemented a number of
v: recent models in NEUT, T2K’s primary neutrino interaction event generator. In this paper, we
i give an overview of the models implemented, and present fits to published νµ and νµ CCQE cross
X section measurements from the MiniBooNE and MINERνA experiments. The results of the fits
r are used to select a default cross section model for future T2K analyses, and to constrain the cross
a section uncertainties of the model. We find a model consisting of a modified relativistic Fermi gas
model and multinucleon interactions most consistently describes the available data.
I. INTRODUCTION
Charged Current Quasi-Elastic (CCQE) scattering
∗ Correspondingauthor,[e-mail] (ν +n → p+µ−) is the dominant neutrino interaction
µ
† Correspondingauthor,[e-mail] process for muon (anti)neutrinos impinging on a nuclear
‡ Presentaddress: ColumbiaUniversity,PhysicsDepartment,New
targetatneutrinoenergiesontheorderof1GeV.Because
York,NewYork10027,USA
CCQE is a two-body process and the incoming neutrino
§ Present address: University College London, Department of
PhysicsandAstronomy,London,UnitedKingdom direction is known for an accelerator experiment, a rea-
¶ Presentaddress: UniversityofManchester,SchoolofPhysicsand sonableapproximationoftheneutrinoenergycanbecal-
Astronomy,Manchester,UnitedKingdom culated using only the outgoing lepton kinematics. Be-
2
cause of this, CCQE is the preferred signal process for tions of the initial ground state of the nucleus; and ad-
neutrino oscillation experiments which generally require ditional nuclear effects, such as multinucleon interaction
some handle on the incoming neutrino energy to extract models, which go beyond interactions with a single nu-
neutrino oscillation parameters due to(–ν) disappearance cleonwithinthenucleus. Thecombinationofthesemod-
µ
or(–ν) appearance in this energy region. However, nu- els would allow for a consistent picture of an axial mass
e
clear effects and interactions which are not distinguish- close to 1.00GeV/c2, with a suppressed cross section at
able from CCQE in the final state bias or smear the re- low-Q2 and larger cross section at higher-Q2 relative to
constructed neutrino energy, so a good understanding of a simple RFG model. Comprehensive reviews of avail-
these effects is important. able CCQE cross section models can be found in Refer-
ences [3, 20–22].
Neutrino interaction generators typically use the rel-
ativistic Fermi gas (RFG) model of the nucleus for all More sophisticated descriptions of the initial state of
neutrino-nucleusinteractionsbecauseofitssimplicity. In the nucleus than the RFG model provides are avail-
the RFG model, all possible nucleon momentum states able from a number of authors [23–26]. These mod-
are filled up to the Fermi momentum, there is a con- els, generically referred to as Spectral Functions (SF),
stant binding energy required to separate the nucleon have a more realistic nucleon momentum distribution
from the nucleus, and the neutrino interacts with a taking into account the shell structure of the nucleus
single bound nucleon. Neutrino-nucleon CCQE scat- and correlated pairs of nucleons within the nucleus, and
tering for free nucleons is described by the Llewellyn- have non-constant binding energies. Note that although
Smith formalism [1], which has been extended to cover these models include correlations between nucleons in
neutrino-nucleus CCQE scattering in the Smith-Moniz the initial state, they still use the impulse approxima-
RFGmodel[2],wherenucleonsboundwithinthenucleus tion and only consider interactions with a single nu-
are described by the RFG nuclear model. The only pa- cleon. More complex models which go beyond the sim-
rameter of the weak current or in the RFG model which ple picture of non-interacting fermions are available [27–
is not well constrained by electron scattering data [3, 4] 31]. However, with the exception of the GiBUU interac-
is the axial mass, M . Results from a global analysis tion model [27, 32], these are not currently implemented
A
of neutrino-deuterium scattering experiments and pion in neutrino interaction generators. In these models, a
electroproductiondatafindM =1.00±0.02GeV/c2 [5], mean field potential due to the presence of other nucle-
A
which is consistent with other analyses [6–8]. These re- ons within the nucleus is calculated, which will generally
sults are also consistent with high energy neutrino beam depend on the position and momentum of the struck nu-
experiments on heavy nuclear targets [9]. cleon. These models are not discussed further as they
Recent differential CCQE cross section results from cannot beeasily implementedin the NEUT neutrino in-
the MiniBooNE collaboration [10, 11] are significantly teraction generator [33].
higher than expectation, which can only be accounted Although alternative nuclear models modify the cross
for in the framework of the Smith-Moniz RFG model by section as a function of the outgoing lepton kinematics
inflating the axial mass, giving rise to the term “Mini- significantly, they do not change the total CCQE cross
BooNE large axial mass anomaly”. This came after an sectionsignificantlyasafunctionofneutrinoenergy[21].
earlierlargeaxialmassmeasurementbyK2K[12],which Additional nuclear effects are also likely to be required
reported a value of MA = 1.20±0.12GeV/c2. Both ex- to explain the current global dataset. Multinucleon in-
perimentsexhibitednotonlyalarger-than-expectedaxial teraction (2p2h) models such as those from Nieves et
mass, but also a supression of low-Q2 events relative to al. [34, 35] and Martini et al. [36] go beyond the impulse
the expection from the Smith-Moniz RFG model. Other approximation and include diagrams where two nucle-
experiments using heavy nuclear targets with beam en- ons are involved in the interaction. This adds significant
ergies in the few-GeV region have also measured cross strengthtotheCCQE-likecrosssectionandexplainsthe
sections which are consistent with an inflation of the ax- difference in normalization observed in the MiniBooNE
ial mass [13–16], although these results do not paint a data, which was previously modelled with a large axial
coherent picture. More recently, the MINERνA experi- mass [37–40]. Because these 2p2h models are not two-
ment[17,18],whichisatasomewhathigherneutrinoen- body processes, they are expected to lead to significant
ergy than MiniBooNE, has shown good agreement with biasesintheneutrinoenergyreconstructionfromtheout-
the Smith-Moniz RFG model with MA = 1.00GeV/c2, going lepton which assumes CCQE kinematics [41, 42].
but requires an enhancement to the transverse compo- Additionally, the Random Phase Approximation (RPA)
nent of the cross section, an effect also seen in electron- is a nuclear screening effect that modifies the propaga-
nucleusscattering[19]. Theseinconsistentresultspresent tor for interactions in nuclear matter [34, 36, 43, 44] and
a considerable challenge to neutrino oscillation experi- has a significant effect on the differential cross section
ments which need to be able to model their signal pro- as a function of Q2, suppressing the cross section in
cesses well. the low-Q2 region and enhancing the cross section for
Recent theoretical efforts which have attempted to re- Q2 >∼0.5GeV2. RPAneedstobeincluded,bothininter-
solve the “MiniBooNE large axial mass anomaly” have actionswithasinglenucleon(1p1h)andthosefrom2p2h
focussed on two main areas: more sophisticated descrip- calculations,tofindgoodagreementwithdata. Notethat
3
both Nieves and Martini calculations are performed in
300
) P
the context of a local Fermi gas (LFG) model, where the V (
e p|
Fermi momentum depends on the local nuclear density, (M 250 E|,
soimprovementstotheinitialstatemodelsofthenucleus R 10-6R
E )
and improvements to the CCQE interaction models can-
200
not necessarily be combined easily.
Whilst there have been rapid experimental and the-
150 10-7
oretical developments relating to CCQE cross sections,
newnuclearmodelsandnucleareffectshaveonlyrecently
100
been implemented into neutrino interaction generators
10-8
or confronted with neutrino-nucleus scattering data, and
no consistent picture has yet emerged. It is not clear 50
which models fit the global data best, and where the de-
ficiencies now lie, which should be a serious concern for 0 10-9
0 100 200 300 400 500 600 700 800
neutrino oscillation experiments. This paper shows the |p| (MeV/c)
effect of fitting current CCQE and multinucleon mod-
els to the MiniBooNE [10, 11] and MINERνA [17, 18]
datasetstoavarietyofmodelsimplementedinNEUTby FIG. 1: The probability distribution for initial state
protons within an oxygen nucleus for Benhar’s SF
membersofT2K’sNeutrinoInteractionsWorkingGroup
model [23] as a function of the removal energy (E ) and
(NIWG). Previous constraints on the CCQE model pro- R
the magnitude of the nucleon momentum (|p|). The SF
duced by the NIWG and used in T2K oscillation anal-
is normalized such that the integral of this distribution
yses only considered an RFG model, and recommended
the NEUT default central value for the axial mass M is 1.
A
= 1.21 GeV/c2 based on the value found by the K2K
experiment [12], with an error large enough to cover fits
Pauli
totheMiniBooNEneutrinomodeCCQEdataset[10],as blocking
is fully described in Reference [45]. This work improves
ontheprevioussituationbyincludingmoresophisticated
effectsproposedtoexplainthelargeaxialmassanomaly, Mean-field
width
and by using all of the newly available CCQE data to
constrain all model parameters without reference to the
default NEUT model. Normalization of
correlated term
The models which have been implemented in the
NEUT generator are discussed in Section II and Sec-
tion III discusses cross-generator validation. Section IV
|p| (MeV/c)
gives a brief overview of the MiniBooNE and MINERνA
data used in the fit. The nominal NEUT predictions FIG. 2: SF parameters in NEUT that may be modified
for these datasets are shown in Section V for a variety
on the SF initial state momentum distribution. This
of models. Section VI discusses the fit procedure. The
figure has been adapted from Reference [46].
results of fake data studies and the fit to external data
aregiveninSectionVII.InSectionVIIIweinterpretthe
results and discuss possible implications in cross section
this work it will specifically refer to the Benhar SF. The
andneutrinooscillationanalysesandSectionIXsumma-
model information is all encoded in the initial state nu-
rizes the results.
cleon distribution shown in Figure 1. Pauli blocking is
implemented as a hard cut-off: final state nucleons with
momenta less than the Fermi momentum pSF are forbid-
II. INTERACTION MODELS IN NEUT F
den. TherearetwotermsintheSFmodel: ashortrange
correlationterm,whichextendstohigherinitialstatenu-
The motivation for, and an overview of, new CCQE cleonmomenta,andameanfieldterm,whichcontributes
models has already been discussed. This section will the main peak at lower momenta. These terms can be
briefly outline the important technical details of the seen in Figure 2, where the two-dimensional SF in terms
models as implemented in NEUT, and highlight any of the removal energy and initial state nucleon momen-
caveats that should be borne in mind when fitting with tumhasbeenprojectedontothemomentumaxis. There
them. The models used in the fits include the SF model, arethreeparametersinNEUTwhichmodifytheSFasil-
multinucleon–neutrino interactions, and RPA. lustratedinFigure2. Thedefaultvaluesfortheseparam-
The NEUT implementation of the SF model from etersaregiveninTableI.Themeanfieldwidthandnor-
Omar Benhar and collaborators [23] is described fully malizationofthecorrelationtermarewell-constrainedby
in Reference [47]. Although SF is a generic term, in electron–scattering data [47] and have little effect on the
4
shape or normalization of the cross section. Thus, they 5 1.4
) s
aisremnoodtificeodnbsiydecrheadngfuinrgthtehreiFnertmhiismwoomrke.ntPuamuliinbtlhoeckfiitnsg. 2GeV4.5 1.3(CC
It should be noted that in the RFG model, the Fermi 2 (Q3.45 1.2QE+
momentum defines the Pauli blocking, but also modifies 1.1R
the width of the initial state nucleon distribution. As a 3 P
A
result,changingpRFFG affectsawiderangeofQ2,whereas 2.5 1 )/s
changing pSF only affects very low Q2 events. 2 0.9(
F C
The multinucleon–neutrino (2p2h) model from Nieves 1.5 C
0.8Q
et al. [34, 35] has been implemented in NEUT as de- 1 E
scribedinReference[48]. Thecrosssectionasafunction 0.5 0.7)
of neutrino energy and the outgoing lepton kinematics 0 0.6
1 2 3 4 5 6 7 8 9 10
was made available by the authors of the model and
E (GeV)
is implemented as a series of lookup tables for various n
nuclear targets and neutrino species. The tables pro- (a) ν – 12C
µ
vided had hadronic variables integrated out, so a generic
5 1.4
model based on Reference [49] for simulating the ini- ) s
2
tNainaEdlUahTnadderovfinenniactlss1hi.maduTrlhoanetiiocdnissctmareatpeksaesnwctyahsebuectsuwerdreeenfnotrtNhgeEenUleepTratotiinmnigc- 2 (GeVQ34..455 11..23(CCQE+
plementationoftheNievesmodelinadequateforcompar- 3 1.1RP
isons with experimental measurements of the final state A
2.5 1 )
hadrons from CCQE events (such as can be found in /s
2 0.9(
Reference [50]). For this reason, only leptonic measure- C
1.5 C
ments are used in this analysis. As the Nieves model is 0.8Q
very complex, the current NEUT implementation does 1 E
0.7)
0.5
not allow fundamental model parameters to be changed.
For simplicity, only a simple scaling parameter which 0 1 2 3 4 5 6 7 8 9 10 0.6
changes the normalization of 2p2h events has been con- E (GeV)
n
sideredinthisanalysis. NotethattheNieves2p2hmodel
included π-less ∆ decay contributions, where a nucleon (b) ν¯µ – 12C
excitedintoa∆(1232)resonancedecayswithoutproduc-
FIG. 3: The ratio of the CCQE cross section including
ing a pion [51, 52]. Contributions from π-less ∆ decay
werepreviouslyimplementedinNEUTandothergener- the non-relativistic RPA model to the CCQE cross
section without RPA, shown for both muon neutrino
ators,andhavebeentreatedasanintrinsicbackgroundin
and muon antineutrino interactions on carbon. An
CCQEselectionsandcorrectedfor. Thisleadstocompli-
enhancement of the ratio can be seen at high Q2, and a
cations when comparing the full Nieves model to CCQE
suppression can be seen at low Q2 (and close to the
cross section measurements.
RPA [34] is implemented into NEUT as a modifica- kinematic boundary for antineutrinos). These Eν and
Q2 dependent tables are used in NEUT to apply the
tion to the 1p1h cross section as a function of E and
ν
Q2. Figure 3 shows the ratio of the Nieves 1p1h cross RPA model. For these plots, an axial mass value of MA
= 1.01 GeV/c2 was used.
section with RPA included over the bare 1p1h cross sec-
tion; these two-dimensional tables of the ratio were sup-
plied by the authors of Reference [34] and are used to
apply the RPA correction in NEUT. The Nieves RPA
SFmodel,andnoRPAcalculationperformedinthecon-
calculation uses the local Fermi gas nuclear model, and
textofSFnuclearmodelisavailable. TwodifferentRPA
NEUT only has a global Fermi gas model implemented
calculations are available from the same authors, termed
for 1p1h interactions, but the authors of the RPA calcu-
relativistic and non-relativistic, which affect the quench-
lationhavenoted[35]thatthesameratiocanbeapplied,
withreasonableprecision,toaglobalFermigas. Because ing of the RPA at high Q2 (>∼ 0.5 GeV2). The ratio
of non-relativistic to relativistic RPA is shown in Fig-
of the model dependence, the same ratios cannot be ap-
ure4. BothRPAmodelsareinvestigatedinthisanalysis
plied to modify the 1p1h interactions calculated with a
as there is no guidance on which model is more physi-
cal. The ‘stray’ points in Figures 3 and 4 are artifacts
from the authors of the RPA model, who provided the
data used to produce these figures. The cause of these
1 Thismodelsimplyenforcesenergyandmomentumconservation,
treats initial nucleons as uncorrelated and drawn from a local artifacts is unknown, but as these points lie outside the
Fermi gas model, and shares momentum equally between final kinematically allowed region of (E , Q2) space, they do
ν
statenucleons[49]. notaffecttheRPAimplementationinNEUTasnoevent
5
outside this region can be generated. it. However, the Nieves model consistently uses a local
Fermigas,whereasNEUTusesaglobalFermigasmodel
for the 1p1h calculation. Currently there is no ability to
5 1.2
) R
2V4.5 1.18P vary the value of MA used in the Nieves model predic-
e A tion as implemented in NEUT, making the fits slightly
2 (GQ3.45 11..1146 (non innocoRnPsiAstecnotrreinctitohnisarpepglaierdd,2.whTichheisSFp+hy2spic2ahllymiondceolnhsiass-
-
3 1.12re tent as the 2p2h enhancement is used (both corrections
2.5 1.1 l.)/R are due to complications in heavy nuclear targets). As
2 1.08P previously noted, no RPA calculation appropriate for a
A
1.5 1.06 ( SF model is currently available, so this inconsistency is
r
1 1.04el.) ucunlaavtoioidnab(SleF.)Tahnedntuhcele2apr2mhocdaellcsuulasteidonfo(rLtFhGe)1pa1rehaclaslo-
0.5 1.02
inconsistent, and it has been remarked that the short
0 1
1 2 3 4 5 6 7 8 9 10 rangecorrelationsincludedtheSFnuclearmodelmaybe
En (GeV) the same as some contributions to the Nieves 2p2h in-
teraction model, so some contributions may be included
(a) ν – 12C
µ
twice.
) 5 1.2 R Additionally, the Effective Spectral Function
2
V4.5 1.18P (ESF) [26, 53] has been implemented in NEUT as
e A
G 4 1.16 ( described in Reference [54], and is included for compar-
( n
2 Q3.5 1.14on ison with the other nominal models in Section V. The
3 1.12-re ESF enforces agreement with the longitudinal response
2.5 1.1 l.)/R fmuondctifiyoningextthreacitneidtiaflrosmtateelencutcrolenonscmatotmereinntgumdatdaistbriy-
2 1.08P
A bution (using a simple parametrization of the Benhar
1.5 1.06 ( SF model), and should be used with the Transverse
r
1 1.04el.) Enhancement Model (TEM), which parametrizes the
0.5 1.02 observed discrepancy between the longitudinal and
0 1 transverse response functions extracted from electron
1 2 3 4 5 6 7 8 9 10
scattering data as an enhancement to the magnetic form
E (GeV)
n factor [19]. By construction, the ESF+TEM agrees
(b) ν¯ – 12C with elastic electron scattering data, and is extended
µ
to neutrino scattering data by modifying the Llewellyn-
FIG. 4: The ratio of the non-relativistic RPA correction Smith interaction formalism for nucleons bound in a
to the relativistic RPA correction, shown for both muon nucleus described by the ESF (and with the modified
neutrino and muon antineutrino interactions on carbon. magnetic form factor from the TEM). This model was
These E and Q2 dependent tables are used to reweight implemented too late to be a candidate model for the
ν
NEUT events from one RPA model to the other. By T2K oscillation analysis, and is not considered further
default, NEUT events are generated with the in the fitting work described in this paper.
non-relativistic RPA model.
Model parameter NEUT default value
With these different ingredients, three distinct candi- MA 1.01GeV/c2
dateCCQEmodelsareavailableinNEUT,whichareall Fermi momentum, pSF 209MeV/c
F
considered in this work: Mean-field width 200MeV/c (Benhar nominal [23])
Norm. of the Benhar nominal [23]
1. RFG+relativistic RPA+2p2h
correlation term (correlated tail ∼20% of total)
2. RFG+non-relativistic RPA+2p2h 2p2h normalization 100% Nieves model [34, 35]
Axial form factor Dipole
3. SF+2p2h. Vector form factors BBBA05 [55]
The default values for all variable model parameters are
TABLE I: Nominal model parameters for the SF+2p2h
listed in Table II and Table I for both RFG+RPA+2p2h
model.
models and SF+2p2h, respectively.
It should be noted that there are deficiencies for
both models as currently implemented in NEUT. The
RFG+RPA+2p2hmodelisverylikethefullNievesmodel 2 Thevalueoftheaxialmassusedforthe2p2hcontributiontothe
as both the RPA and 2p2h calculations are taken from crosssectionwasfixedtoMA=1.01GeV/c2.
6
Model parameter NEUT default value IV. EXTERNAL DATASETS
M 1.01GeV/c2
A
Fermi momentum, pRFG 217MeV/c Four datasets are used in the CCQE fits presented in
F
this work: the MiniBooNE neutrino [10] (2010) and an-
RPA Nieves relativistic or
tineutrino [11] (2013) results; and the MINERνA neu-
non-relativistic model [34]
trino[17](2013)andantineutrino[18](2013)results. All
2p2h normalization 100% Nieves model [34, 35]
experimentaldetailsandinformationabouttheseresults,
Axial form factor Dipole
which is reproduced here, are taken from the references
Vector form factors BBBA05 [55]
cited above unless otherwise stated.
The single-differential cross section results are given
TABLE II: Nominal model parameters for the intermsofQ2 , thefour-momentumtransfercalculated
QE
relativistic and non-relativistic RFG+RPA+2p2h from lepton kinematics under the quasi-elastic hypothe-
models. sis, which is calculated using the equations:
2M(cid:48)E −(M(cid:48)2+m2 −M2)
EQE = n µ n µ p , (1)
ν (cid:113)
We note that both of our candidate models are ex- 2(M(cid:48) −E + E2 −m2 cosθ )
n µ µ µ µ
pectedtobreakdownatlowmomentumtransferbecause
theydonotincludenucleareffectssuchasnuclearexcita-
(cid:113)
tions and collective resonances. In other analyses which Q2 =−m2 +2EQE(E − E2 −m2 cosθ ), (2)
QE µ ν µ µ µ µ
fit models to CCQE data, bins which are dominated by
low momentum transfer events are excluded [56]. In this where E is the muon energy; M , M and m are
µ n p µ
analysis we have not followed any such bin masking pro- the neutron, proton and muon masses, respectively; and
cedure. Arguably,toobtainarealisticvalueofthemodel M(cid:48) = M −V where V is the binding energy of carbon
n n
parameters,oneshouldonlyfitthemodelinitsstatedre- assumed in the analysis3. For both MiniBooNE datasets
gion of validity. However, the main focus of this analysis and the MINERνA neutrino dataset, V = 34MeV; for
istoobtaincentralvaluesanderrorsfortheT2Koscilla- the MINERνA antineutrino dataset, V =30MeV.
tionanalysis,wherethecrosssectionmodelisusedforall In the MiniBooNE analysis, Q2 is calculated from
QE
regions of phase-space, so some pragmatism is required. theunfoldedT andcosθ distributions. TheMINERνA
µ µ
analysisunfoldstheQ2 distributioncalculatedwiththe
QE
reconstructed p and cosθ values. The errors on the
µ µ
Q2 distributions for both experiments include the un-
QE
certaintiesrelatingtothemuonreconstruction,soshould
cover the difference in the method used to produce the
III. NUWRO AS A VALIDATION TOOL FOR Q2 crosssection results. We notethatthemain results
NEW INTERACTION MODELS QE
ofouranalysisusetheMiniBooNEdouble-differentialre-
sultsonly,sothereisnopossibletensionfromdifferences
The NuWro Monte Carlo generator for neutrino inter- betweenthemethodsusedtoproduceQ2QE distributions.
actions has been developed over the past ∼10 years at
the University of Wrocław [57]. It was the first MC gen-
A. MiniBooNE neutrino
erator to have an implementation of the Benhar SF [23]
and the Nieves 2p2h model included [34, 35], and served
as the benchmark for the NEUT development of both The MiniBooNE CCQE data has been released as
models. The implementation of the SF model in NuWro a double-differential cross section as a function of
was based on the code written for Reference [58] and (Tµ,cosθµ), where Tµ is the kinetic energy of the out-
subsequently optimized for NuWro. The Nieves model going muon and θµ is the angle between the incoming
implementation in NuWro used a series of lookup ta- neutrino and outgoing muon. Differential cross sections
bles for the 2p2h cross-section as a function of leptonic were also released as a function of Q2 or EQERFG, but
QE ν
variablesforvariousnucleartargetsandneutrinospecies the double-differential result was preferred as it is con-
so is very similar as in NEUT, although it has since tains the most information and has minimal model de-
been improved to use a more general formalism which pendence. The MiniBooNE data release included cen-
dependsonanumberofnuclearresponsefunctionswhich tral values for each bin and the diagonal elements of the
can be extracted from the Nieves code, and therefore re-
duces the number of lookup tables required. The same
genericmodel[49]wasusedtosimulatetheinitialandfi-
3 NotethatthebindingenergyV isjustthevalueassumedwhen
nalhadronicstatesinNuWroaswasusedinNEUT.For calculating Q2 , so we must use the same value as the exper-
boththeSFandNieves2p2hmodels,NuWroandNEUT iments whenQpEroducing comparable Q2 distributions, but it
QE
areingoodagreement,whichprovidesausefulvalidation neednotbeconsistentwiththebindingenergyusedinoursim-
of the NEUT implementations of these models. ulation.
7
shape-only covariance matrix; correlations between bins pendently of ν¯ -induced CC1π− as most π− mesons are
µ
werenotreleased. Additionally,theoverallnormalization absorbed. Unfortunately, this property makes CC1π− a
uncertainly was given as 10.7% for neutrino running. biggerbackgroundtotheCCQEanalysisinantineutrino
The MiniBooNE CCQE cross sections are released as mode, and means that there is no sample with which to
both CCQE-corrected, and CCQE-like measurements. directly tune the CC1π− production from the NUANCE
The CCQE-like sample is obtained by selecting events resonancemodel,sotheneutrinomodeCC1π+ hastobe
in which a muon was detected with no pions, but no used (as was done for the neutrino mode sample). Other
requirement was made on the proton. The CCQE- backgrounds are subtracted using the NUANCE interac-
correctedmeasurementisproducedbysubtractingback- tionmodelaftersometuningandcorrections. Asaresult
ground events (where the primary interaction was not of the two large backgrounds in the antineutrino sample,
CCQE) based on the NUANCE [59] generator predic- the purity of the CCQE-like sample is 61%, making the
tion. The dominant background is CC1π+, and a dedi- correction larger than for the neutrino mode sample.
cated sample was used to tune the NUANCE prediction
whichwasusedinthebackgroundsubtraction. Itshould
benotedthattheNUANCECC1π+ simulationincluded C. MINERνA
π-less ∆ decay. The published signal purity for the neu-
trino dataset is 77%.
The CCQE datasets from MINERνA are released
CCQE-like results are less model dependent than
asCCQE-correctedsingle-differentialflux-averagedcross
CCQE-corrected results (as they do not rely on the ex- section as a function of Q2 , where the flux has been
QE
periment’s own MC correction strategy), but make the
averaged over the region 1.5 ≤ E ≤ 10GeV. There is
ν
analysis dependent on the simulation of the background an additional requirement that 1.5 ≤ EQE ≤ 10GeV,
ν
in the MiniBooNE detector, which cannot be tuned to with EQE as defined in Equation 1. Covariance matri-
ν
theMiniBooNEdatainthesamewayMiniBooNE’sback-
ces and central values have been released to perform fits
groundmodelcouldbe. CCQE-correctedresultsareused
to both shape-only and absolutely normalized neutrino
inthisanalysis. AdownsideofusingtheCCQE-corrected
and antineutrino datasets. In this work, the absolutely
dataistheexplicitsubtractionofπ-less∆decayeventsin
normalized distributions have been used in the fit.
the MiniBooNE analysis, which forms part of the Nieves
The correction strategy for the MINERνA data is to
multinucleon–neutrino prediction which we treat as sig-
fit the relative normalizations of simulated background
nal in the analysis. Unfortunately, there is no obvious
distributions to the data in terms of the recoil energy,
waytoaccountforthiseffect,soweignoreitfortheanal-
energy deposited outside a vertex region (the recoil re-
ysis presented. We note that Nieves et al. also used the
gion), and then subtract the predicted background from
CCQE-corrected dataset to compare to their full mod-
theCCQE-likesample. Thepublishedpurityfortheneu-
els [37, 39]. trinodatasetrangesfrom65%atlowQ2 to40%athigh
QE
Q2 (with an overall purity of 49%). The purity for the
QE
antineutrinodatasetisgivenas77%. Thepurityislower
B. MiniBooNE antineutrino
for the neutrino analysis because events with a proton
from the initial interaction are more complicated to re-
The MiniBooNE antineutrino data has been released construct than those with a neutron4.
in the same format as the neutrino mode data. Again, IntheMINERνACCQEanalyses,theefficiencyforse-
the double-differential CCQE-corrected results are used. lecting events with θ >20◦ is very low because the MI-
µ
Theoverallnormalizationuncertaintywasgivenas13.0% NOS near detector, downstream of MINERνA, is used
forantineutrinorunning. Thisislikelytobestronglycor- to tag muons. This introduces a small model depen-
related with the normalization uncertainty for the neu- dence on the results because an RFG model was used
trino mode data, as the uncertainly comes mostly from to correct for the unsampled region of phase-space. The
the flux normalization uncertainty. However, as this in- MINERνA collaboration subsequently released a distri-
formation was not released, no correlation is assumed in bution where the cross section is measured for CCQE
this analysis. events with θ ≤ 20◦. As this dataset is less model-
µ
The correction strategy for the antineutrino dataset dependent, it has been used in the fits, and will be con-
is more complicated than for the neutrino mode sam- sistently used in this analysis. MINERνA also made
ple because of the relatively high νµ contamination in cross-correlations between the neutrino and antineutrino
the ν¯µ beam, which is the largest background in the an- datasets available in a data release after the publication
tineutrino CCQE sample (MiniBooNE is an unmagne-
tizeddetector). ThereisalsoalargeCC1π− background,
the analogue of the CC1π+ contamination in the neu-
trino dataset. Two properties are used to measure the
4 Theantineutrinoanalysishasanadditionalcutrequiringnoad-
νµ background [60]: 8% of νµ-induced CC interactions ditional (other than the muon) tracks from the vertex, and al-
produce no decay electron due to muon-nucleus capture; lowsonlyoneisolatedenergyshower,whereastheneutrinomode
andtheν -inducedCC1π+ eventscanbeidentifiedinde- analysisallowstwo[17,18].
µ
8
oftheirCCQEpapers. Thecorrelationmatricesreleased and 8 for the MINERνA, MiniBooNE single-differential
include both shape and normalization errors, but it is andMiniBooNEdouble-differentialsamples,respectively.
possible to extract shape-only correlation matrices using TheNieves2p2hcontributionisalsoshownontheseplots
the method given in Reference [61]. The full matrix in- for reference.
cluding both shape and normalization errors included is To produce a meaningful nominal χ2 for the Mini-
shown in Figure 5. BooNE datasets, it is necessary to fit the MiniBooNE
normalization parameters. The single and double-
differential plots shown in Fig. 7 and 8 are scaled ac-
1
utrino 000...468 ctrahaollmreyd,ebitntehegsretstnoλfiotMνmthBpienoaaiMnnldtpi.nrλieBMν¯TdoiBhcoetaNiorbEenessgntfiovofirermntthaivnelaizlMTuaaetinisboilnBeofoIpIotaIhN.reaEAmpddeudotliueltribpolanaet---
e differential datasets, without the scaling factor applied,
N 0.2
o -00.2 aeyree.shown in Figure 9, which are easier to interpret by
n -0.4 · 10-39
utri -0.6 2)V 18 2p2h Only
ne Ge 16 RFG (c 2 = 10.80)
Anti Antineutrino Neutrino --10.8 2/ (cmE1142 SREFSP+FA2++pT22Eph2M h( c ((2cc 2=2 = =6 513.541..163)05))
2QQ10 DATA
d 8
/
6
FIG. 5: Cross-correlation matrix including both shape sd
4
and normalization uncertainties for the MINERνA
2
neutrino and antineutrino samples. The eight neutrino
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
and eight antineutrino bins shown here correspond to
Q2 (GeV2)
the eight Q2 bins from the MINERνA datasets. QE
QE
(a) Neutrino
· 10-39
2)V 16 2p2h Only
V. MONTE CARLO PREDICTION Ge 14 RFG (c 2 = 12.07)
2/m 12 SF+2p2h (c 2 = 60.61)
For each of the four experimental results included in c RPA+2p2h (c 2 = 31.09)
the fit, one million CCQE and 2p2h events were gener- 2 (QQE180 EDSAFT+ATEM (c 2 = 13.56)
ated with NEUT for each model using the default pa- d
/ 6
rameters given in Tables II and I and the published flux
sd
4
for each dataset. The flux averaged cross section predic-
2
tions were produced using the following method:
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1. For each event apply experiment-specific cuts and, Q2 (GeV2)
if the event passes, calculate the relevant recon- QE
structed quantity and fill the 1D or 2D event rate (b) Antineutrino
histogram.
FIG. 6: Nominal model predictions for the MINERνA
2. Calculate the event rate by integrating the MC datasets with M =1.01GeV/c2 and all other model
A
event rate histogram (flux × cross section).
parameters at their default values. The relativistic RPA
model is shown.
3. Integrate the published flux histogram to get the
average flux.
Note that the double-differential cross section plots
4. Scalethefilledhistogrambytheeventratedivided shown in Figures 9 have been rebinned. In the distribu-
by the average flux to get the flux averaged cross tions released by MiniBooNE, and used in the fits, there
section per target nucleon. are 20 cosθ bins uniformly distributed between -1 and
µ
1. For ease of presentation, these have been rebinned
5. Divide the content of each bin by the bin width.
andtheresultsareshownineightcosθ slicesofvarying
µ
sizes, where merged bins have been averaged and their
Thedefaultpredictionsforavarietyofmodelsavailable
in NEUT, as well as the data, are shown in Figures 6, 7 errors combined in quadrature.
9
2) 25· 10-39 Fit type λMνB λMν¯B
V 2p2h Only RFG 0.732±0.007 —
2/Gem 20 RSFF+G2 (pc22h = ( c123 6=. 7380)1.46) Neutrino 1D SF+2p2h 0.741±0.007 —
c RPA+2p2h (c 2 = 46.70) RPA+2p2h 0.760±0.007 —
(E15 ESF+TEM (c 2 = 109.59) ESF+TEM 0.804±0.008 —
2QQ DATA
d 10 RFG — 0.805±0.011
/
SF+2p2h — 0.826±0.011
sd Antineutrino 1D
5 RPA+2p2h — 0.774±0.010
ESF+TEM — 0.803±0.011
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 RFG 0.725±0.011 —
Q2 (GeV2)
QE SF+2p2h 0.756±0.011 —
Neutrino 2D
RPA+2p2h 0.760±0.011 —
(a) Neutrino
ESF+TEM 0.827±0.012 —
· 10-39
2)V 12 2p2h Only RFG — 0.808±0.015
Ge RFG (c 2 = 83.55) Antineutrino 2D SF+2p2h — 0.838±0.015
2/m 10 SF+2p2h (c 2 = 111.55) RPA+2p2h — 0.802±0.015
c 8 RPA+2p2h (c 2 = 43.23) ESF+TEM — 0.833±0.015
(E ESF+TEM (c 2 = 74.95)
2QQ 6 DATA
TABLE III: Table of best fit MiniBooNE normalization
d
/ 4 parameter values for the nominal model comparisons
sd
shown in Figures 7 and 8. The relativistic RPA
2
calculation is shown.
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Q2 (GeV2)
QE
(b) Antineutrino
FIG. 7: Nominal model predictions for the MiniBooNE
single-differential datasets with M =1.01GeV/c2 and
A
all other model parameters at their default values. The
relativistic RPA calculation is shown. Normalization
parameters are applied as given in Table III.
10
2p2h Only
6 -1. < cosq m < 0.0 8 0.0 < cosq m < 0.3 10 0.3 < cosq m < 0.6
RFG (c 2=247.9) 7
5 8
) 6
V
e SF+2p2h (c 2=457.8) 4 5 6
G
2/m RPA+2p2h (c 2=130.9) 3 43 4
2
39 c ESF+TEM (c 2=220.9) 1 21 2
-0 DATA 0 0 0
1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
24
· ( 20 0.6 < cosq m < 0.7 22 0.7 < cosq m < 0.8 0.8 < cosq m < 0.9 30 0.9 < cosq m < 1.0
m 18 20 25
qs 16 18 25
s2ddco 1142 1146 20 20
Tm 10 12 15 15
10
d 8
6 8 10 10
6
4 4 5 5
2 2
0 0 0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2
T (GeV)
m
(a) Neutrino
2p2h Only 0.16 -1. < cosq m < 0.0 0.7 0.0 < cosq m < 0.3 1.4 0.3 < cosq m < 0.6
RFG (c 2=91.8) 0.14 0.6 1.2
) 0.12 0.5
V 1
e SF+2p2h (c 2=118.5) 0.1 0.4
G 0.8
0.08
2/m RPA+2p2h (c 2=49.0) 0.06 0.3 0.6
c ESF+TEM (c 2=91.4) 0.04 0.2 0.4

39 0.02 0.1 0.2
-0 DATA 0 0 0
1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
10
·( 4 0.6 < cosq m < 0.7 6 0.7 < cosq m < 0.8 0.8 < cosq m < 0.9 16 0.9 < cosq m < 1.0

m 3.5 5 8 14
qs
o 3 12
s2 c 2.5 4 6 10
dd
Tm 2 3 8
d 1.5 4 6
2
1 4
2
1
0.5 2
0 0 0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2
T (GeV)
m
(b) Antineutrino
FIG. 8: Nominal model predictions for the MiniBooNE double-differential datasets with M =1.01GeV/c2 and all
A
other model parameters at their default values. The relativistic RPA calculation is shown. Normalization
parameters are applied as given in Table III.