Determining the Neutrino Flux from Accelerator Neutrino Beams

Mary Bishai

Physics Department, Brookhaven National Laboratory, P.O. Box 5000, Upton, NY 11973, USA.

Abstract

Man made sources of neutrinos, from reactors and proton accelerators, are providing the best experimental sensi-tivities to determining the unknown neutrino oscillation parameters such as θ13, the mass hierarchy, and the CP phase.In addition, these experiments enable the measurements of the known neutrino oscillation parameters with higherprecision and the search for new neutrino oscillation phenomena. A critical component of any neutrino oscillationexperiment is the precision determination of the neutrino flux from the source, and its composition. I will summarizethe different techniques used by current short and long baseline neutrino accelerator experiments to determine theunoscillated neutrino flux, and discuss the implications for future experiments.

Keywords: neutrino, oscillation, beam

1. Neutrino Oscillation Experiments at Fermilab

A critical component of any neutrino oscillation ex-periment is the precision determination of the neutrinoflux from the source, and its composition. There are cur-rently two neutrino oscillation experiments at Fermi Na-tional Accelerator Laboratory (Fermilab) in Batavia, IL:the Booster Neutrino Experiment (MiniBooNE) operat-ing in the Booster Neutrino Beamline (BNB) [1] andthe Main Injector Neutrino Oscillation Search (MINOS)Experiment operating in the Neutrinos at the Main In-jector (NuMI) beamline [2]. In this report I will com-pare and summarize the different techniques by whichthe MiniBooNE and MINOS experiments model theneutrino flux from the NuMI and BNB beamlines.

Both the BNB and NuMI beamlines utilize protonbeams incident on low-Z targets to produce chargedmesons that are charge selected and focused using mag-netic focusing horns. The BNB utilizes an 8 GeV protonbeam from the Fermilab Booster incident on a thin Betarget of length 71cm that is embedded in a single 174kA pulsed magnetic horn. The focused mesons are al-lowed to decay in an air filled cylindrical region that is3 feet in radius and 45 meters long. The resulting neu-trino beam then travels through 450 meters of dirt to

the MiniBooNE detector [3] which is located at a dis-tance of 541 meters from the target. The NuMI beam-line utilizes a 120 GeV proton beam incident on a thingraphite target 95cm in length. The resulting mesonsare focused by two 185 kA pulsed horns placed 10 me-ters apart. The NuMI decay volume is He filled, 1min radius and 675m long. The MINOS experiment [4]comprises two detectors in the NuMI beamline: a NearDetector (ND) located 1.04 km from the target and aFar Detector (FD) located 735 km from the target. TheBNB and NuMI beamlines produce a neutrino flux thatis more than 90% νμ with small contaminations of ν̄μand νe/ν̄e. The fluxes of the different neutrino speciesfrom the BNB and NuMI beamline in the MiniBooNEand MINOS ND respectively are shown in Figure 1. Inaddition to the on-axis BNB neutrinos, the MiniBooNEdetector also recieves a significant flux of off-axis neu-trinos from the NuMI beamline [5]. The MiniBooNEdetector is located at a distance of 745m from the NuMItarget, at an off-axis angle of 110mrads. The flux ofmuon neutrinos in the MiniBooNE detector from NuMIand BNB is shown in Figure 2.

The MiniBooNE experiment is a short baseline neu-trino oscillation experiment whose primary goal is to

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0920-5632/$ – see front matter © 2012 Published by Elsevier B.V.

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Figure 1: Neutrino beams at Fermilab. The top figure is the BNBneutrino flux at the MiniBoone detector. The bottom figure is theNuMI beam neutrino flux at the MINOS ND. The νμ, ν̄μ, νe and ν̄ecomponents are shown.

Figure 2: A comparison of the νμ flux in the MiniBooNE and MI-NOS ND from the different neutrino beamlines. The NuMI off-axis atMiniBooNE is shown as a solid line.

search for νμ to νe oscillations at large Δm2 using base-lines of order 1km. The MiniBooNE experiment com-

prises a single 800 ton mineral oil Cerenkov detector[3] placed 541m from the BNB target and 745m fromthe NuMI target. The determination of the expected νμflux and the νe contamination in MiniBooNE from theBNB beam is obtained from a detailed simulation of thebeamline using GEANT4 [6] tuned using external mea-surements of hadron production cross-sections in thetarget and beamline elements. The MINOS experimentis a long baseline two-detector neutrino oscillation ex-periment. The MINOS detectors are magnetized ironand scintillator tracking calorimeters [4]. The determi-nation of the neutrino flux in the MINOS Far Detectoris obtained from a FLUKA 08 [7]/GEANT4 simulationof the beamline which is tuned to match the observedneutrino interaction rate in the Near Detector using thetechnique described in [8, 4]. The NuMI simulationtuned to match the on-axis higher energy neutrino ratein the MINOS ND is then used to predict the off-axisNuMI νμ rate observed in the MiniBooNE detector.

The BNB and NuMI focusing horns can operate inreversed polarity to produce a ν̄μ beam. This enablesthe MiniBooNE and MINOS experiments study neu-trino and anti-neutrino oscillations in the same exper-iment.

2. Neutrino Flux Predictions in MiniBooNE andMINOS

As mentioned in Section 1, the techniques used byMiniBooNE and MINOS to predict the unoscillated νμevent rate in the detectors differ significantly.

To simulate the interaction of the primary 8 GeVBooster proton beam with the Be target and secondaryinteractions in the Al horn, the MiniBooNE experimentuses custom tables describing the double differentialcross-sections for the production of protons, neutrons,pions and Kaon as a function of pz and pT based on ex-ternal measurements [9]. As discussed in [9], the ex-isting external measurements of pion and Kaon produc-tion from p-Be interactions cover the same kinematicregions in xF and pT as the BNB mesons that contributeto the majority of the νμ flux in the MiniBooNE de-tector. The total p-Be meson production cross-sectionsare obtained from the data compiled by the ParticleData Group [10]. A GEANT4 simulation is used tomodel the BNB beamline geometry and meson trans-port which includes the Al focusing horn, the targethall, and the 50 meter meson decay volume. The ge-ometry model matches the actual constructed beamline.The Horn magnetic field generated by the 174 kA mod-eled in GEANT4 includes the skin-depth effect. Ter-tiary interactions of the hadrons from the target with the

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beamline material are modeled in GEANT4. The pre-dicted BNB νμ interaction rates and the observed ratesin MiniBooNE are shown in Figure 3. The shape ofthe νμ event rate in the MiniBooNE detector matchesthe prediction very well, but an overall normalizationfactor of 1.21 was required to match the observed abso-lute event rate. The estimated uncertainties on the BNB

Figure 3: The νμ event rates from the NuMI beamline as seen in theMINOS ND and the tuned MC predictions (top). νμ event rates fromthe BNB as observed in the MiniBooNE detector and the tuned MCpredictions scaled up by 1.21 (bottom). In both figures the pointswith error bars are the observed events and the histograms are the MCpredictions.

νμ flux from the proton beam modeling, the p-Be dif-ferential production cross-sections, the horn field mod-eling, and the nucleon and pion total cross-sections aresummarized in Table 1. The estimated flux model un-certainties are dominated by the p-Be production cross-sections which are estimated to be 15%.

The MINOS experiment is a two detector long-baseline neutrino oscillaton experiment. The neutrinointeraction rate in the near detector (ND) is used to pre-dict the unoscillated neutrino rates in the far detector(FD). Since the ND sees an extended source of neutri-

Source of Uncertainty MINOS ND MiniBooNEProton delivery 2% 2%Horn field 8% 2%Horn material budget 3%Target hadro-production 2% 15%Target degradation 4% N/ANucleon cross-sections 2.8%Pion cross-sections 1.2%

Table 1: Sources of uncertainty on the νμ flux predictions from theNuMI beamline in the MINOS ND and the BNB in the MiniBooNEdetector.

nos, while the FD sees a point source, the unoscillatedneutrino spectrum in both detectors is significantly dif-ferent [4]. A reliable simulation of the NuMI beam-line is therefore needed to extrapolate the ND eventrate to the FD. The NuMI beamline is modeled usinga detailed GEANT4 simulation of the as-built geome-try. The horn field modeling, and meson transport in thebeamline also uses the GEANT4 simulation. The pri-mary 120 GeV p-C interactions in the graphite target aswell as tertiary hadron interactions in the beamline ma-terial are modeled using the FLUKA 08 simulation [7].Although the FLUKA 08 hadron production models aretuned to existing measurements, they do not include re-liable measurements of p-C and p-Al meson productionin the xF and pT range of the mesons that contribute tothe NuMI neutrino flux in the MINOS detectors. In MI-NOS, the only data used to tune the beamline simulationto produce a reliable prediction of the unoscillated neu-trino rate at the far detector is the observed MINOS NDneutrino interaction rate. The meson differential pro-duction from the NuMI target in FLUKA08 as a func-tion of xF and pT was parameterized. The parameters ofthe meson production model, as well as the expected ef-fects from the modeling of the horn currents, skin-deptheffects and target and horn misalignments were allowedto vary in a fit of the predicted ND neutrino rate fromthe simulation to the observed rate. The fit included anoverall detector energy scale and offset parameter to ac-count for ND detector mismodeling effects. To betterseparate detector and beam modeling effects, the NuMIbeam tune was varied by changing the target positionwith respect to the horns and the νμ and ν̄μ data from 3different tunes : low-energy, medium-energy, and high-energy were simultaneously fit [8]. The tuned simu-lation results and the observed MINOS ND data fromtwo different NuMI beam tunes are shown in Figure3. The tuned simulation model matches the ND datawell. The estimated uncertainties on the ND νμ eventrate obtained from varying the target hadron production

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parameterization, the horn field modeling, and the hornmaterial budget is shown in Table 1. In 2008 and 2009,the ND event rate was observed to decline. The effectwas best modeled in the FLUKA simulaiton of the tar-get by radiation damage to the NuMI target core [11].As a result, an uncertainty on the ND event rate due totarget degradation is also included in the predicted NDrate uncertainties from the simulation. The uncertaintiesin the MINOS ND rate thus obtained from the targetproduction and beamline simulation are dominated bythe horn field and skin-depth effect uncertainties whichare 8%. Variations in the target hadron production pa-rameterized model produced an uncertainty of around2% in the predicted ND rate. It is worthwhile to notethat this technique assumes that the neutrino interac-tion cross-sections in the MINOS ND simulation arecorrectly modeled. Since both detectors are iron scin-tillator sampling calorimeters, the neutrino interactioncross-section uncertainties - which are large in the fewGeV range of MINOS - cancel out in the extrapolationof the observed rates from ND to FD. The NuMI beam-line simulation tuning technique described here cannotbe used as a reliable prediction of the absolute NuMIflux in the ND. The technique is used to improve themodeling of the target hadron production, horn focus-ing and beamline geometry in the beamline simulationto allow a reliable extrapolation of the observed MINOSND event rate to the FD. The technique is also usedto determine the residual uncertainty from the beam-line geometry and hadron production uncertainties inthe extrapolation from ND to FD. The dominant beam-line modeling uncertainties as a function of the νμ en-ergy in the ND are shown in Figure 4. The residualuncertainty on the near to far extrapolation as a func-tion of the neutrino energy in the far detector is alsoshown in Figure 4. It is significant to note that in a twodetector long-baseline oscillation like MINOS, the fluxuncertainties do not cancel out entirely since a beamlinesimulation is still needed to extrapolate from near to far.The largest residual beamline modeling uncertainties onthe predicted FD event rate in MINOS are from the hornfield effects and are of order ∼ 3%.

3. Measurement of the NuMI Beam in the Mini-BooNE Detector

The NuMI beamline simulation tuned to the on-axisMINOS ND as described in Section 2 was used topredict the NuMI neutrino flux in MiniBooNE detec-tor which is at a distance of 745m from the NuMI targetand 110 mrad off-axis. The NuMI off-axis flux in Mini-BooNE covers the same neutrino energy region as the

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Figure 4: The dominant uncertainties on the MINOS ND neutrinorate predictions (top) obtained from tuning the MC to the observedND event rate and the residual uncertainties on the Near to Far extrap-olation (bottom). The gray histogram represents the uncertainty fromthe modeling of the horn material budget. The black histogram is theuncertainty from parameterization of the meson production from thetarget. The blue histogram is the total uncertainty from the horn fieldmodeling which includes the horn current uncertainty, the skin-deptheffect, and the two horn misalignments.

BNB on-axis beam as shown in Figure 2. The NuMIdecay region is very long at 675m in length and theMiniBooNE detector sits very close to the beam dumpat the end of the decay region. Therefore, the Mini-BooNE detector sees a very extended source of off-axisneutrinos from NuMI. The observed NuMI νμ and νeneutrino interaction rates in MiniBooNE with the pre-duction from the tuned NuMI beam simulation overlaid[13] are shown in Figure 5. The data and prediction arein very good agreement for both νμ and νe. The uncer-tainties on the predicted event rates are shown as a gray

M. Bishai / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 210–214 213

band and are dominated by the neutrino cross-sectionuncertainties. More details on the measurement of theNuMI beam in the MiniBooNE detector can be found in[12] and [13].

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Figure 5: The νμ (top) and νe (bottom) event rates from the NuMIbeamline as seen in the MiniBooNE detector with the tuned NuMIsimulation predictions overlaid as solid lines. The gray bands arethe total uncertainties on the predicted event rate including the cross-section uncertainties.

4. Conclusions

The MiniBooNE and MINOS experiments have de-veloped detailed simulations of the BNB and NuMIneutrino beamlines respectively. MiniBooNE uses p-Behadron production data from other experiments (HARP,BNL E910) to tune the BNB simulation and predict theexpected νμ and beam νe event rates in the MiniBooNEdetector. The predicted flux uncertainty is large ∼ 20%and is dominated by p-Be meson production model un-certainties. MINOS uses the near detector (ND) datato constrain meson production kinematics and beamlinegeometry mismodeling in the simulation. ND data usingdifferent tunes of the NuMI beamline are used to con-strain horn focusing and beamline geometry uncertain-ties in the simulation and to separate beam from detec-tor effects. The uncertainty on the predicted ND event

rate from the simulation after tuning is < 10% and isdominated by focusing uncertainties. Most, but not all,neutrino flux uncertainties cancel when using a near de-tector to extrapolate to a far detector. In MINOS, can-cellation is good to 3%. Due to large modeling uncer-tainties in the propagation of π → μ, MINOS is unableto use νμ to constrain beam νe. The event rate of νμ in-teractions in MiniBooNE from the NuMI beamline hasbeen successfully predicted using the on-axis MINOSND to tune the NuMI beamline simulation.

5. Acknowledgements

The results summarized in these proceedings arebased on the work of the MiniBooNE and MINOS col-laborations. The work was supported by the US DOE;the UK SFTC; the US NSF; the State and Universityof Minnesota; the University of Athens, Greece; andBrazil’s FAPESP, CNPq and CAPES. I would partic-ularly like to thank Sacha Kopp, Zarko Pavlovich andPatricia Vahle from MINOS for their superb work onthe NuMI beam tuning, and Zelimir Djurcic from Mini-BooNE who lead the effort on the joint MiniBooNE-NuMI analysis and supplied me with the data plots in-cluded here.

References

[1] 8 GeV Technical Design Report, http://www-boone.fnal.gov/publicpages/8gevtdr 2.0.ps.gz.

[2] S. Kopp, AIP Conf. Proc. 773, 276 (2005).[3] A. A. Aguilar-Arevalo et al., Nucl. Inst. Meth. A 599, 28 (2009).[4] P. Adamson et al., Phys. Rev. D 77, 072002 (2008).[5] A. A. Aguilar-Arevalo et al., AIP Conf. Proc. 842, 834 (2006).[6] S. Agostinelli et al., Nucl. Inst. Meth. A 506, 250 (2003).[7] G. Battistoni et al., AIP Conf. Proc. 896, 31 (2007).[8] Z. Pavlovic. FERMILAB-THESIS-2008-59, (2008).[9] A. A. Aguilar-Arevalo et al., Phys. Rev. D 79, 072002 (2009).

[10] K. Nakamura et al., J. Phys. G 37, 075021 (2010).[11] N. Simos, Poster presentation at Neutrino 2010. To be published

in Nuc. Phys. B. Proc. Supp. (2011).[12] P. Adamson et al., Phys. Rev. Lett. 102, 211801 (2009).[13] Z. Djurcic. Poster presentation at Neutrino 2010. To be pub-

lished in Nuc. Phys. B. Proc. Supp. (2011).

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