Advances in High Energy Physics
Volume 2018 (2018), Article ID 2547358, 11 pages
https://doi.org/10.1155/2018/2547358

Research Article

Degeneracy Resolution Capabilities of NOνA and DUNE in the Presence of Light Sterile Neutrino

Akshay Chatla,¹ Sahithi Rudrabhatla,² and Bindu A. Bambah¹

¹School of Physics, University of Hyderabad, Hyderabad 500046, India
²Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA

Correspondence should be addressed to Akshay Chatla; chatlaakshay@gmail.com

Received 10 April 2018; Accepted 15 August 2018; Published 6 September 2018

Academic Editor: Hiroyasu Ejiri

Copyright © 2018 Akshay Chatla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

Abstract.

We investigate the implications of a sterile neutrino on the physics potential of the proposed experiment DUNE and future runs of NOA using latest NOA results. Using combined analysis of the disappearance and appearance data, NOA reported preferred solutions at normal hierarchy (NH) with two degenerate best-fit points: one in the lower octant (LO) and = 1.48 and the other in higher octant (HO) and = 0.74. Another solution of inverted hierarchy (IH), which is 0.46 away from best fit, was also reported. We discuss chances of resolving these degeneracies in the presence of sterile neutrino.

1. Introduction

Sterile neutrinos are hypothetical particles that do not interact via any of the fundamental interactions other than gravity. The term sterile is used to distinguish them from active neutrinos, which are charged under weak interaction. The theoretical motivation for sterile neutrino explains the active neutrino mass after spontaneous symmetry breaking, by adding a gauge singlet term (sterile neutrino) to the Lagrangian under where the Dirac term appears through the Higgs mechanism, and Majorana mass term is a gauge singlet and hence appears as a bare mass term [1]. The diagonalization of the mass matrix gives masses to all neutrinos due to the See-Saw mechanism.

Some experimental anomalies also point towards the existence of sterile neutrinos. Liquid Scintillator Neutrino Detector (LSND) detected transitions indicating which is inconsistent with (LSND anomaly) [2]. Measurement of the width of Z boson by LEP gave number of active neutrinos to be [3]. Thus the new neutrino introduced to explain the anomaly has to be a sterile neutrino. MiniBooNE, designed to verify the LSND anomaly, observed an unexplained excess of events in low-energy region of spectra, consistent with LSND [4]. SAGE and GALLEX observed lower event rate than expected, explained by the oscillations of due to (Gallium anomaly) [5–7]. Recent precise predictions of reactor antineutrino flux have increased the expected flux by 3% over old predictions. With the new flux evaluation, the ratio of observed and predicted flux deviates at 98.6% C.L (Confidence level) from unity; this is called “reactor antineutrino anomaly” [8]. This anomaly can also be explained using sterile neutrino model.

Short-baseline (SBL) experiments are running to search for sterile neutrinos. SBL experiments are the best place to look for sterile neutrino, as they are sensitive to new expected mass-squared splitting . However, SBL experiments cannot study all the properties of sterile neutrinos, mainly new CP phases introduced by sterile neutrino models. These new CP phases need long distances to become measurable [9, 10] and thus can be measured using long baseline (LBL) experiments. With the discovery of relatively large value for by Daya Bay [11], the sensitivity of LBL experiments towards neutrino mass hierarchy and CP phases increased significantly. In this context, some phenomenological studies regarding the sensitivity of LBL experiments can be found in recent works [12–16]. Using recent global fits of oscillation parameters in the 3+1 scenario [17], current LBL experiments can extract two out of three CP phases (one of them being standard ) [10]. The phenomenological studies of LBL experiments in presence of sterile neutrino is studied by several groups [18–23]. Now, the sensitivity of LBL experiments towards their original goals decreases due to sterile neutrinos. It is seen in case of the CPV measurement; new CP phases will decrease the sensitivity towards standard CP phase (). This will reduce degeneracy resolution capacities of LBL experiments. In this paper, we study hierarchy-- degeneracies using contours in - plane and how they are affected by the introduction of sterile neutrinos. We attempt to find the extent to which these degeneracies can be resolved in future runs of NOA and DUNE.

The outline of the paper is as follows. In Section 2, we present the experimental specifications of NOA and DUNE used in our simulation. We introduce the effect of sterile neutrino on parameter degeneracies resolution in Section 3. Section 4 contains the discussion about the degeneracy resolving capacities of future runs of NOA and DUNE assuming latest NOA results—NH- (normal hierarchy-) LO (lower octant); NH-HO (higher octant); and IH- (inverted hierarchy-) HO—as true solutions for both 3 and 3+1 models. Finally, Section 5 contains concluding comments on our results.

2. Experiment Specifications

We used GLoBES (General Long Baseline Experiment Simulator) [24, 25] to simulate the data for different LBL experiments including NOA and DUNE. The neutrino oscillation probabilities for the 3+1 model are calculated using the new physics engine available from [26].

NOA [27, 28] is an LBL experiment which started its full operation from October 2014. NOA has two detectors: the near detector is located at Fermilab (300 ton, 1 km from NuMI beam target) while the far detector (14 Kt) is located at Northern Minnesota 14.6 mrad off the NuMI beam axis at 810 km from NuMI beam target, justifying “off-axis” in the name. This off-axis orientation gives us a narrow beam of flux, peak at 2 GeV [29]. For simulations, we used NOA setup from [30]. We used the full projected exposure of p.o.t (protons on target) expected after six years of runtime at 700 kW beam power. Assuming the same runtime for neutrino and antineutrino modes, we get p.o.t for each mode. Following [31] we considered 5% normalization error for the signal and 10% error for the background for appearance and disappearance channels.

DUNE (Deep Underground Neutrino Experiment) [32, 33] is the next generation LBL experiment. Long Base Neutrino Facility (LBNF) of Fermilab is the source for DUNE. Near detector of DUNE will be at Fermilab. Liquid Argon detector of 40 kt to be constructed at Sanford Underground Research Facility, situated 1300 km from the beam target, will act as the far detector. DUNE uses the same source as of NOA; we will observe beam flux peak at 2.5GeV. We used DUNE setup give in [34] for our simulations. Since DUNE is still in its early stages, we used simplified systematic treatment, i.e., 5% normalization error on signal and 10% error on the background for both appearance and disappearance spectra. We give experimental details described above in tabular form in Tables 1 and 2.

Table 1: Details of experiments.

Name of Exp
NOA
DUNE

Location
Minnesota
South Dakota

POT()
x
x

Baseline(Far/Near)
812 km/1km
1300 km/500 m

Target mass(Far/Near)
14 kt/290 t
40 kt/8 t

Exposure(years)
6
10

Detector type
Tracking Calorimeters
LArTPCs

Table 2: Systematic errors associated with NOA and DUNE.

Name of Exp
Rule
Normalization error

signal(%)
background(%)

NOA
appearance
5
10

disappearance
2
10

appearance
5
10

disappearance
2
10

DUNE
appearance
5
10

disappearance
5
10

appearance
5
10

disappearance
5
10

Oscillation parameters are estimated from the data by comparing observed and predicted and interaction rates and energy spectra. GLoBES calculates event rates of neutrinos for energy bins taking systematic errors, detector resolutions, MSW effect due to earth’s crust, etc. into account. The event rates generated for true and test values are used to plot contours. GLoBES uses its inbuilt algorithm to calculate values numerically considering parameter correlations as well as systematic errors. In our calculations we used as

where are the event rates for the bin in the detectors of different experiments, calculated for true values of oscillation parameters; are the expected event rates for the bin in the detectors of different experiments for the test parameter values; are the uncertainties associated with the flux and detector mass; and are the respective associated standard deviations. The calculated function gives the confidence level in which tested oscillation parameter values can be ruled out with referenced data. It provides an excellent preliminary evaluation model to estimate the experiment performance.

3. Theory

In a 3+1 sterile neutrino model, the flavour and mass eigenstates are connected through a 4 4 mixing matrix. A convenient parametrization of the mixing matrix is [36]

Here and represent real and complex 4 4 rotation in the plane containing the 2 2 subblock in (i, j) subblock

where, , , , and are the CP phases.

There are three mass-squared difference terms in 3+1 model: (solar), (atmospheric), and (sterile). The mass-squared difference term towards which the experiment is sensitive depends on L/E of the experiment. Since SBL experiments have a very small L/E, for and . term survives. Hence, SBL experiments depend only on sterile mixing angles and are insensitive to the CP phases. The oscillation probability, for LBL experiments in 3+1 model, after averaging oscillations and neglecting MSW effects, [37] is expressed as sum of the four terms

These terms can be approximately expressed as follows:

with the parameters defined as

The CP phases introduced due to sterile neutrinos persist in the even after averaging out lead oscillations. Last two terms of (4) give the sterile CP phase dependence terms. depends on the sterile CP phases and , while depends on a combination of and . Thus, we expect LBL experiments to be sensitive to sterile phases. We note that the probability is independent . One can see that will effect if we consider earth mass effects. Since matter effects are relatively small for NOA and DUNE, their sensitivity towards is negligible. The amplitudes of atmospheric-sterile interference term (8) and solar-atmospheric interference term (6) are of the same order. This new interference term reduces the sensitivity of experiments to the standard CP phase ().

In Figure 1, we plot the oscillation probability () as a function of energy while varying (-180° to 180°) and keeping for the three best-fit values of latest NOA results [35], i.e., NH-LO-1.48[], NH-HO-0.74, and IH-HO-1.48, where HO implies and LO implies . For the flux peak of NOA, E 2GeV, we observe a degeneracy between all best-fit values due to the presence of band for neutrino case, while only NH-HO and IH-HO bands overlap in antineutrino case. We see that phase decreases both octant and hierarchy resolution capacity for neutrino case and only mass hierarchy resolution capacity for antineutrino case. The second row plots for DUNE at baseline 1300 km. We observe smaller overlap between bands compared to NOA. Thus, the decrease of degeneracy resolution capacity for DUNE is less than NOA. Similarly we plot while varying (-180° to 180°) in Figure 2 and keeping . We see that has similar effect to that of ; the only change is reversal of band extrema; i.e., gives the same result as and vice versa. This can be explained using (4) in which we see and are always together with opposite signs. Overall from the probability plots, we observe that the addition of new CP phases decreases octant and mass hierarchy resolution capacities.

Figure 1: The oscillation probability as a function of energy. The top (bottom) panel is NOA (DUNE). The bands correspond to different values of , ranging from -180° to 180° when . Inside each band, the probability for = 90° ( = -90°) case is shown as the solid (dashed) line. The left (right) panel corresponds to neutrinos (antineutrinos).

Figure 2: The oscillation probability as a function of energy. The top (bottom) panel is NOA (DUNE). The bands correspond to different values of , ranging from -180° to 180° when . Inside each band, the probability for = 90° ( = -90°) case is shown as solid (dashed) line. The left (right) panel is for neutrinos (antineutrinos).

In the next section, we explore how parameter degeneracies are affected in the 3+1 model and the extent to which these degeneracies can be resolved in future runs of NOA and DUNE.

4. Results for NOA and DUNE

We explore allowed regions in - plane from NOA and DUNE simulation data with different runtimes, considering latest NOA results as true values. Using combined analysis of the disappearance and appearance data, NOA reported preferred solutions [35] at normal hierarchy (NH) with two degenerate best-fit points: one in the lower octant (LO) and and the other in higher octant (HO) and . Another solution of inverted hierarchy (IH), 0.46 away from best fit, is also reported. Table 3 shows true values of oscillation parameters and their marginalization ranges we used in our simulation. By studying the allowed regions, we understand the extent to which future runs of NOA and DUNE will resolve these degeneracies, if the best-fit values are true values.

Table 3: Oscillation parameters considered in numerical analysis. The and are taken from latest NOA results [35].

Parameter
True value
Marginalization Range

0.304
Not Marginalized

0.085
0.075,0.095]

0.623(HO),0.404(LO)
0.32,0.67]

0.025
Not Marginalized

0.025
Not Marginalized

0.025
Not Marginalized

135(NH-HO),-90(NH-LO,IH)
-180,180]

-180,180]
-180,180]

-180,180]
-180,180]

e
Not Marginalized

(NH)
e
Not Marginalized

(IH)
e
Not Marginalized

1 e
Not Marginalized

In the first row of Figure 3, we show allowed areas for NOA3+]. In first plot of first row, we show 90% C.L allowed regions for true values of and and normal hierarchy. We plot test values for both NH and IH, of 3 and 3+1 neutrino models. We observe that introducing sterile neutrino largely decreases the precision of . The WO-RH region, for 3 case confined between and of , confines the whole region for 4 case. The WH-RO region of 3 case doubles, covering the entire region of for 4 case. The 3+1 model also introduces a small WH-WO region, which was absent in 3 model. In the second plot of first row (true value , and normal hierarchy), for the 3 case, we see RH-RO region excluding to of , while RH-WO region covers the whole of the region. In 3+1 model, both RH-RO and RH-WO regions cover the whole of the region. WH-RO solution occupies a small region for 3 case, covering half of region for 4 case. WH-WO region covers the whole of the region for 4 case. In the third plot of first row, true values are taken as , and inverted hierarchy. The RH-RO region covers the entire range of for both 3 and 4 case, whereas RH-WO region almost doubles from 3 case to 4 case. A small range of excluded from WH-RO for 3 case is covered in 4 case. WH-WO region of 3 case excludes to of while full range is covered for 4 case.

Figure 3: Contour plots of allowed regions in the test plane, versus , at 90% C.I with top, middle, and bottom rows for NOA runs of , and years, respectively.

In the second row of the figure, we plot allowed regions for NOA3+]. We take true values as best-fit points obtained by NOA. We observe an increase in precision of parameter measurement, due to an increase in statistics, from added 1 yr of antineutrino run. In the first plot of the second row, the RH-RO octant region covers entire range for both 3 and 4 case. RH-WO region includes to of for 3 case, while the whole range of is covered in 4 case. A slight increase in the area of WH-RO is observed form 3 to 4 case. 4 introduces WH-WO region which was resolved for 3 case. In the second plot, RH-RO region allows full range of for 4 case, while it was restricted to lower half of CP range in 3 case. We see that WH-RO solution, which was resolved in 3 case, is reintroduced in 4 case. We also see a slight increase in the size of WH-WO solution from 3 to 4. In third plot, RH-RO region covers the whole CP range for 4 while to of are excluded in 3 case. The almost resolved RH-WO solution for 3 doubles for 4 case. WH-RO and WH-WO cover the entire region of for 4 case.

In the third row, we show allowed regions for NOA3+]. In the first plot, it can be seen that small area of RH-WO in case of 3 now covers the whole of region for 4 case. While the 3 case has WH-W degeneracy, 4 case introduces equal sized WH-WO-W degeneracy. In second plot, for 3 case most of values above are excluded, but for 4 case we see that contour covers the whole of range. Already present small area of RH-WO of 3 is also increased for 4 case. 4 case also introduces a small region of WH solutions which were not present in 3 case. In the third plot, we see that 4 introduces RH-WO region of the almost equal size of RH-RO region of 3 case. We observed a slight increase in WH-RO region for 4 over 3 case, while the WH-WO region almost triples for 4 case.

In Figure 4, we show allowed parameter regions for DUNE experiment for different runtimes. DUNE, being the next generation LBL experiment, is expected to have excellent statistics. Hence, we plot 99% C.L regions for DUNE. In the first row of Figure 4, we show 99% C.L for DUNE1+]. In the first plot, RH-RO region covers the entire range for both 3 and 4 case. The RH-WO region which covers only lower half of region for 3 case covers the whole range for 4 case. A small region of WH is also observed. In the second plot we see that all WH solutions are resolved. RH-WO covers the whole range of for both 3 and 4 case. RH-RO solutions exclude to of for 3 case, while to of are excluded for 4 case. In third plot, we see that 4 case extends RH-RO to the whole range of while to of were excluded for 3 case. We can see that DUNE clearly has better precision than NOA experiment. In the second row, we show allowed regions for DUNE1+]. We see the WH solutions are resolved for both 3 and 4 cases for all the best-fit values. In the first plot, 4 case introduces RH-WO solution of similar size as RH-RO region of 3 case. In the second plot, there is no considerable change in 4, compared to 3 case for RH-RO region, while RH-WO octant is approximately doubled for 4 case compared to 3 case. In the third plot, 4 case introduces small region of RH-WO which covers to of . In the third row, we combine statistics of DUNE1+] and NOA3+]. There is a small improvement in precision from the combined result over the result from DUNE1+] alone. In the first plot, we see that a small RH-WO region is introduced by 4 case. In the second plot, there is no considerable change between 3 and 4 case for RH-RO region, while RH-WO octant almost doubles over 3 case for 4 case. In the third plot, 4 case introduces small region of RH-WO which covers to of .

Figure 4: Contour plots of allowed regions in the test plane versus at 99% C.L with top, middle, and bottom rows for DUNE runs of years and DUNE]+NOA], respectively.

In Figure 5, we show allowed parameter regions for DUNE experiment, at 99% C.L for DUNE5+]. We see that WH regions completely disappear for all the true value assumptions. In the first plot, RH-RO region covers a small range for both 3 and 4 case indicating high precision measurement capacity of DUNE. We see that range for 4 case is approximately doubled as compared to the 3 case. A small region of RH-WO is observed for 4 case. In the second plot, RH-RO region covers small range of equal area for both 3 and 4 case. A small region of RH-WO is observed for 4 case. In the third plot, the RH-WO solution is resolved. There is an increase in precision due to an increase in statistics. DUNE5+] clearly has a better precision compared to the NOA3+] experiment. In the second row, we combine full run of NOA and DUNE to check their degeneracy resolution capacity. The WH solutions are resolved for both 3 and 4 cases for all the best-fit values. In the first plot, RH-WO solution is almost resolved for 4 case. In the second plot, RH-RO region covers small range of equal area for both 3 and 4 case. A small region of RH-WO is observed for 4 case. We observe a slight improvement in degeneracy resolution, on consideration of combined statistics of full run DUNE and NOA, over DUNE5+].

Figure 5: Contour plots of allowed regions in the test plane versus at 99% C.L with top and bottom rows for DUNE[] and NOA[] + DUNE[], respectively.

5. Conclusions

We have discussed how the presence of a sterile neutrino will affect the physics potential of the proposed experiment DUNE and future runs of NOA, in the light of latest NOA results [35]. The best-fit parameters reported by NOA still contain degenerate solutions. We attempt to see the extent to which these degeneracies could be resolved in future runs for the 3+1 model. Latest NOA best-fit values are taken as our true values. First, we show the degeneracy resolution capacity, for future runs of NOA. We conclude that NOA3+] could resolve WH-WO solutions for first two true value cases, at 90% C.L for 3 case, but not for 4 case. DUNE1+] could resolve WH and RH-W solutions for both 3 and 4 case. WO degeneracy is resolved for 3 case at 99% C.L except for small RH-WO region for the second case of true values. DUNE1+] combined with NOA3+] shows increased sensitivity towards degeneracy resolution. Finally, for the full planned run of DUNE5+], all the degeneracies are resolved at 99% C.L for 3 case while a tiny region of WO lingers on for 4 case. For combined statistics of DUNE5+] and NOA3+], we observe that all the degeneracies are resolved at 99% C.L for both 3 and 4 case except for the NH-LO case. Thus, we conclude that NOA and DUNE experiments together can resolve all the degeneracies at 99% C.L even in the presence of sterile neutrino, if one of the current best-fit values of NOA is the true value.

Data Availability

The data used to support the findings of this study are based on published data and licensed open access software.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

Akshay Chatla would like to thank the Council of Scientific & Industrial Research, Government of India, for financial support. The work of Sahithi Rudrabhatla was supported by theDepartment of Science & Technology, Government of India. We would like to thank Dr. Monojit Ghosh, Dr. C Soumya, and K Siva Prasad for their valuable help.

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