Muon Neutrino Oscillation to Electron Neutrino with a Large Water Cherenkov Detector

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Background Study on e Appearance from a Beam in Very Long Baseline Neutrino

Oscillation Experiments with a Large Water Cherenkov Detector

C. Yanagisawa, C. K. Jung, P. T. Le

Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, U.S.A.

B. VirenDepartment of Physics, Brookhaven National Laboratory, Upton, NY 11973, U.S.A.

(Dated: August 6, 2010)

There is a growing interest in very long baseline neutrino oscillation experimentation using ac-celerator produced neutrino beam as a machinery to probe the last three unmeasured neutrinooscillation parameters: the mixing angle 13, the possible CP violating phase CP and the masshierarchy, namely, the sign of m232. Water Cherenkov detectors such as IMB, Kamiokande andSuper-Kamiokande have shown to be very successful at detecting neutrino interactions. Scaling upthis technology may continue to provide the required performance for the next generation of exper-iments. This report presents the latest effort to demonstrate that a next generation (> 100 kton)water Cherenkov detector can be used effectively for the rather difficult task of detecting es fromthe neutrino oscillation e despite the large expected potential background resulting from

0sproduced via neutral current interactions.

PACS numbers: 13.15.+g, 14.60.Lm,14.60.Pq

Keywords: neutrino oscillation, water Cherenkov

I. INTRODUCTION

It has been shown that there are certain advantages ina wideband neutrino beam over a now traditional narrow-band neutrino beam for neutrino oscillation experiments,especially for the observation of e oscillation, pro-vided that the baseline is reasonably long (over 1,000km) [1].

By broadening the range of energies with which multi-ple oscillations can be resolved, a richer parameter space

can become accessible than is available to an experimentfocused on only the first oscillation maximum.

In the original paper proposing the use of a wide-bandneutrino beam for a very long baseline neutrino oscil-lation (VLBNO) experiment [1] by the Brookhaven Na-tional Laboratory (BNL) neutrino working group (NWG)some simplifying assumptions were used. The sensitivi-ties presented in the paper relied on calculations basedon 4-vector level Monte Carlo (MC) simulations, a sim-ple model for energy resolution and certain assumptionsabout reconstruction capabilities. Namely, a detaileddetector simulation for the proposed water Cherenkovdetector was not included. In addition it was assumedthat the signal events were only from quasi-elastic (QE)charged current (CC) scattering (e + n e + p) andthe background events were only from single 0 neutral

email: [email protected]; Also at Science De-

partment, BMCC, City University of New York,199 Chambers

Street, New York, NY 10007, U.S.A.Currently, Department of Physics and Astronomy,Rutgers, the

State University of New Jersey,136 Frelinghuysen Rd, Piscataway,

NJ 08854

current (NC) interactions +N +0 +N where Nand N are nucleons.

In order to gain a better insight on this idea of theVLBNO experiment with a wide-band neutrino beam for e oscillation, we performed a more sophisticatedand elaborate multivariate likelihood based analysis us-ing a full MC simulation that included inelastic neu-trino interactions, water Cherenkov detector response,and well-tuned event reconstruction algorithms. ThisMC simulation and reconstruction programs were devel-oped and fine-tuned for the Super-Kamiokande-I experi-ment (SK-I) [2].

II. ENERGY RECONSTRUCTION AND EVENTDESCRIPTION

For the discussions in this paper, we calculate a recon-structed neutrino energy using the formula

Erec =mNEe

mN (1 cose)Ee,

where mN

, Ee

and e

are the nucleon mass, the recoilelectron energy and the scattering angle of the recoil elec-tron with respect to the incident neutrino beam, respec-tively. In a strict sense, this quantity represents the in-cident neutrino energy only when the event is producedby CC QE scattering and the Fermi motion of targetnucleons is ignored. Nonetheless, we show in Figure 1the neutrino energy and Erec for CC QE (top) and allCC (bottom) events to compare the two energy distribu-tions for the two classes of CC events. Although Erec forthe CC events does not reproduce the incident neutrino

arXiv:1008.1

019v1

[hep-ex]5

Aug2010


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FIG. 1: The distributions of neutrino energy (solid lines) andreconstructed neutrino energy (dotted lines) of single ring e-like events originating from CC QE interactions (top figure)and from all CC interactions (bottom figure). Note that adip at about 2 GeV is due to e neutrino oscillation.The open square boxes with error bars indicate statisticaluncertainties.

spectrum as well as it does for CC QE events, it stillreproduces it quite well.

The initial event selection is made to maximize thenumber of interactions that are consistent with comingfrom e appearing at the far end of the baseline in thebeam while minimizing events such as CC or anyevents from NC interactions. Needless to say, the clear-est event signature comes from e CC QE interactions.Inelastic e CC events also carry information about os-

cillations but are more difficult to cleanly select and havesomewhat worse energy resolution as shown in Figure 1.Regardless of the interaction, a recoil proton will rarelybe above its Cherenkov threshold of about 1.25 GeV/cand will not contribute notably to the event signature.For these reasons, a e appearance candidate event willbe initially selected if its signature is consistent with be-ing a Cherenkov radiation pattern from a single electron

(termed single ring, e-like).A CC QE event will usually be distinguishable from

one arising from a e CC QE interaction as the result-ing Cherenkov ring produced by will have a sharperrise and fall in the amount of Cherenkov light at theedges of the ring than one due to an electron. This isbecause a muon presents a relatively straight line sourceof Cherenkov light while an electron initiates an elec-tromagnetic shower. This shower consists of a distribu-tion of track directions due to the number of particles inthe shower and that they experience larger multiple scat-tering. As the muon energy approaches the Cherenkovthreshold there is an increasing chance that multiple

scattering and the collapsing Cherenkov light cone willsmooth the rise of the edge of the ring and potentiallymimic an electron.

Likewise, inelastic and NC interactions with a non-zeropion multiplicity can have additional light that is not con-sistent with the pattern of a single e-like ring. Dependingon the exact event topology these events are either easilyruled out or present challenging backgrounds. Chargedpions above their Cherenkov threshold of 160 MeV/c pro-duce a -like ring and are rejected. Events with visiblelight from both pions and the primary charged lepton arestrongly rejected based on ring counting.

Events with a final state consisting of only a single neu-tral pion present a particular challenge. The 0 decays toa pair of gamma rays, each of which initiate an electro-magnetic shower and produce an e-like ring of varying in-tensity and direction. These 0 events can become back-ground depending on how the 0 decays to two gammarays. At one extreme, the decay is symmetric such thatthe gamma rays have similar energies. If the original 0 isboosted enough, the two gamma rays are nearly collinearand produce mostly overlapping rings. They can then beimpossible to be distinguished single electron events withan energy equal to the sum of the two gammas. At theother extreme, a highly asymmetric 0 decay results inone strongly boosted and one strongly retarded gammaray. In the lab frame, the higher energy gamma will pro-

duce a single e-like ring while the other may produce nodiscernible light.

The events with a 0 in the final state can come fromtwo sources: (1) NC interactions and (2) charge ex-changes of charged pions inside the target nucleus or withan oxygen or a hydrogen nucleus while traveling in water.

Finally, there are events from electron neutrino inter-actions that are not from e that appeared in the beamfrom neutrino oscillation e. Rather, there is anintrinsic e component in the unoscillated neutrino beam


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originating from muon or kaon decays. The beam used inthis study has an intrinsic e component which is 0.7% ofthe flux. The background events from these neutrinosare irreducible.

In this analysis, to classify the events for the initial se-lection, the reconstruction algorithms used for the SK-Iatmospheric neutrino analysis are employed. In addition,a special algorithm called POLfit [8] is used. This algo-

rithm has been found to be extremely useful for removingsingle 0 background events in samples containing eventsthat are classified as single-ring and e-like [9] by the stan-dard SK-1 reconstruction. This paper describes how in-formation provided by POLfit, together with other usefulvariables, can be effectively used to significantly reducethe 0 background while retaining a sufficient efficiencyfor the signal.

III. MONTE CARLO EVENT SAMPLE

The Monte Carlo event sample used in this study was

originally produced by the SK-I collaboration to simulateatmospheric neutrino events detected by the SK-I detec-tor and corresponds to about 100 years of the exposure.The detailed description of the Monte Carlo generation aswell as the event reconstruction is described elsewhere [3].

The energy spectra for and e produced in theEarths atmosphere are different from those in the neu-trino beam proposed by the BNL NWG. To account forthis, each event is given a weight based on the neu-trino energy such that the shape of the resulting spec-trum matches that expected from the beam. An addi-tional normalization is applied so that the total numberof CC QE events are as expected.

Assuming no oscillations, it is expected that there willbe 12,000 such events for a detector with SK-I efficien-cies and fiducial volume of 500 kton (22.2 SK-I) whichis placed 2,540 km from the neutrino production targetand for five years of running as described in the paper byBNL NWG [1]. When oscillations are applied, this sam-ple is weighted by the oscillation probability taking intoaccount full three-neutrino mixing and matter effects.

The oscillated e sample is prepared by similarlyweighting and normalizing the e atmospheric MC eventsto what is expected from the component of the beam,that is, under the assumption of 100% e oscilla-tion. Actual oscillation parameters are then applied tothis sample by weighting to the appropriate oscillationprobability. The intrinsic e component in the beam istaken to be the same shape as and normalized to be 0.7%that of the component.

The anti- components of the beam are ignored in thisstudy. Both ( and e) are small in number comparedto their partners in the beam.

To select MC e appearance candidate events an initialset of cuts based on the standard SK-I codes is used: (a)there is one and only one e-like ring, (b) the reconstructedevent vertex is at least 2 m from any inner PMT surface

and (c) there is no activity in the outer (veto) detector.In addition to these standard cuts, events produced by

neutrinos with energies greater than 10 GeV are ignoreddue to lack of statistics in the atmospheric MC sample.The beam has a tail that extends up to 15 GeV but itscontribution to the background is negligible as will beshown below.

IV. NEUTRINO OSCILLATIONPROBABILITIES

The oscillation probabilities applied to the componentsof the beam neutrino flux use the following parameters:

m221

= 7.3 105eV2,m2

31= 2.5 103eV2,

sin2 212 = 0.86,sin2 223 = 1.0,sin2 213 = 0.04, and

CP = 0,45,135.

Note that the sign convention of CP follows that ofthe paper by BNL NWG [1]. Unless otherwise stated, inthis paper the value of CP is +45

and the baseline is2,540 km which corresponds to the distance from BNLto Homestake Mine in South Dakota. Later we will de-scribe the results with different values for CP as wellas with the baseline of 1,480 km which corresponds tothe distance from Fermilab to Henderson Mine in Col-orado. The result with the baseline of 1,480 km was forthe UNO detector proposed first in 1999 and later to bebuilt in Henderson Mine. See the references [4] for thedetail of the UNO detector. These results are similar towhat is expected for the Fermilab to Homestake baseline

of 1,300km. This shorter baseline is considered by apply-ing inverse-square scaling of the flux and recalculation ofoscillation probabilities.

The neutrino oscillation probabilities were calculatedby the nuosc [5] package. The calculator assumes 3- os-cillation with possible CP symmetry violation and mat-ter effects. The matter densities can be vacuum, non-zeroconstant or stepwise-constant matter densities. The non-constant PREM [6] and arbitrary user provided densityprofiles are also supported. It calculates the probabili-ties either analytically for constant matter densities orfor any density profile it can use a 5th order adaptiveRunge-Kutta stepper. The package has been validatedagainst published calculations [7].

V. POLFIT

In this section we briefly describe the 0 fitter calledPattern Of Light fit (POLfit) [8]. POLfit is applied toevents which are initially classified as single-ring and e-like by the standard SK-I analysis codes in order to iden-tify 0 background events in this event sample. It as-sumes the event is a 0 event and that the ring found


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FIG. 2: 0 reconstruction efficiency with the standard SK-I codes (open circles) and after accepting additional eventswith missing gamma found by POLfit (solid circles).

by the standard codes is one of the gammas from the0 decay. It will then determine the direction and en-ergy of a secondary gamma that, along with the primaryone, is most consistent with the pattern of light collectedby the PMTs. POLfit produces two possible secondarygammas by employing two algorithms. One is optimizedassuming the secondary ring is overlapping with the pri-mary ring (forward-algorithm). The other is optimizedto find a second ring in the wider angular region (wide-algorithm).

In each algorithm, the pattern of light expected fromthe full 0 decay is calculated from a set of templates andcompared to the collected light and a likelihood is formed.These templates are pre-determined using the detectorsimulation. The energy and direction phase-space of thesecondary gamma is searched to find the point that leadsto the maximum likelihood. Each algorithm supplies thedirection of two photons, their energies, the two photoninvariant mass, and the maximum likelihood value ob-tained. It was found that the wide-algorithm methodmore reliably finds a real second ring more often thanthe forward-algorithm. Therefore, in this report we usemostly the information provided by the wide-algorithmunless otherwise stated.

To demonstrate the power of POLfit, Figure 2 showsthe relative 0 reconstruction efficiencies with (solid cir-cles) and without (open circles) POLfit employed as afunction of the opening angle between the two recon-structed gammas from the 0 decay in the lab frame andfor single 0 events produced by the NC interactions. Tobe accepted in this sample, the event must have a two-photon invariant mass (m ) within 2 of the expectedvalue given the event came from a 0. Here, the neutrinoenergy spectrum is that of the original SK-I atmospheric

muon neutrinos. In the case without POLfit, only eventsidentified as having two e-like rings by the standard SK-Isoftware can be candidates to be a 0. With POLfit in-formation, 0 events that are classified as single-ring bythe standard selection may now be selected.

Depletion of0 detection efficiencies at a small open-ing angle is due to overlap of the two e-like rings. Atlarge opening angle it is due to the second ring being too

faint. As clearly seen in Figure 2, POLfit improves the0 reconstruction efficiency significantly.

VI. USEFUL VARIABLES TO DISTINGUISHTHE SIGNAL FROM THE BACKGROUND

A cut on m reduces background from single 0 NC

events but it also reduces signal efficiency somewhat.Alone, it is not enough to reduce the background to alevel comparable to the oscillation signal. It is, there-fore, desirable to find additional distinguishing features.

In this section, nine such features (variables) including

m are described. Distributions of these variables areshown for events that are oscillated e CC (labeled sig-nal and with solid lines) and NC, CC and beam-eCC events (background, dotted lines). The distribu-tions are plotted for different Erec regions in steps of 0.5GeV from 0 to 2 GeV, 2 GeV Erec < 3 GeV and Erec 3 GeV.

In general, at lower energies (sub-GeV range), thebackground is largely from the misidentified single-0

events discussed above. At higher energies, non-QE in-teractions become dominant leading to additional waysfor background to mimic e CC QE events.

A. Reconstructed 0 mass (m)

As shown above, this variable is useful to remove back-ground events that come from single 0 NC production.In Figure 3 the distributions of m are shown. In thelower reconstructed neutrino energy region (Erec 2GeV), the distributions show a prominent 0 peak. Athigher energies, the contribution from multi-pion produc-tion increases and POLfit begins to reconstruct the cor-rect second gamma poorly or returns an arbitrary resultthat is not associated with any physical particle. Becauseof this, the 0 peak disappears in the higher energy re-

gion.

B. Fraction of energy in the second ring (Efrac)

In general, the second e-like ring found by POLfit hasless energy than the one found by the standard SK-I re-construction software. Furthermore, POLfit must find asecond ring and if the event does not in fact have one,this wrongly reconstructed ring tends to have much less


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energy than the primary one. This effect is shown in Fig-ure 4 where the ratios of the energy of the second ring tothe sum of two ring energies are plotted.

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FIG. 5: The distributions of the difference in log0 likelihoodbetween the two algorithms. The larger this variable, themore likely an event is the 0 background. The distributionsin solid lines are for the signal and those in dotted lines arefor the background.

C. Difference in log 0 likelihood ratio (log 0-lh)

As mentioned above, POLfit employs two algorithms,the wide- and forward-algorithm. Each provides a log-likelihood that the event is a 0. Signal events actuallycontain only a single ring. Nevertheless, with such events,POLfit will return a second, fake ring. In such cases, both

algorithms tend to place this fake ring in the vicinity ofthe single primary ring. Therefore, the two algorithmstend to find similar fake rings. This makes the two like-lihoods similar to each other and the log-likelihood ratio(difference between two log-likelihoods) tends to be sym-metric around zero. On the other hand, in the case of a 0

background event the secondary photon from a 0 decayis not necessarily confined in the direction of the primaryphoton. This makes the log-likelihood ratio asymmetricwith a long left tail, especially at lower energies. The dif-ference is significant in the lower energy region as shownin Figure 5. However, this trend changes above Erec =1.0 GeV where the contribution from multi-pion produc-

tion starts to increase and dilutes this effect.

D. Direction cosine of the e-like ring (cos)

The direction cosine of the primary e-like ring with re-spect to the neutrino beam is a good discriminator to sep-arate the signal from the background. Its distributionsare shown in Figure 6. This variable does not depend onthe information from POLfit.


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FIG. 6: The distributions of the directional cosine of the pri-mary e-like ring with respect to the neutrino beam direction.The distributions in solid lines are for the signal and that indotted lines are for the background.

As the energy of the neutrino decreases, the outgoingelectron direction is distributed over a wider angle withrespect to the neutrino direction. As the energy becomescomparable to that of Fermi motion, the distribution isfurther widened because the momentum of the target nu-cleon becomes significant and will tend to randomize theelectrons direction. This latter effect is less for the more

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E. Total charge to ring energy ratio (Q/E)

Light collected in an event that is not consistent withthe single ring found by the standard SK-I codes is an in-dication of unreconstructed or missed particles and thusa non-QE interaction. A measure of this light is the ra-tio of the total charge, in unit of PE (photoelectron),collected by all PMTs to the energy associated with theprimary reconstructed ring in MeV. Some backgroundevents where only one ring is found are expected to pro-duce some light which is not identified as a ring. Thedistributions of this variable are shown in Figure 7. Theseparation is most pronounced at lower reconstructed en-ergy where any 0s are likely to be less boosted and notput all their light in the forward direction. Thus in anasymmetric 0 decay the second ring tends to be weakerthan the standard SK codes can detect.

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F. log particle-identity-likelihood (log pid-lh)

The standard SK-I reconstruction software provideslikelihoods of a Cherenkov ring to be e-like (Le) and -like (L). From these two likelihoods, the logarithm ofthe ratio of likelihoods, log(L/Le) (log pid-lh) is used asa good measure to separate electrons from muons. Themore negative log pid-lh is, the more e-like a Cherenkov

ring is. When two e-like rings, such as the photons froma 0 decay, overlap and reconstruct as a single ring theycan produce a log pid-lh that is more e-like than a singleelectron at a comparable energy would have. Figure 8shows this small but noticeable effect.

G. log 0-likelihood (log 0-lh)

POLfit provides the logarithm of a likelihood that theevent consists of a single 0. For events that actuallydo consist of a single 0 this variable is expected to besmaller (more negative), namely more 0-like, than that

for a signal event. This trend shows up in lower energyregion (Erec 1 GeV) as shown in Figure 9. In the higherenergy region, the distribution tends to be narrower forthe signal events.

H. Cherenkov angle (Cangle)

The distribution of reconstructed Cherenkov angle isexpected to be different between the signal and back-


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FIG. 9: The distributions of the log 0-likelihood of single e-like ring events. The distribution in solid line is for the signaland that in dotted line is for the background.

ground events and it depends on whether there is overlapbetween two Cherenkov rings and on the energy of theprimary ring. In Figure 10 the Cherenkov angle distri-butions for different Erec regions are shown. The shapeof the distribution for the signal events differs from thatfor the background events in most of the energy regions,although degrees of differences vary from energy region

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FIG. 10: The distributions of the measured Cherenkov angleof the primary e-like ring. The distribution in solid line is forthe signal and that in dotted line is for the background.

to region.

I. Log ring-count likelihood ratio (log ring-lh)

To decide how many Cherenkov rings there are in anevent, two hypotheses are compared: the first hypothesisis that there is only one Cherenkov ring and the second isthat there is an additional ring in the event. The compar-ison is made using log-likelihood ratio, calculated by thestandard SK-I codes, of the two hypotheses. In Figure 11this log-likelihood ratio is plotted for different Erec re-gions. The shape of the distribution for the signal eventsdiffers from that for the background events in most ofthe energy regions, although degrees of differences againvary over the different energy regions.

VII. DISCRIMINATOR: LIKELIHOODFUNCTION AND LIKELIHOOD RATIO

A series of cuts on the variables described in the pre-vious section can reduce the background well. However,too many cuts in series reduce the signal selection effi-ciency. The problem for this analysis is that none of thevariables alone can separate the signal from the back-ground powerfully. Thus, this situation is well suitedfor a multivariate analysis where a likelihood functionis defined and utilizes all variables that have noticeabledistinguishing power. We have shown that the nine vari-ables described above are distributed differently depend-ing on the source of the events (signal or background),


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FIG. 11: The distributions of log-likelihood ratio of two hy-potheses on the number of Cherenkov ring in an event: thereis only one Cherenkov ring or there are more. If the log-likelihood ratio is negative, the event is less likely to havean additional ring. The distributions in solid line are for thesignal and that in dotted line are for the background.

although the differences may not be large. As we willsee, an accumulation of relatively small differences, whenthe correlations among the variables are small, can makea bigger difference.

From each distribution shown in Figures 3-11, aprobability is calculated for an event to have a value

of the corresponding variable i as signal p

s

i and asbackground pbi . Then the log-likelihood is defined bylog(Ls) = i=1,..,9 log(p

si ) as signal and by log(Lb) =

i=1,..,9 log(pbi) as background. These probabilities arecalculated in the same bins ofErec as used in Figures 3-11.

Then the difference between two log-likelihoods,log(L) = log(Lb) log(Ls), is calculated to decidewhether to accept or reject the event. Figure 12 showslog(L) distributions for the different Erec regions forthe signal events (solid line) and the background events(dotted line). The smaller log(L) is, the more likely anevent is a signal event. It is clearly seen that the log(L)distribution of the signal events differ significantly from

that of background events over wide range of Erec.

VIII. RECONSTRUCTED NEUTRINO ENERGYDISTRIBUTIONS WITH A CUT ON log(L)

The final acceptance of an event is determined by itsvalue of log(L). As the distributions of the nine vari-ables used to define the likelihood depend on Erec, sodoes the distribution of log(L). Therefore, in order not

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FIG. 12: The distributions of log-likelihood ratio of two hy-potheses on the origin of events: signal vs. background. Thedistributions in solid line are for the signal and those in dottedline are for the background.

to change the energy spectrum unnecessarily, we adopt astrategy to keep the signal detection efficiency constantover a wide range of Erec by changing the log(L) cutaccording to Erec. The cut is selected to retain 40% ofthe signal that passes the standard SK-I cuts for all Erec.

In presenting the results, first we illustrate the per-formance of the traditional analysis represented by thestandard SK-I codes for comparison. Figure 13 (top)

shows the Erec distributions of the signal (dashed line),of the background (background-1) mostly from NC inter-actions (dotted line), and of the irreducible background(background-2) from the e contamination in the neu-trino beam (dash-dotted line). The signal is overwhelmedby the background, especially in the low energy region.In this case, we find 700 signal events, 1,877 backgroundevents from background-1, and 127 background eventsfrom background-2.

On the contrary, if we retain 40% of the signal eventsafter the cut on log(L) introduced in this paper, thebackground-1 events are strongly suppressed as shownin Figure 13 (right figures). We find 280 signal, 87background-1, and 49 background-2 events.

The analysis presented here uses nine variables todefine the likelihood. The usefulness of all nine vari-ables is evaluated by examining how much the signal-to-background (S/B) ratio changes when each variable isremoved in turn from the overall likelihood function. Ta-ble I summarizes the numbers of events and the S/B ratiofor each case where only the contribution to background-1 is considered. The S/B ratio is always appreciablysmaller when one of the nine variables is removed fromthe likelihood function than when all nine are included.


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FIG. 13: Top: The distributions of the reconstructed neu-trino energy with the standard Super-Kamiokande cuts. Thedistributions in dashed line are for the signal and thosein dotted (dash-dotted) line are for the background-1(-2).CP = +45

and the baseline is 2,540 km. Bottom: Thesame distributions except that, in addition to the standardSuper-Kamiokande cuts, the cut on logL is applied.

Each variable helps to enhance the signal.

IX. Erec DISTRIBUTIONS AND CP-VIOLATINGPHASE CP

In the previous section we showed that with a set ofappropriate cuts, the background contribution can besuppressed down to a reasonable level, while retaining

TABLE I: Summary of the numbers of the signal and back-ground events, and the signal-to-background ratio usingevents from background-1 with the cut on log(L) to retain40% of the signal events. The signal-to-background ratio withone variable removed is compared to the ratio with all ninevariables. Note that the numbers of the signal (background-2) events are not always 280 (49) due to the finite bin sizeused for the distribution of the variable removed.

Variable removed Sig Bkg-1 Bkg-2 Sig/Bkg-1None 280 87 49 3.22

log 0-lh 281 102 50 2.75Q/E 281 94 49 2.98

log 0-lh 278 94 51 2.98log pid-lh 277 94 46 2.96

Efrac 281 98 49 2.85m 280 105 50 2.66cos 279 101 49 2.76

Cangle 280 98 49 2.86 log ring-lh 277 95 49 2.93

TABLE II: Summary of the numbers of the signal and back-ground events for different values of CP using events frombackground-1 (Bkg-1) and background-2 (Bkg-2) with the cuton log(L) chosen to retain 40% of the signal events.

CP Sig Bkg-1 Bkg-2

+135 386 89 50+45 280 87 49

0 197 90 48-45 159 87 48

-135 263 87 49

enough statistics for the signal. In this section, we seewhether this set of the cuts is still useful for other valuesof the CP-violating phase CP. Table II lists the numbersof events from the signal, background-1 and background-2 for various values of CP.

X. Erec DISTRIBUTIONS AND BASELINE

It is interesting to see how the baseline will changethe results of similar analyses presented in the pre-ceding section. For this study, the cut on log(L)is used again to retain 40% of signal and the base-line is assumed to be 1,480 km (Fermilab to Hender-son Mine). Figure 14 shows the Erec distribution of

the signal (dashed line), background-1 (dotted line) andbackground-2 (dash-dotted) for = +45. Table III liststhe numbers of events from the signal, background-1 andbackground-2 for different values of CP.

XI. SOURCES OF BACKGROUND EVENTS

It is important to know where the background eventscome from. Information such as the true energy of neutri-


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FIG. 14: The distributions of the reconstructed neutrino en-ergy is shown for events that pass the standard SK-I cuts andthe cut on log(L) such that 40% of the signal events are re-tained. The distributions in dashed line are for the signal andthose in dotted (dash-dotted) line are for the background-1(background-2). CP = +45

and the baseline is 1,480 km.

TABLE III: Summary of the numbers of signal and back-ground events for different values for CP using events frombackground-1 (Bkg-1) and background-2 (Bkg-2) with the cuton log(L) to retain 40% of the signal events and using abaseline of 1,480 km.

CP Sig Bkg-1 Bkg-2

+135 646 238 142+45 699 233 141

0 498 230 140-45 357 247 142

-135 609 237 142

nos and nature of interaction of neutrinos that producethe background events is very useful for design of theneutrino beam for a VLBNO experiment.

Figures 15-16 show the neutrino energy distributions ofthe signal, background-1 and background-2 events for thebaseline of 2,540 km and 1,480 km, respectively. These

events are chosen with the log(L) cut that retains 40%of the signal events after the first set of the cuts (thestandard SK-I cuts).

As mentioned earlier, for the most of the results pre-sented in this report, we apply the cut on the neutrinoenergy at 10 GeV. To justify this cut, we checked to seehow much more the background contribution would in-crease if we allowed events produced by neutrinos whoseenergies were greater than 10 GeV and less than 15 GeV.For these additional events we fixed the weight value to

TABLE IV: The percent contributions from events pro-duced by different interactions for signal events and for thebackground-1 events are summarized for CP = +45

withthe cut on log(L) to retain 40% of the signal events andwith the baseline of 2,540 km.

Interaction Erec range (GeV)

Sig 0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-

CC QE 86% 79% 63% 82% 28% 46%CC 0 2% 3% 4% 2% 5% 6%CC 11% 15% 28% 13% 37% 30%CC n 1% 3% 3% 4% 25% 14%CC others 0% 0% 1% 0% 3% 2%

Bkg-1 0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-CC QE 7% 5% 6% 0% 0% 0%CC 0 0% 1% 4% 6% 4% 0%CC 2% 5% 0% 1% 0% 0%CC n 0% 0% 3% 6% 0% 0%CC others 0% 0% 0% 0% 21% 3%NC 0 23% 53% 60% 59% 18% 0%NC 64% 10% 6% 0% 0% 0%NC n 0% 13% 5% 16% 55% 92%NC co0 5% 14% 16% 12% 2% 5%NC elastic 0% 0% 1% 0% 0% 0%

that used at 10 GeV. The atmospheric e flux times thee cross section decreased by about 60% while that forthe wideband beam by about 50% in this energy re-gion. Therefore the atmospheric e and spectrum areonly slightly softer than the wideband spectrum from10 GeV to 15 GeV. This argument, therefore, gives areasonable estimate of the extra contribution from high

energy neutrinos. All the neutrino oscillation parametersare the same as in the case with CP = +45, the base-

line of 2,450 km, and the 40% log(L) cut. The numbersof the signal, background-1, and background-2 events ac-cepted are 281, 91 and 49, respectively, which should becompared with 280 for the signal, 87 for the background-1 and 49 for the background-2 with the neutrino energycut at 10 GeV. Thus the percent increases in the numberof the signal, background-1 and background-2 events are1%, 4%, and 0%, respectively.

Tables IV and V summarize all neutrino interactionsthat produce candidate events passing all cuts with 40%efficiency for the baseline of 2,540 km and 1,480 km, re-spectively. In these tables, 0,, and n stand for sin-gle 0, single and multiple production, respectively.The co label stands for production via coherent inter-action with the oxygen nucleus. The others includeseta and kaon production as well as deep inelastic scatter-ing (DIS). However, for the background, the lable nincludes DIS. Note that in the tables there is no contribu-tion from NC interaction for signal events by definition.CC QE contributions to background-1 are due to in-teractions.


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FIG. 15: The distribution of the energies of neutrinos thatproduce the signal, background-1 and background-2 events.In addition to the standard Super-Kamiokande cuts, the cuton log(L) is applied in such a way to retain 40% of thesignal events that survive by this cut. The distribution indashed line is for the signal and that in dotted (dash-dotted)is for the background-1(-2). CP = +45

and the baseline is2,540 km.

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FIG. 16: The distribution of the energies of neutrinos thatproduced the signal, background-1 and background-2 events.In addition to the standard Super-Kamiokande cuts, the cuton log(L) is applied in such a way to retain 40% of thesignal events that survive by this cut. The distribution indashed line is for the signal and that in dotted (dash-dotted)is for the background-1(-2). CP = +45

and the baseline is1,480 km.

TABLE V: The percent contributions from events producedby different interactions for the signal events and for thebackground-1 events are summarized for CP = +45

withthe cut on log(L) to retain 40% of the signal events andwith the baseline of 1,480 km.

Interaction Erec range (GeV)

Sig 0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-

CC QE 82% 77% 52% 42% 54% 53%CC 0 3% 3% 6% 7% 4% 5%CC 14% 18% 30% 36% 30% 30%C n 1% 2% 12% 13% 11% 10%CC others 0% 0% 0% 2% 1% 2%

Bkg-1 0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-CC QE 8% 4% 1% 3% 0% 0%CC 0 0% 2% 6% 4% 0% 0%CC 6% 6% 2% 1% 1% 0%CC n 0% 0% 1% 1% 0% 0%CC others 0% 0% 0% 4% 2% 7%NC 0 23% 58% 61% 29% 23% 0%NC 59% 5% 6% 0% 0% 0%NC n 0% 11% 5% 23% 65% 93%NC co0 4% 14% 17% 35% 9% 0%NC elastic 0% 0% 1% 0% 0% 0%

XII. DETECTOR SIZE AND GRANULARITY

It is interesting to see what the effect of the detectorsize has on the performance of POLfit. Although theresults reported so far are based on the analyses of theMonte Carlo events generated for the Super-Kamiokandedetector with 40% PMT coverage, we can make someassessment of the effect of a larger, more granular de-tector by imposing a cut on the distance to the PMTsurface from the 0 production point in the direction ofthe 0 (Dwall). For this study we use single

0 eventsproduced by NC interactions. When the 0 energy isabout 1 GeV, the minimum opening angle of two pho-tons is about 20 and less at higher energies. As Dwallgets larger, the number of PMTs that detect Cherenkovphotons increases (improved granularity) which can helpto resolve light patterns. Two negative impacts competewith this effect. The Cherenkov cone is more spread outso less light is seen by any one PMT. The light musttravel further and is thus more subject to absorptionand scattering (attenuation) in the water. These bothlead to a decrease in the number of detected photons per

PMT which may degrade the pattern of light that theCherenkov cone produces. In the first case, since infor-mation is not lost and is just spread out to more PMTsthe problem can likely be handled in improvements to re-construction codes. In the second case, some informationabout the original Cherenkov light emitting particles isunrecoverable.

Figure 17 shows the 0 detection efficiency as a func-tion of the opening angle for Dwall ranges: 5 m - 10 m,15 m - 20 m, and 25 m - 30 m and includes POLfit infor-


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FIG. 17: The 0 detection efficiency as a function of the twophoton opening angle for three ranges of the distance fromthe 0 production vertex to the closest PMT surface in thedirection of0.

mation. It is clearly seen that when the opening angle issmaller (less than 60), the efficiency is improved as thedistance to the PMT surface in the 0 direction increases.Note that above the opening angle of 60, the 0 detec-tion efficiency seems more or less independent of Dwall.Because of the finite size of the detector and at such largeopening angles selecting events based on Dwall becomesa less capable means of emulating a larger detector.

Nevertheless, this indicates that the granularity of thedetector in terms of the PMT density is an importantfactor to improve the 0 detection efficiency. It also ap-pears that the effect of light attenuation is not a majorissue at least for Cherenkov light traveling up to 30-40 min SK-I water which has an attenuation length of 80-100m (depending on wavelength).

Therefore for the same PMT coverage using the samePMTs, a larger detector than SK-I will perform better,on average, to reconstruct 0. Limitations may be ex-pected once the typical path length for Cherenkov lightapproaches attenuation length.

A similar study can be done by looking at how theS/B ratio varies as a function of Dwall for other event

types. In this case we look at the S/B ratio for values

of Dwall for the primary e-like ring. For Dwall > 20 mthe S/B ratio changes from the average of 1.4 to 3.8 forevents with Erec 1.2 GeV, and for events with 2 GeV Erec < 4 GeV the S/B ratio essentially stays the same.

The large improvement in the S/B ratio for events withErec 1.2 GeV results from an increase in the number ofPMTs (pixels) in a Cherenkov ring. This improvementis significant as in the energy region Erec 1.2 GeV the

contribution from the NC events is reduced to a levelas low as that from the irreducible background. This im-provement, however, is not realized for events with 2 GeV Erec < 4 GeV presumably because in this energy re-gion multi-pion events are the major background.

This observation is also true if the minimum distanceDwall is set at 10 or 15 m, although the improvement inthe S/B ratio is less than the case of the 20-m cut. Fora SK-I sized detector, this 20-m cut reduces the numberof the signal events by 41%. However, if the detector islarger, this loss of efficiency can be greatly reduced. Inother words, for a given detector size, the finer granu-larity, not necessarily the number of Cherenkov photons

collected by individual PMT, improves the S/B ratio.

XIII. CONCLUSION

We have demonstrated that a large water Cherenkovdetector can be used to detect efficiently the signal eventsby es from the neutrino oscillation e while keep-ing the background at a reasonably low level in a VLBNOexperiment for the baseline of over 1,400 km with a wide-band beam.

Acknowledgments

The authors gratefully acknowledge the work of theSuper-Kamiokande collaboration in developing the mostof tools used for this analysis. However, the result andits interpretation are responsibility of the authors ofthis paper. The work is partially supported by fund-ing from Stony Brook University Office of the Vice Pres-ident for Research, DOE grant DEFG0292ER40697 atStony Brook University and DOE contract DE-AC02-98CH10886 at Brookhaven National Laboratory, andthe City University of New York PSC-CUNY ResearchAward Program at Borough of Manhattan Community

College/the City University of New York.

[1] D. Beavis et al., Report of the BNL neutrino workinggroup, BNL-69395, hep-ex/0211001; M. V. Diwan et al.,Phys. Rev. D68 (2003) 012002, also hep-ex/0306081.

[2] M. Shiozawa, Nucl. Instr. Meth. A433 (1999) 240.[3] Y. Ashie et al., Phys. Rev. D71 (2005) 112005.

[4] C. K. Jung, Feasibility of a Next Generation Under-ground Water Cherenkov Detector: UNO, Talk atNNN99, Stony Brook, New York, 1999, available atarXiv:hep-ex/0005046. Also see the expression of interestand the proposal by the UNO collaboration,
http://lanl.arxiv.org/abs/hep-ex/0211001http://lanl.arxiv.org/abs/hep-ex/0306081http://lanl.arxiv.org/abs/hep-ex/0005046http://lanl.arxiv.org/abs/hep-ex/0005046http://lanl.arxiv.org/abs/hep-ex/0306081http://lanl.arxiv.org/abs/hep-ex/0211001


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http://nngroup.physics.sunysb.edu/uno/publications/EOI.pdfandhttp://nngroup.physics.sunysb.edu/uno/publications/uno-rnd-proposal05-DOE 111105.pdf.

[5] B. Viren. http://www.phy.bnl.gov/trac/nuosc/.[6] Dziewonski and Anderson, Preliminary Reference Earth

Model, Phys. Earth. Planet. Int., 25, 297-356 (1981).[7] I. Mocioiu, R. Shrock, Matter Effects on Neutrino Oscilla-

tions in Long Baseline Experiments, Phys.Rev. D62 (2000)

053017 and I. Mocioiu, R. Shrock, Neutrino Oscillationswith Two m2 Scales, JHEP 0111, (2001) 050.

[8] T. Barszczek, Ph.D Thesis, University of Califor-

nia, Irvine, unpublished (2005). Available at theSuper-Kamiokande website at http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.html.

[9] Y. Itow et al., The JHF-Kamioka neutrino project, KEKreport 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05,hep-ex/0106019 (2001); C. Yanagisawa, Background Un-derstanding and Supression in Very Long Baseline Neu-trino Oscillation Experiments with Water Cherenkov De-tectors Talk at NNN05, Aussois, France, 2005, available

at http://nnn05.in2p3.fr/schedule.html/.
http://nngroup.physics.sunysb.edu/uno/publications/EOI.pdfhttp://nngroup.physics.sunysb.edu/uno/publications/uno-rnd-proposal05-DOE_111105.pdfhttp://nngroup.physics.sunysb.edu/uno/publications/uno-rnd-proposal05-DOE_111105.pdfhttp://www.phy.bnl.gov/trac/nuosc/http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://lanl.arxiv.org/abs/hep-ex/0106019http://nnn05.in2p3.fr/schedule.html/http://nnn05.in2p3.fr/schedule.html/http://lanl.arxiv.org/abs/hep-ex/0106019http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://www.phy.bnl.gov/trac/nuosc/http://nngroup.physics.sunysb.edu/uno/publications/uno-rnd-proposal05-DOE_111105.pdfhttp://nngroup.physics.sunysb.edu/uno/publications/uno-rnd-proposal05-DOE_111105.pdfhttp://nngroup.physics.sunysb.edu/uno/publications/EOI.pdf

Muon Neutrino Oscillation to Electron Neutrino with a Large Water Cherenkov Detector

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