JHEP07(2018)079 Springer July 4, 2018 May 4, 2018 July 28, 2017 July 11, 2018 Boson

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JHEP07(2018)079 Springer July 4, 2018 May 4, 2018 July 28, 2017 July 11, 2018 boson. This : : : : Z Revised Accepted Received Published , through the observation of 34 [email protected] θ , a Published for SISSA by https://doi.org/10.1007/JHEP07(2018)079 and Stephen J. Parke b,c [email protected] , . 3 1707.05348 David V. Forero The Authors. a c Beyond Standard Model, Neutrino Physics, CP violation

Light sterile neutrinos can be probed in a number of ways, including elec- , [email protected] Instituto de Gleb F´ısica Wataghin —13083-859, UNICAMP, Campinas, SP, Brazil Center for Neutrino Physics,Blacksburg, Virginia VA Tech, 24061, U.S.A. E-mail: Theoretical Physics Department, Fermi NationalP.O. Accelerator Laboratory, Box 500, Batavia, IL 60510, U.S.A. b c a Open Access Article funded by SCOAP Keywords: ArXiv ePrint: constrain the mixing angle whichneutral-current parametrizes events this at mixing, the farnificantly detector. over current We find constraints thanks that to DUNEbetween its will neutral- large be and statistics able charged-current and to events. excellent improve discrimination sig- neutral-current data sample is expectedchannel since offers they a do direct notneutrino, avenue interact to which with is probe the currently only the weakly mixingand constrained between by NOvA, current a data however, sterile from these SuperK, neutrinoby constrains IceCube and these will the experiments. continue tau to In improve this as work, more we data study is the collected potential of the DUNE experiment to Abstract: troweak decays, cosmology andiments, neutrino the oscillation neutral-current experiments. datatrinos: At is long-baseline directly once exper- sensitive the to active the neutrinos presence have of oscillated light into sterile a neu- sterile state, a depletion in the Pilar Coloma, DUNE sensitivities to thetau mixing neutrinos between sterile and JHEP07(2018)079 ] ], 10 15 18 , , 14 17 [ 4 µ ] for recent U 2 , 1 ], reactor [ 12 13 , 6= 0 . Hence, if there are 14 Z 12 34 , θ 24 θ 3 ] for a detailed discussion of these 10 , 9 ], MiniBooNE [ parameter space 11 34 θ − – 1 – 24 θ ). Light sterile neutrinos can lead to observable 11 ], see e.g., refs. [ 8 sterile – = 0 16 3 24 θ ]. The current and next generation of oscillation experiments 16 , for 34 θ 18 1 18 7 -function 2 In recent years, the eV-scale has recently been put on the spot due to a set of experimen- parametrization χ 4.3 Expected allowed regions in the 4.1 Sensitivity to 4.2 Rejection power for the three-family hypothesis, for tal anomalies independently reportedand in Gallium LSND experiments [ [ will attempt to refuteimpressive limits or on confirm the these mixing between hints. sterile neutrinos The and muon Icecube neutrinos experiment has recently put beta decay and chargedglobal lepton fits flavor using violating these transitionsthey observables). (see are Nevertheless, kinematically e.g., if accessible refs. their inenergies [ masses these and are processes, the light bounds unitarity enough from isare so electroweak effectively derived processes from restored that oscillation fade at data away. low [ constraints. In this case the best limits LEP data places severeadditional neutrinos constraints below on the electroweak the scale,weak they invisible cannot bosons couple decay to (i.e., of the they Standard the phenomena Model should in be a numberof of the electroweak leptonic processes mixing through matrix, their including impact meson on decays, the muon decay, unitarity neutrinoless double 1 Introduction In the pastconstrain decade, scenarios a with tremendous experimental additional effort neutrinos has with been masses carried below out the in electroweak order scale. to B 5 Summary and conclusions A Complete expressions for the relevant mixing matrix elements in our 3 Simulation 4 Results Contents 1 Introduction 2 Oscillation probabilities in the 3 + 1 framework JHEP07(2018)079 ∼ 34 θ 2 41 m 18 (at . and 0 ] (among < 24 21 θ 2 events at the | 4 τ τ ν U | oscillations driven τ ν flux has oscillated into A non-zero → µ µ 1 ν ν ] or STEREO [ ]. beam. 4 [ 20 τ ν 2 has been obtained by combining IceCube 1 eV . 34 However, to the best of our knowledge θ have been set by the Daya Bay exper- 2 ]. Future long-baseline experiments, with can be derived from the observation of 4 ]. e 116 (at 90% CL) for an active-sterile mass- . τ ]. Conversely, placing equally competitive U 28 36 0 . ν , – 2 ]. However, the constraint is given for a specific value 23 [ < 27 24 – 2 – 30 2 2 , | | 4 9 4 τ µ ]. On the other hand, a more direct test for the U U | | 2 25 2 | | 4 4 ]. However, their results are severely limited by statistics, µ e U U | | 26 [ 15 (at 90% CL) for an active-sterile mass splitting equal to ]. 2 . 0 37 < 1 eV . 2 | ]. Previous studies of sterile neutrino oscillations using the DUNE far 4 τ 29 U | parameter space [ ] and short baseline data in ref. [ 34 θ 18 charged-current cross section is still low at multi-GeV neutrino energies. τ ]. In the near future, experiments such as SOX [ ν ] while the Super-Kamiokande experiment have set the bound 19 18 ]. A joint analysis of Bugey-3, Daya Bay and MINOS data has also been performed [ we refer the reader to ref. [ 2 22 Alternatively, the mixing between sterile neutrinos and tau neutrinos can be tested Indirect constraints on the mixing with An important constraint on the tau-sterile mixing angle For a sensitivity study using the DUNE near detector to probe sterile neutrino oscillations at ∆ 2 1 2 benchmark to conduct a search for sterile neutrino mixing using neutral-currentDeepCore data. data [ of the sterile mass squared difference larger than1eV 1 eV the neutral-current data sample hasArgon not detector been technology considered has in excellentvery any particle good of identification these discrimination capabilities works. power and betweenthe The therefore charged- statistics liquid a and collected neutral-current at events. DUNEthe In will addition, number exceed considerably of (by a events rough collected order of at magnitude) MINOS or NOvA. Thus, DUNE offers an excellent competitive constraints using this approach [ larger detectors, more powerful beams andbe a better able control to of systematic pushDUNE uncertainties, these experiment may [ limits even further.detector data In can be this found, work, e.g., we in refs. focus [ on the potential of the squared splitting above 0 since the at long-baseline experiments searchingat for the a far depletion detector. in In the fact, neutral-current both event the rates MINOS and the NOvA experiments have provided experiments. At long-baselinetau experiments neutrinos most by of the time theby it initial the reaches atmospheric the far mass-squared detector,impact splitting. of thanks sterile The to neutrinos OPERA on this experimentfar oscillation detector, channel, has setting using constrained the charged-current bound the 4 90% CL) for anactive-sterile active-sterile mixing mass produces splitting strikingcascade signatures above in events 0 the in zenith IceCubeto and DeepCore, probe energy and distribution the of aftermixing some between years sterile neutrinos of and data tau taking neutrinos it can is be possible performed using long-baseline limits on the mixing withchallenges tau associated neutrinos to is the a production much and more detection difficult of task, a duematter to effects the in technical atmospherichave neutrino set oscillations. the For limit example,1 the eV IceCube experiment iment [ others) will constrain furtherneutrino the mixing program with at electron Fermilabnos neutrinos, will [ while tighten the the short-baseline to bounds constrain on the the cross-product mixing with muon neutri- while in the electron sector strong bounds on JHEP07(2018)079 , , 2 k 4 m . (2.1) ]. If a − A } 2 4 ) 19 τ m ν occurs for a ≡ → k µ is the neutral- 2 4 µ ν ν m ( NC ν P σ and e ) + ν ’s similar to what Daya µ disappearance as well as ν 2 µ m ν → µ , ν ( and } we derive the oscillation proba- ) e P s ν channel. Here, 2 ν s ) + ν e → ν , µ → i ν ( → ν µ ν ∗ P µ αi ν U ( − – 3 – P 1 = { { α ν 4. In this work we are interested in the effect of NC NC ν ν , σ σ 3 oscillation channels at the far detector of long-baseline µ µ , , then searches using ν ν s 2 τ summarizes the main features of the DUNE experiment ¯ ν φ φ , ν 3 1 (i.e., assuming no beam contamination from other neutrino disappearance search for sterile neutrinos, see ref. [ = = → e µ ≡ µ ν ν ν τ NC i φ N and ¯ beam will not constrain such sterile-tau mixing. + and s µ ν ν µ NC N → we summarize and draw our conclusions. Some useful expressions for the , in this paper we consider a broader range of ∆ µ + 3. Given the values of the neutrino energy and distance corresponding to 2 5 ν , e, µ, τ, s 2 , e ]. NC that changes from the flavor to the mass basis in the 3 + 1 neutrino framework ≡ N 28 4 unitary matrix: = 1 U α = × of 0.1 eV k In addition to the standard solar and atmospheric mass-squared differences, in the 3+1 The manuscript is organized as follows. In section Although current hints of sterile-active neutrino mixing with 2 NC appearance in a m N e channel [ framework the oscillation probabilitieswith depend on three newthe splittings far ∆ detector at DUNE, for illustration purposes we can effectively neglect the solar current cross section for theIn active the neutrinos, absence which is ofand independent near a of detectors sterile up the to neutrino neutrino,detector a flavor. mass, the known normalization efficiency, NC factor and event comingsites. the from rates In different the should fact, different geometric distance, be the acceptanceefficient combined the of cancellation fit same the of between beam systematic at near at errors the and the associated far far two detector to data the should flux provide and a cross very section in this and is therefore sensitive to oscillations in the Assuming that nosearching oscillations for have a taken depletion in placewith the respect at number to of the the neutral-currentmuon near (NC) prediction neutrinos detector, events obtained with at this flux using theflavors), near far can the detector detector be number data. of done NC For events a at perfect the far beam detector of can be expressed as: matrix is a 4 where oscillations into sterile states on the event rates measured at the DUNE far detector. 2 Oscillation probabilities inIn the this section 3 we + derive 1 approximatebe expressions framework for useful the oscillation in probabilities, understanding which will the results of our numerical simulations later on. The mixing bilities in the experiments, and discussmass-squared the splitting. different Section limitsand of the details interest relevant to depending our numericaland on simulations. in the Our section results active-sterile are presentedelements in of section the mixing matrix using our parametrization can be found in appendix ∆ Bay has performed forsterile the neutrino only mixes with ν JHEP07(2018)079 and (2.4) (2.5) (2.2) (2.3) 4 2 j s 4 unitary × , 31 31 31 , , the oscillation sub-block of the ∆      41 considered in this 2 j , sin ∆ sin ∆ 24 ∆ , 2 41 iδ sin 24 41 41 , − 2 31 24 iδ m | and e c 3 − ∆ 24 i s e 24 c s U sin ∆ sin ∆ | 24 34 2 s 0 0 c | 43 43 3 21 = µ = 24 4 iδ U 4 | . µ s e 24 phase, which disappears from the sin ∆ cos ∆ are the new mixing angles with the 12 c 24 4 ,U s + 4 3 3 O 14 i ∗ ∗ s s δ θ − affecting the 24 13 41 U U 3 sub-block of the matrix shows only iδ V 3 3 10 000 0 0 0 1 0 ij ∆ e µ µ θ 23 × = 0, which is a valid approximation given 2      U U 23 O 4 4 s s s 14 sin = 14 θ 13 U U 2 c V | 4 4 24 ∗ ∗ 4 – 4 – µ µ 34 24 s U U c . V U rotation corresponds to the standard CP-violating | 24 E 34 2 ,V | s 4 4 13 O      , and the 3 µ − V L/ ]. = . In this notation, U ,U 34 | 34 2 ij 8 23 + 8 Re + 8 Im CP ij Under the approximation ∆ c s c U δ θ 23 m ) is completely general, but does not allow to see the num- 3 s 13 34 ∆ c ≡ 34 s 13 ) = 4 cos 2.2 c c s 34 ≡ channel is given (in vacuum) by: − ν s 13 ≡ 24 s ij δ c are the two new CP-violating phases. In this parametrization, the − denotes a similar rotation but this time including a complex phase. ν ij → 1 00 0 10 0 0 0 0 0 0 c ij = 24 = µ → V 3      ν 3 , δ µ s ( µ and ν 14 = U U P δ ij 34 ≡ θ O µs sin P denotes a real rotation with an angle can be parametrized in terms of six mixing angles and three Dirac CP-violating In the following, we choose to parametrize it as the product of the following ≡ ]. In this case there is no sensitivity to the ij ij U 4 s 23 O For simplicity, from now on we consider The probability in eq. ( In our numerical simulations the full Hamiltonian is diagonalized toIf extract neutrinos the are oscillation Majorana, probabilities additional CP-phases enter the matrix. However, neutrino oscillations are 3 4 exactly. insensitive to these and therefore they will be ignored here. the strong constraints set bywork reactor [ experiments in themixing range matrix, of and the ∆ relevant elements of the mixing matrix read complex phase associated withphase the in three-families, small deviations from a unitarytherefore matrix, within which current at bounds leading [ order are proportional to where fourth state, and Here, mixing matrix, while For example: matrix phases. consecutive rotations: where we have defined ∆ ber of independent parameters which enter the oscillation probability. A 4 sterile mass-squared splittings. probability in the mass splitting and focus on the effects of the oscillation due to the atmospheric and the JHEP07(2018)079 (2.8) (2.9) (2.6) (2.7) ]. . 38 31 31 ), as ∆ 31 ∆ 31 . 2 31 2 ∆ 2.2 ∆ ∆ 31 sin 2 2 2 sin ∆ 2 sin sin sin 2 34 c 2 24

sin ] s 24 ] 24 2 24 3 3 θ ∗

δ s ∗ s 2 34 s 2 c . U 24 U 2 2 23 3 δ 3 2 23 s 31 cos 2 µ µ s ) sin U U 4 2 23 4 + 2 s 2 34 s 2 23 s ) cos phase is now evident. Depend- + 2 c s U U ) 24 2 13 2 23 4 sin 2∆ 4 24 δ 24 ) c 2 13 ∗ s µ ∗ , the following three limiting cases 2 23 µ δ δ c 24 , s 24 U 2 13 U 2 41 − δ δ c cos − 31 2 13 cos m c (1 − 1 2 − 24 sin 24 s 24 − ): 43 s θ + Re[ (1 34 34 oscillation probability, eq. ( sin ∆ ): 2 31 + 2 Re[ θ 2 (1 34 34 θ 34 | s 2 31 θ θ 2 θ ∆ 41 31 3 | 2 23 ν s 2.6 3 s ∆ s sin ≈ cos(∆ U sin 2 sin 2 | 2 13 – 5 – 2 → U sin 2 sin 2 2 sin 2 c | 2 34 ): 34 | 24 41 sin ∆ µ 23 2 c 3 θ θ | sin 23 24 θ ν ): 31 24 − ] sin 2∆ µ 3 θ θ 2 θ 3 + µ 31

43 ∗ U ∆ 0 there is a signiﬁcant cancellation in the probability. s 2 34 | 3 U s s sin 2 U 2 34 ∆ | sin 2 ≈ 3 s sin 2 U sin 2 2 24 µ 31 24 + 3 23 3 + sin 2 c 2 24 s θ ∗ θ cos ∆ µ U 41 23 + sin 2 2 c + 4 23 ∆ | 4 23 U θ 2 34 θ U s 4 41 2 2 3 θ 24 23 | 2 34 s 24 s ∗ µ 41 θ 2 θ U 4 s θ + sin 2 sin 2 U s 4 2 2 23 2 2 sin U 2 | ∆ ∗ 4 µ c 2 23 sin 2 2 2 sin 2 2 U 2 s 2 23 24 c 2 | | 2 | + U θ c sin 4 2 2 U 3 23 4 24 | s µ sin sin 4 c s (i.e., ∆ sin c 4 2 13 sin ∗ 4 13 µ 2 24 U U µ c U 2 13 c | 5 | c 2 34 2 24 4 13 2 13 34 2 U 4 c 1 4 sin 2 2 U c c c 24 c ∗ c | | µ 2 23 θ 3 2 1 2 23 2 23 − s 24 U 2 + − − + 2 Im[ µ s s c 2 4 13 U = 4 = 4 = = = 2 | c 2 13 4 13 2 13 c c c sin µs µs P = 4 = 2 ). Then we can rewrite the P 2 34 − + 2 + 2 c µs A.1 = P This will be discussed in more detail later in this section. the far detector Note that if distance to the far detector (i.e., ∆ at the far detector (i.e., ∆ µs The oscillations due to the active-sterile mass-splitting are already averaged-out at The oscillation maximum due to the active-sterile mass-squared splitting matches the The oscillations due to the active-sterile mass-squared splitting have not developed P A similar expression in this limit, but assuming a real mixing matrix, can be found in ref. [ 3. 2. 1. 5 where the dependence with theing new on CP-violating the phase value of thecan new be mass-squared considered splitting, ∆ for the probability in eq. ( see eq. ( JHEP07(2018)079 = 10 2 2 23 θ (2.10) 2 2 31 . This π 5 m = ] 23 0.002 eV 0.004 eV Δ 24 s = = = δ ; sin 2 41 2 41 2 41 GeV 34 [ 2 m m m s Δ Δ Δ 0.1, = eV . This is shown = 2 34 3 s 24 − = Energy 23 δ 2 24 1 c the cancellation in s 10 4 24 × , as indicated in the leg- s and, most importantly, 2 41 48 . 0.5 m 24

0.6 0.4 0.2 0.0 1.0 0.8

s μ 1 - = 2 P 31 . 2 31 ∆ 2 31 angle by the oscillation exper- 2 = 0 and m m . In this case, the contribution 10 24 2 2 sin 24 ∆ θ 1 δ ): , while the different lines shown in each 2 34 2 2 31 / s 5 24 π m ] δ 2.6 = Δ 0.002 eV 0.004 eV 23 2 41 = = = θ 24 2 41 2 41 2 41 δ 2 GeV m [ m m m 2 Δ Δ Δ 1. channel, in vacuum. The different panels corre- . 0.1, = s sin )) is negative and cancels almost exactly the ν 2 34 s – 6 – = 0 Energy 4 13 = c 2.8 1 → 2 24 34 . In the most general case, the dependence of the s around the atmospheric scale, when the oscillation θ µ 0. Under this assumption, the probability simplifies ν 1 2 41 2 0) = = 1, the amplitude of the oscillation is proportional → 0.5 m

1.0 0.8 0.6 0.4 0.2 0.0 24

→ 34

= sin ). The solid lines in all panels have been obtained for s

μ 1 - θ P c 24 24 2.8 θ θ = ( 2 , which vanishes exactly if 10 µs 24 2 2 2 | c P ), in this case there is no sensitivity to 24 2 31 0 = 5 iδ m = ] 2.6 e Δ 0.002 eV 0.004 eV 24 = = = 13 δ 23 2 41 2 41 2 41 c GeV s [ m m m 084 ; and sin Δ Δ Δ . 34 0.1, = s : notice that a cancellation of the oscillation amplitude takes place in this 2 34 s = 0 2 31 − = 0, as shown in the left panel in ﬁgure = Energy 2 24 m 13 1 23 s for diﬀerent values of ∆ 24 θ c δ . Oscillation probability in the 2 1 2 24 = ∆ s | 0.5 Given the strong limits that have been set on the As mentioned above, a destructive interference between the standard and non-standard 2 23 2 41

0.2 0.0 1.0 0.8 0.6 0.4

s μ 1 - P m 5 ; sin . In contrast with eq. ( there is no dependencecase are with solely the driven by sterile the mass-squared atmospheric mass-squared splitting. splitting, and The the oscillations size of in the this effect the probability can also be severe in the limitiments ∆ looking for oscillationsaddress involving explicitly the a case sterile when considerably neutrino with in respect the to eV the scale, expression in it eq. is ( worth to cancellation is only partialand (or this negligible) can be for seen otheractive-sterile from mass values the splitting middle of the and oscillation the right patternblue CP panels is and more in phase, dashed complex, the as as figure. yellow shown expected, probability lines For by other with the in values dotted the figure of energy the oscillating becomes at non-trivial different due frequencies. to Moreover, the as interference we will of see different in terms section case for from the interference (lasttwo other term contributions in to eq. thethat, oscillation ( probability. in In the fact, limit itto is straightforward to show contributions to the oscillation amplitudemixing is parameters possible and, for in particular, certainin for values figure certain of values the of active-sterile theprobability CP phase simplifies to eq.∆ ( panel correspond to different values ofend. the active-sterile The mass rest splitting of ∆ the0 oscillation parameters have been fixed to: ∆ Figure 1 spond to different values of the new CP-violating phase JHEP07(2018)079 . ]. The 3 ] library ], which − 41 43 40 cm , · 39 ], with 50 MeV 96 g 43 . CC events that might τ ν and µ ] accounting for the far detector ν , 44 e ν NC interactions at the detector. For τ ν ]. In the present work we have considered ] used bins in visible energy of 50 MeV for 29 43 and – 7 – µ ν , e ν = 1300 km from the source. In particular, we focus ]. (1). L 42 ∼ O . Moreover, the dependence with the standard oscillation 23 2 34 θ s 2 2 sin 4 13 c ). We have checked that the size of these modifications is relatively small and, 2.6 The main backgrounds for this search would be In our simulation of the signal, we have computed separately the contributions to the Finally, it is worth to mention that matter effects will modify the oscillation probability following we will adopt the more conservative 250 MeV bin size asbe our default mis-identified configuration. as NC events.for We CC have events assumed is thatfor the at instance, background the muons rejection leave level efficiency long of tracks in 90%. liquid Argon However, (LAr) this that are is difficult probably to a misidentify conservative estimate: the reconstructed energy ofwhere wider the bins hadron of 125 shower,two MeV were as sets considered opposed of [ matrices: tobins, the and the a DUNE original (more CDR setincreased conservative) to rebinned studies provided 250 version MeV. by of We performed the theseand our matrices authors 250 simulations MeV for where of bins) the the and two ref. bin options found (with [ size similar 50 results was MeV bins for the two sets of matrices. Therefore, in the trino interactions and detectorTo reconstruction this of the end, particles wewere produced use obtained in using the the the final migrationgeometry, LArSoft state. matrices neutrino-argon simulation interactions provided software and by [ detector propagation the active of volume. authors the of The final authors ref. state of [ ref. particles [ in the simplicity, we have assumed aenergy. 90% flat The efficiency experimental as observable avisible for function energy a of (energy the NC reconstructed deposited eventlight). visible is in The a the correspondence hadronic detectorvisible between shower in a with energy the given a deposited incident certain form in neutrino of the energy a detector and track has the and to amount scintillation of be obtained from the simulation of neu- which includes a newneutrino implementation oscillation of probabilities systematic inphysics a errors engine 3+1 as available scenario described from have ref. in been [ ref. implemented [ using thetotal new number of events coming from detector, located at aon distance the of potential ofscenarios. NC To measurements this toto end, discriminate discriminate between we between charged-current the relycurrent (CC) 3-flavor work on and have and the been NC performed 4-flavor events. excellent using capabilities All a modified the of version simulations of the in the DUNE GLoBES the far [ detector effects have been properly included using a constant matter density3 of 2 Simulation In contrast to usualdistances, analyses in searching for this signals work of we sterile want neutrino to oscillations take at advantage short of the capabilities of the DUNE far parameters goes as in eq. ( therefore, the vacuum probabilitiesnumerical are simulations precise in the enough following to sections. understand However, in the our behavior numerical of analysis, matter the is directly proportional to JHEP07(2018)079 , τ ]. 1 45 flux will τ ν 65%), the ≈ CC events mis- µ ν τ ν CC N µ ν CC , as a function of the (recon- N 2 e ν CC background contributions, following N e ν ) and the rest of the oscillation parameters in and τ ◦ ν NC leptons. In most of the cases ( CC events would be largely suppressed since µ N ν µ τ – 8 – ν = 42 + 23 µ θ ν NC N Signal Background + , the number of events already includes the branching ratio for e ν NC τ ν CC ] from LArSoft simulations, while the hadronic showers pro- N ( N 43 CC events are much smaller and approximately of equal size. In τ ν mode 2901 22 301 39 mode 6489 129 751 140 yr. In all cases, signal and background rejection efficiencies have already been · ¯ ν ν and e ]. MW ν · 45 decays. Usual oscillations (in the three-family scenario) have been considered in the , τ 29 . Expected total number of events with a (reconstructed) visible energy between 0.5 and The expected NC event distributions are shown in figure The expected total number of signal and background events is summarized in table in refs. [ structed) visible energy, forwhen the there three-family is scenario a (white sizableAs mixing histogram) expected, angle and a with for depletion the the in sterile case the neutrino (blue/light number gray of histogram). events can be observed in the 3 + 1 case with all cases, both signalneutrino and events backgrounds due receive tohas contributions the been from intrinsic computed right- contamination forused and of visible in wrong-sign the energies our beam. between analysis,Additional 0.5 experimental GeV using The details and the number for 8 the of beam GeV, DUNE events which configuration setup is with considered the in 80 GeV this region work protons can as be found in ref. [ where the different backgroundseen contributions from are shown this separately table,identified for the as clarity. largest NC, due As background to can contributioncoming the be comes from large from flux available at the far detector, while the contributions decays hadronically producing a shower:and these consequently events no constitute rejection an efficiency irreducibleGaussian has background been energy assumed resolution in function this forthe case. the values We derived have assumed in a duced ref. from [ hadronic tau decaysfor have the been NC smeared signal. using the same migration matrices as the detector. On the otheroscillations. hand, Consequently, the the active number neutrino of most flavors would of be the affected initial by muonthe standard neutrinos detector. have Given oscillated the to energeticinteract neutrino tau at flux neutrinos the at by DUNE, detector the some via time of CC, they the producing oscillated reach hadronic computation of the backgrounds,agreement with setting their current best-fit values. as NC events, except when they have very low energies or are not completely contained in Table 1 8 GeV at thecontributions DUNE separately. far This detector. correspondsand The to antineutrino number 7 running of yrs modes) of eventstotal is data with of taking shown 300 a (equally for kt 40 splitaccounted the kton for. between signal detector neutrino and In and background the 1.07 case MW of beam power, yielding a JHEP07(2018)079 ) within 2 31 04. Unless . m ∆ = 0 , 13 2 31 θ 2 m 2 ∆ / sin ) , 2 31 23 θ m = 0. The expected distribution 2 2 1 24 (∆ . θ σ BG = 0 = 0 = 34 θ 34 14 2 θ θ 2 sin 1, 05 and . sin . . In addition to an overall normalization [GeV] = 0 rec . In practice, however, the cancellation of B 2 34 E ) = 0 θ χ 23 – 9 – 2 ]. Specifically, we consider the following Gaus- θ 2 48 2 – 46 in the visible (deposited) energy in the detector, with (sin channel is enhanced when some energy information is 2 σ 1 2 3 4 5 6 7 8 s χ ). ν is obtained after marginalization over the nuisance param- 0 B.1 005, → 2 . 900 600 300 χ

1800 1500 1200 µ

5 MeV 250 / Events ) = 0 13 θ 2 2 , as specified in the appendix 2 (sin χ σ . Expected signal and background event distributions, as a function of the reconstructed function defined in eq. ( The effect of systematic uncertainties is accounted for through the addition of pull- 2 χ eters and the relevantcurrent standard experimental oscillation uncertainties parameters [ sian (sin priors: otherwise specified, we haveparameters, assumed included a as conservative 10% pull-terms Gaussian in prior the for all nuisance uncertainty for the signal andtainty for background the (which signal is (bin-to-bin bin-to-bin uncorrelated)tematic correlated), has uncertainties been a related included to shape to the uncer- account shapeparameters for of are possible the taken sys- event to distributions. be Moreover, uncorrelatedwell all between as nuisance the between neutrino the and different antineutrinootherwise contributions channels to as stated, the the signal final and/or background events. Unless included in the fit,analysis as implementing we a will binned seea in the next section. This is exploitedterms in to our the numerical the energy distribution ofdictated the by the background standard (shown oscillationsthe by suffered far the by detector, the green/dark active whichbe gray neutrinos is observed, histogram) as well-known. and they is propagate there Inity to is this to practically case, no oscillations pile-up all in at particles the low in energies. the Due final to state this, would the sensitiv- shows the expected number of NCfor events for background sin events (CC mis-identified as NC) is given by the greenrespect (dark gray) to histogram. the three-familythe scenario. energy carried Moreover, away the by events the pile outgoing up neutrino in at the low final energies state. due One to can also see that Figure 2 visible energy, after efficienciespected and number of detector NC events reconstruction. in the The 3-family standard white scenario, while histogram the shows blue (light the gray) ex- histogram JHEP07(2018)079 ) β ν = 0 → 24 θ α ν = 0 there = drops from 24 14 θ θ 2 41 might be very = m 24 θ 14 θ . . By the time DUNE and 34 appearance channels. In 2 θ 14 e θ ¯ ν the three-family hypothesis 41 2 → m µ ν . Next we proceed to turn on the ∆ 34 − θ of the flux and cross section as in the and ¯ 24 sterile mixing angle, which is currently θ e ν 34 (500) m, this is a valid approximation as θ ), the dependence with ∆ → ∼ O µ 2.10 ν L – 10 – same convolution In spite of these difficulties, the DUNE collaboration expects to 6 . Under this assumption, the near detector measurements will provide ]. 2 49 and determine for which values of 1 eV 24 < θ 2 41 m Before concluding this section, let us comment on the relevance of the near detector For a recent review of the challenges that long-baseline experiments have to meet regarding systematic 6 consider the simpler caseand where study two the of sensitivity the of newmixing the angle mixing DUNE angles experiment fixed to to zero, uncertainties see ref. [ In this sectionmixing we parameters show in our the numericalstarts different taking results scenarios data for discussed the thetight. in constraints Nevertheless expected on section DUNE is the sensitivities also sterile sensitivethe to to mixing less the the angles constrained new among the three sterile-active mixing angles. Therefore, we initially the oscillation probabilities: this guaranteesdetector no data effect the at oscillation the wouldthe near be effect detector, in driven while by the at the oscillation the atmospheric would far be scale. observable Thus, for in4 large this enough case Results rates. Thus, theyhave correspond to to be estimates propagated onaccounted to the for. the size Finally, far it of detector,would should the be once also final no be the systematic effect stressed near errors onThe that detector the that reason in data near the is has detector case that, data already that as regardless been it of the was new shown mass-squared in splitting. eq. ( long as ∆ a clean determination offlux, the which convolution can of then the bepoint, NC it extrapolated should cross to be section the mentioned thatin far and our detector the assumed the prior with muon fit uncertainties a for neutrino would small the correspond systematic uncertainty. errors At to this the values used for the analysis of the far detector event unclear yet. A detailed simulationscope of of the this work near-far and detector canIn data ultimately this combination be work, is performed instead, beyond only we the bydeveloped have the yet assumed experimental at collaboration. the that near the detector.for oscillations For a due neutrino near to energies detector the in located the new region at state around a have 2-3 GeV, distance not and of reach a precision at theview percent of level this, in we the be expect conservative. the 5%–10% values considered in this workdata for and the its NC sample possibledetector to explicitly: impact its on design the is fit. still undecided In and its this expected work, performance we is have therefore not simulated the near detector can be used to measurefar the detector. This contrastsusing with oscillation CC measurements data, in where appearanceto the mode the initial impact ( and of standard finalextremely oscillations, neutrino challenging. making flux the spectrum cancellation (and of systematic flavor) uncertainties differ due systematic errors in the NC channels is expected to be extremely efficient, since the near JHEP07(2018)079 ], 4 ) and 12, at . 0 . norm 34 ∼

σ θ Kbound SK 34 13 θ θ 2 = = 0. The different 24 24 , θ θ true 34 13 027 θ θ = . . Also, as shown in the 2 = 34 15 (at 90% CL) translates 14 = 5% . As seen in the figure, 2 . θ = 0 θ sin 24 ) = 0 0 3 , θ 24 14 , for different values of the 5 eV θ θ < norm . = 0 σ (2 = = 0 34 2 2 | 24 θ = = 0 90% C.L 4 δ 14 14 τ sin θ θ 2 41 = U | m shape 14 and σ δ ∆ 0 0.05 0.1 0.15 0.2 0.25 24

θ 8 6 4 2 0

16 14 12 10

χ ∆ 2 under the assumption = 0. The horizontal dotted line indicates the value 34 – 11 – 24 θ θ = ) and does not depend on any of the new oscillation ] and whose limit on 14

= 0

4 θ Kbound SK 2.10 24 = 0, the expression for the vacuum sterile neutrino appear- θ 14 15, for θ = 0, and are then fitted using increasing values of . is shown in the left panel of figure 34 0 4 θ = 10% = 5% = i , for 2 θ < 34 24 34 θ norm norm sin θ 34 θ σ σ θ . If prior uncertainties could be reduced to the 5% level for both 2 = = 2 = 5%, Rate only = 10%, Rate only norm norm shape shape 1 eV σ σ σ σ . 0 ), we find that DUNE will be sensitive down to values of sin 90% C.L > corresponding to 90% C.L. for 1 d.o.f.. 0 0.05 0.1 0.15 0.2 0.25 -discovery reach analysis where 4-flavor event rates were calculated in ‘data’ and fit, with 2 shape . Left panel: expected sensitivity to 8 6 4 2 0 2 41 χ σ 34

16 14 12 10

m χ ∆ 2 The sensitivity to , assuming that the experiment will measure event distributions in agreement with the 34 90% C.L. (1 d.o.f.).from For atmospheric comparison neutrino we data also collected byfor show the the ∆ Super-Kamiokande limit (SK) collaboration on [ normalization this and mixing shape angle errors, obtained weconstraint find by that more DUNE than would be a able factor to of improve two. over the It SK should be stressed that the DUNE constraint are simulated setting all our results show a considerableerrors. dependence Assuming a on (conservative) the 10%shape size systematic error and ( on implementation both of normalization systematic ( Under the assumption ance probability is givenfrequencies by eq. induced ( byquestion the to sterile, ask in nor thisθ any case of is if the DUNEexpectation CP-violating will in be phases. the able to three-family An improve scenario. over interesting current In constraints this on case, the “observed” event distributions derived simultaneously on theactive-sterile two mass-squared mixing splitting. angles 4.1 Sensitivity to Super-Kamiokande atmospheric data [ into the constraint sin of the ∆ could be rejected. We finalize this section by showing the expected limits that could be Figure 3 lines correspond to differentpanel: assumptions of systematical uncertainties,all see the text 4-flavor for parametersplot, details. fixed we Right to fixed the the values systematical in errors the to plot, 5%. except for The shaded region is disfavored at 90% C.L. from JHEP07(2018)079 , ) 2 2 41 24 we 34 θ θ m 2 5 eV plane . ). It is and 34 5 eV θ . = 0 14 . Different − θ 4.3 2 41 input values. 3 = 0 24 6= 0 . The change m θ 2 for the assumed 2 41 . The true value χ 34 true , it is relevant to m σ 24 24 θ 2 , θ θ 2 24 ∼ θ do not include a binned and 6= 0) there is a dependence . For ∆ 3 34 and sin 5 24 θ 0. In the next subsections we θ 2 41 ' m 6= 0) is marginal, as shown in the 14 0 is of particular relevance. In this show the dependence of our results 6= 0 or , θ 24 4 ≈ θ 24 6= 0. 14 θ θ 24 24 θ θ ≈ ) with a significance of ◦ 14 – 12 – θ 18 = 0 is assumed for simplicity. In all panels, the ∼ , as long as 14 2 41 θ m is tightly constrained by reactor experiments for the ∆ , using equally-sized bins in visible energy, as described in 2 ) for which the three-family hypothesis would be successfully 14 χ θ 2 41 m 6= 0 leads to a more interesting phenomenology, since in this case , ∆ . Thus, since by the time DUNE will be running smaller values of ). In fact, is in this regime where constraints in the 24 24 θ 3 θ 2.9 taking all systematical errors at the 5% level. In this case, we assume that ] and therefore its impact (even for 34 are expected, the case when θ 19 , as a function of the possible true values of ∆ 24 . θ 4 3 is set to be nonzero, while Finally, we comment on the analysis shown in the right panel of figure The lines labeled as “Rate only” in the left panel of figure 34 and (i.e. if it happens to be as large as and only consider the total event rates in the computation of the θ 2 34 14 expected events distributions are computed usingThe the obtained indicated “observed” values event as distributionsthe are three-family then scenario, compared i.e.,sets to in of the absence true expected of values result ( arejected in sterile at neutrino. 90% C.L.. The contours The indicate different the panels in figure The scenario where the oscillation probability also dependscase, on the assuming active-sterile as mass-squared splitting. ourask In true if this hypothesis the experiment ain would 3+1 figure be with able nonzero toof reject the three-family hypothesis. This is shown θ systematical errors. 4.2 Rejection power for the three-family hypothesis, for then worth to mention that considered [ right panel of figure θ last case DUNE, with the considered configuration, will produce a ‘indication’ of a nonzero with the sterile masswhich squared is difference, one and ofare we the therefore have values in fixed considered the its regime inin where value relation our the to to results sterile ∆ eq. oscillation inare ( is figure averaged-out reported at by the far different detector, the collaborations (as will be addressed in section to the analysis shownanalysis in for the left panel,the in experiment the will right measure panelfour-family event we scenario. distributions performed in a In agreement order discovery withfor reach to the simplicity, quantify the the expectation four-flavor impact in parameters ofwith the where also the fixed having values in to a the their nonzero plot ‘true’ labels. values In (except this for case (for blue lines, for 5%leads systematic to errors). a As noticeable canwill improvement be in only seen, the consider results. the asection inclusion Therefore, binned of in energy the information rest of this section we will study in detail the phenomenology in case χ in sensitivity can bedashed appreciated red from lines, the for 10% comparison systematic between errors the (or dashed between the pink dot-dot-dashed and green dot- and solid would be valid for any value of ∆ JHEP07(2018)079 . 4, 4, 4, 34 π 0 θ 10 π/ π/ π/ = (4.1) : the ) the − . Right 24 2 31 = = 24 1 δ − δ and it is 23 34 m 10 23 θ θ = 0 23 θ 31 ∆ 2 θ 24 δ ≡ 24 2 1, θ . − 2 10 23 = 0 , corresponding sin 34 2 41 θ δθ 4 2 3 − m sin 10 5% syst. there can be a large : for negative values 10% syst. 4 2 31 2 31 − 10 m 1 2 3 4 5 m , − − − − −

)

2), where ∆

. Such dependence can be ∆

10 10 10 10 10

[eV ] m

∆ /

2 2 2 34 24 c . 2 13 δ and the same implementation s . This can be easily explained 2 24 0 2 41 2 41 s (left panel), the true value of − 24 34 10 m δ m θ = 1) the oscillation probability in + 23 24 δ δ δθ 31 ( 1 are diﬀerent from zero, the oscillation ∆ − cos = 0 2 10 24 34 24 δ 34 'O θ θ 71. Left panel: dependence of the results with c 2 . has been set to a non-zero value in all cases, as 05 1 2 , this leads to a decreased sensitivity in this . . 2) 34 sin 2 / s 34 − = 0 = 0 2 31 > θ 1 10% syst. and 10 34 34 24 θ θ 2 – 13 – m 2 2 s − χ 24 sin sin ∆ 2 23 θ s )), for values of ∆ + 2 3 = 0 with respect to the results obtained for ' ) is negative and suppresses the probability, leading − 2 13 1 2 3 4 5 10 2 34 c 2.8 − − − − − 24 2 41

2.7

10 10 10 10 10

41 (

] [eV m

∆ m 2 2 2 24 = 0 for simplicity. The contours indicate the sets of true values c , if both . The same true value of ), which shows two terms that depend on the value of 0 14 ≈ . In fact, it can be easily shown that, in the limit 2 10 24 θ δ 2.9 π µs . The true value of P = 1 24 . θ 1 − = 0 2 24 (see also eq. ( 10 34 δ θ 24 2 θ 1 . Central panel: dependence of the results with the true value of sin 2 24 also depends on the value of the CP phase sin 2 2 . For values of ∆ δ − and sin π π/ 24 10 = = = 0 µs δ 10% syst. sin 2 41 24 24 24 P δ δ δ m ) for which the three-family hypothesis would be successfully rejected at 90% C.L.. In the second term in eq. ( . Rejection power for the three-family hypothesis, as a function of the assumed true 3 = 0) would be disfavored with a ∆ 2 41 − ) approximates to 24 4 1 2 3 4 5 m 10 i δ − − − − − θ

10 10 10 10 10

2.7 41 Conversely, in the limit where the new frequency is averaged-out (∆ As explained in section

] [eV m

∆ = 1 and at the first oscillation maximum (sin , ∆ 2 2 24 2 13 θ results show a veryfrom mild the dependence expression in with eq. ( thefirst one value is of directly proportional toand ( is therefore very suppressed;completely while off-peak the second at term the is first proportional oscillation to maximum. sin 2∆ In fact, in the same limit ( eq. ( where the effect of the interference term can be easily appreciated. region of the parameter spaceThe for interference has theof opposite cos effect in theto region worse ∆ results for c to different true valuesof of systematic uncertainties haveAs been shown assumed in figure forinterference all between lines the different (indicated contributions bythe to value the the of oscillation top amplitude, label). depending on with respect to different parameters:(central the panel); true and value the of assumed priors for the systematicprobability uncertainties (right panel). appreciated by comparing the three lines shown in the left panel in figure ( other words, they indicatepoint the fraction of parameterthe space true value where of thepanel: SM hypothesis dependence (namely, of the the results with the assumed priors for the systematic uncertainties. Figure 4 values of ∆ indicated in the labels, while JHEP07(2018)079 , 23 θ and have 24 34 δ θ there is a 2 31 and m 24 ∆ δ 0 than for larger → plane if the observed 2 41 . However, as we saw in m 2 41 = 0). 34 θ 34 m θ 24 δ and , it has been kept fixed during and 2 41 24 , while the contours do not show function, for a given pair of test 24 θ m θ 34 . 2 θ parameter space χ 2 ) the interference term would not be ◦ 34 θ 25 . Therefore, in this case it is not possible ) is additionally suppressed with cos 2 − & (which is very difficult to reject, since this 4.2 2.9 34 24 2 31 θ , θ m – 14 – 0 ∆ in the averaged-out regime. In the former case, a → ' 2 41 shows the dependence of the results with the assumed 24 m 2 41 4 θ and section m shows the dependence of the results with the true value 2 4 or a ∆ 2 31 , the resulting allowed regions are very different if the results are m 5 ∆ near maximal mixing. 23 θ 2 41 , is obtained after minimization over the new CP-violating phase m = 0. As shown in the figure, in the region where ∆ 34 θ shows the expected allowed regions in the 24 δ 5 − , as outlined in section in the oscillation probability in eq. ( , and strong cancellations between the different contributions may occur. The the oscillation probabilities show a large dependence with the new CP-violating π 24 24 24 θ 2 δ δ ∼ . In this case, all priors for the systematic uncertainties are set at the 10% and we As shown in figure Figure Finally, the right panel in figure The central panel in figure 34 24 = 1) and at the first oscillation maximum it is easy to show that the term proportional θ δ 2 13 different values (e.g., in the region tested using ∆ strong cancellation in theof oscillation probability can alwaysto be disfavor achieved large setting values the of value the new mixing angles. Only if the two mixing angles have very over all nuisance parameters. Asthe for fit the mass to splitting the ∆ simplicity, test we value have indicated also inprocedure; each kept however, panel all minimization to the over show standardsignificantly the the the parameters standard difference results parameters fixed in shown is during the here. not results. the expected minimization For to affect a function of this parameter. event distributions are found tocase, be the in “observed” agreement event with distributionsesis, the are and three-family simulated fitted hypothesis. assuming in Invalues the a this three-family 3+1 hypoth- scenario. The value of the one would proceed to derive asection limit on the mixing angles phase effect of thevalues cancellations of is the active-sterile much mass more splitting and, severe therefore, in we expect the very limit different results ∆ as exception of the regionis around the ∆ region where significant cancellations can4.3 take place for Expected allowedIf regions the in observed the event distributions show an agreement with the three-family expectation, for the systematic uncertainties,normalization where and all for priorshand, both are shows signal set the to and room 10%5%. background. for for As improvement can both if The be the all dot-dashedrejection seen prior shape of from line, the uncertainties the and three-family on figure, can hypothesis the be the in improvement practically reduced is other all dramatic down the and parameter to leads space, to with a the sole successful strong dependence of the resultslarge with variations the for true value larger of to mass the splittings. approximate oscillation This probabilities behavior in can section again bepriors easily for traced the back systematicbeen uncertainties. set In as this indicated panel, the in true the values top of label. The solid line uses our default implementation to cos which is small for of have fixed c JHEP07(2018)079 7 is ]. 041 . 24 = 1) 18 com- 0 δ 11 and 14 . 2 41 < θ 0 2 7(stat.) 2 2 m . | SK < 4 9 NOvA 5 eV µ . 2 | U 5 4 | ). This results . = 0 µ 2 U 2 41 | m ) 5 eV ∆ ] (darker gray regions ◦ . ( 0 18 34 θ ] as well as from atmo- are valid for an sterile mass ≤ 5 28 2 41 m ∆ (right panel). The shaded regions

IceCube at 90% of C.L for a ∆ 2 ≤ ◦ 10% sys. 5% sys. DUNE 2 2 ]. Similarly, IceCube, by the use of ] and IceCube DeepCore data [ . 4 4 5 eV plane, for an active-sterile mass-squared 0 5 10 15 20 25 30 POT and a total systematical errors . 31 5 0 ] (gray region), and from atmospheric data 34 30 25 20 15 10 20 ]. For comparison, in the right panel of

< 05 eV

= 0

28 24 ) ( θ ◦ 10 18 − 34 2 41 θ × 24 m θ 05 . and – 15 – the impact of the new CP-violating phase ◦ 2 ] and IceCube DeepCore data [ 8 . 2 31 at 90% of C.L [ 4 eV 2 4 m 20 − ∆ < at 90% of C.L [ 1 eV = 10 . 24 2 0 θ and therefore they do not apply to the case shown in left panel. 2 41 2 41 2 m > ) ∆ ◦ m ( 2 41 (left panel) and for ∆ 1 eV 34 . = 1 eV 2 θ m 0 2 41 > eV 4 m 2 41 − m

18 for ∆

%sys. 5% .

= 10 ]. Experiments observing atmospheric neutrinos like the Super-Kamiokande 0 sys. 10% 0 = 0 as true input values. The lines labeled as “10% sys” (“5% sys”) have been DUNE 28 2 41 4 < 15 for ∆ i . m 0 5 10 15 20 25 30 θ 2 0 . Expected sensitivity projected in the | 5 0 4 we show the currently allowed NOvA regions from ref. [ 30 25 20 15 10

τ <

) ( θ 5

U ◦ 2 | NOvA has observed 95 neutral current events at the far detector while 83 | It is worth to notice that all constraints shown in the right panel of figure 4 7 12% ref. [ τ 438 live-days of data, found no evidence for sterile neutrinos constraining 4(syst.) events where expected in the three-flavor case. Since no evidence for an sterile , . U squared difference ∆ with three-flavor neutrinos, placed a| bound on the active-sterile mixing: figure spheric data from the Super-Kamiokande experiment [ ∼ experiment have also constrained4 the tau-sterile mixingand angle. SK,three after years of an atmospheric analysis neutrino data of from the DeepCore detector, which was consistent 9 neutrino oscillation was found, they placed thefor following the constraints (assuming active-sterile cos mixings: patible with no oscillation atcorrespond the to near an detector exposure-equivalent (0 of 6 large enough to allowDUNE for an could efficient disfavor cancellation justConversely, in the in the upper the probability. left limit Thus,much ∆ and in milder lower this and right regime does cornercontour not of is allow therefore the for obtained parameter a in cancellation space. this in case. the oscillation probability. A closed 10% for the backgroundresults from (normalization the only). NOvA experimentfrom from For the a comparison, NC Super-Kamiokande the search experiment [ labeled right [ with panel red shows lines), the also latest at the 90% C.L.. Figure 5 splitting ∆ correspond to theassuming expected confidence regionsobtained allowed assuming 10% at (5%) 90% prior uncertainties C.L. for the (2 signal d.o.f.), (both shape for and a normalization) and simulation JHEP07(2018)079 ; . 2 ◦ 14 9 θ (our eV < 0; (ii) 1 24 − 24 δ → θ with 10% ◦ 2 41 and m 30 and 10 14 . 2 δ , taking advantage 24 eV , shown in the right θ 5 34 − . θ does not change at all. ◦ current constraint were 34 14 θ θ far detector is tightly constrained by Daya . At long-baseline experiments, τ 14 ν θ ) and two CP-violating phases – 16 – 34 . θ 2 31 channel guarantee that most of the beam will have m )). The oscillation probabilities will generally depend τ ν and ∆ range where the current limits on . Even in the case where 2.3 . First, we have derived the oscillation probabilities in 24 2 41 → 1) is affected. However, 5 θ 2 41 and a fourth neutrino. m µ , 2 41 ν m τ 14 m ν θ due to cancellations in the probability. 34 θ 2 31 ) we provide approximate expressions for the oscillation probabilities m ∆ ] for the ∆ 2.9 by the time it reaches the far detector, thanks to the atmospheric mass- 19 , apply. On the other hand, in the left panel of the same figure (with )–( τ ν ; and (iii) ∆ 5 2 41 bound (for 2.7 2 31 m m 24 θ ∆ ' We have then proceeded to simulate the expected sensitivity of the DUNE experiment In this work, we have studied the potential of the future DUNE experiment to conduct a Finally, we want to comment on the impact of having a nonzero electron-sterile mixing 2 41 m using the expected NC events collected at the far detector. We have studied the variation around) the eV scale,thus, in here eqs. ( we havein allowed three it different regimes, to∆ depending vary on between the 10 mass of the sterile state: (i) ∆ additional mixing angles ( parametrization is given byon eq. an ( additional oscillationactive frequency dictated and by sterile thedifferent mass-squared states, regimes splitting ∆ paying between particular the attentionphases. to the dependence Unlike with in the other new CP-violating studies where the mass of the sterile was required to be at (or search for sterile neutrinos using theof NC data the expected excellent at the capabilitiesNC of events. liquid For simplicity, Argon we to haveneutrino focused discriminate is on introduced. between a 3+1 charged-current In and this scenario, case, where the only mixing one matrix extra has sterile to be extended including three however, oscillations in the oscillated into squared splitting. Byevents measured searching at for the a farprobe detector, depletion the experiments mixing in like between NOvA the or number MINOS of have been neutral-current able (NC) to intense scrutiny. Income the near online future to amixing refute new of or generation a confirm of lightbounds these short-baseline on sterile experiments the hints, neutrino mixing will and with withchallenges tau associated will electron neutrinos to place is and the a production muon strong much and neutrinos. more constraints detection difficult of on task, Achieving given the similar the technical 5 Summary and conclusions The experimental anomalies independentlyGallium experiments reported have in put LSND, the possible MiniBooNE, existence reactor of and an eV-scale sterile neutrino under Only the Bay experiment [ panel of figure unconstrained) DUNE is notsystematical able to errors. exclude the This,power small also for window reinforces ∆ 24 our conclusion about the loose of constraining the current allowed region set by5% NOvA with systematics a DUNE good will control also of systematics improve below over 5%. the current With in IceCube constraint the for resultscompletely shown relaxed in in figure the analysis (i.e. ‘free’), our result for As shown in the figure, DUNE is expected to improve over a factor of two with respect to JHEP07(2018)079 , ), 2 34 θ 2 31 and eV m 4 34 − ∆ θ , where 4 = 10 2 41 . 41 2 . m 3 m 4.2 , the mixing angle 24 δ the experimental results would 2 31 . In this case, the oscillation prob- m 34 ∆ θ 6= 0. In this case, the oscillation prob- = 0, we have determined the sensitivity . The reason is, again, the possibility ◦ 24 ’s, measurement or limiting this fraction θ 14 τ (and assuming the same value for θ 2 41 ν π m = = 24 – 17 – θ 24 δ . First, we considered the 3+1 scenario as the true 2 41 implementation can be found in section 2 m χ ). We find that DUNE will be able to improve over current to be as large as 30 . The simulated data were tested using two very different values 34 2.10 5 and ∆ θ fraction of a possible sterile neutrino(s). Given the difficulties = 0, DUNE would be able to reject the three-family scenario for ; conversely, for 24 τ 2 δ ν 24 and eV δ 3 24 − θ , see eq. ( 10 2 31 1 and m × 12 (at 90% CL) for our default implementation of systematic uncertainties. If 07 (at 90% CL). . could be almost two orders of magnitude larger and the three-family scenario . . . 4 0 0 τ 24 ν θ = 0 . ∼ ∼ ), 34 24 34 34 The DUNE experiment has unprecedented discrimination between neutral-current and Finally, we considered the opposite situation, and assumed that the experiment will find Next we proceeded to study the case where First, working under the assumption θ θ θ θ 2 41 2 2 2 2 m or constraint ofassociated the to the productionby and other detection means of iscan very provide challenging. an excellent In constrainonly or this the discover paper, a we sterile neutrino show that that primarily the mixes DUNE with experiment errors assumed. Conversely, inallow the case values of of ∆ of having a strongobservable cancellation effect in in the the event oscillation distributions probability, even which in could presencecharged-current of lead events very to for large a a mixing non- angles. long-baseline experiment: this will allow for a measurement the allowed confidence regions that wouldresults turn are from shown the in analysis figure of theof simulated the data. active-sterile Our mass-squareda splitting. closed In contour the is averaged-outconstraints regime obtained; in (∆ this we place find by a that factor DUNE of two would or be more, depending able on to the size improve of over the NOvA systematic ∆ would not be rejectedin by terms the of data. the oscillation The probabilities, behavior as of explained our ina results detail result can that in is be section in easily agreement with understood the three-family expectation. In this case, we determined and the size ofthe the presence systematic errors. of anario, We found sterile depends that heavily neutrino, the on measuredsin the sensitivity as value of of its the the ability experiment CPsin to to phase. reject For the example, three-family for ∆ sce- more complicated and, in particular,for strong certain cancellations in values the of hypothesis, probability can and take determined place forable which to values reject of thewe the three-family show mixing the scenario. parameters dependence DUNE Our of would results the be are sensitivity summarized with in the CP figure phase constraints on this parameter setsin by the SK experiment,systematic and errors will could be be sensitivesin reduced to down values to of 5%, the experimental sensitivity wouldabilities reach depend on the active-sterile mass-squared splitting. The phenomenology becomes numerical simulations and the of the DUNE experimentability to is the independent third of mixingdriven the angle by new ∆ CP-violating phases; furthermore, oscillations are solely of our results with the implementation and size of the systematic errors. The details of our JHEP07(2018)079 (B.1) (A.1) (A.2) , . 2 , 24 θ . 2 j 2 λ 34 2 34 j s c − σ sin 23 2 24 j c s ¯ 2 34 λ c 13 2 23 c s 2 23 s j − + X 2 13 c 34 24 c 2 + δ 2 24 − s cos 24 , 23 s 34 iδ i 24 θ e c 13 s shape c 34 σ 14 θ 24 s sin 2 iδ 13 e 24 s i sin 2 ) s − X ), the mixing matrix elements needed for the 24 n-bins 23 24 δ 14 θ θ + + s : 2.3 – 18 – 14 2 34 δ c sin 2 sin 2 − k 24 k 1 2 b 23 c CP b σ δ θ ( i + 13 i i s T − O -function ) 2 34 , e 2 sin 2 s 14 ), we find the following useful expressions: χ ln δ k 24 − , i 2 23 X 24 − s c c bg-chls O A.1 24 34 14 CP c c 2 13 c δ + + ( c i 23 2 13 24 24 2 i c − c s − iδ O e − 14 13 k = = k c c − e a − a 2 3 σ i ∗ Poissonian | s = = = = 3 T U s 4 3 3 4 3 s s U µ µ µ | k U U U U U i X s-chls 4 X s n-bins + U 4 ∗ µ -function = 0, and using eq. ( = 2 2 U 2 14 parametrization χ 8 χ θ B The results of our differentwith analyses, the including following spectral information, have been performed For A Complete expressions for the relevant mixing matrixStarting elements from in the parametrization our incalculation eq. of ( the sterile appearance probability are given by: with the U.S. Department ofUnited Energy, Office States of Government Science, retains Office andtion, of the acknowledges High that publisher, Energy the by Physics. United accepting Statesrevocable, The the world-wide Government retains license article to a for publish non-exclusive, or publica- paid-up,or reproduce ir- allow the published others form to of this do manuscript, so, for United States Government purposes. Fermilab where this project started.Energy under DVF was contracts also DE-SC0013632 supportedtial and support by DE-SC0009973. the from U.S. the This European Departmentunder work Of Union’s the has Marie Horizon received Sklodowska-Curie 2020 grant par- research agreementauthored and No. innovation by 674896. programme This Fermi manuscript Research has been Alliance, LLC under Contract No. DE-AC02-07CH11359 We warmly thank Michel Sorel forulate providing the us liquid with Argon theEnrique detector smearing Fernandez-Martinez reconstruction matrices for needed for useful to discussions. neutral-current sim- Paulo events. DVF Research is PC Foundation thankful also (FAPESP) for funding thanks the6., Grant support No. and of São 2014/19164-6 also and for 2017/01749- the URA fellowship that allowed him to visit the theory department at Acknowledgments JHEP07(2018)079 , , ]. Phys. (B.2) τ corre- ν , O → SPIRE e -meters ν IN ]. 95 ][ and ]. ) are penalties to τ ) plus background SPIRE are the bin-to-bin ν IN i B.1 → [ ]. a, c c ( ]. SPIRE µ s . ν IN Global constraints on -meters and ][ SPIRE (2015) 052019 40 SPIRE norm IN σ IN oscillations in the NOMAD ][ (1995) 503 ), and also due to the standard k i e arXiv:1607.01176 ][ = , s ν [ D 91 ) ]. k i ]. b i B.2 → c -meters, σ bg µ ) 15 B 434 + ν ]. k Limits on sterile neutrino mixing using = k b SPIRE SPIRE a a IN IN σ ][ Phys. Rev. ][ arXiv:1605.08774 SPIRE (1 + , [ (1 + (2016) 151803 IN Search for sterile neutrinos mixing with muon hep-ex/0306037 arXiv:1407.6607 k ][ Search for Final NOMAD results on k [ – 19 – [ X . The last four terms in eq. ( Nucl. Phys. X s-chls bg-chls 117 , shape ) := ) := (2016) 033 σ b Unitarity and the three flavor neutrino mixing matrix is the result of the sum of signal ( i (2003) 19 a, c 08 T (2014) 094 ), which permits any use, distribution and reproduction in ( hep-ex/0106102 bg i ]. [ Non-unitarity of the leptonic mixing matrix: present bounds and s arXiv:1508.05095 10 [ B 570 JHEP that are marginalized over assuming they have been measured SPIRE collaboration, K. Abe et al., arXiv:1609.08637 , Phys. Rev. Lett. [ IN , λ (2001) 3 JHEP Non-unitarity, sterile neutrinos and non-standard neutrino interactions ][ , CC-BY 4.0 Search for neutrino oscillations at are total normalization systematical errors in signal and background, This article is distributed under the terms of the Creative Commons b B 611 Phys. Lett. σ (2016) 113009 , collaboration, P. Astier et al., collaboration, P. Astier et al., (2017) 153 collaboration, P. Adamson et al., 04 and . D 93 are the theoretical events (depending on the model parameters) while j a σ σ function due to the systematics included in eq. ( T 2 arXiv:1410.2008 Nucl. Phys. Rev. JHEP neutrinos in MINOS NOMAD experiment NOMAD oscillations including a new search for tau-neutrino appearance using hadronic tau decays from a nuclear power reactor atSuper-Kamiokande Bugey atmospheric neutrinos in Super-Kamiokande [ MINOS heavy neutrino mixing future sensitivities j ), where the systematical errors where included in the usual form: χ S. Parke and M. Ross-Lonergan, M. Blennow et al., S. Antusch and O. Fischer, E. Fernandez-Martinez, J. Hernandez-Garcia and J. Lopez-Pavon, Y. Declais et al., b ¯ λ ( [8] [9] [6] [7] [4] [5] [1] [2] [3] Attribution License ( any medium, provided the original author(s) and source are credited. References uncorrelated systematics with error the oscillation parameters as Open Access. Where respectively. For simplicity we have assumed sponds to the ‘observed’ events. bg where JHEP07(2018)079 , ] C , ] C 83 ] C 83 ]. A Phys. Rev. , SPIRE ]. ]. IN Phys. Rev. (2017) 093005 arXiv:0704.1500 , Phys. Rev. ][ [ , 19 SPIRE SPIRE arXiv:1007.1150 ]. 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