jaydeep datta s.uma sankar arxiv:1907.08966v1 [hep-ph] 21 ... · e-mail:...

Prepared for submission to JHEP

Matter vs Vacuum Oscillations in AtmosphericNeutrinos

Mohammad Nizama,b Jaydeep Dattac,b Ali Ajmid S.Uma Sankare

aTata Institute of Fundamental Research,Mumbai 400005, IndiabHomi Bhabha National Institute,Anushakti Nagar, Mumbai 400094, IndiacSaha Institute of Nuclear Physics,Bidhannagar, Kolkata 700064, IndiadDepartment of Physics and Astronomy, Kyoto University,Kyoto 606-8502, JapaneDepartment of Physics, Indian Institute of Technology Bombay,Mumbai 400076, India

E-mail: [email protected], [email protected],[email protected], [email protected]

Abstract: Atmospheric neutrinos travel very long distances through earth matter. Itis expected that the matter effects lead to significant changes in the neutrino survivaland oscillation probabilities. Intial analysis of atmospheric neutrino data by the Super-Kamiokande collaboration is done using the vacuum oscillation hypothesis, which provideda good fit to the data. In this work, we did a study to differentiate the effects of vacuumoscillations and matter modified oscillations in the atmospheric neutrino data. We find thatmagnetized iron detector, ICAL at INO, can make a 3 σ discrimination between vacuumoscillations and matter oscillations, for both normal and inverted hierarchies, in ten years.

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Contents

1 Introduction 1

2 Vacuum vs. Matter Modified Oscillations 2

3 Methodology 3

4 Results 6

5 Conclusions 11

1 Introduction

The pioneering water Cerenkov detectors, IMB [1, 2] and Kamiokande [3, 4], observed theup down asymmetry of atmospheric muon neutrinos and established atmospheric neutrinoanomaly. The next generation experiment, Super-Kamiokande [5], measured the zenithangle dependence of atmospheric muon and electron neutrinos and established atmosphericneutrino oscillations. The analysis of Super-Kamiokande data has determined, to a goodprecision, the larger mass-squared difference |∆31| and the mixing angle sin 2θ23 of the threeflavour neutrino oscillations1. This determination played an important role in the design ofthe accelerator neutrino experiments T2K [6] and NOνA [7].

In the beginning, the data of Super-Kamiokande was analyzed using the hypothesis ofvacuum oscillations, which provided a good fit to the data. The determination of |∆31| andsin 2θ23 was done, in fact, under this hypothesis. The up going atmospheric neutrinos travelthousands of kilometers through earth matter. During their travel, they are expected toundergo forward elastic scattering, which modifies their propagation properties. In such asituation, the data should be analyzed under the hypothesis of matter modified oscillations.A number of studies [8–11] considered such oscillations and explored the sensitivity of futureatmospheric neutrino detectors to determine whether ∆31 is positive or negative. Recently,Super-Kamiokande experiment analyzed their data using the hypothesis of matter modifiedoscillations and they disfavour, at 2 σ, both vacuum oscillations as well as matter oscillationswith negative values of ∆31[12].

At present, the most precise determination of |∆31| and sin 2θ23 comes from the muonneutrino disappearance data of the accelerator neutrino experiments, such as MINOS[13],T2K [14] and NOνA [15]. Vacuum oscillations as well as matter oscillations with eitherpositive ∆31 or negative ∆31 provide an equally good fit to this data and give essentially thesame values of oscillation parameters. The νe/νe appearance data in accelerator neutrino

1 The definitions of various neutrino oscillation parameters for three flavour mixing are given at thebeginning of section 2.

– 1 –

experiments is sensitive to matter effects [16, 17]. A precise measurement of the oscillationprobabilities, Pµe and Pµe, is expected to lead to a determination of the sign of ∆31. Thepresent appearance data from T2K [18] and NOνA [19] favour positive sign for ∆31 but donot rule out the negative sign. Since vacuum oscillations provide a good fit to the νµ dis-appearance data, one must consider that hypothesis also in analyzing the νe/νe appearancedata. Consideration of vacuum oscillation hypothesis introduces unwanted complicationsin the search for CP violation at accelerator neutrino experiments. Therefore, it is desirableto make a distinction between vacuum oscillations versus matter oscillations through otherexperiments, such as the atmospheric neutrino experiments, which are not very sensitive tothe CP violation.

2 Vacuum vs. Matter Modified Oscillations

Neutrinos are produced in three flavours: νe, νµ and ντ . These mix to form three masseigenstates ν1, ν2 and ν3, with masses m1,m2 and m3 respectively. The mixing betweenthe flavour eigenstates and the mass eigenstates is given by νeνµ

ντ

= U

ν1

ν2

ν3

, (2.1)

where U is a 3 × 3 unitary matrix called PMNS matrix. It is parametrized by the threemixing angles θ12, θ13 and θ23 and the CP violating phase δCP as

U =

1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13e

−iδCP

0 1 0

−s13eiδCP 0 c13

c12 s12 0

−s12 c12 0

0 0 1

(2.2)

For neutrino propagation in vacuum, the oscillation probabilities depend on the six parame-ters: the two mass-squared differences, ∆21 = m2

2−m21 and ∆31 = m2

3−m21, the three mixing

angles and the CP violating phase (δCP). At present, ∆21, |∆31|, θ12 and θ13 are measuredquite precisely. In case of the third mixing angle, sin2 2θ23 is measured to be closed to 1 butsin2 θ23 has a rather large range of (0.4 − 0.64). The sign of ∆31 is not known at present.Therefore, we consider both the possibilities of positive and negative sign.Recently, the twolong baseline oscillation experiments, T2K [18] and NOνA [19], have measured the valueof CP violating phase. However, the best fit δCP values of these two experiments are verydifferent. A combined analysis of all neutrino data gives the following allowed ranges at 3 σ[20]: (135◦ − 366◦) for NH and (196◦ − 351◦) for IH. For neutrino propagation in matter,the oscillation probabilities are modified due to matter effects. These are parametrized bythe Wolfenstein matter term A = 0.76× 10−4 ρ(in gm/cc)E(in GeV) [21, 22]. Inclusion ofmatter effects induces a change in the mass square differences and the mixing angles andhence in the probabilities. This change depends on not only the matter term but also onthe sign of ∆31. By measuring the change in the probabilities it is possible to determinethe sign of ∆31.

– 2 –

The modification of neutrino oscillation probabilities by matter effects is a hypothesis,based on the fact that neutrino-electron elastic forward scattering occurs. Till now thishypothesis is tested only in the solar neutrino data, through the Mikheyev-Smirnov reso-nance effect [23, 24]. In fact, the sign of ∆21 is determined through this mechanism. It isdesirable to establish the existence of the matter modification of neutrino probabilities in asmany experiments as possible. As explained in the introduction, the present atmosphericneutrino data of Super-Kamiokande disfavours vacuum oscillations only at 2 σ. Therefore,it is desirable to firmly establish the distinction between matter and vacuum oscillationswith atmospheric neutrino data.

We first study the difference between matter and vacuum oscillation probabilities fortwo representative path-lengths for atmospheric neutrinos, L = 5000 km and L = 8000

km. Fig:1 shows the neutrino oscillation probabilities Peµ and Pµµ and Fig:2 shows theanti-neutrino oscillation probabilities Peµ and Pµµ. In each case, the vacuum probability aswell as the matter modified probabilities for positive and negative signs of ∆31 are plotted.The matter modified probabilities, for both signs of ∆31, are calculated numerically usingthe code nuCraft [25], which uses the earth density profile of the PREM model [26]. When∆31 is positive, Pµµ for matter oscillations is lower than Pµµ for vacuum oscillations over awide range of energies and path-lengths. But Pµµ is essentially the same for both the cases.For ∆31 negative, the situation is reversed. Therefore, to study the difference of vacuumoscillations from matter oscillations of either sign, it is important to measure neutrino andanti-neutrino event rates separately.

In this work, we study the sensitivity of Iron Calorimeter (ICAL) at the India-basedNeutrino Observatory (INO) to make a distinction between vacuum and matter modifiedoscillations using atmospheric neutrino data. The charge identification capability of ICALleads to a very high sensitivity for this distinction [27].

3 Methodology

Atmospheric neutrinos are produced through the decay of pions and kaons and the subse-quent decay of muons. Pions and kaons are produced in the interactions of primary cosmicrays with atmospheric nuclei. Hence the atmospheric neutrinos consist of νµ, νµ, νe andνe. The ICAL at INO is a 50 kton magnetized iron calorimeter whose iron plates are inter-spersed with the active detector elements, Resistive Plate Chambers (RPCs). The chargecurrent (CC) interactions of the neutrinos in the detector produce µ− or µ+ or e− or e+

depending on the flavour of the initial neutrino [27].We have used NUANCE event generator [28] to simulate the atmospheric neutrino

events used in this study. It generates neutrino events using atmospheric neutrino fluxesand the relevant cross sections. For a generated event, NUANCE gives the informationon the particle ID and the momenta of all interacting particles. The information of thefinal state particles is given as an input to a GEANT4 simulator of ICAL. This simulatormimics the response of ICAL and generates the hit bank information as the output. Areconstruction program sifts through the hit bank information of each event and tries toreconstruct a track. Electrons and positrons in the final state produce a shower and quickly

– 3 –

0 5 10 15 20Energy (in GeV)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

µe

P vs. Energy for 5000 kmµe P

µe P

for matter (NH)µe P

for vacuum (NH)µe P

for matter (IH)µe P

for vacuum (IH)µe P


0

0.1

0.2

0.3

0.4

0.5

µe

P

vs. Energy for 8000 kmµe P

µe P

for matter (NH)µe P

for vacuum (NH)µe P

for matter (IH)µe P

for vacuum (IH)µe P


0

0.2

0.4

0.6

0.8

1

µ µP

vs. Energy for 5000 kmµ µP

µ µP

for matter (NH)µ µP

for vacuum (NH)µ µP

for matter (IH)µ µP

for vacuum (IH)µ µP


0

0.2

0.4

0.6

0.8

1

µ µP


µ µP





Figure 1. Left top describes Peµ with respect to energy for L = 5000 km, Right top describes Peµwith respect to energy for L = 8000 km, Left bottom describes Pµµ with respect to energy for L =5000 km, Right bottom describes Pµµ with respect to energy for L = 8000 km

lose their energy. Identifying such particles and reconstructing their energy is an extremelydifficult problem. Muons, being minimum ionizing particles, pass through many layers ofiron, leaving behind localized hits in the RPCs. Using this hit information, the track ofthe muon can be reconstructed. Because of the magnetic field, this track will be curvedand the bending of the track is opposite for negative and positive muons. Thus ICAL candistinguish between the CC interactions of νµ and νµ. If a track is reconstructed, the eventis considered to be a CC interaction of νµ/νµ. The charge, the momentum and the initialdirection (cos θtrack), of a reconstructed track, are also calculated from the track properties[29].

We have generated unoscillated atmospheric neutrino events for 500 years of exposure,using NUANCE. In generating these events, the neutrino fluxes at Kamioka are used asinput along with ICAL geometry. The νµ/νµ CC events are given as input to GEANT4and reconstruction code. Events for which one or more tracks are reconstructed are stored

– 4 –


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

µ eP

vs. Energy for 5000 kmµ eP

µ eP

for matter (NH)µ eP

for vacuum (NH)µ eP

for matter (IH)µ eP

for vacuum (IH)µ eP


0

0.1

0.2

0.3

0.4

0.5

µ eP

vs. Energy for 8000 kmµ eP

µ eP

for matter (NH)µ eP

for vacuum (NH)µ eP

for matter (IH)µ eP

for vacuum (IH)µ eP


0

0.2

0.4

0.6

0.8

1

µ µP


µ µP






0

0.2

0.4

0.6

0.8

1

µ µP


µ µP





Figure 2. Left top describes Peµ with respect to energy for L = 5000 km, Right top describes Peµwith respect to energy for L = 8000 km, Left top describes Pµµ with respect to energy for L = 5000km, Right top describes Pµµ with respect to energy for L = 8000 km

along with the charge, the momentum and the initial direction of the track with the largestmomentum. In the case of νe/νe CC events, the electron/positron are redefined to be µ−/µ+

and the events are processed through GEANT4 and the reconstruction code. Once againthe charge, the momentum and the initial direction of the track with the largest momentumare stored. This redefinition of νe/νe CC events is done so that the events which undergoνe(νe)→ νµ(νµ) oscillation are properly taken into account in our analysis.

We used accept/reject method on the unoscillated sample to obtain the oscillated eventsample. We calculated the vacuum oscillation probabilities, Pµµ, Pµµ, Peµ and Peµ, usingthe formula for three flavour oscillations. The corresponding matter modified probabili-ties, for both signs of ∆31, are calculated numerically using the code nuCraft [25]. Theaccept/reject method is applied to νµ(νµ) CC events using Pµµ(Pµµ) to obtain the muonevents due to the survival of νµ/νµ. The same method is applied to νe(νe) CC events usingPeµ(Peµ) to obtain the muon events due to the oscillation of νe/νe. The track informa-

– 5 –

tion for each of the selected events is taken from the simulation described in the previousparagraph.

4 Results

Using the procedure described in the previous section, we generate the muon event samplefor matter modified oscillations with ∆31 positive. In calculating the oscillation proba-bilities for this case, we used the following values of neutrino parameters as inputs [20]:sin2 θ12 = 0.310, sin2 θ13 = 0.02240, sin2 θ23 = 0.582, ∆31 = 2.525 × 10−3 (eV2) and∆21 = 7.39 × 10−5 (eV2). The matter effects in atmospheric neutrino oscillations arenot sensitive to δCP [9]. We first do our calculation with the input value δCP = 0. Thegenerated sample is divided into µ− and µ+ samples and is further subdivided into 17

track momentum bins and 90 track direction bins. The momentum bins are (1, 2), (2, 2.2),(2.2, 2.4), (2.4, 2.6), (2.6, 2.8), (2.8, 3.0), (3.0, 3.5), (3.5, 4.0), (4.0, 4.5), (4.5, 5.0), (5.0, 6.0),(6.0, 7.5), (7.5, 9.0), (9.0, 11.0), (11.0, 14.0), (14.0, 20.0), (20.0, 100.0). We considered onlythose events with track momentum greater than 1 GeV because such events lead to goodtrack reconstruction. The signature of oscillations is very small for the down going eventsand it is almost impossible to reconstruct tracks of muons moving in horizontal direction.Therefore, we considered only the up going events with cos θtrack in the range (0.1, 1). SinceICAL can reconstruct the muon direction very accurately, we have subdivided the aboverange into bins of equal width 0.01. Using this procedure, we have two binned event sam-ples, Ndata,µ−

ij and Ndata,µ+

ij , which we treat as data. Here i refers to the track momentumbin and varies from 1 to 17 and j refers to cos θtrack bin and varies from 1 to 90.

We consider the vacuum oscillations as a hypothesis to be tested against the datasamples described above. Using the vacuum oscillation hypothesis, two other event samples,Nvac,µ−

ij and Nvac,µ+

ij , are generated using the same procedure described in the previousparagraph. In calculating the vacuum oscillation probabilities the five inputs, sin2 θ12 =

0.310, sin2 θ13 = 0.02240, ∆31 = 2.525× 10−3 eV2, ∆21 = 7.39× 10−5 eV2 and δCP = 0, areheld fixed. The test values of sin2 θ23 are varied in the range (0.4, 0.64). To quantify thedifference between matter and vacuum oscillations, we define ∆Nµ−

ij = Ndata,µ−

ij −Nvac,µ−

ij

and ∆Nµ+

ij = Ndata,µ+

ij − Nvac,µ+

ij . In Fig:3, we plot ∆Nµ−

i = Σj∆Nµ−

ij and ∆Nµ+

i =

Σj∆Nµ+

ij as a function of track momentum. Fig:4 gives the plots of ∆Nµ−

j = Σi∆Nµ−

ij and

∆Nµ+

j = Σi∆Nµ+

ij as a function of track direction. We see that ∆Nµ∓

i negative because the

matter effects suppress the peak values of Pµµ. We also see that the magnitude of ∆Nµ−

i islarger than that of ∆Nµ+

i for ∆31 positive. The situation is reversed when ∆31 is negative.This, of course, is a reflection of the fact that the matter effects are more pronounced inPµµ for positive value of ∆31 and in Pµµ for negative values of ∆31. A similar pattern isalso seen in ∆Nµ∓

j , for the same reasons.

We calculate the test event samples N test,µ−

ij and N test,µ+

ij as

Ntest,µ−/µ+

ij = Nvac,µ−/µ+

ij [1 + πijξ], (4.1)

– 6 –

11− 10− 9− 8− 7− 6− 5− 4− 3− 2− 1−Track momentum (in GeV)

800−

700−

600−

500−

400−

300−

200−

100−- µ ij

N∆ jΣ =

i- µ

N∆

matter - vacuum)µν → µν +µν → eν(

1 2 3 4 5 6 7 8 9 10 11Track momentum (in GeV)

240−220−200−180−160−140−120−100−

80−60−40−20−

+ µ ij N∆ jΣ

=

i+ µ N∆

matter - vacuum)µν → eν + µν → eν(

11− 10− 9− 8− 7− 6− 5− 4− 3− 2− 1−Track momentum (in GeV)

250−

200−

150−

100−

50−

0

- µ ij N∆ jΣ

=

i- µ N∆


1 2 3 4 5 6 7 8 9 10 11Track momentum (in GeV)

400−

350−

300−

250−

200−

150−

100−

+ µ ij N∆ jΣ

=

i+ µ N∆


Figure 3. The difference between the number of muon events for matter vs. vacuum oscillations(∆Nµ∓

i ) as a function of track momentum. The plots in the left (right) panels are for µ−(µ+)

events. The plots in the top (bottom) panels are for ∆31 positive and negative.

where we introduced a systematic error through the pull parameter ξ. In principle thesystematic errors πij depend on the track momentum and the track direction. However,these have not yet been calculated for ICAL. Therefore we assume a common systematicerror for each ij bin and do our calculations for two different values, πij = 0.1 or 0.2. Wecomputed the χ2 between the data and the test event samples by

χ2 = χ2(µ−) + χ2(µ+) + ξ2, (4.2)

– 7 –

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1trackθcos

140−

120−

100−

80−

60−

40−

20−

0- µ ij

N∆ iΣ =

j- µ

N∆


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1trackθcos

50−

40−

30−

20−

10−

0

10

+ µ ij N∆ iΣ

=

j+ µ N∆


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1trackθcos

40−

30−

20−

10−

0

10

20

30

40

- µ ij N∆ iΣ

=

j- µ N∆


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1trackθcos

60−

50−

40−

30−

20−

10−

0

10+ µ ij

N∆ iΣ =

j+ µ

N∆


Figure 4. The difference between the number of muon events for matter vs. vacuum oscillations(∆Nµ∓

j ) as a function of cos θtrack. The plots in the left (right) panels are for µ−(µ+) events. Theplots in the top (bottom) panels are for ∆31 positive and negative.

where

χ2(µ−) = Σ17i=1Σ90

j=12

(N test,µ−

ij −Ndata,µ−

ij

)−Ndata,µ−

ij ln

N test,µ−

ij

Ndata,µ−

ij

(4.3)

χ2(µ+) = Σ17i=1Σ90

j=12

(N test,µ+

ij −Ndata,µ+

ij

)−Ndata,µ+

ij ln

N test,µ+

ij

Ndata,µ+

ij

, (4.4)

and a prior on the pull parameter ξ2 is added. For each test value of sin2 θ23, the minimumvalue of χ2 is computed by varying the pull parameter ξ in the range (−3, 3) in steps of0.1. We obtain the χ2 for a ten year exposure by dividing the minimum χ2 by 50. This χ2

is a measure of ICAL sensitivity to distinguish vacuum oscillations from matter oscillationswith ∆31 positive.

– 8 –

In calculating the vacuum oscillation probabilities, we held five neutrino parametersfixed. However, each of these parameters have an associated uncertainty. Varying twoof these parameters, sin2 θ12 and ∆21, has very little effect on the atmospheric neutrinooscillation probabilities. The variation in the two parameters, sin2 θ13 and ∆31, can lead toa noticeable change. Therefore we generated test event samples by varying these parametersin the following ranges:

• sin2 θ13 is varied in its 2 σ range and we computed the corresponding χ2 with theaddition of the appropriate prior. We found that the minimum χ2 occurred when thevalue of sin2 θ13 in both the matter and the vacuum oscillation probabilities is thesame.

• The variation of ∆31 is done in two steps. First we used the following two test values:2.525× 10−3 eV2 and −2.438× 10−3 eV2, which are the positive and negative best fitvalues of the global fits. We found that the minimum χ2 always occur when the signof test ∆31 matched that of input ∆31. Later we varied the magnitude of test ∆31 inits 2 σ range and computed the χ2 again with the addition of appropriate prior. Herealso, the minimum χ2 occurred when the test value is equal to the input value.

• Variation in δCP is studied later.

After calculating ICAL sensitivity to distinguish vacuum oscillations from matter oscil-lations with ∆31 positive, we repeat this calculation for the case where ∆31 is negative. Ourresults are shown in Fig:5 where the left panel is for ∆31 positive and the right panel is for∆31 negative. Each panel shows the variation of χ2 for different test values of sin2 θ23 forthree different values of the systematic error, πij = 0, 0.1, 0.2 2. We see that χ2

min = 11.8 for∆31 positive and is 9.5 for ∆31 negative. Hence, ICAL can rule out vacuum oscillations atbetter than 3 σ confidence level, if the matter effects, as prescribed by Wolfenstein [21, 22],are present. This sensitivity is there for both the signs of ∆31.

The results presented in Fig:5 assumed δCP to be zero for both matter and vacuumoscillations. However we should check the sensitivity if the test value of δCP is variedover its full range (0, 360◦). We performed this calculation where we kept the true valueof δCP = 0 for matter oscillation probabilities and considered the four test values δCP =

0, 90◦, 180◦, 270◦ for vacuum oscillations. The minimum χ2, as a function of test δCP isshown in Fig:6. We see that this marginalization over δCP has essentially no effect on theminimum χ2. The χ2

min values are 11.7 for positive ∆31 and 9.5 for negative ∆31.Recent global fits to neutrino oscillation data yield the best fit value of δCP ≈ 270◦

for both signs of ∆31 [20]. We have redone our calculations with δCP = 270◦ as our inputvalue in matter oscillation probabilities. We obtained χ2

min of 12.8 for ∆31 positive and 9.3

for ∆31 negative. Thus we see that changing the true value of δCP has only a small effecton χ2

min. We did a marginalization over the full range of the test values of δCP in this case

2For test values of sin2 θ23 > 0.6 the corresponding values of sin2 2θ23 differ from 1 significantly. In sucha situation, Pµµ (vacuum) will have measurable non-zero values near its minimum. This, we believe, is thereason for the sharp increase in χ2 for sin2 θ23 > 0.6.

– 9 –

0.4 0.45 0.5 0.55 0.6 0.65

23θ2sin

0

5

10

15

20

25

30

2 χ

positive)31∆ (23θ2 vs. sin2χ

Systematics 0.2

Systematics 0.1

Systematics 0.0

0.4 0.45 0.5 0.55 0.6 0.65

23θ2sin

0

5

10

15

20

25

30

2 χ

negative)31∆ (23θ2 vs. sin2χ

Systematics 0.2

Systematics 0.1

Systematics 0.0

Figure 5. Sensitivity of ICAL to matter vs. vacuum oscillations assuming charge identification.δCP is set equal to 0 for both matter and vacuum oscillations.

also. The minimum χ2 occurred for the test value 180◦. The values of minimum χ2 are11.8 for ∆31 positive and 9.3 for ∆31 negative.

0 50 100 150 200 250

CPδ

0

5

10

15

20

25

30

2 χ

positive)31∆ (CPδ vs. 2χ

Systematics 0.2

Systematics 0.1

Systematics 0.0

0 50 100 150 200 250

CPδ

0

5

10

15

20

25

30

2 χ

negative)31∆ (CPδ vs. 2χ

Systematics 0.2

Systematics 0.1

Systematics 0.0

Figure 6. Sensitivity of ICAL to matter vs. vacuum oscillations assuming charge identification.δCP is set equal to 0 for matter oscillations and is varied over four test values for vacuum oscillations.

It is worth exploring the role of charge identification capability of ICAL in the discrim-ination sensitivity. To do this, we combined the µ− and µ+ event samples into a singlesample and computed the χ2 between the matter and vacuum oscillated distributions. The

– 10 –

results are shown in Fig:7, which show that the sensitivity reduces a factor of 2 if the chargeidentification is not there.

0.4 0.45 0.5 0.55 0.6 0.65

23θ2sin

0

5

10

15

20

25

302 χ

positive)31∆ (23θ2 vs. sin2χSystematics 0.2

Systematics 0.1

Systematics 0.0

Systematics 0.2, without charge ID



0.4 0.45 0.5 0.55 0.6 0.65

23θ2sin

0

5

10

15

20

25

30

2 χ

negative)31∆ (23θ2 vs. sin2χSystematics 0.2

Systematics 0.1

Systematics 0.0




Figure 7. Sensitivity of ICAL to matter vs. vacuum oscillations assuming no charge identifi-cation

5 Conclusions

In this paper, we have considered the sensitivity of ICAL at INO to make a distinction be-tween matter modified oscillations and vacuum oscillations in atmospheric neutrino data.We find that a ten year exposure leads to a better than 3 σ sensitivity, whether ∆31 is pos-itive or negative. The difference between the matter and vacuum oscillations is significantfor neutrinos if ∆31 is positive and for anti-neutrinos if ∆31 is negative. Hence, the chargeidentification capability of ICAL has an important role in giving rise to such good sensitiv-ity. This sensitivity is independent of the true value of δCP. With no charge identification,the sensitivity is reduced by half.

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