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4  Very Long Baseline Experiment



Figure 1: BNL wide band spectrum with the new graphite target and horn design. This spectrum is at 0 degrees with respect to the proton beam on target and the normalization is at 1 km from the target.

We calculate the event rate without oscillations assuming a 1.0 MW proton beam power with 28 GeV protons (1.1 × 1014 protons per pulse), a 0.5 MT fiducial mass water Cherenkov detector and 5 years of running. Because BNL's Alternating Gradient Synchrotron (AGS) can run in a parasitic mode to the Relativistic Heavy Ion Collider (RHIC), we expect to get beam for as much as 1.8× 107 sec per year. However, we conservatively assume only 1.0× 107 sec of AGS running per year here. Using these parameters, the 0∘ flux from Figure 1 and the relevant cross sections, we calculate that the number of quasi-elastic charged current muon neutrino events in a detector located at 2540 km will be ∼ 12000 in five years running. Table 1 shows the number of different kinds of events we expect in the absence of oscillations. The large statistics combined with the long baseline make many of the following important measurements possible.

Table 1: Number of events of different types for the very long baseline experiment. The parameters are 1 MW of beam, 0.5 MT of fiducial mass, and 5 years of running with 107 seconds of live time each year. CC, NC, QE, stands for charged current, neutral current, and quasielastic, respectively. The νe interaction rate is from the electron neutrino contamination in the beam.


Reaction Number
CC νµ+ N → µ- + X 51800
NC νµ+ N → νµ+ X 16908
CC νe + N → e- + X 380
QE νµ+ n → µ- + p 11767
QE νe + n → e- + p 84
CC νµ+ N → µ- + π+ + N 14574
NC νµ+ N → νµ+ N + π0 3178
NC νµ+ O16 → νµ+ O16 + π0 574
CC ντ+ N → τ- + X 319
(if all νµ→ ντ)  

4.1  νµ disappearance


Figure 2: [

Neutrino produced muon angle distribution, data and Monte Carlo.] Angular distribution of muons from the process νµn → µ- p (top curve) and background from νµN → µ- N' π (bottom curve). The histogram is data from AGS experiment E734 (year 1986) and the lines are Monte Carlo.


Figure 3: [

Oscillation nodes vs. distance.] Nodes of neutrino oscillations for disappearance (Not affected by matter effects) as a function of oscillation length and energy for Δ m322 = 0.0025 eV2. The distances from FNAL to Soudan (the distance from BNL to Morton salt works is approximately the same[36]) and from BNL to Homestake are shown by the vertical lines.

Figure 4: [

Expected νµ disappearance spectra, Δ m322 = 0.0025] Spectrum of detected events in a 0.5 MT detector at 2540 km from BNL including quasielastic signal and CC-single pion background. We have assumed 1.0 MW of beam power and 5 years of running. The top histogram is without oscillations; the middle error bars are with oscillations and the bottom histogram is the contribution of the background to the oscillated signal only. This plot is for Δ m322 = 0.0025 eV2. The error bars correspond to the statistical error expected in the bin. A 10 % detector energy resolution is assumed. At low energies the Fermi movement, which is included in simulation, will dominate the resolution.

Figure 5: [

Expected νµ disappearance spectra, Δ m322 = 0.001] Spectrum of detected events in a 0.5 MT detector at 2540 km from BNL including quasielastic signal and CC-single pion background. We have assumed 1.0 MW of beam power and 5 years of running. The top histogram is without oscillations; the middle error bars are with oscillations and the bottom histogram is the contribution of the background to the oscillated signal only. This plot is for Δ m322 = 0.001 eV2. The error bars correspond to the statistical error expected in the bin. A 10 % detector energy resolution is assumed. At low energies the Fermi movement, which is included in simulation, will dominate the resolution.
The angular distribution of the muons from the quasi-elastic process νµ + n → µ- + p produced by the 0o beam in Figure 42 was measured in experiment E734 (1986) at BNL. It is shown again in Figure 2 along with the principal background, νµ + N → µ- + N + π [13]. A variety of strategies is possible to reduce this background further in a water Cherenkov detector. Knowing the direction of an incident νµ accurately and measuring the angle and energy of the observed muon allows the energy of the νµ to be calculated, up to Fermi momentum effects. This method is used by the currently running K2K experiment [8]. The known capability of large water Cherenkov detectors indicates that at energies lower than 1 GeV the νµ energy resolution will be dominated by Fermi motion and nuclear effects[14]. The contribution to the resolution from water Cherenkov track reconstruction depends on the photo-multiplier tube coverage. With coverage greater than ∼ 10%, we expect that the reconstruction resolution should be more than adequate for our purposes [21]. In the following discussion we assume a 10% resolution on the νµ energy. This is consistent with the resolution projected for 10% coverage from the K2K experience [15].

The range of Δ m322 ∼ 1.24Eν[GeV] /L[km] covered by the proposed experiment using the beam in Figure 1 extends to the low value of about 5 × 10-4  eV2. The lower end of this extensive range of values is considerably below the corresponding values for other long baseline terrestrial experiments [11, 12]. If the value of Δ m322 turns out to be towards the lower end (∼ 10-3) of its current range, or if the value of Δ m212 turns out to be towards its high end (∼ 10-4 eV2), then large and very interesting interference effects in the very long baseline experiment will be possible.

Extra-long neutrino flight paths open the possibility of observing multiple nodes (minimum intensity points) of the neutrino oscillation probability in the disappearance experiment. Observation of one such pattern will for the first time directly demonstrate the oscillatory nature of the flavor changing phenomenon. The nodes occur at distances Ln = 1.24 (2n-1) Eν/Δ m322, n= 1,2,3, .... In Figure 3, as an example, we show the flight path L versus Eν relationship of the nodes for Δ m2 = 0.003  eV2, a value close to the value measured in atmospheric neutrino experiments [4]. An advantage of having a very long baseline is that the multiple node pattern is detectable over a broad range of Δ m2. For Δ m322 as small as 0.001 eV2, the oscillation effects will be very large.

The two single charged pion reactions νµ+ p → µ- + p + π+ and νµ + n → µ- + n + π+ produce a signal which is somewhat larger than the quasi-elastic total in Table 1. For these events, if both the muon and the pion produce more than 50 photoelectrons each, the event can be easily identified as a two ring event in a water Cherenkov detector and rejected. 50 photoelectrons corresponds to about 170 MeV/c (250 MeV/c) for muons (pions) for a detector with 10% photo-multiplier coverage. An additional cut to require the muon to be within 60o of the neutrino direction reduces the background further. With such a cut, we find that 18% of the events will show one ring (principally the µ-). The detection of two muon decays, one from the µ- the other from the decay chain π → µ → e, could be used to further suppress this background by approximately a factor of 2. More importantly, background events can be tagged by the two muon decays to determine the shape of the background from the data itself. This will greatly increase the confidence in the systematic error due to this background. The reaction νµ + n → µ- + p + π0 (the only allowed CC-π0 reaction) is ∼15% of the total quasi-elastic rate. The momentum distribution of µ- and π0 are essentially the same as those for CC-charged pion production. Only 0.5% of the CC-π0 events will look like quasi-elastic muon events because at least one of the gamma rays from the π0 decay is usually visible. Thus this background is negligible in the quasi-elastic sample.

The expected plot of signal and background is shown in Figures 4 and 5. They show the disappearance of muon type neutrinos as a function of neutrino energy measured in quasi-elastic events. The background, which will be mainly charged current, will also oscillate, but the reconstructed neutrino energy will be systematically lower for the background. Nevertheless, the main effect will be to slightly broaden the large dips due to disappearing muon neutrinos.

In Figure 6 we show the statistical precision expected on the measurement of Δ m322 and sin2 2 θ23 for several different points in the parameter space. It is clear that since the signal and the statistics are large, the systematic error in fitting the spectrum will dominate the final error. We list various effect that must be considered for the measurement with brief comments about each.

Figure 6: [

Statistical uncertainty for Δ m322 and sin22θ23] Statistical resolution at 68%, 90% and 99% confidence level on Δ m322 and sin2 2θ23 for the 2540 baseline experiment; assuming 1 MW, 0.5 MT, and 5 years of exposure.

Figure 7: [

Statistical and systematic uncertainty for Δ m322 and sin22θ23, includes other's allowed regions.] Resolution including statistical and systematic effects at 68%, 90% and 99% confidence level on Δ m322 and sin2 2θ23 for the 2540 baseline experiment; assuming 1 MW, 0.5 MT, and 5 years of exposure. We have included a 5% bin-to-bin systematic uncertainty in the energy calibration as well as a 5% systematic uncertainty in the normalization. The expected resolution from the MINOS experiment at Fermilab and the allowed region from SuperK is also indicated.

Figure 8: [

The allowed region from the K2K experiment.] The allowed region for Δ m322 and sin22θ23 from the K2K experiment. From thesis by Eric Sharkey, SUNY at Stony Brook.
With the assumption on the systematic errors as above we obtain Figure 7. The systematic errors introduce a small correlation in the Δ m322 vs. sin2 2 θ32 measurement. The error on the determination of Δ m322 at 0.0025 eV2 increases to about ± 1.2% at maximum mixing, but there is only a small effect on the determination of sin2 2 θ23. As mentioned before, the energy scale uncertainty must be added in quadrature to the calculated uncertainty on Δ m322. The precision of this experiment can be compared with the precision expected from MINOS (Figure 7) and the precision obtained so far from the K2K experiment (Figure 8). It is expected that K2K will obtain twice as much data; therefore we could naively estimate that the precision on the parameter determination will improve as 2-0.5.

Finally, we note that the flux normalization is usually obtained by placing a detector close to the neutrino source. For example, both K2K and MINOS have large near detectors to determine the flux. Since absolute flux determination is not very important for parameter determination in our case, we argue that the requirements on a near detector need not be very severe for this measurement. It may not be necessary to build a near detector until sufficient statistics are obtained in the far detector to demand the required systematic error reduction of a near detector.

4.2  νµ→ νe appearance

The oscillation of νµ→ νe is discussed is several recent papers [16, 17, 18, 19]. This oscillation in vacuum is described fully by the following equation:
  P(νµ→νe) =
4(s232s132c132 +JCPsinΔ21) sin2
Δ31
2
 
    +2(s12s23s13c12c23c132 cosδ -s122s232s132c132) sin Δ31 sinΔ21       (1)
   
+4(s122c122c232c132 +s124s232s132c132 -2s123s23s13c12c23c132 cosδ -JCP sinΔ31) sin2
Δ21
2
 
   
+8(s12s23s13c12c23c132 cosδ - s122s232s132c132) sin2
Δ31
2
sin2
Δ21
2
 
where
  JCP ≡ s12s23s13c12c23c132sinδ       (2)

JCP is an invariant that quantifies CP violation in the neutrino sector. The abbreviations sij ≡ sinθij, cij ≡ cosθij, and Δij ≡ Δ mij2 L / 2 Eν are used. The formula for P(anti-νµ→anti-νe) is the same as above except that the JCP terms have opposite sign. The vacuum oscillations for a baseline of 2540 km are illustrated in Figure 9 as a function of energy for both muon and anti-muon neutrinos. The main feature of the oscillation is due to the term linear in sin2Δ31/2. The oscillation probability rises for lower energies due to the terms linear in sin2 Δ21/2. The interference terms involve CP violation and they create an asymmetry between neutrinos and anti-neutrinos. The vacuum oscillation formula (Eq.1) and Figure 9 show that the CP asymmetry also grows as 1/E in the 0.5-3.0 GeV region. The parameters listed in the figure are sin2 2 θ12=0.8, sin2 2 θ23=1.0, and sin2 2 θ13=0.04 and Δ m212=5.0× 10 -5 eV2, Δ m322=0.0026 eV2. Similar notation for parameters will be followed in the rest of the document. Because of this effect it is argued that the figure of merit for measuring CP violation is independent of the baseline. For very long baselines the statistics for a given size detector at a given energy are poorer by one over the square of the distance, but the CP asymmetry grows linearly in distance [17]. The background to the electron neutrino signal comes from contamination in the beam (νe/νµ∼ 0.7%) and neutral current events. At small distances the systematic error on this background could limit the ability to extract the CP violating effect, but at large distance the background reduces as 1/(distance)2 and allows us to greater sensitivity to CP violating effects. We rely on this important observation in the rest of this section.


Figure 9: Probability of νµ→ νe and anti-νµ→ anti-νe oscillations at 2540 km in vacuum assuming a δCP=+45o CP violation phase. It can be seen that the CP asymmetry between νµ and anti-νµ increases for lower energies because the CP asymmetry is proportional to Δ m212 L /E which increases for lower energies. The parameters listed in the figure are sin2 2 θ12=0.8, sin2 2 θ23=1.0, and sin2 2 θ13=0.04 and Δ m212=5.0× 10 -5 eV2, Δ m322=0.0026 eV2.


Figure 10: Probability of νµ oscillating into νe after 2540 km. The parameters assumed are listed in the figures. The upper and lower curves correspond to CP phase angle of +45o and 0o respectively. We point out that the effect of CP phase increases for lower energies.


Figure 11: Probability of νµ oscillating into νe after 2540 km. The parameters assumed are listed in the figures. This plot assumes a CP violation phase of +45o. The upper and lower curves are for neutrinos and anti-neutrinos, respectively. We see that for distance of 2540 the matter effects will be large and will lead to almost complete reversal of nodes and anti-nodes for neutrinos and anti-neutrinos. The probability for neutrinos with Δ m322 < 0 will be similar to (but not exactly the same as) anti-neutrinos.

The vacuum oscillation formulation must be modified to include the effect of matter [18]. The νµ→ νe probability in the presence of matter is shown in Figures 10 and 11. When compared to Figure 9 we can see that matter will enhance (suppress) neutrino (anti-neutrino) conversion at high energies and will also lower (increase) the energy at which the oscillation maximum occurs. The effect is opposite (enhancement for anti-neutrinos and suppression for neutrinos) if the sign of Δ m322 is negative. The Figures 9 to 11 gives us hints about possible strategies in understanding neutrino oscillation parameters.

In the low energy region from 0 to 1.0 GeV, the probability for νµ→ νe is dominated by the effects of Δ m212 if the solution to the solar neutrino deficit is the large mixing angle (LMA) solution. An excess of electron like events in this region would be sensitive to Δ m212 and sin2 2 θ12.

In the intermediate energy region from 1.0 to 3.0 GeV, we see that the CP violating phase δCP has a large effect on the oscillation probability and the effects of matter are relatively small. Therefore this energy region could be used to measure the CP violating phase δCP from the observed spectrum of electron like events.

The higher energy region with energy greater than 3.0 GeV is clearly the region of discovery for νµ→ νe oscillations as well as the sign of Δ m322. In the case of the normal mass hierarchy (m3 > m2 > m1) the oscillation signal in the high energy region for neutrinos will be enhanced by more than a factor of 2. Moreover, as we will discuss below, the backgrounds from both neutral currents and intrinsic νe will fall in this region. Therefore the appearance signal will have a distinctive shape to distinguish it from the background. In the case of (m2 > m1 > m3) the oscillation signal in the high energy region will be almost completely suppressed. However, there will be a peak between 2 and 3 GeV. If sin2 2 θ13 is sufficiently large, this will be a clear signature for Δ m322 < 0, a very important result in particle physics.

Finally, matter enhancement of the oscillations has been postulated for a long time without experimental confirmation [20]. Detection of such an effect by measuring a large asymmetry between neutrino and anti-neutrino oscillations or by measuring the spectrum of electron neutrinos is a major goal for neutrino physics. This measurement will also yield the sign of Δ m322.

4.3  Backgrounds

While the νµ disappearance result will be affected by systematic errors, the νµ→ νe appearance result will be affected mainly by the backgrounds. The signal we are looking for consists of clean, single ring electron events in the detector. The signal will mainly result from the quasielastic reaction νe + n → e- + p. The main backgrounds will be from neutral current reactions and the intrinsic electron neutrinos in the beam. Most of the ∼ 17000 neutral current reactions from Table 1 are either elastic scattering off nucleons or single pion production channels. Of these, the channels that produce single π0 will be the major source of backgrounds. We estimate that approximately 2800 NC events will have multiple pions in the final state. Half of these will have at least one π0. We expect that these can be rejected much more effectively than the single π0 production channels which will have ∼ 3700 events (see Table 1). This number includes the coherent production channel of νµ+ O16 → νµ+ O16 + π0. The charged current background channel, νµ+ n → µ- + p + π0, in which the muon remains invisible was shown to be small for a similar beam spectrum in the E889 proposal [21].

Figure 12: The q2 distribution of νµ+ N → νµ+ N + π0 channels. Here q2 = ((p'N + p'π) - pN)2. pN is the initial 4 momentum of the target nucleon (assumed to be at rest in the lab frame). p'N and p'π are the 4-momenta of the final state nucleon and pion, respectively. The peak of the distribution is independent of neutrino energy. The neutrino energy only determines the physical cutoff of the q2 distribution. The slightly negative behavior of the distribution is caused by the Fermi motion of the target nucleus which was assumed to be at rest in the above formula.


Figure 13: The π0 energy distribution of νµ+ N → νµ+ N + π0 channels with no cuts. The peak of the distribution is independent of neutrino energy. The neutrino energy determines the high energy cutoff of the distribution. The distribution is about 3 orders of magnitude suppressed above 2.5 GeV where we expect the signal from νµ→ νe appearance.

For a baseline of 2540 km, the matter enhanced oscillation signal will be above 3 GeV. Our strategy for obtaining a unique, clear signal therefore depends on the observation that neutral current background will peak at low energies and fall rapidly as a function of observed energy. This is demonstrated in Figures 12 and 13 for the neutral current single pion production channel. In Figure 12 we see that the q2 distribution peaks at low values and is nearly independent of the neutrino energy. The neutrino energy only determines the kinematic limit of the q2 value. This behavior leads most neutral current events to be at low energies.

Figure 13 shows the distribution of total π0 energy for single pion production events with no detector cuts. We see that the distribution is about 3 orders of magnitude suppressed above 2.5 GeV where we expect the signal from νµ→ νe appearance (see Figure 10). Therefore, we propose that even a modest rejection of neutral current background above 2.5 GeV is sufficient to provide us with good sensitivity for νµ→ νe appearance.

This modest rejection can be obtained by first cutting all events with visible energy less than 500 MeV. Further rejection is obtained by getting rid of events with two showers each with energy greater than 150 MeV separated by more than 9 degrees in angle and by cutting events with angle between the shower and the neutrino direction of greater than 60 degrees; this was calculated using a fast Monte Carlo with appropriate angle and energy resolution corresponding to a water Cherenkov detector. At high energies, above 3 GeV, a full simulation of a large water Cherenkov detector showed us that it is possible to obtain about a 50% rejection based on the Cherenkov ring characteristics. The overall rate of π0 misidentification is shown in Figure 14.

It should be noted that the advantage of the very long baseline is in applying a simple cut on the total visible energy to eliminate most of the background. The rate of π0 misidentification for neutral current events (Figure 13) above 500 MeV is 6%. The efficiency for electrons is shown on the right hand side of Figure 14. The efficiency for quasielastic electron neutrino events is 64% at energy less than 1.5 GeV. Above 1.5 GeV the efficiency is 90%. Using appropriate resolution and efficiency factors we obtain the predicted background spectrum of electron like showering events in Figure 15. The reconstructed electron energy and the angle of the electron with respect to the neutrino direction is used to reconstruct the neutrino energy assuming a quasielastic scattering event. Figure 15 includes backgrounds from the neutral current single π0 production off nucleon as well as coherent π0 production off O16, which has a much more energetic spectrum. The spectrum also includes the background from νe contamination in the beam.

The predicted number of total background events is 146 with the beam-νe contamination accounting for 70 events. It should be remarked that above 2 GeV the background is dominated by the beam-νe contamination: there are 35 νe events versus 17 π0 events. This is despite the rather poor rejection of NC(π0) events at high energies. Below 2 GeV the background will be dominated by the NC(π0) events: with 35 νe events and 59 π0 events. Therefore any error in the determination of the NC(π0) background including contamination from other neutral current background channels (which will have similar energy dependence) will not significantly affect the high energy region above 2 GeV where we expect to see a distinct signal for electron neutrino appearance.

Figure 14: On the left: the rate of misidentification of π0 events as electrons versus total π0 energy for the calculations in this paper. On the right: electron efficiency used in this calculation.


Figure 15: Spectrum of reconstructed electron neutrino energy (assuming quasielastic events) of the background for νµ→ νe search. This is for 1 MW beam power, 0.5 MT detectors mass and 5× 107 sec of running. The top histogram includes both the NC(π0) and electron contamination backgrounds. The electron neutrino contamination is also shown separately.

4.4  Sensitivity to sin2 2 θ13

Figures 16 and 17 show the spectrum of electron like events that will be detected at 2540 km. The signal for Δ m322=0.0025 eV2 and sin2 2 θ13 ∼ 0.04 will be about 200 events. The advantages of the very long baseline are in obtaining a large enhancement at higher energies and creating a nodal pattern in the appearance spectrum. Both of these can be used to further improve the sensitivity of the experiment. It should be noted that the value of Δ m322 will be known very precisely from the disappearance measurement; this value can then be used to precisely predict the shape of the spectrum of electron-like events. Unlike past experiments in which only a simple counting of signal over background was performed, the node pattern in this experiment will be a strong confirmation of νµ→ νe. The broadband beam also allows for sensitivity over a broad range of Δ m322. This can be seen in Figure 17.

Figure 16: Spectrum of detected quasi-elastic electron neutrino charged current events in a 0.5 MT detector at 2540 km from BNL. We have assumed 1 MW of beam power and 5 nominal years of running. This plot is for Δ m322 = 0.0025 eV2. We have assumed sin2 2 θ13 = 0.04 and Δ m212 = 6× 10-5 eV2. The error bars correspond to the statistical error expected in the bin. The spectrum includes effects of Fermi motion, energy resolution and efficiency.


Figure 17: Spectrum of detected quasielastic electron neutrino charged current events in a 0.5 MT detector at 2540 km from BNL. We have assumed 1 MW of beam power and 5 nominal years of running. This plot is for Δ m322 = 0.0015 eV2. We have assumed sin2 2 θ13 = 0.04 and Δ m212 = 6× 10-5 eV2.

We calculated the background electron spectrum assuming sin2 2 θ13=0; then we varied the parameters, Δ m312 and sin2 2 θ13, and calculated the χ2 with respect to the background spectrum. The other parameters in this calculation were set as follows: Δ m212=6× 105 eV2, sin2 2 θ12=0.8, sin2 2 θ23=1.0 and δCP=0. We assumed that the remaining parameters will be well-known from other experiments. However, the small uncertainty on Δ m212 will cause us to lose sensitivity to sin2 2 θ13 at values of Δ m322 < 0.001 eV2, outside the region favored by SuperK. For the calculation we assume a 10% systematic error (in addition to the statistical error) on the background spectrum of events. This level of systematic uncertainty is attainable with a modest sized near detector and it compares well with proposals for other such experiments. The 90% confidence level upper limit obtained from this calculation is shown in Figure 18. The same figure also shows the sensitivities of several other proposed experiments as well as the current best limit from the CHOOZ reactor experiment. The current upper limit at Δ m312 = 0.0025 eV2 is sin2 2 θ13 = 0.12. It should be noted that if Δ m322 is lower the current limit becomes much poorer. (We will use the values sin2 2 θ13 = 0.04 and sin2 2 θ13 = 0.06, which are a factor 1/3 and 1/2 below the current limit as benchmark points for some of the plots.)

The sensitivity shown in Figure 18 can be divided in two regions: above Δ m322 = 0.0015 eV2 (in the parameter region preferred by the SuperK data) the electron spectrum shape will be very distinct and show at least two clear nodes; below Δ m322 = 0.0015 eV2 the statistics will be larger and we will get a better limit, however the signal will not have the distinct shape that will be a strong confirmation of an oscillation signal. Moreover, the sin2 2 θ13 measurement in the lower region could be correlated with Δ m212.

The sensitivity for the BNL-to-Homestake experiment declines as Δ m322 becomes larger and the first oscillation node moves to higher energies where our spectrum has much lower flux. This can be improved by adding more focusing elements to the horn-produced beam to increase the high energy flux; however, this will increase the background for the lower energy events. We are in the process of performing these optimization studies to determine the best spectrum shape for this experiment. Lastly, we note that the sensitivity does not depend strongly on the amount of neutral current background. This is shown in Figure 19 where we have calculated the 90% confidence level upper limit assuming that the the neutral current background is twice as high as in Figure 15. This is because the spectrum is already dominated by the intrinsic νe background in the higher energy region above 2 GeV. Therefore any additional NC background makes little difference to the statistical sensitivity. Much higher NC background will affect the spectrum below 2 GeV and this could lower the sensitivity to CP parameters as well as Δ m212.

Figure 18: Expected 90% confidence level upper limit on sin2 2 θ13 versus Δ m312 for the BNL-to-Homestake experiment compared to other proposed experiments. The current limit from the CHOOZ reactor experiment is also shown on the same plot.


Figure 19: Expected 90% confidence level upper limit on sin2 2 θ13 versus Δ m312 for the BNL-to-Homestake experiment. The two curves are with the background as predicted in Fig. 15 (the left hand curve) and assuming the neutral current background to be a factor of two larger (the curve to the right).

4.5  Sensitivity to the CP violation parameter

As shown in Figure 9, the effect of CP violation grows linearly as energy is decreased (or the baseline increased). For a very long baseline experiment, it is possible to compare the signal strength in the π/2 node versus the 3π/2 or higher nodes. Such a comparison will yield a measurement of the CP violation parameter δCP. Such a measurement can be done with only neutrino beam running over most of the parameter region (anti-neutrino running not necessary). Any such measurement of CP should eventually be augmented by data using a muon anti-neutrino beam in the same experiment. Nevertheless, we have calculated the sensitivity to CP parameter δCP with only neutrino running. In Figure 20 we plot the reconstructed neutrino spectrum for electron-like events including background for 3 different values of δCP. The effect of δCP is clearly large for the lower energy signal region as pointed out earlier. In Figure 21 we further examine the effect of CP on the electron spectrum. This plot shows that both the size of the modulation and the phase shifts as we examine different energy bins. The phase shift is due to the presence of terms involving both sinδ and cosδ in the νµ→ νe probability over the entire spectrum. The broadband beam, therefore, allows us to fit the entire spectrum and gives us good sensitivity to δCP with much reduced correlation with sin2 2 θ13.

Figure 20: The observed electron neutrino spectrum including background contamination for 3 different values of the CP parameter δCP. The error bars are for δCP = 135o; the errors bars indicate the statistical error on eah bin. The red histogram below the error bars is for δCP = 45o, and the blue histogram is for δCP = -45o. The green hatched histogram shows just the background (Figure 15). This plot is for Δ m322 = 0.0025 eV2. We have assumed sin2 2 θ13 = 0.06 and Δ m212 = 6× 10-5 eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.


Figure 21: The event rate in 3 energy bins from Fig. 20 as a function of δCP. This plot also includes the background in each of the 3 energy bins. This plot shows that both the phase and the size of the modulation changes as we examine different energy bins. Thus a fit to the entire spectrum should give us good sensitivity to δCP.

It is clear from Figure 20 that sensitivity to νµ→ νe depends on both sin2 2 θ13 and δCP. Therefore, we have calculated the 90% confidence level upper limit on sin2 2 θ13 as a function of δCP with all other parameters fixed in Figure 22. The region on the right hand side of the curves in Figure 22 can be excluded if no excess of electrons is found as expected for the parameters shown in the figure.

Figure 22: 90% and 95% confidence level upper limit in sin2 2 θ13 as a function of δCP if no excess of electron is found as expected for Δ m322 = 0.0025 eV2, and Δ m212 = 6× 10-5 eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.

If sin2 2 θ13 is reasonably large then a good measurement of δCP is possible from the neutrino data alone. 68% and 90% confidence level error contours are shown in Figure 23 with statistical errors only for δCP=45o and sin2 2 θ13 = 0.06 (the other parameters are listed in the figure caption). Systematic errors on the background will mainly affect the low energy (0.5 to 2 GeV) region, which has large sensitivity to the CP parameter. We have calculated the error contours assuming 10% systematic uncertainty on the background in Figure 24. We believe that with the use of a near detector as well as clearly tagged background events we can achieve 10% determination of the expected background. Figures 25 and 26 show the expected error contours at sin2 2 θ13 = 0.04, δCP=135o and sin2 2 θ13 = 0.06, δCP=-90o, respectively. Two important observations considering these results are: if we perform the measurement without using a wide band beam in a narrow region of L/E the result will have a severe correlation between sin2 2 θ13 and δCP; this correlation is broken by the use of a wide band beam. Secondly, the expected error on δCP is ± 20o over a wide range of sin2 2 θ13; it can be improved considerably with modest amount of anti-neutrino data running. We will examine the consequences of the anti-neutrino running in an update to this paper.

For the result in this section on the CP measurement we have assumed that the values of Δ m212 and sin2 2 θ12 will be well known. The measurement of δCP is, of course, correlated to these quantities. On the other hand, we could fit the observed electron distribution for the quantity JCP× Δ m212 to simply detect the presence of CP-violating terms in the spectrum without attempting to measure δCP. We will examine these and other subtleties in the next update to this paper.

Figure 23: 68% and 90% confidence level error contours in sin2 2 θ13 versus δCP for statistical errors only. The test point used here is sin2 2 θ13=0.06 and δCP=45o. Δ m322 = 0.0025 eV2, and Δ m212 = 6× 10-5  eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.


Figure 24: 68% and 90% confidence level error contours in sin2 2 θ13 versus δCP for statistical and systematic errors. The test point used here is sin2 2 θ13=0.06 and δCP=45o. Δ m322 = 0.0025  eV2, and Δ m212 = 6× 10-5  eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.


Figure 25: 68% and 90% confidence level error contours in sin2 2 θ13 versus δCP for statistical and systematic errors. The test point used here is sin2 2 θ13=0.04 and δCP=135o. Δ m322 = 0.0025  eV2, and Δ m212 = 6× 10-5  eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.


Figure 26: 68% and 90% confidence level error contours in sin2 2 θ13 versus δCP for statistical and systematic errors. The test point used here is sin2 2 θ13=0.06 and δCP=-90o. Δ m322 = 0.0025  eV2, and Δ m212 = 6× 10-5  eV2. The values of sin2 2 θ12 and sin2 2 θ23 are set to 0.8, 1.0, respectively.

4.6  Sensitivity to mass hierarchy

There are three possible neutrino mass hierarchies possible with the existing data on atmospheric and solar neutrinos. For most of this paper we have assumed the normal mass hierarchy (NH): m3 > m2 > m1. The reversed mass hierarchy (RH), m1 > m2 > m3, will be ruled out if the preferred Solar-LMA solution is confirmed in the near future. The LMA solution depends on m2 > m1 through the MSW mechanism. The third possibility, m2 > m1 > m3, called the unnatural hierarchy (UH), will result in a very different appearance spectrum in the case of the BNL to Homestake experiment. This is illustrated in Figure 27; the UH possibility causes a suppression νµ→ νe oscillation in the high energy region. However, the second oscillation maximum is still present and it is quite sensitive to the CP phase. In the case of UH, therefore, we will still obtain reasonable sensitivity to sin2 2 θ13 with neutrino running, but it will depend strongly on δCP as shown in Figure 28.

Figure 27: Probability for νµ→ νe oscillations as a function of neutrino energy for a baseline of 2540 km. The three curves correspond to regular mass hierarchy (RH) with δCP = 0o (black), irrational mass hierarchy (IRH) with δCP = 0o (red), and irrational mass hierarchy (IRH) with δCP = 180o (blue). The other parameters are indicated in the figure.


Figure 28: Expected 90% confidence level upper limit on sin2 2 θ13 versus Δ m312 for the BNL-to-Homestake experiment for the UH hypothesis for running with neutrinos for 5 years. We have used δCP = 0o and δCP = 180o for the two curves labeled BNL-HS-UH-CP0 and BNL-HS-UH-CP180, respectively. The limit that can be obtained for the NH possibility with δCP = 0o is also shown labeled BNL-HS-NH.

For a large region of parameter space, the UH and NH possibilities can be separated with good significance using the spectrum obtained from the neutrino running only. Nevertheless, anti-neutrino running may be essential if sin2 2 θ13 is small. The probability of anti-νµ→ anti-νe for the UH case in the of anti-neutrinos is shown in Figure 29. In the UH case the oscillation probability is enhanced in the high energy (> 3 GeV) region. This could be detected easily by changing the polarity of the horn focussed beam to make an anti-neutrino beam.

For this report we have concentrated on first running the beam with the neutrino polarity. In an updated to this report we will examine the event rates, and sensitivities for anti-neutrino running. Nevertheless, we can make a few remarks based on experience from [13]. The horn focussed anti-neutrino flux will be about 80% of the neutrino flux. However, the event rate from anti-neutrino will be suppressed because of the lower cross section. The event rate will also have about 10% contamination from neutrinos. An important feature, however, for the very long baseline experiment can be seen in Figure 30, which shows the cross section for quasielastic events for neutrinos and anti-neutrinos. In the interesting energy region about 3 GeV where we expect the matter enhanced signal for anti-neutrino running, the quasielastic cross section for anti-neutrino running is about 70% of the neutrino cross section. This implies that the sensitivity to sin2 2 θ13 in the UH case using anti-neutrinos could be quite good with similar amount of running as in the neutrino case for NH.

Figure 29: Probability for anti-νµ→ anti-νe oscillations as a function of anti-neutrino energy for a baseline of 2540 km. The two curves correspond to unnatural mass hierarchy (UH) with δCP = 0o (black), and unnatural mass hierarchy (UH) with δCP = 180o (red). The other parameters are indicated in the figure.


Figure 30: Cross section for quasielastic events. νe + n → e- + p for neutrinos and anti-νe + p → e+ + n for anti-neutrinos.

4.7  Sensitivity to Δ m212

The distance of 2540 km is sufficient to obtain an appreciable signal for νµ→ νe because of the dominant mixing due to Δ m212 and sin2 2 θ12 if the LMA (Large Mixing Angle) solution holds for the solar neutrino anomaly. This is shown in Figures 31 and 32. The parameters for the best fit point in the LMA solution contour were used for Figure 31. An excess of 62 events is expected in the lower part of the energy spectrum. If the true value of Δ m212 is at the upper end of the LMA solution (12.0× 10-5 eV2) then a rather large excess of 230 events is expected. This signal can result in a reasonably good measurement of Δ m212; at the LMA best fit point the expected accuracy is ± 20%. The confidence level contours are shown in Figure 33 where the LMA allowed contour is approximated as a rectangle. Statistical and 10% systematic error on the background are included in this determination. The accelerator experiment by itself will yield a result with a correlation between Δ m212 and sin2 2 θ12; therefore another experiment must provide a measurement of sin2 2 θ12 to give the best result on Δ m212.

If there is no excess of electron-like events in the spectrum such as Figure 31 then an upper limit can be obtained on the parameters Δ m212 versus sin2 2 θ12. Such a 90% confidence level limit is shown in Figure 34. This limit was obtained using statistical errors and a 10% systematic error on the background. This experiment can cover most of the LMA solution; if the background can be measured better or suppressed further then all of the LMA region could be covered.

Such a measurement of the parameters governing the solar neutrino anomaly in the νe appearance mode is qualitatively very different from measurements in the SNO experiment or long baseline reactor experiments such as KAMLAND [22] and confirms the neutrino oscillation picture in a useful new mode.

Figure 31: Spectrum of electron-like events for sin2 2 θ13=0. The other important parameters are Δ m212 = 6× 10-5 eV2 and sin2 2 θ12 =0.8.


Figure 32: Spectrum of electron-like events for sin2 2 θ13=0. The other important parameters are Δ m212 = 6× 10-5 eV2 and sin2 2 θ12 =0.8.


Figure 33: 68, 90, and 99 percent confidence level contours for a measurement at the LMA best fit point. Both statistical and systematic errors are included. We assume a 10% systematic error on the background.


Figure 34: Expected 90% confidence level limit on Δ m212 versus sin2 2 θ12 if there is no excess of electron-like events. Both statistical and systematic errors are included.

4.8  The Experimental Strategy and Program

For most of this document we have shown the possible results of running with a neutrino beam for a total of about 5 years of practical operation. The actual running conditions will, of course, depend on the physics results that will be produced as the experiment progresses. The great advantage of this proposed program is that it is so rich in its physics reach that important new physics results will come forth after every year of running. These results, in turn, will determine the character of running for the next period.

For example, after only about 2 years of running we will have a very accurate determination of Δ m322 and sin2 2 θ23. At this stage, if we see a substantial peak in the electron spectrum at the expected energy, we will have strong evidence for the natural mass hierarchy (NH) and then continue running with neutrinos to detect the presence of CP violating terms. But if we see no electron signal, we would then switch to antineutrino running. Since at higher energies (> 3 GeV), the antineutrino quasielastic cross section is 70% of the neutrino quasielastic cross section, it will not take a very large amount of antineutrino running to see a peak in the positron spectrum at the expected energy if sin2 2 θ13 is > 0.01 with the unnatural mass hierarchy. Determination of the mass hierarchy is by itself a major goal of this experimental program.

If the value of sin2 2 θ13 is too small, one will still complete the experimental program to determine Δ m212 in the appearance mode, a qualitatively different mode from the SNO or the KAMLAND experiments, and a confirmation of the oscillation picture we now have.

It should also be pointed out that although the absolute determination of Δ m322 may be limited by systematic errors on the energy scale, this systematic error is eliminated when we compare the values of Δ m322 obtained from neutrino versus anti-neutrino running. Such a comparison will yield a truly unique test of CPT conservation and more new physics.

Other unexpected results cannot be ruled out because of the spectacular physics reach of such an experiment. These results will influence the running conditions as well as future accelerator, beam, and detector upgrade paths.

We also emphasis that this all-inclusive neutrino oscillations program can be completed in a single facility. Other proposed methods that feature a sequential experiments approach will take much longer to perform and will ultimately cost more. This is an important strategic point for the US particle physics program.

4.9  Detectors for the very long baseline experiment

The conversion of Homestake Gold Mine in Lead, South Dakota, into the National Underground Science and Engineering Laboratory (NUSEL), tentatively to take place in the next few years, will provide a unique opportunity for a program of very-long baseline neutrino oscillation experiments. As explained above, these experiments are possible only due to the length of the baseline, 2540 km, from the Brookhaven National Laboratory (BNL) to Lead. It is proposed that the NUSEL facility will accommodate either an array of detectors or a single monolithic one both with total masses approaching 1 Megaton. Most of these will be water Cherenkov detectors that can observe neutrino interactions in the desired energy range with sufficient energy and time resolution [23]. Details of underground construction of these detectors is provided in Appendix II.

An alternative to Homestake also exists at the Waste Isolation Pilot Plant (WIPP) located in an ancient salt bed at a depth of ∼ 700 meters near Carlsbad, New Mexico. One advantage of the WIPP site is that it is owned by the DOE and now has a program of underground science. We note that the recent Neutrino Factory Study [24] at BNL identified the WIPP site as one possible location for a far detector, and the current BNL neutrino beam could use the same concept. The distance from BNL to WIPP is about 2880 km. The cosmic ray background will be higher at WIPP because the facility is not as deep as Homestake, which has levels as deep as ∼ 2500 meters. The increased background, although undesirable, is not an insurmountable problem. However, the mechanical design of a large cavity in a salt bed has to be very different because of the slow movement of salt that causes a cavity to slowly collapse.

The issue of depth is not one that greatly impacts this experiment. A modest overburden is needed so that the detector is not swamped by cosmic ray muon events and thus overwhelmingly dead. Because the beam spill times are well known, simple timing gates suffice to remove virtually all direct cosmic ray backgrounds. This method is successfully used in the K2K experiment. The background from cosmic ray muon spallation events as well as electrons from muon decay are both well below the analysis energy threshold. However, there is a very rich array of physics that a large underground detector can do in the time between beam spills many of which either benefit from or require depths of greater than 3000 meters water equivalent[26]. Figure 35 shows the cosmic ray muon intensity as a function of depth.

Figure 35: Cosmic ray muon intensity as a function of depth in meters water equivalent (m.w.e) (from ref [25]).

In this report we will not address the detailed issues of detector design and cost. A more detailed study of a very large water Cherenkov detector has been done by the UNO collaboration [26]. Figure 36 shows a conceptual design drawing of their detector layout.

Figure 36: Conceptual design of baseline UNO detector (from ref [26]).

Another option for detector technology is a liquid Argon (LAR) time projection chamber. Although a massive LAR detector (500 kT) cannot be ruled out at this stage, a near LAR detector to precisely measure the beam spectrum appears to be a very attractive possibility.

The viability of a large liquid argon detector is presently being demonstrated by the ICARUS collaboration [37] in cosmic-ray tests of a 300-ton module located on the Earth's surface. Currently, a study is in progress to site the LANNDD, 70 KT liquid Argon detector at WIPP [38, 39]. The key issue at this stage is of safety and a proposal to the DOE to study this is in preparation. The LANNDD detector can be used for neutrino physics, as well as the search for proton decay and other astro-particle physics goals. Currently, the ICARUS detector at the Gran Sasso is being constructed with a 3kT detector as a goal. The operation of this detector will provide key information for the eventual construction of LANNDD and for the neutrino physics identified in this paper. A magnetized liquid argon detector would give the maximal discrimination against backgrounds in a neutrino beam, would enhance the ability to perform CP violation experiments, and would permit use of a beam produced by a solenoid focusing scheme [40] that contains both neutrinos and antineutrinos. An R&D experiment is proposed to use a prototype liquid argon detector in a magnetic field to determine the sign of electrons via analysis of their electromagnetic showers up to several GeV [41].




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