Measurement of the neutrino component of an anti-neutrino beam observed by a non-magnetized detector

0.3 MB·English

by  A. A. Aguilar-Arevalo

Measurement of the neutrino component of an anti-neutrino beam observed by a
non-magnetized detector
A. A. Aguilar-Arevalo12, C. E. Anderson15, S. J. Brice6, B. C. Brown6, L. Bugel11, J. M. Conrad11,
R. Dharmapalan1, Z. Djurcic2, B. T. Fleming15, R. Ford6, F. G. Garcia6, G. T. Garvey9, J. Grange7,
J. A. Green8,9, R. Imlay10, R. A. Johnson3, G. Karagiorgi11, T. Katori8,11, T. Kobilarcik6, S. K. Linden15,
W. C. Louis9, K. B. M. Mahn5, W. Marsh6, C. Mauger9, W. Metcalf10, G. B. Mills9, J. Mirabal9,
C. D. Moore6, J. Mousseau7, R. H. Nelson4, V. Nguyen11, P. Nienaber14, J. A. Nowak10, B. Osmanov7,
A. Patch9,11, Z. Pavlovic9, D. Perevalov1, C. C. Polly6, H. Ray7, B. P. Roe13, A. D. Russell6,
M. H. Shaevitz5, M. Sorel5∗, J. Spitz15, I. Stancu1, R. J. Stefanski6, R. Tayloe8, M. Tzanov4,
R. G. Van de Water9, M. O. Wascko10†, D. H. White9, M. J. Wilking4, G. P. Zeller6, E. D. Zimmerman4
(The MiniBooNE Collaboration)
3
1 1University of Alabama; Tuscaloosa, AL 35487
0 2Argonne National Laboratory; Argonne, IL 60439
2 3University of Cincinnati; Cincinnati, OH 45221
4University of Colorado; Boulder, CO 80309
n
5Columbia University; New York, NY 10027
a
6Fermi National Accelerator Laboratory; Batavia, IL 60510
J
7University of Florida; Gainesville, FL 32611
9 8Indiana University; Bloomington, IN 47405
2
9Los Alamos National Laboratory; Los Alamos, NM 87545

10Louisiana State University; Baton Rouge, LA 70803
]
x 11Massachusetts Institute of Technology; Cambridge, MA 02139
e 12Instituto de Ciencias Nucleares,
- Universidad Nacional Auto´noma de M´exico, D.F. 04510, M´exico
p
13University of Michigan; Ann Arbor, MI 48109
e
14Saint Mary’s University of Minnesota; Winona, MN 55987
h
[ 15Yale University; New Haven, CT 06520

3 (Dated: January 31, 2013)
v
4 Two methods are employed to measure the neutrino flux of the anti-neutrino-mode beam ob-
6 served by the MiniBooNE detector. The first method compares data to simulated event rates in
9 a high purity νµ induced charged-current single π+ (CC1π+) sample while the second exploits the
1 difference between the angular distributions of muons created in νµ and ν¯µ charged-current quasi-
. elastic(CCQE)interactions. Theresultsfrombothanalysesindicatethepredictionoftheneutrino
2
flux component of the pre-dominately anti-neutrino beam is over-estimated - the CC1π+ analysis
0
1 indicates the predicted νµ flux should be scaled by 0.76±0.11, while the CCQE angular fit yields
0.65±0.23. The energy spectrum of the flux prediction is checked by repeating the analyses in
1
: bins of reconstructed neutrino energy, and the results show that the spectral shape is well mod-
v eled. These analyses are a demonstration of techniques for measuring the neutrino contamination
Xi of anti-neutrinobeams observed byfuture non-magnetized detectors.
r
a
I. INTRODUCTION purely neutrino nor anti-neutrino in content, detectors
must be able to separate the two contributions. Most
commonly, this is achieved by employing a magnetic
If θ is non-zero, next generation neutrino oscillation field to identify the final-state µ− (or µ+) produced in
13
experiments will embark on a program to measure the charged-currentν (or ν¯ ) interactions. A handle onthe
µ µ
neutrinomassorderingandlookforevidenceofCPviola- overall level and energy dependence of ν versus ν¯ in-
µ µ
tionintheneutrinosector. Thiseffortwillrequireprecise duced events, however, is also possible in unmagnetized
oscillation measurements with both neutrino and anti- detectors with a suitable choice of reaction channels.
neutrino beams in order to isolate these effects. Since
Accelerator-basedneutrinobeamsaretypicallycreated
beams producedinanacceleratorenvironmentarenever
by colliding proton beams with thick nuclear targets.
Mesons produced at a variety of energies and angles are
focused by a magnetic horn before entering a decay tun-
nel. Mesondecayscanbecalculatedsufficientlywellfora
∗Presentaddress: IFIC,UniversidaddeValenciaandCSIC,Valen-
givenbeamgeometrythattheneutrinofluxuncertainties
cia46071,Spain
†Present address: Imperial College; London SW7 2AZ, United arise mainly from uncertainties in the meson production
Kingdom cross sections. In particular,to avoidextrapolating data
2
takenwithdiversenucleartargetmaterialsorprotonen-
ergies, neutrino experiments require dedicated hadron
production cross-section measurements taken with the 12000
same beam energy and target to obtain a reliable flux
prediction. If an accelerator-based neutrino experiment 10000
lacks such hadron production data, it may be able to
s
meetitsoscillationanalysisgoalsusingcalibrationsfrom nt8000
e
a near detector; however the secondary physics goal of Ev n mode
measuring neutrino-nucleon absolute cross sections will ed 6000
ct
still be limited by flux uncertainties. di
e
To avoid ambiguity, in this paper references to “neu- Pr4000
trinos” are not meant to also refer to anti-neutrinos,
(a)
and “mode” refers to the polarity of the magnetic fo- 2000
cusing horn used in the beamline. In this way, for
example, “anti-neutrino events” refers to anti-neutrino 0
0 0.05 0.1 0.15 0.2 0.25
induced events exclusively while “anti-neutrino-mode q p (rad)
events” refers to data obtained when the horn polarity
focuses negatively charged particles, which is a mix of
neutrino and anti-neutrino induced events.
2000
The Mini Booster Neutrino Experiment (MiniBooNE) p+Be fi p + fi n m
1800
is located at Fermilab in Batavia, Illinois and has made p+Be fi p - fi n m
1600
many oscillation [1–5] and cross section [6–13] measure-
ments. For MiniBooNE, the pion production data cru- nts1400
e
cial to the flux model come from proton-beryllium cross Ev1200 n mode
sections on a 5% interaction length target reported by cted 1000
the HARP experiment [14]. However, even with dedi- edi 800
cateddataappropriatetotheexperimentalsetupofMini- Pr
600
BooNE, there remain small regions of phase space rele-
vant to MiniBooNE not covered by these HARP mea- 400 (b)
surements. Of particular importance is the production 200
of very forward pions with respect to the direction of 0
0 0.05 0.1 0.15 0.2 0.25
the incoming proton beam. This is the dominant pro- q p (rad)
duction regionof parent particles contributing neutrinos
to the anti-neutrino-mode beam, or vice versa. Mini-
BooNE uses a magnetic horn to defocus the majority of
FIG. 1: (Color online) Predicted angular distributions of pi-
these background parent particles, but as Figure 1 sug-
onswith respect to theincidentproton beam (θπ) producing
gests, the very forward pions can escape magnetic de- νµ and ν¯µ in (a) neutrino mode and (b) anti-neutrino mode.
flection. This same angular region suffers from a sizable Only pions leading to νµ and ν¯µ events in the detector are
beam-related proton background and would also require shown, and all distributions are normalized to 5.66 × 1020
a model-dependent acceptance correction[15]. For these protons on target. Arrows indicate the region where HARP
reasons, pion cross sections in the θ <30 mrad region, data[14] are available.
π
where θ is the angle the outgoing pion makes with re-
π
spect to the incoming proton beam, are not reported by
HARP and the majority of the MiniBooNE flux predic- energy range (∼ 1 GeV) [16]. For these reasons anti-
tionarisingfromπ+(π−)decaywhilefocusingπ−(π+)is neutrinoinducedeventsarenotaseriouscomplicationfor
extrapolatedfromthe available hadronproduction data. neutrino-mode running, as these flux and cross-section
Thehadronproductiondatacover∼90%ofsignselected effects conspire to suppress their contribution, while the
pions,while lessthan25%ofoppositelychargedpionsin same effects amplify the neutrino contamination in anti-
thesamebeamareconstrained. Someoftheseacceptance neutrino-mode data. Simulation predicts anti-neutrino
limitations could be reduced by use of the long-target events account for ∼ 1% of neutrino-mode data while
data takenby HARP, whichareactivelybeing analyzed. neutrinos are responsible for ∼ 30% of anti-neutrino-
modedata. Thismotivatesadedicatedstudyoftheneu-
The overall contamination rate is more significant in trino flux contribution to the anti-neutrino-mode data.
anti-neutrino mode due to effects from both flux and A data set corresponding to 5.66 ×1020 protons on tar-
cross section: the leading-particle effect at the target get is analyzed here and is important for both the on-
preferentially produces about twice as many π+ as π−, going MiniBooNE anti-neutrino oscillation search [4, 5]
andtheneutrinocrosssectionisaboutthreetimeshigher and anti-neutrino cross-sectionmeasurements.
than the anti-neutrino cross section in the MiniBooNE Two approaches for measuring the neutrino flux in
3
anti-neutrino-mode are taken. In the first method, a Ageant4-basedmodel[19]isusedtopredicttheneu-
highpuritysampleofcharged-currentsingleπ+(CC1π+) trino and anti-neutrino flux at the detector. The simu-
events isolate the ν contribution in the beam. The sec- lation considers proton travel to the target, p-Be inter-
µ
ondmethodexploitstheinterferenceterminthecharged- actions in the target including meson production, mag-
currentquasi-elastic(CCQE)crosssection,wherethean- netic horn focusing, particle propagation, meson decay,
gulardistributionoffinal-statemuonsarepredictedtobe and finally neutrino and anti-neutrino transport to the
distinct for ν compared to ν¯ interactions. Both tech- detector. As mentioned earlier, measurement of pion
µ µ
niqueswereintroducedintheMiniBooNEanti-neutrino- cross sections from p-Be interactions are obtained from
moderunproposal[17]. Thesetwoapproachesoffercom- the HARP experiment. The HARP double differential
plementarymeansofmeasuringtheneutrinofluxcompo- cross-section error matrix is used to set pion production
nentinanti-neutrino-modedata,withtheCCQEsample uncertainties [20]. Even with valuable data constraints,
providing a constraint at lower neutrino energies while meson production at the target contributes the largest
the CC1π+ measurement covers higher energies. They systematic error to the flux prediction. The fractional
providebothacheckoftheMiniBooNEbeamsimulation uncertainty on pion production is ∼8% around the flux
inaregionnotcoveredbyexternaldataanddemonstrate peak,whiletheuncertaintygrowssignificantlyinregions
a set of techniques for measuring the ν contamination dominated by pions unconstrained by HARP data. The
µ
in an anti-neutrino-mode beam in the absence of a mag- flux prediction in neutrino and anti-neutrino modes is
netized detector. It has been arguedelsewherethat even presented in Figure 2. Details of the beamline and flux
modeststatisticalseparationofcharged-currentneutrino prediction are given in Ref. [20].
and anti-neutrino events, afforded by the kind of analy-
ses presented here, may be sufficient to meet the physics
goals in proposed future experiments such as neutrino B. Detector
factories [18].
This paper is organized as follows: the MiniBooNE
TheMiniBooNEdetectorisa6.1mradiusspherefilled
experiment is described in Section II while Section III
with 818 tons of pure Marcol7 mineral oil. It houses
details the neutrinoandanti-neutrinoscatteringmodels.
1520 8-inch Hamamatsu photomultiplier tubes (PMTs)
Two techniques to measure the neutrino contribution to
segregated into two optically isolated regions: an inner
theanti-neutrinofluxarepresentedinSectionsIVandV.
signal region of 575 cm radius and an outer veto shell
The results are compared in Section VI, implications for
of thickness 35 cm. The former contains 1280 PMTs
other neutrino experiments are discussed in Section VII
(11.3% coverage) while the latter holds 240 PMTs. The
and this work is summarized in Section VIII.
veto region is used to enforce containment of charged
particles produced by neutrinos and anti-neutrinos from
the beam and reject charged particles entering the tank.
II. THE MINIBOONE EXPERIMENT Themineraloilhasadensityof0.845g/cm3withanin-
dexofrefractionof1.47at20◦C. Chargedparticleswith
A. Beamline and flux velocity β>0.68 produce Cherenkov radiation. Particle
identification and reconstruction is principally obtained
The Booster Neutrino Beamline (BNB) provides the throughthepatternandtimingofthispromptCherenkov
neutrino and anti-neutrino flux to MiniBooNE. A beam light; however, delayed scintillation light present due to
of 8 GeV kinetic energy protons is extracted from the fluorescentcomponentsintheoilhasalsobeenusedeffec-
Booster synchrotron in “spills” of 5×1012 protons over tivelytoprovideenergyinformationforchargedparticles
1.6 µs at a maximum rate of 5 Hz. A lattice of alterna- produced below Cherenkov threshold [10].
tively focusing and defocusing quadrupole magnets steer MiniBooNE electronics record PMT charge and time
the proton bunches to a beryllium target 71 cm (1.75 informationbeginning about 5µs before the 1.6µs BNB
interaction lengths) long. The protons collide with the protondelivery. Data are recordedfor a total of 19.2µs.
target to create a spray of secondary particles. An alu- The 5 µs interval before the beam spill is primarily
minum electromagnetic horn surrounding the target is present to minimize data contamination caused by cos-
pulsed to coincide with the p-Be collisions, creating a mic ray muons stopping in the signal region prior to the
toroidal magnetic field to focus mesons of the desired start of the DAQ window. PMT activity is recorded for
charge. The hornpulses are suchthat the magnetic field morethan10µsafterbeamdeliverytoobserveelectrons
is constant for the duration of the proton spill. In neu- from the at-restdecay of muons (hereafter referred to as
trinomode,themagnetichornfocusespositivelycharged “Michel” electrons) subsequent to the initial neutrino or
secondary particles while defocusing those with nega- anti-neutrino induced interaction.
tivecharge;the horneffectsarereversedinanti-neutrino The detector response to muons is measured using a
mode. Thefocusedmesonsareallowedtodecayina50m dedicatedmuontaggingsystemthatindependently mea-
air-filled decay region which terminates at a steel beam surestheenergyanddirectionofcosmicraymuonsupto
dump. Thedominantdecaymodesofthemesons,mostly 800 MeV. MiniBooNE employs a scintillator hodoscope
pions, produce muon neutrinos and anti-neutrinos. directly above the detector and seven internal scintilla-
4
addition, the surrounding environment composed of dirt
externaltotheMiniBooNEenclosure,theconcretecylin-
dricalhousingandtheair-filledgapbetweenthedetector
10-11
and walls is treated. Of critical importance is the treat-
n mode ment of particle transport in the detector medium. The
V)10-12 geant3 program takes as input the final-state particles
e
M emerging from the nucleus and simulates their propaga-
0
T/510-13 tion in the detector.
PO With a few exceptions, MiniBooNE uses the standard
2/m geant3 settings to simulate physics processes. Devia-
c10-14
1/ tions include a custom model for light propagation in
(
F the detector oil and a substitution of the hadronic in-
10-15 teraction model. The default gfluka hadron model is
(a)
replacedbythegcalor[23]package,whichbettermod-
10-16 elspionabsorption(π±+X →X′)andchargeexchange
0 0.5 1 1.5 2 2.5 3 3.5 4
En (GeV) (π±+X ↔π0+X′) processes. This is particularly rel-
evant for the present analysis,where the predicted event
compositionofthe twointeractionsamplesstudiedisde-
pendent on the pion survival model. Based on compar-
10-11 n m isons with external data [24] and the gcalor predic-
n mode n m tion,anuncertaintyof35%(50%)isassignedtothepion
V)10-12 absorption (charge exchange) interaction in the detector
T/50 Me10-13 nn e tmheedniuumcl.euTshies duinscceurstsaeidntiynfSoercttihoensIaImICe.processes inside
O e The model for light propagation in the oil is formed
P
2/m using a combination of external measurements and cal-
c10-14
1/ ibration data. Photon emission through Cherenkov and
(
F scintillation processes is simulated and propagated until
10-15 the photon either is absorbed or hits a PMT photocath-
(b)
ode,possibly leading to photoelectronproduction. Light
10-16 emmission,attenuationandscatteringareincluded. The
0 0.5 1 1.5 2 2.5 3 3.5 4
En (GeV) optical model of the detector describes the wavelength,
time, and angular dependence of these processes [25].
FIG. 2: (Color online) The MiniBooNE flux prediction for
III. PREDICTED NEUTRINO AND
(a) neutrino mode and (b) anti-neutrino mode. Due to the
ANTI-NEUTRINO INTERACTIONS
leading-particle effect, the neutrino contribution to the anti-
neutrino-mode flux is more significant compared to the anti-
neutrinocomponentoftheneutrino-modebeam. Plotstaken MiniBooNE uses the nuance [16] event generator to
from Ref. [20]. simulate neutrino and anti-neutrino interactions in the
detector. nuance includes a comprehensive neutrino
and anti-neutrino cross section model which considers
tor cubes at different depths, each connected to a dedi- knowninteractions inthe neutrino andanti-neutrinoen-
cated one-inch PMT for readout. The measured ranges ergy range from ∼ 100 MeV to 1 TeV. Ninety-nine reac-
and directions of muons traversing the hodoscope and tions are modeled separately and combined with nuclear
stopping in cubes are used to verify muon reconstruc- models describing bound nucleon states and final-state
tion algorithms. The energy (angle) resolution improves interactions to predict event rates and kinematics.
from12%(5.4 deg)at 100MeV to 3.4%(1.0 deg) at 800 Bound nucleons in the detector medium are described
MeV. Full detector details and calibrations are available by the Relativistic Fermi Gas model [26]. This assumes
in Ref. [21]. thenucleonstobeindependentandquasi-free. Alsospec-
ifiedis a hardcut-offinavailablestruck nucleonenergies
as dictated by the exclusion principle.
C. Detector simulation The neutrino and anti-neutrino interaction types rele-
vant to the analysis presented here are charged-current
The detector response to particle interactions and quasi-elastic (Section IIIA) and pion production (Sec-
propagation is simulated using geant3 [22]. The en- tion IIIB). The neutrino-induced absolute cross sections
tire detector geometry is considered, including the steel for both processes have been measured at MiniBooNE
tank, external supports and main inner components. In using a flux prediction well determined by HARP data.
5
Thesecross-sectionmeasurementsareutilizedintheanti- considered, however the ∆(1232) is dominant in the en-
neutrino-mode simulation. ergy range spanned by MiniBooNE. Multi-pion produc-
tion mechanisms are also considered, though their con-
tribution is predicted to be small.
A. Charged current quasi-elastic scattering The axial masses in the resonance channels are set
simultaneously to reproduce inclusive non-MiniBooNE
To model CCQE interactions, this analysis uses mea- charged-current data [37]. The extracted values are
suredcrosssectionsfromthe MiniBooNEneutrinomode MA1π = 1.10± 0.27 GeV (single pion production) and
CCQEdata[9]andamodelwhichhasbeenfoundtowell- Mmulti−π =1.30±0.52 GeV (multi-pion production).
A
reproduce the kinematics of such events. Specifically, In the present analysis the charged-current single π+
MiniBooNE adopts the CCQE scattering formalism of (CC1π+) prediction with these assumptions is adjusted
Smith-Moniz [26]. The vector component of the interac- to reproduce the kinematic distributions measured in
tion is measured by electron scattering experiments and MiniBooNE neutrino-mode data [9, 12].
is assumed to have a non-dipole form [27]. The axial-
vector form factor employs a dipole construction, con-
taining an “axial mass”, M , taken either from Mini- C. Final state interactions
A
BooNE or external data, depending on the neutrino tar-
get. For a neutrino or anti-neutrino interaction with a nu-
The MiniBooNE mineral oil is composed of C H , cleon bound in carbon, nuance propagates the outgo-
n 2n+2
n∼20,andthepredictionforCCQEscatteringis differ- ing hadrons including nucleons, mesons and baryonic
ent for the two flavors of target. In the present analysis, resonances, and simulates their re-interaction as they
Meff = 1.35 ± 0.17 GeV together with a Pauli blocking exit the nucleus. The initial interaction model employs
A
adjustment,κ=1.007±0.012areassumedforboundnu- the impulse approximation which assumes an instan-
cleonscattering. Thesevaluescomefromahighstatistics taneous exchange with independent nucleons. Subse-
analysis of MiniBooNE ν CCQE events on carbon [9] quent to the initial neutrino or anti-neutrino interac-
µ
and are consistent with values recently determined from tion, particles produced inside the nucleus are propa-
an independent MiniBooNE neutral-current elastic scat- gated step-wise in 0.3 fm increments until they emerge
tering sample [10]. A previous shape-only study has from the ∼ 2.5 fm radius sphere. Intermittently, the
shown that these CCQE model parameters reproduce probability for hadronic re-interaction is calculated us-
the MiniBooNEanti-neutrino-modedatashape[28],and ingaradially-dependentnucleondensitydistribution[38]
thereforethe sameMeff andκvaluesareappliedtoboth alongwithexternalπ−N,N−N cross-sectionmeasure-
A
ν and ν¯ CCQE scattering events on carbon. ments [39]. For ∆ re-interactions(∆+N →N +N), an
µ µ
Forfreescatteringoffhydrogen,aprocessaccessibleto energy-independent probability of 20% (10%) is taken
anti-neutrino and not neutrino CCQE events, a value of for ∆++N, ∆0+N (∆+++N,∆−+N)basedonK2K
M = 1.03 ± 0.02 GeV is used based on a global fit to data [37] and is assigned 100% uncertainty.
A
previous light target data [29]. Asmentionedearlier,outofallhadronicre-interaction
In the case of carbon scattering, the superscript ”eff”, processes, pion absorption and charge exchange (π± +
short for “effective”, on MA is introduced to allow for X ↔ π0 +X′) are the most relevant in predicting the
the possibilitythatnucleareffects areresponsibleforthe composition of the CC1π+ (Section IVA) and CCQE
apparent discrepancy between the MiniBooNE carbon- (Section VA) samples studied in this analysis. Intranu-
basedmeasurementsandlighttargetresults. Thisisalso clear fractionaluncertaintiesonpionabsorption(charge-
theoretically motivated by a possible reconciliation be- exchange)aresetto25%(30%)basedoncomparisonsbe-
tween the measurements through a mechanism resulting tweenexternaldata[24]andnuance. The simulationof
in intranuclear correlations of greater importance than these two processes in the detector medium is addressed
previouslythought[30–34]. Such amechanismwouldin- separately in the detector simulation (Section IIC).
dicate a larger CCQE cross section for nuclear targets
thanfor free scattering,whichinthis case,is reflectedin
the higher M choice for carbon versus hydrogen scat- IV. MEASURING THE NEUTRINO FLUX
A
tering. COMPONENT IN THE CC1π+ SAMPLE
A. The CC1π+ sample
B. Pion production
TheeventsintheCC1π+sampleinanti-neutrinomode
Baryonic resonances are the dominant source of sin- originatealmostexclusivelyfromν interactions,making
µ
gle pion production at MiniBooNE. The formalism to it anexcellentcandidate for measuringthe ν contentof
µ
describe these events is taken from the Rein-Sehgal the anti-neutrino-mode beam. In the few-GeV energy
model [35], where the relativistic harmonic oscillator range,the dominant charged-currentsingle pion produc-
quark model is assumed [36]. Eighteen resonances are tionchannelscontainafinal-state π+ (π−)inthe caseof
6
ν (ν¯ )scattering. MiniBooNEcleanlyidentifiesCC1π+
µ µ
eventsbyselecting3“subevents”,attributedtothemuon TABLE I: Summary of selection cuts in the CC1π+ sample.
Purity and efficiency numbers are sequential and are calcu-
from the primary ν interaction and two subsequent de-
µ lated for the “observable CC1π+” event signature - 1 µ−, 1
cayelectrons,one eachfromthe µ− andπ+ decaychain:
π+.
Efficiency Purity
1: νµ+p(n)→µ−+p(n)+π+ Cut # Description (%) (%)
֒→µ++νµ 0 Nocuts 100 10
2: ֒→e−+ν¯ +ν
e µ 1 Three subevents 30 29
3: ֒→e++ν +ν¯ .
e µ 1st subevent in event time window
(1) 2 28 34
4000 < T(ns) < 7000
The mono-energetic µ+ from the decay of stopped π+
All subevents: reconstructed
doesnotleadtoaseparatesubeventduetotheshortlife- 3 23 36
vertex< 500 cm from tank center
time ofthe π+. Subevents aredefinedasclustersintime
4 1st subevent: tank hits > 200 22 39
of PMT activity (or PMT “hits”). A hit is any PMT
pulse passing the discriminator threshold of ∼ 0.1 pho- 5 2nd, 3rd subevents: 19 65
tank hits < 200
toelectrons. A temporal cluster of PMT activity with
at least 10 hits within a 200 ns window and individ- 6 All subevents: vetohits < 6 16 78
ual hit times less than 10 ns apart, while allowing for Distance between reconstructed
at most two spacings of 10 - 20 ns, defines a subevent. 7 end of 1st subeventand nearest 12 82
Apart from detection efficiencies, some neutrino-induced Michel electron vertex < 150 cm
CC1π+ events do not enter the three subevent sample
as ∼ 8% of µ− are captured in carbon [40] and there-
fore do not lead to the production of a Michel electron. marily due to decay-in-flightπ−. Starting from an event
Other selectioncuts made to enhance sample purity and population that is ∼ 70% ν¯ , this simple two decay
µ
improve reconstruction are given with efficiencies in Ta- electron requirement remarkably yields a sample that is
ble I. Cut 1 is the three subevent criterion previously ∼ 80% pure ν .
µ
detailed. Cut 2 requires that the first subevent occur
during a 3 µs time window centered on the BNB proton
spill. Cut 3 rejects eventsclose to the detectoredge that TABLEII:PredictedeventcompositionoftheCC1π+sample
are likely to be poorly reconstructed. Selection cuts on in anti-neutrinomode.
the number of tank hits are based primarily on the ob-
Interaction Channel Contribution (%)
servation that Michel electrons produce fewer than 200 νµN →µ−π+N (resonant) 64
tankhits. Cut4ensuresthefirstsubeventisnotaMichel νµA→µ−π+A (coherent) 7
electron and rejects low energy muons that might be re- ν¯µN →µ+π−N (resonant) 6
constructed poorly. Cut 5 requires that the number of νµn→µ−p 6
hitsforthesecondandthirdsubeventsisconsistentwith νµn→µ−π0p 2
a Michel electron. Veto PMT activity is monitored si- ν¯µp→µ+π0n 1
multaneously with the main tank PMTs, thus Cut 6 en- Other(mostly DIS) 14
suresnosubeventisduetochargedparticlesenteringthe “ObservableCC1π+”
82
tank and that all charged particles produced inside the (1 µ−, 1 π+)
detector are contained. Cut 7 enforces spatial corre-
lation between the end of the muon track and the clos-
est Michel electron vertex. This reduces a class of back-
groundswhereneither the secondnorthe thirdsubevent
arise from the decay of the muon to a Michel electron. B. CC1π+ event reconstruction
This cut is applied only to the Michel closest to the end
ofthereconstructedprimarymuontrackasthepionlife- In this analysis, charged-current single π+ event re-
time compared to the muon is short enough that either construction relies exclusively on the observation of the
Michel can occur temporally first. outgoing muon. Muon kinematics are obtained by the
Charged-current single π− events induced by ν¯ are pattern, timing, and total charge of prompt Cherenkov
µ
largely rejected by the primary requirement of three radiation collected by PMTs in the first subevent of the
subeventsbecausemostπ−cometorestandarecaptured interaction. The topology and timing of the observed
by carbon nuclei [41], yielding no decay electron. The PMT hits are compared to a likelihood function operat-
predicted event composition after this selection is pre- ing under a muon hypothesis. This likelihood function
sentedinTableII.Thesampleis82%observableCC1π+ predicts hit patterns and timing based on the interac-
events (i.e., events with a single muon, a single π+, and tion vertex and the momentum four-vector of the muon.
anynumberofnucleonsexitingtheinitialtargetnucleus). Thelikelihoodfunctionsimultaneouslyvariestheseseven
Some ν¯ CC1π− events do make it into the sample, pri- parameters while comparing to the observed PMT hits.
µ
7
The parameters from the maximized likelihood function
yield the reconstructed muon kinematics. TABLE III: Anti-neutrino-mode CC1π+ sample details and
Undertheassumptionof∆(1232)productionbyaneu- νµ flux component measurement. The measured cross sec-
trinoscatteringoffastationarynucleontargetincarbon, tion has been applied to simulation, and the νµ flux scale is
foundbycalculating(observedevents-expectedν¯µ events)/
the neutrino energy is given by:
expected νµ events. The reported error is discussed in more
detail in Section IVD. The Monte Carlo sample is generated
so that theassociated statistical error is negligible compared
2(M −E )E − E2 −2M E +m2 +∆M′2 to theother sources of uncertainty.
p B µ (cid:16) B p B µ (cid:17)
Eν∆ = 2[(Mp−EB)−Eµ+pµcosθµ] E∆ν Range Mean Gen. Events Expected νµ Flux
(2) (MeV) Eν (MeV) in Data νµ ν¯µ Scale
600 - 700 961 465 556 104 0.65 ± 0.10
where E = 34 MeV is the binding energy, m is the 700 - 800 1072 643 666 118 0.79 ± 0.10
B µ
muon mass, ∆M′2 = M2−M2, where M (M ) is the 800 - 900 1181 573 586 97 0.81 ± 0.10
p ∆ ∆ p 900 - 1000 1285 495 474 78 0.88 ± 0.11
∆(1232) (proton) mass, p is the muon momentum, and
µ 1000 - 1200 1426 571 646 92 0.74 ± 0.10
θ is the outgoing muon angle relative to the incoming
µ 1200 - 2400 1685 521 614 74 0.73 ± 0.15
neutrino beam. Effects not accounted for in the recon- Inclusive 1266 3268 3542 563 0.76 ± 0.11
struction include non-resonant pion production, contri-
butions from higher mass ∆ resonances and scattering
off the quasi-free protons in hydrogen instead of carbon.
A shape comparison of reconstructed E∆ in data and
ν
simulation is presented in Figure 3.
flux measurement. Results are presented in Table III.
Events in the anti-neutrino mode CC1π+ sample indi-
catetheneutrinofluxinanti-neutrinomodeislowerthan
800 thesimulationpredicts. Theextractedcalibrationis0.76
± 0.11 of the nominal prediction over all reconstructed
700
energies, while the analysis applied to individual energy
600 Simulation ranges does not indicate any significant energy depen-
500 dence.
s
nt Data
e400
v
E
300
200
100
0
0 0.5 1 1.5 2 2.5 3 D. Systematic errors
EDn (GeV)
FIG. 3: (Color online) The reconstructed energy spectrum
The systematicerroronthe neutrino flux measurment
for simulation versus data in the anti-neutrino-mode CC1π+
usingtheanti-neutrino-modeCC1π+ samplecomesfrom
sample. Simulationisnormalizedtodata,andonlystatistical
errors are shown. two sources that are treated as uncorrelated with each
other: the uncertainty on the CC1π+ cross section ob-
tained from [12] and the uncertainty in the background
prediction. The largest contribution to the uncertainty
on the CC1π+ cross section comes from the neutrino-
C. Measuring the neutrino flux component in the mode flux uncertainty, which is the only systematic er-
anti-neutrino-mode CC1π+ sample ror associated with the cross-section measurement that
is also independent of the measurement made here. Be-
The simulation sample is separated into two compo- cause the other CC1π+ uncertainties are treated as un-
nents: observable CC1π+ events and background. All correlated, a partial cancellation of errors is ignored in
observable CC1π+ events in the simulation are modeled the presentneutrino flux measurement. This results in a
using the CC1π+ cross section that has been measured slightoverestimateoftheneutrinofluxuncertainty. Both
in MiniBooNE neutrino-mode data [12]. Given that the ν and ν¯ background events in the sample are assigned
µ µ
majority of the CC1π+ sample in anti-neutrino mode is 30% uncertainties to conservatively recognize the model
induced by neutrinos, with this cross-section measure- dependence of the sample composition. The fractional
ment appliedany remainingnormalizationdifference be- uncertainty contributions to the flux measurement are
tween data and simulation is interpreted as a neutrino presented in Table IV.
8
TABLE IV: Fractional uncertainty (%) contributions to the TABLEV:Summaryof selection cutswith efficiencies inthe
neutrino flux measurement in the CC1π+ sample. The νµ CCQE sample. “Purity” refers to ν¯µ CCQE only,and purity
uncertainty is dominated bythe CC1π+ cross-section error. and efficiency numbersare sequential.
EQE Range Total Efficiency Purity
ν(MeV) Statistical ν¯µ νµ Fractional Error Cut # Description (%) (%)
600 - 700 6 9 11 15 0 Nocuts 100 32
700 - 800 5 7 10 13 1 Two subevents 49 41
800 - 900 5 6 10 13
1st subevent in event time window
900 - 1000 5 6 10 13 2 47 42
4000 < T(ns) < 7000
1000 - 1200 5 6 11 13
1200 - 2400 5 5 19 20 3 1st subevent: reconstructed 38 43
vertex< 500 cm from tank center
Inclusive 2 6 13 14
4 1st subevent: tank hits > 200 35 45
5 2nd subevent: tank hits < 200 33 45
V. MEASURING THE NEUTRINO FLUX 6 Both subevents: veto hits < 6 29 49
THROUGH MUON ANGULAR DISTRIBUTIONS
Distance between reconstructed
IN THE CCQE SAMPLE
7 end of 1st subeventand 2nd 25 54
subeventvertex < 100 cm
A. The CCQE sample
The CCQE interaction is the dominant channel in
TABLEVI:Predictedcomposition oftheanti-neutrino-mode
MiniBooNE’senergyrange. CCQEeventstypicallyhave
CCQE sample.
two subevents, attributed to the primary muon and the
associated decay positron: Channel Contribution (%)
ν¯µp→µ+n 54
12:: ν¯µ+p → µ֒→+e++n+νe+ν¯µ. (3) νν¯µµNN →→νµµµ+−nππ→−+NNµ−((rrpeessoonnaanntt)) 2860
The CCQE sample is therefore similar in formation to ν¯µA→µ+π−A (coherent) 4
theCC1π+ samplewithonemajordivergence: arequire- ν¯µN →µ+Λ,Σ 3
ment of two subevents instead of three. As shown in ν¯µp→µ+π0n 2
Other 3
Table V, the CCQE selection cuts closely follow those
All ν¯µ 71
motivated in Section IVA, with a few exceptions appro-
All νµ 29
priate to the inclusion of a single Michel electron. The
Michel tank hit and veto PMT hit cuts apply to the sec-
ond subeventonly now (Cuts 5 and6, respectively), and
the muon endpoint-electron vertex cut in Cut 7 is tight- including µ−, π− capture and final-state interactions;
ened to 100 cm in light of larger backgrounds. The se- however, in the case of anti-neutrino induced CC1π−
lectioncutsoutlinedhereareidenticaltothoseemployed scattering, due to π− nuclear capture almost 100% of
in a previous shape-only extraction of CCQE model pa- CC1π− events have only two subevents and are exper-
rameters[6]andcloselyfollowthoseusedinthe absolute imentally indistinguishable from CCQE. This implies a
measurement of the ν induced CCQE cross section [9], direct background measurement of CC1π− events (anal-
µ
with only minor differences that result in approximately ogoustowhatwasdoneinRef.[9])isimpossible. There-
the same sample efficiency and purity. fore,thoughtheCC1π+ yieldconstraintmadeinRef.[9]
Despite the selection cuts, there are formidable back- isstrictlyappropriatetoneutrinoinducedCC1π+ events
grounds to the anti-neutrino-mode CCQE sample. Prior only, it is applied to both predicted CC1π+ and CC1π−
to this analysis, simulation estimates the anti-neutrino- backgroundevents in the CCQE sample.
mode CCQE sample has a purity just above 50% as Many backgrounds to the CCQE sample peak in the
shown in Table VI. The major backgrounds include most forward scattering region of the muon angular dis-
CC1π+ and CC1π− events, which account for a total tribution with respect to the incoming neutrino beam.
of ∼ 20% of the sample, and the ν processes, predicted ThisincludespionproductionandhydrogenCCQEscat-
µ
toberesponsiblefor∼30%ofthesample. The30%pre- tering - while the latter is technically not a background,
dicted ν contamination is investigated and ultimately theproperhandlingofthedifferenceinnucleareffectsbe-
µ
constrained in this analysis. tweenboundandfreetargetsisnotstraightforward. Ad-
A few additional modifications to the simulation are ditionally,theforwardscatteringregionisstronglycorre-
made to accommodate the backgrounds. The largest lated with low-Q2 events, a problematic region both ex-
non-CCQE background in the sample is single pion pro- perimentallyandtheoretically[42]. SuchlowQ2dataare
duction which enters the sample due to nuclear effects, dominated by ν¯ interactions, while the present analysis
µ
9
is principally interested in backwards scattering muons C. Neutrino flux measurement using CCQE
whichisdominatedbyν . Forthesereasons,eventswith
µ
cos θµ > 0.91 are not included in the fit to data, where Neutrino and anti-neutrino CCQE cross sections dif-
θµ is the outgoing muon angle relative to the incoming fer exclusively by an axial-vector interference term that
neutrino beam. amplifies ν scatteringwhile suppressingν¯ events. Apar-
ticularlycleanwaytoexploitthiscrosssectiondifference
is to fit the angular distribution of the primary muon.
B. CCQE event reconstruction
The contribution from ν¯ is suppressed in the backward
µ
scatteringregion. Figure5showsthepredictedν andν¯
µ µ
Eventreconstructionintheanti-neutrino-modeCCQE contributions to the cosine of the outgoing muon angle.
sample proceeds similar as in the CC1π+ sample, de- To measure the neutrino content in the anti-neutrino
scribed in Section IVB. As in the CC1π+ reconstruc- mode beam, the Monte Carlo (MC) sample is separated
tion,measurementofmuonkinematics fromthe primary into two cos θ templates, one arising from all ν inter-
µ µ
interaction is solely responsible for recreating the inci- actions and the other from ν¯ , regardless of interaction
µ
dent neutrino energy. No requirement is made on the channelandnucleartarget. Alinearcombinationofthese
ejected nucleon; this is an important distinction from two templates is then formed,
theCCQEdefinitionsusedbyotherexperiments[43,44],
where a single proton track may be required in the case
ofneutrino-inducedCCQE.Asimilarenergyreconstruc-
tion as described in Section IVB is implemented, but in TMC(αν,αν¯)≡αννMC +αν¯ν¯MC (5)
this sample a ν¯ probe is assumed:
µ
2(M −E )E − E2 −2M E +m2 +∆M2
EQE = p B µ (cid:0) B p B µ (cid:1)
ν¯ 2[(Mp−EB)−Eµ+pµcosθµ] 104
(4) P r e d i c t e d n C o m p o s i t i o n
nm: 29 %
nm: 71 %
where the same definitions from Equation 2 apply and
∆M2 = Mp2 − Mn2, where Mn is the neutron mass. 103
Figure 4 presents the reconstructed energy distributions
s
insimulationanddataintheCCQEsample. CCQEscat- ent
v
teringwithfreeprotonsinhydrogenareindistinguishable E
from those on bound protons in carbon, so all events in 102 n MC
n MC
data and simulation are reconstructed using the carbon TMC(a n = 1,a n = 1)
scattering assumption implicit in Equation 4. data
10
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
cos q
m
3500
3000 FIG. 5: (Color online) The cos θµ distribution of the CCQE
Simulation sample by neutrino type before fitting. As printed on the
2500 figure, 29% of the sample is predicted to be induced by neu-
nts2000 trinos. TheMonteCarlo samplehasbeennormalized to5.66
ve Data × 1020 protonson target.
E
1500
1000
where T is the total predicted cos θ distribution to
MC µ
500 be compared to data, α and α are neutrino and anti-
ν ν¯
neutrinoratescales,andνMC andν¯MC aretheMCneu-
0
0 0.5 1 1.5 2 2.5 3
EQE (GeV) trinoandanti-neutrinoscatteringangularpredictions,re-
n
spectively. The modified simulation sample is compared
todatabyformingagoodness-of-fitχ2 testasafunction
FIG. 4: (Color online) The reconstructed energy spectrum of the rate scales:
for simulation versus data in the anti-neutrino-mode CCQE
sample. Simulationisnormalizedtodata,andonlystatistical
errors are shown. χ2 = (T (α ,α ) −d )M−1(T (α ,α ) −d )
X MC ν ν¯ i i ij MC ν ν¯ j j
i,j
(6)
10
whereiandj labelbins ofcosθ , disdataandM isthe nucleon CCQE scattering and κ = 1.022. When the
µ
symmetric error matrix given in Equation 7. The error muonangularfittechniquedescribedinthissectionisre-
matrix is used to propagate correlated uncertainties on peatedwiththisprediction,yieldratesofα =0.99±0.23
ν
parameters and processes to the quantities reported in and α = 1.20±0.23 are found, as reported in Ref. [5].
ν¯
the analysis. It is made by first forming weights corre- With this alternate CCQE scattering model, the angu-
sponding to simulation excursions set by Gaussian vari- lar fit over all reconstructed energies reports a neutrino
ations of parameters within their associated error. The contaminationinthe sampleof23±6%,consistentwith
difference of these weighted events from the simulated the 21 ± 8% contamination found with the scattering
central value forms the error matrix, assumptions described in Section IIIA.
The results from this technique depend on knowing
the angular distributions of neutrino and anti-neutrino
K
M = 1 (Ns−NCV)×(Ns−NCV). (7) CCQEinteractionsin the detector. While the procedure
ij K sP=1 i i j j relies on exploiting the effect of the interference term in
theCCQEcrosssection,theangulardistributionsmaybe
Here K simulation excursions are used (K = 100 in this
somewhat altered by nuclear effects. In this analysis the
analysis), Ns is the re-weightednumber of entries corre-
measuredangulardistributionofneutrinointeractionson
sponding to the sth simulation set and NCV represents
carbon [9] is employed, but the measurement relies on
theMiniBooNEsimulationcentralvalue. Thistechnique
thescatteringmodeldescribedinSectionIIIAtopredict
is further describedin Ref.[45]. Bin-by-bincos θ corre-
µ anti-neutrino interactions. This model does not include
lations between ν and ν¯ are also treated. The specific
µ µ two body current effects which may be larger than pre-
systematic errors are discussed in the next section.
viously expected [30] and may introduce additional neu-
Thefitisperformedanalyticallyinthreebinsofrecon-
trino and anti-neutrino angular differences. Despite this
structed energy and also in an inclusive energy sample.
inherentmodeldependence,theresultspresentademon-
Resultsincludingstatisticalandsystematicuncertainties
strationofa techniqueaimedatinforming future experi-
are presented in Table VII. The fits to data are shown
ments looking to separately constrainneutrino and anti-
in Appendix A, where Figure 7 contains both the fitted
neutrino events in an unmagnetized environment. By
distributions and the fractional differences between the
that time, the effect of additional nuclear processes on
simulation and data before and after the fits. The ad-
the angular dependence of anti-neutrino CCQE scatter-
justed contributions of ν and ν¯ to the CCQE sample
µ µ ing should be better known.
are compared to the prediction in Table VIII.
The χ2 value for the angular fit in the reconstructed
energy range EQE>900 MeV is unusually low at χ2 =
ν
D. Systematic errors
7 for 21 degrees of freedom. This is believed due simply
to chance,as the statisticalerroronly fit agreeswith the
data exceptionally well within the error, returning χ2 = As the presentanalysisdirectly measuresthe neutrino
13 for 21 degrees of freedom. component in the anti-neutrino-mode beam, systematic
As the ν angular template has been correctedfor the errors relating to beam geometry and meson production
µ
observed cross section per Ref. [9], α may be inter- at the target are not considered. The remaining system-
ν
preted as a flux scale factor, and significant deviations atic errors include those arising from detector modeling,
from unity would imply a flux mismodeling. Consistent thesinglepionproductionbackground,andthecrosssec-
withtheresultsreportedinSectionIVC,fitsintheanti- tion parameters in the underlying model. Contributions
neutrino-mode CCQE sample indicate the true neutrino propagated from these errors to the uncertainty on the
flux to be somewhat lower than the simulation predicts. parameterαν in the inclusive energysample aregivenin
Over all reconstructed energies, the neutrino flux com- Table IX.
ponent ofthe anti-neutrino-mode beam shouldbe scaled Apartfromfinal-stateinteractionuncertaintiesleading
by 0.65 to match the observed data. Fits in individual to errors on the cross section, the error on the CC1π+
reconstructed energy bins show that the neutrino flux background contributes to the systematic error through
component shape is well-modeled. Finding the calibra- the errorlabeled “CC1π+ Constraint”in Table IX. This
tion on the neutrino flux component inconsistent with measurement uncertainty is based on a Q2-dependent
unityisnotsurprising,astheneutrinoparentpionsorig- shape-onlyscalefactortoimprovedata-simulationagree-
inateprimarilyinapoorlyconstrainedproductionregion mentintheneutrino-modeCC1π+ sample[3]. Thecross
(cf. Figure 1). The rate scale α is ambiguous in inter- section (both CCQE and CC1π+) uncertainty is domi-
ν¯
pretation, as the cross section is yet unmeasured. nant in these fits and warrants further discussion. Ta-
Care must be taken when comparing these results to ble X offers a breakdown of cross section parameters
the µ+/µ− yield numbers reported in the MiniBooNE and associated errors. The error on carbon Meff has
A
ν¯ → ν¯ oscillation analysis [4, 5], since the interaction been reduced from that reported in Ref. [9] to avoid
µ e
predictionisdifferent. Intheoscillationanalysisthecross double-counting MiniBooNE systematic errors applica-
section parameters measured in Ref. [6] are employed, ble to both the measurement of Meff and the measure-
A
which includes Meff = 1.23(1.13) GeV for bound (free) ment reported here. The 26% uncertainty due to cross-
A