Neutrino Mass Hierarchy in Future Long-baseline Experiments

Sanjib Kumar Agarwalla

Instituto de Fısica Corpuscular, CSIC-Universitat de Valencia, Apartado de Correos 22085, E-46071 Valencia, Spain

Abstract

In this talk, we discuss the prospects of determining the neutrino mass hierarchy in future long-baseline oscillationexperiments in the light of recently discovered moderately large value of θ13.

Keywords: Neutrino mass hierarchy, Long-baseline experiments

1. Introduction and Motivation

Our knowledge of the 1-3 lepton mixing angle θ13 hasenhanced quite a lot in last one year or so and finally ithas been discovered by the reactor experiments DayaBay [1] and RENO [2] with unprecedented confidence.They have found a reasonably large value of 1-3 mixing:sin2 2θ13|DayaBay = 0.089±0.010 (stat)±0.005 (syst) [3],and sin2 2θ13

∣∣∣RENO

= 0.113 ± 0.013 (stat) ± 0.019 (syst)[4], in agreement with the measurements performed ear-lier by T2K [5, 6], MINOS [7, 8], and Double Chooz[9, 10] experiments. Combined analyses of all the neu-trino oscillation data available [11, 12, 13] imply a non-zero value of θ13 at more than 10σ and predict a best-fitvalue of sin2 θ13 � 0.023 with a relative 1σ precisionof 10%. This large value of θ13 opens the window todirectly determine the neutrino mass hierarchy1 (NMH)using the Earth matter effects in accelerator based long-baseline neutrino oscillation experiments [14].

Settling the issue of NMH is very important in or-der to determine the structure of neutrino mass ma-trix which in turn can give crucial piece of informationtowards the underlying theory of neutrino masses andmixing [15]. This is also a key ingredient for neutrino-less double beta decay searches probing the Majorananature of neutrinos. If Δm2

31 < 0, and yet no neutri-noless double beta decay is observed even in the very

1Two possibilities are there: it can be either normal (NH) ifΔm2

31 ≡ m23 − m2

1 > 0, or inverted (IH) if Δm231 < 0.

far future experiments, that would be a strong evidencethat neutrinos are not Majorana particles [16]. With therecent discovery of large value of θ13, it seems that thefundamental measurement of NMH is not a dream any-more.

2. Present Generation Experiments: T2K & NOνA

The experiments T2K [17, 6] & NOνA [18, 19] ex-pect to probe NMH by measuring the νμ → νe oscilla-tion probability Pμe and its charge conjugate νμ → νeoscillation probability Pμe. Since these experimentshave moderately long-baselines (295 km for T2K and810 km for NOνA), the matter effects due to neutrinopropagation through the Earth are important. The matterterm modifies Pμe (and also Pμe) differently for NH andfor IH. Matter effects increase Pμe for NH and decreaseit for IH and vice verse for Pμe. For δCP in the lowerhalf-plane (LHP, −180◦ ≤ δCP ≤ 0), Pμe is larger andfor δCP in the upper half-plane (UHP, 0 ≤ δCP ≤ 180◦),Pμe is smaller. Hence, for the combination (NH, LHP),the values of Pμe are much higher than those for IH (andPμe values are much lower). Similarly, for the combina-tion (IH, UHP), the values of Pμe are much lower thanthose of NH (and Pμe values are much higher). Thus,LHP is the favourable half-plane for NH and UHP is forIH.

The combined data from presently running T2K (5years of ν run) and upcoming NOνA (3 years of ν + 3

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years of ν run) can resolve the NMH for 55% (45%) ofthe allowed values of true δCP at 90% (95%) C.L. if NHis the true hierarchy [20]. The addition of a 5 kt liquidargon detector placed close to NOνA site and exposedto the NOνA beam would increase the CP coverage forNMH. It is shown in [20] that combined data from 5 ktliquid argon detector (3 years of ν + 3 years of ν run),NOνA (6 years of ν + 6 years of ν run) and T2K (5 yearsof ν run) can give 90% C.L. hint of hierarchy discoveryirrespective of the true hierarchy and δCP. These resultsare obtained with the true value of sin2 2θ13 = 0.1 andthe true value of sin2 θ23 = 0.5.

3. Option for Next Generation LBL Experiments

One of the main goals of the next generation long-baseline experiments is to provide a more than 5σ dis-covery of NMH for 100% values of true δCP and forboth the choices of true hierarchy. There are several fu-ture long-baseline neutrino oscillation experiments arein R&D phase or under discussion world-wide. For thesake of discussion, we can classify these experimentalproposals into two categories: the experimental set-upswith baselines < 1000 km and > 1000 km.

The baseline choices which are smaller than 1000 kmare: a) CERN to Frejus (130 km) [21], b) J-PARC toKamioka (295 km) [22], c) CERN to Canfranc (630 km)[23], and d) CERN to Gran Sasso (730 km) [24]. Veryhigh power intense neutrino beam (1.5 to 4 MW) andlarge size water Cherenkov detector (∼ fiducial mass of500 kton) are the key and common components of theseexperimental proposals. Since the Earth matter effect isnot large enough for these experimental set-ups, noneof these future facilities would be able to provide > 5σdiscovery of NMH for all the allowed values of true δCP.

The baselines which are above 1000 km and are be-ing studied actively are CERN to Pyhasalmi (2290 km)[25] and Fermilab to Homestake (1290 km) [26]. TheLBNO collaboration in Europe is pursuing the feasi-bility study of an experimental set-up where neutrinosproduced in a conventional wide-band beam facility atCERN would be observed in a proposed 20 kton LiquidArgon detector at the deep underground of Pyhasalmimine (∼ 4000 m.w.e), at a distance of 2290 km. Dueto the strong matter effects and the high detection effi-ciency at both the first and second oscillation maxima,this particular setup would have unprecedented sensi-tivity to the neutrino mass ordering. With an exposureof 2.25 × 1020 protons on target (p.o.t) from the SPSmachine at 400 GeV, a conclusive determination (> 5σC.L.) of the NMH is possible for any value of δCP. With3.75×1020 p.o.t which is four times smaller compared to

LBNE

2

δ (true)

χ

CP

σ

σ

5

10

Mass Hierarchy Discovery, NH true

LBNO

4 times small LBNO

2 times small LBNO

Δ

10 90 0−90−180

1000

100

180

Figure 1: Mass hierarchy discovery as a function of true value of δCP.

the full run of LBNO, a 10σ NMH discovery is achiev-able with the CERN - Pyhasalmi set-up. On the otherhand, in the United States, the LBNE collaboration isexploring the prospects of sending a wide-band neu-trino beam from Fermilab to Homastake, at a distanceof 1290 km. As the LBNE proposal stands now, theyare planning to build a 10 kton LArTPC which will beplaced on surface. In this proposal, a neutrino beamwith a power of 700 kW which delivers 6 × 1020 p.o.twith 120 GeV proton beam energy has been consideredand they have plans for 5 years of ν run and 5 years ofν run. With the full run of LBNE, one can expect tohave a 5σ NMH discovery for 85% values of δCP. Fig.1 (taken from [27]) shows the comparison between theLBNO and LBNE facility for the NMH discriminationsensitivity as a function of the true value of δCP.

In [28], we have explored a new strategy to deter-mine the NMH that employs a superbeam with an av-erage neutrino energy of ∼ 5 GeV, as those being pro-posed at CERN, focused towards the existing and well-understood Super-Kamiokande detector, 8870 km away.We have shown that the neutrino beam resulting from aproton source with a total exposure of 5.4 × 1021 p.o.tcan reveal the NMH at 5σ irrespective of the true hi-erarchy and CP phase. This measurement relies on thenear resonant matter effect in the νμ → νe oscillationchannel, and can be done counting the total number ofappearance events with just a neutrino beam.

S.K. Agarwalla / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 196–198 197

4. Other Probes of Neutrino Mass Hierarchy

Large value of θ13 allows us to explore NMH withatmospheric neutrinos using the resonant Earth mattereffects. The proposed iron calorimeter detector at INOfacility [29], IceCube Deepcore and PINGU [30] are theinteresting future possibilities to explore NMH with at-mospheric neutrinos. Cosmology can also weigh neutri-nos with precision and future CMB and LSS cosmolog-ical measurements have a chance to determine the lightneutrino spectrum [31].

5. Conclusions

Recent discovery of large θ13 has created a lot of ex-citement in neutrino physics. The neutrino mass hier-archy is one of the fundamental unsolved issues in theneutral lepton sector and in the light of large θ13, boththe LBNO and LBNE experimental set-ups would beable to settle this issue with > 5σ confidence level.

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