Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198

A method for detecting nt appearance in the spectra ofquasielastic CC events

A.E. Asratyan*, G.V. Davidenko, A.G. Dolgolenko, V.S. Kaftanov,M.A. Kubantsev1, V.S. Verebryusov

Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya St. 25, Moscow 117259, Russia

Received 6 February 2002; received in revised form 6 June 2002; accepted 13 June 2002

Abstract

A method for detecting the transition nm-nt in long-baseline accelerator experiments, that consists in comparing the

far-to-near ratios of the spectra of quasielastic CC events generated by high- and low-energy beams of muon neutrinos,

is proposed. The test may be accessible to big water Cherenkov detectors and iron-scintillator calorimeters, and is

limited by statistics rather than systematics. In the NuMI program with the MINOS detector, only the Dm2 values

above some 4� 10�3 eV2 can be probed.

r 2002 Published by Elsevier Science B.V.

PACS: 14.60.Pq; 14.60.Fg

Keywords: Neutrino oscillations; nt Appearance

The data of Super-Kamiokande [1] favor thetransition nm-nt as the source of the deficit ofmuon neutrinos from the atmosphere. However,this still has to be verified by directly observing ntappearance in accelerator long-baseline experi-ments. The options discussed thus far, all invol-ving fine instrumentation on a large scale, are todetect the secondary t by range in emulsion [2], byCherenkov light of the t [3], or by the transversemomentum carried away by the decay neutrino(s)[4]. By contrast, in this paper we wish to formulate

a t signature that is solely based on the energyspectra of CC events, and therefore, should beaccessible to water Cherenkov detectors and torelatively coarse calorimeters with muon spectro-metry. We assume that the experiment includes anear detector of the same structure as the fardetector, irradiated by the same neutrino beam butover a short baseline that rules out any significanteffects of neutrino oscillations [5]. Thereby, thesystematic uncertainties in comparing the interac-tions of primary and oscillated neutrinos arelargely eliminated. Our aim is to distinguish themuonic decays of t leptons against the backgroundof nm-induced CC events. In order to minimize theeffects of nm disappearance, the data collected witha harder t-producing beam are compared withthose for a softer reference beam in which t

*Corresponding author. Tel.: +7-095-237-0079; fax: +7-

095-127-0837.

E-mail address: asratyan@vxitep1.itep.ru (A.E. Asratyan).1Now at Department of Physics and Astronomy, North-

western University, Evanston, IL 60208, USA.

0168-9002/02/$ - see front matter r 2002 Published by Elsevier Science B.V.

PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 1 3 4 6 - 3

production is suppressed by the threshold effect.The analysis is restricted to quasielastics (QE), thatis, to neutrino events featuring a muon and smallhadronic energy.

As soon as the first maximum of the oscillationlies below the mean energy of muon neutrinos inthe beam, or Dm2L=/EnSo1:24 eV2 km=GeV;much of the signal from QE production andmuonic decay of the t is at relatively low values ofvisible energy E: That is because the t neutrinosarising from nm-nt are softer on average thanmuon neutrinos, the threshold effect is relativelymild for QE, and a large fraction of incidentenergy is taken away by the two neutrinos fromt�-m�n%n: Let f ðEÞ be the spectrum of QE eventsobserved in the far detector, nðEÞ is the spectrumof similar events in the near detector that has beenextrapolated and normalized to the location of thefar detector, and RðEÞ is the ratio of the two:RðEÞ ¼ f ðEÞ=nðEÞ: In the case of nm disappearancethrough the transitions nm-ne or nm-ns; where nsis the hypothesized sterile neutrino, the ratio R forthe harder beam should be identically equal to thatfor the softer beam: RhardðEÞ ¼ RsoftðEÞ: However,in the case of nm-nt this equation is violated bythe process of t production and muonic decay,that predominantly occurs in the harder beam andshows up as a low-E enhancement of thecorresponding ‘‘far’’ spectrum fhardðEÞ: This causesthe ratio Rhard to exceed Rsoft towards low valuesof visible energy E: The latter effect, that mayprovide a specific signature of nt appearance, isinvestigated in this paper.

In the simulations reported below, the harder(or t-producing) and softer (or reference) beams ofmuon neutrinos are respectively assigned as thehigh- and low-energy beams from the MainInjector (MI) at Fermilab, as foreseen by theNuMI program [5]. The mean nm energies in thesebeams are close to 12 and 5 GeV; respectively.Again as in the NuMI program, a baseline of730 km is assumed throughout. That the neutrinosource is not pointlike gives rise to a systematicuncertainty on the far-to-near ratio RðEÞ: For theMI low- and medium-energy beams, this has beenestimated [6] as 0.02 in the En regions of bestfocusing (below some 5 and 8 GeV; respectively).We assume a similar uncertainty on RðEÞ for the

high-energy beam.2 Note however that, for thestatistics considered in this paper, the overalluncertainty on the effect is still dominated bystatistical errors. The two detector types consid-ered are an iron-scintillator calorimeter and awater Cherenkov detector.

Charged- and neutral-current interactions of thenm and nt are generated using the NEUGENpackage that is based on the Soudan-2 MonteCarlo [7]. This generator takes full account ofexclusive channels like QE proper and excitationof baryon resonances, that are important for ouranalysis of CC events with small hadronic energy.

The iron-scintillator calorimeter is assumed tobe the MINOS detector [5] that is in constructionstage. The detector response is not simulated infull detail; instead, the resolution in muon energyis approximated as dEm ¼ 0:11� Etrue

m and inenergy transfer to hadrons—as dn ðGeVÞ ¼ 0:55�ffiffiffiffiffiffiffiffiffi

ntruep

[8]. QE events are selected as those withEm > 1 GeV and no1 GeV; where Em and n are thesmeared values of muon energy and of energytransfer to hadrons, respectively.3 The visibleenergy of a CC event, E; is estimated in terms ofsmeared quantities: E ¼ Em þ n: The lower cutoffon muon energy, that corresponds to a minimumrange of 4.4 nuclear interaction lengths in iron, isaimed at suppressing the background from pionpunchthrough. In the region Em > 1 GeV; thedominant background is pion decay in flight inNC events and in CC events with soft primarymuons. In the simulation, each spurious muontrack is assigned an energy according to its totalrange in iron.

We also analyze the performance of a waterCherenkov detector, in which nm-induced QE havea characteristic signature of muonlike single-ringevents [9]. Analyzing the multi-GeV exitingmuons, particularly, in the smaller near detector,may require a device of the AQUA-RICH type

2We may expect that systematic uncertainties on RðEÞ for thehigh- and low-energy beams are correlated and, therefore, will

partially cancel in the difference. Such correlation is neglected

here.3These selections should be viewed as illustrative. The actual

selections will be based on a detailed simulation of detector

response to CC events with small hadronic energy.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198 191

[10] or an instrumented muon absorber down-stream of the water tank. In our simulation for thewater Cherenkov detector, QE events are selectedas those featuring a single muon with momentumabove 800 MeV; no additional charged second-aries with momenta above the Cherenkov thresh-old in water, and no p0 mesons in the final state. Ahigher cutoff on muon energy than in Ref. [9] isdictated by the pion-decay background thatincreases with decreasing Em (see below). For theQE reaction nmn-m�p; the above selections imply

an energy transfer to the nucleon of less than0:47 GeV: (Some 70% of thus selected events aredue to quasielastics proper.) Muon energy issmeared according to dEm ¼ 0:05� Etrue

m ; andneutrino energy is estimated as E ¼ Em þ200 MeV: The background arises from pions inNC events that feature no other charged second-aries above the Cherenkov threshold and no p0

mesons, and is largely due to single-pion produc-tion via excitation of baryon resonances. In awater Cherenkov detector, punchthrough pions

0 5 10 15 20 25 30 35 4010

-2

10-1

1

10

102

Iron-Sc., High Beam

CC 5443 <E>=12.1 GeV

10 Kton*Year

E (GeV)

even

ts /

200

MeV

0 5 10 15 20 25 30 35 4010

-2

10-1

1

10

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Water Ch., High Beam

CC 8258 <E>=11.7 GeV

50 Kton*Year

E (GeV)

even

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MeV

0 5 10 15 20 25 30 35 4010

-2

10-1

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Iron-Sc., Low Beam

CC 1589 <E>=5.7 GeV

10 Kton*Year

E (GeV)

even

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MeV

0 5 10 15 20 25 30 35 4010

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10-1

1

10

102

Water Ch., Low Beam

CC 2831 <E>=5.0 GeV

50 Kton*Year

E (GeV)

even

ts

/ 200

MeV

Fig. 1. The oscillation-free ‘‘near’’ spectra of nn-induced QE events, nðEÞ; for the iron-scintillator (on the left) and water Cherenkov

(on the right) detectors irradiated by the MI high- and low-energy beams (top and bottom panels, respectively). The pion background

to QE events is shown by shaded histograms. The assumed exposure is 10 ð50Þ kton yr for the iron-scintillator (water Cherenkov)

detector.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198192

will be efficiently rejected by secondary interac-tions, but the background of pion decays in NCevents will be relatively bigger because of longerpion paths in water than in iron. Therefore, weneglect the pion-punchthrough background to QEin a water Cherenkov detector, and only considerthe ‘‘irreducible’’ background due to pion decay inflight.

Shown in Fig. 1 are the oscillation-free nearspectra of selected QE events, nðEÞ; for the twobeams and two detectors considered. Also illu-strated are the E-distributions of backgroundevents (see above). In the absence of oscillations,10 ð50Þ kton yr exposures of the iron-scintillator(water Cherenkov) detector in the softer andharder beams will yield some 1600 (2900) and

0 0.5 1 1.5 2 2.5 3 3.5 40

2

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14 2=0.003 eV 2m∆

12τ N 69µ N

1π N

E (GeV)

Iron - Sc.

even

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0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

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25

2=0.003 eV 2m∆

32τ N 126µ N

6π N

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Water Ch.

even

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2

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14 2=0.007 eV 2m∆

49τ N 46µ N

1π N

E (GeV)

Iron - Sc.

even

ts /

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0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

2=0.007 eV 2m∆

114τ N 90µ N

6π N

E (GeV)

Water Ch.

even

ts /

200

MeV

Fig. 2. The low-energy region of the far spectrum for the high-energy beam, assuming nm-nt with maximal mixing and Dm2 of 0.003

or 0:007 eV2 (top and bottom panels, respectively). The contributions from the decays t�-m�n%n; nm-induced CC events, and the pion

background are depicted as the open, shaded, and dark areas, respectively. The left-hand panels are for the iron-scintillator calorimeter

ð10 kton yrÞ; and the right-hand panels are for the water Cherenkov detector ð50 kton yrÞ: Statistical fluctuations are suppressed.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198 193

0 1 2 3 4 5 6 7-0.5

0

0.5

1

1.5

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R(E

)

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E (GeV)

R(E

)

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)

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0

0.5

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1.5

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2.5Water Ch., Low Beam

E (GeV)

R(E

)8

Fig. 3. The far-to-near ratio RðEÞ ¼ f ðEÞ=nðEÞ for quasielastic events produced by the MI high- and low-energy beams (top and

bottom panels, respectively) in the iron-scintillator and water Cherenkov detectors (left- and right-hand panels, respectively). The solid

(open) dots are for the transition nm-nt ðnm-nsÞ with maximal mixing and Dm2 ¼ 0:007 eV2: The error bars on RðEÞ for the

transition nm-nt are the statistical uncertainties corresponding to 10 ð50Þ kton yr exposures of the iron-scintillator (water Cherenkov)

detector in either beam.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198194

0 1 2 3 4 5 6 7 8

-0.4

-0.2

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2=0.003 eV 2m∆

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Dif

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-0.4

-0.2

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0 1 2 3 4 5 6 7 8

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-0.2

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-0.4

-0.2

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-0.4

-0.2

0

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2=0.007 eV 2m∆

E (GeV)

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Fig. 4. The difference DRðEÞ between the far-to-near ratios for the MI high- and low-energy beams. The solid (open) dots are for

nm-nt ðnm-nsÞ with maximal mixing. The top, middle, and bottom panels are for Dm2 ¼ 0:003; 0:005; and 0:007 eV2; respectively.The left- and right-hand panels are for the iron-scintillator calorimeter and for the water Cherenkov detector, respectively. The error

bars are statistical errors for 10 ð50Þ kton yr exposures of the former (latter) detector in either beam.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198 195

5400 (8300) nm-induced QE events, respectively.4

The low-energy region of the far spectrum, thatis relevant to our analysis, is depicted in Fig. 2for the high-energy beam assuming nm-ntwith Dm2 ¼ 0:003 and 0:007 eV2: (Here andin what follows, maximal mixing of sin2 2y ¼ 1is assumed.) Qualitatively, the decays t�-m�n%nare seen to form an appreciable fraction ofthe spectrum towards low values of E;

0 2 4 6 8 10 12 14-2

0

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Iron-Sc.

Inte

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)2 eV-3(102m∆0 2 4 6 8 10 12 14

-2

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l

0 2 4 6 8 10 12 140

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40 KY

20 KY

10 KY

0 2 4 6 8 10 12 140

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Sig

nif

ican

ce

200 KY

100 KY

50 KY

)2 eV-3(102m∆

)2 eV-3(102m∆)2 eV-3(102m∆

Fig. 5. The integrated difference S (see text) as a function of Dm2 for the iron-scintillator (top left) and water Cherenkov (top right)

detectors. The solid and open dots are for nm-nt and nm-ns; respectively. Shown by successive error bars are the combined (statistical

and systematic) errors on SðDm2Þ corresponding to 10 (50), 20 (100), and 40 ð200Þ kton yr exposures of the iron-scintillator (water

Cherenkov) detector in the t-producing beam. The bottom panels show the statistical significance of the t signal for either exposure ofeither detector.

4 In all numerical estimates, we do not take into account the

discussed upgrade of the proton driver at Fermilab [11] that

may result in a substantial increase of neutrino flux from the

Main Injector.

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198196

though the total number of events is relativelysmall.

Assuming either nm-nt or nm-ns driven byDm2 ¼ 0:007 eV2; the far-to-near ratios RðEÞ foreither beam and either detector are illustrated inFig. 3.5 That the ratios RðEÞ for the transitionsnm-nt and nm-ns diverge towards low values ofE is evident for the harder beam in which tproduction is not suppressed. Again consideringnm-nt and nm-ns; in Fig. 4 we plot the difference

DRðEÞ ¼ Rhard � Rsoft

for various values of Dm2: Indeed, at visibleenergies below some 4 GeV DRðEÞ deviates fromzero for the transition nm-nt; while staying closeto zero for nm-ns: This deviation may be viewed asa signature of nt appearance. The naive expectationfor nm-ns; DRðEÞ ¼ 0; is violated by the smearingof neutrino energy and by the pion background.

By the time the proposed test can be implemen-ted, the actual value of Dm2 will probably beestimated to some 10% by analyzing the nmdisappearance in the MI low-energy beam [8].Given the value of Dm2; a consistent approachwould be to fit DRðEÞ to the predicted shape inorder to estimate the mixing between the muonand tau neutrinos. A cruder measure of the effectis provided by the integral S ¼

RDRðEÞ dE; which

we estimate between E ¼ 1 and 4 GeV: Allowingfor either nm-nt and nm-ns; the respectiveintegrals Sðnm-ntÞ and Sðnm-nsÞ are plotted inFig. 5 as functions of Dm2:

Since the reference beam produces many morelow-energy events than the harder beam, thestatistical error on the integral S is largelydetermined by the statistics accumulated with thelatter. Therefore, we fix the exposure of the iron-scintillator (water Cherenkov) detector in thereference beam at 10 ð50Þ kton yr; and assume asimilar or bigger exposure in the harder beam: 10(50), 20 (100), or 40 ð200Þ kton yr: The respectiveuncertainties on Sðnm-ntÞ; that also include theaforementioned systematics on RðEÞ; are illu-

strated by successive error bars in Fig. 5. Andfinally, dividing the difference between Sðnm-ntÞand Sðnm-nsÞ by the total error on Sðnm-ntÞ; weestimate the statistical significance of the enhance-ment that is also depicted in Fig. 5.

We estimate that at a level of 4s; the 10 (50), 20(100), and 40 ð200Þ kton yr exposures of the iron-scintillator (water Cherenkov) detector in the MIhigh-energy beam will allow to probe nt appear-ance down to the Dm2 values of some 0.009(0.005), 0.006 (0.0035), and 0:0045 ð0:003Þ eV2;respectively. Thus in the NuMI program with the5:4 kton MINOS detector and with the existingProton Booster [5], the proposed test may besensitive to Dm2 values in the Kamiokande-allowed region [12], but not below some 4�10�3 eV2 as suggested by the more recent resultsof Super-Kamiokande [13]. On the other hand,a big ðB100 ktonÞ water Cherenkov detectorwould allow to probe the transition nm-nt overa large portion of the Dm2 region favored by theanalysis of atmospheric neutrinos in Super-Kamiokande.6

With an AQUA-RICH device capable ofdetecting multiple rings and of momentum-analyz-ing hadrons [10], the single-ring selection may berelaxed to allow a few soft hadrons above theCherenkov threshold. This will allow to increasethe acceptance to ntn-t�p as well as to embraceresonant mechanisms like ntpðnÞ-t�DþþðDþÞ;thereby enhancing the t�-m�n%n signal andboosting the sensitivity to nm-nt:

To conclude, we have proposed a test of ntappearance that consists in comparing the far-to-near ratios of the spectra of QE CC eventsgenerated by different beams of muon neutrinos,and therefore, may be accessible to water Cher-enkov detectors and to calorimeters with muonspectrometry. The test is limited by statistics ratherthan systematics.

5 In the figures, statistical fluctuations are suppressed for the

data points themselves, but the error bars are for the statistics

as indicated.

6Apart from muonic decays of QE-produced t leptons, a

water Cherenkov detector may also allow to detect the

electronic decays t�-e�n%n in the spectra of single-ring

electronlike events. This will require good understanding of

the contribution of neutral-current p0 production to electron-

like events (see, for example, [14]).

A.E. Asratyan et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 190–198 197

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