Non-unitarity, sterile neutrinos, and non-standard neutrino interactions

Journal of High Energy Physics, Apr 2017

Abstract The simplest Standard Model extension to explain neutrino masses involves the addition of right-handed neutrinos. At some level, this extension will impact neutrino oscillation searches. In this work we explore the differences and similarities between the case in which these neutrinos are kinematically accessible (sterile neutrinos) or not (mixing matrix non-unitarity). We clarify apparent inconsistencies in the present literature when using different parametrizations to describe these effects and recast both limits in the popular neutrino non-standard interaction (NSI) formalism. We find that, in the limit in which sterile oscillations are averaged out at the near detector, their effects at the far detector coincide with non-unitarity at leading order, even in presence of a matter potential. We also summarize the present bounds existing in both limits and compare them with the expected sensitivities of near-future facilities taking the DUNE proposal as a benchmark. We conclude that non-unitarity effects are too constrained to impact present or near future neutrino oscillation facilities but that sterile neutrinos can play an important role at long baseline experiments. The role of the near detector is also discussed in detail.

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Non-unitarity, sterile neutrinos, and non-standard neutrino interactions

Received: October Non-unitarity, sterile neutrinos, and non-standard neutrino interactions Mattias Blennow 1 2 4 7 8 9 10 Pilar Coloma 1 2 4 6 8 9 10 Enrique Fernandez-Martinez 1 2 3 4 8 9 10 Josu Hernandez-Garcia 1 2 3 4 8 9 10 Jacobo Lopez-Pavon 0 1 2 4 5 8 9 10 Open Access 1 2 4 8 9 10 c The Authors. 1 2 4 8 9 10 Cantoblanco E-28049 Madrid, Spain 0 CERN, Theoretical Physics Department 1 via Dodecaneso 33 , 16146 Genova , Italy 2 P. O. Box 500, Batavia, IL 60510 , U.S.A 3 Instituto de F sica Teorica UAM/CSIC 4 KTH Royal Institute of Technology, Albanova University Center , 106 91 Stockholm , Sweden 5 INFN , Sezione di Genova 6 Theoretical Physics Department, Fermi National Accelerator Laboratory 7 Department of Theoretical Physics, School of Engineering Sciences 8 nd that , in the limit 9 Calle Nicolas Cabrera 13-15 , Cantoblanco E-28049 Madrid , Spain 10 [21] G.H. Collin, C.A. Arguelles, J.M. Conrad and M.H. Shaevitz , Sterile neutrino ts to short The simplest Standard Model extension to explain neutrino masses involves the addition of right-handed neutrinos. At some level, this extension will impact neutrino oscillation searches. In this work we explore the di erences and similarities between the case in which these neutrinos are kinematically accessible (sterile neutrinos) or not (mixing matrix non-unitarity). We clarify apparent inconsistencies in the present literature when using di erent parametrizations to describe these e ects and recast both limits in the popular neutrino non-standard interaction (NSI) formalism. We in which sterile oscillations are averaged out at the near detector, their e ects at the far detector coincide with non-unitarity at leading order, even in presence of a matter potential. We also summarize the present bounds existing in both limits and compare them with the expected sensitivities of near-future facilities taking the DUNE proposal as a benchmark. We conclude that non-unitarity e ects are too constrained to impact present or near future neutrino oscillation facilities but that sterile neutrinos can play an important role at long baseline experiments. The role of the near detector is also discussed in detail. neutrino; interactions; cDepartamento de F sica Teorica; Universidad Autonoma de Madrid - Non-unitarity and sterile neutrino phenomenology comparison 1 Introduction Sterile neutrino case Present constraints on deviations from unitarity DUNE sensitivities A Current constraints on sterile neutrinos The simplest extension of the Standard Model (SM) of particle physics able to account for the evidence for neutrino masses and mixings is the addition of right-handed neutrinos to its particle content. A Majorana mass term for these new singlet fermions is then allowed by all symmetries of the Lagrangian. This new mass scale at which lepton number is violated could provide a mechanism to also explain the origin of the observed matterantimatter asymmetry of the Universe [1] and is a necessary missing piece to solve the mysterious avour puzzle. However, given that this new mass scale is not related to the electroweak symmetry breaking mechanism, there is no theoretical guidance for its value. A large Majorana scale leads to the celebrated seesaw mechanism [2{5], providing a very natural explanation of the lightness of neutrino masses. On the other hand, it also leads to unnaturally large contributions to the Higgs mass, worsening the hierarchy problem [6]. Conversely, a light neutrino mass could also naturally stem from a symmetry argument [7{ 13]. Indeed, neutrino masses are protected by the lepton number symmetry and, if this is an approximate symmetry of the theory, a large hierarchy of scales is not required to naturally accommodate the lightness of neutrinos. Thus, the value of this scale of new physics can only be probed experimentally and, depending on its value, very di erent and interesting phenomenology would be induced in di erent observables. In this work we analyze the phenomenological impact of these new physics in neutrino oscillation facilities. If the new mass scale is kinematically accessible in meson decays, the sterile states will be produced in the neutrino beam. On the other hand, if the extra neutrinos are too heavy to be produced, the e ective three by three PMNS matrix will show unitarity deviations. We will refer to these situations as sterile and non-unitary neutrino oscillations, respectively. The aim of this work is to discuss in which limits these two regimes lead to the same impact on the oscillation probabilities, and reconcile apparently inconsistent results in previous literature. This work is organized as follows. In section 2 we will compare the non-unitarity and sterile neutrino phenomenology and discuss in which cases both limits are equivalent. In section 3 we will present and solve the apparent inconsistency present in the literature studying non-unitarity e ects in di erent parametrizations, and provide a mapping between the two. In section 4 we will recast both scenarios using the popular NSI parametrization. The existing bounds, applicable in both regimes, from present observables are summarized in section 5. Finally, in section 6 we present the sensitivity of the prospective Deep Underground Neutrino Experiment (DUNE) to these e ects, and our conclusions are summarized in section 7. Non-unitarity and sterile neutrino phenomenology comparison In this section we will show how, under certain conditions, the phenomenology of nonunitarity and sterile neutrino oscillations are equivalent to leading order in the activeheavy mixing parameters, not only in vacuum but also in matter. If n extra right-handed neutrinos are added to the SM Lagrangian, the full mixing matrix (including both light and heavy states) can be written as U = where N represents the 3 longer be unitary.1 Here, 3 active-light sub-block (i.e., the PMNS matrix), which will no n sub-block that includes the mixing between active and heavy states, while the R and S sub-blocks de ne the mixing of the sterile states with the light and heavy states, respectively. Note that both R and S are only de ned up to an unphysical rotation of the sterile states and that neither of them will be involved when considering oscillations among active avours. Non-unitarity case In the case of non-unitarity, only the light states are kinematically accessible and the amplitude for producing one of these states in conjunction with a charged lepton of avour particular decay is proportional to the mixing matrix element N i. In the mass eigenstate basis, the evolution of the produced neutrino state is given by the Hamiltonian [14] H = VNC 1Note that this is true regardless whether the extra states are kinematically accessible or not. where VCC = p GF nn= 2 are the charged-current (CC) and neutralcurrent (NC) matter potentials, respectively. The oscillation evolution matrix S0 in this basis is now de ned as the solution to the di erential equation = P Sterile neutrino case In the sterile neutrino scenario, all of the states are kinematically accessible and the full oscillation evolution matrix S, involving both light and heavy states, takes the form denotes the \theoretical" oscillation probabilities (although it should be noted that they do not add up to one), de ned as the ratio between the observed number of events divided by the product of the SM-predicted ux times cross section. In other words, is the factor that would be needed to obtain the number of events after convolution with the standard model ux and cross sections. However, in practice neutrino oscillation experiments do not measure P . present and future experiments rather determine the ux and cross sections via near detector data and extrapolate to the far detector by correcting for the di erent geometries, angular apertures, and detection cross sections. In this scenario, the oscillation probability would then inferred from the ratio where R and R are the observed event rates at the far detector and the corresponding extrapolation of the near detector result, respectively. For the near detector, we assume that the phases corresponding to the propagation of the light neutrinos have not yet developed potential, this equation has the formal solution S0 = exp( iHL) : The amplitude for a neutrino in the mass eigenstate j to interact as a neutrino of avour is given by the mixing matrix element N j , which means that the oscillation probability will be given by = j(N S0N y) j2: iS_ 0 = HS0 S = U S0U y; where S0 is the full (3 + n) (3 + n) evolution matrix expressed in the mass eigenbasis. For vacuum oscillations, we nd that S 3 sub-block S can be simpli ed to 0 = diag exp( i mj21L=2E) . Therefore, the active where ; stand for active neutrino avors, J is the phase factor acquired by the heavy state J as it propagates, and S0 is de ned in the same way as in the non-unitarity case. mi2J L=E In the limit of large mass squared splitting between the light and heavy states (i.e., 1) the oscillations are too fast to be resolved at the detector and only an averaged-out e ect is observable. In this averaged-out limit, the cross terms between the rst and second term in the evolution matrix average to zero and we nd = jS j2 = which recovers the same expression as eq. (2.5) up to the O( 4) corrections.2 Thus, we can conclude that averaged-out sterile neutrino oscillations in vacuum are equivalent to non-unitarity to leading order (this equivalence is indeed lost at higher orders). We will therefore concentrate on this averaged-out limit for the rest of this paper. For oscillations in the presence of matter, the sterile neutrino oscillations will be subjected to a matter potential that in the avour basis takes the form Hmat = V3 3 = B@ If the matter potential is small in comparison to the light-heavy energy splitting the light-heavy mixing in matter will be given by ~ J = to rst order in perturbation theory. In the limit mi2J =2E VCC; VNC, we can therefore neglect the di erence between the heavy mass eigenstates in vacuum and in matter, and apply eq. (2.10). Thus, we conclude from this that the matter Hamiltonian in the light sector can be computed in exactly the same way as for the non-unitarity scenario and we therefore nd the very same expressions for the \theoretical" probability in eq. (2.5) as for the non-unitarity case, at leading order in 2Note that this expression is also applicable whenever the light and heavy states decohere due to wave mi2J =2E, In the case of sterile neutrinos one also needs to consider the impact of the near detector measurements on the extraction of the experimentally measurable probability. In this work we will always assume that the oscillations due to the additional heavy states are averaged out at the far detector. However, this might not be the case at the near detector. Ideally, both sets of observables should be simulated and analyzed together consistently. Nevertheless, the following simpli ed limiting cases can be identi ed: 1. The light-heavy oscillations are averaged out already at the near detector. For practical purposes, the oscillation phenomenology in this case is identical to the nonunitarity case and eq. (2.7) also applies. For the experimental setup of DUNE, that will be studied as an example of these e ects in section 6, with a peak neutrino en2:5 GeV and a near detector distance of 0:5 km, this is the case when m2 & 100 eV2. 2. The light-heavy oscillations have not yet developed at the near detector, but are averaged out at the far detector. In this case, the near detector would measure the uxes and cross sections, and therefore the denominator in eq. (2.7) would be equal to one. In this case, the experimental probability would coincide with the \theoretical" probability in eq. (2.5). This scenario is the one implicitly assumed in many phenomenological studies, given the simplicity of eq. (2.5). However, it is typically only applicable in a very small part of the parameter space, i.e., for very particular values of m2 (which depend on the neutrino energy and on the near and far detector baselines). For DUNE, since the far detector baseline is 1300 km, this would be the case only in the region 0:1 eV2 . m2 < 1 eV2. This scenario will nevertheless be explored in section 6 to highlight its di erences relative to the previous one, which is applicable in a larger fraction of the m2 parameter space. 3. The oscillation frequency dictated by the light-heavy frequency matches the near detector distance. In this case, oscillations could be seen at the near detector as a function of neutrino energy, leading to more striking signals. At DUNE, this regime is matched for values of m2 in the range presently favoured by the LSND/MiniBooNE [15, 16] and reactor anomalies [17, 18] (see [19{21] for recent reviews). We expect that the sensitivity to this part of the parameter space will be dominated by the dedicated experiments to explore these anomalies, such as the Fermilab shortbaseline neutrino program [22], leaving little room for their averaged-out e ects to be observed at the far detectors in long-baseline oscillation experiments, not optimized for these searches. Therefore, this scenario will not be discussed further. Parametrizations The two most widely used parametrizations to encode these non-unitarity e ects stemming from the heavy-active mixing are N = (I N = T U = (I is a Hermitian matrix [23, 24] and T is a lower triangular matrix [25{28]. In eq. (3.1) both U and U 0 are unitary matrices that are equivalent to the standard PMNS matrix up to small corrections proportional to the deviations encoded in = B@ e = (1 T ) = B@ lead to a lower triangular matrix. For 3 extra neutrinos we can use U36U26U16U35U25U15 U34U24U14 (where we have not included unphysical rotations among the sterile neutrinos), leading to [25]: Majorana mass scales. Thus, (1 ) is just the rst term in the cosine series correcting the unitary rotation U 0. It is also straightforward to obtain the relation between the heavy-active neutrino mixing and the parameters in the triangular parametrization, if one considers that the heavy-active mixing can also be encoded by introducing additional complex rotations characterized by new mixing angles ij , with j > 3. For example, U14 = BBB 00 1. Note that we choose to label the matrix elements with avour indices for notation ease instead of using numbers as in [27]. Furthermore, in [27] the identity matrix is not singled out from as in our eq. (3.2) so that the diagonal elements ii in [27] are close to 1 instead of small. Therefore, in practice, . These changes are only cosmetic and the following discussion applies to [27] with the above-mentioned The deviations from unitarity are directly related to the heavy-active neutrino mixing. For instance, in the hermitian parametrization one can directly identify [29] ' B@s^14s^24 + s^15s^25 + s^16s^26 s^14s^34 + s^15s^35 + s^16s^36 s^24s^34 + s^25s^35 + s^26s^36 21 (s234 + s235 + s236) which is accurate to second order in the (small) extra mixing angles. In principle, the two parametrizations should be equally valid. However, the alternative use of each of them seemingly leads to inconsistent results. As an illustrative example, let us compare the disappearance probability in the atmospheric regime in the two 21 = 0 = 1 = 1 ij = mi2j L=4E. Here, P vacuum including the normalization factors as discussed in section 2. denotes the \experimental" oscillation probability in The naive conclusion derived from eq. (3.6) is that for the Hermitian parametrization good sensitivity to the non-unitarity parameter is expected in this channel, since it appears at linear order. Conversely, the triangular parametrization does not show this e ect. This apparent inconsistency stems from the fact that the unitary matrices U and U 0 are, in fact, di erent. This is the case even though these matrices are traditionally identi ed with the standard unitary PMNS matrix in each parametrization. However, this identi cation is only accurate up to the small corrections stemming from the deviations from unitarity. As we will show below, the di erences between the two are indeed linear in the non-unitarity parameters, and the two matrices can be easily related to each other. The relevant question is therefore which of these matrices, if any, that more closely matches the one that is determined through the present neutrino oscillation data. Starting from eq. (3.1) a unitary rotation V can be performed to relate U and U 0 From the rst relation in eq. (3.8) the elements of V can be identi ed as at linear order in . Substituting again in eq. (3.8) the relations N = (I )U = (I = (I U = V yU 0: V = I 0 C = B2 e 102 = 203 = C0P = 103 = Re( s23ei CP e are found. This implies the following mapping between the two sets of mixing angles3 in When the relations given in eqs. (3.10) and (3.12) are taken into account the predictions for the di erent oscillation channels coincide at leading order in the non-unitarity parameters, as they should. An important conclusion derived from this is that the determination of the mixing angles themselves will generally be a ected by non-unitarity corrections. However, the size of these corrections is, at present, negligible compared to the current uncertainties on the determination of the mixing angles themselves. These corrections are parametrization-dependent but, when taken into account and propagated consistently, the predictions derived from both schemes agree. For neutrino oscillation studies it seems advantageous to adopt the triangular parametrization, since it leads to fewer corrections given its structure. For instance, in the example shown in eq. (3.6) there are no corrections coming from non-unitarity for this parametrization, and thus the angle 23 in U can be identi ed with the angle determined in present global ts to a good approximation. Indeed, this is also the case for 12 and 13, since the Pee oscillation probabilities in the solar regime (KamLAND) and in the atmospheric regime (Daya Bay, RENO, Double-Chooz) are also independent of any non-unitarity corrections at linear order when the triangular parametrization is considered and when the appropriate normalization is taken into account, see section 2. Thus, the U matrix from the triangular parametrization corresponds, to a good approximation, with the unitary matrix obtained when determining 12, 23 and 13 through present (disappearance) neutrino oscillation measurements. Since we are here interested in the impact of non-unitarity and sterile neutrinos on neutrino oscillation phenomenology we will therefore use the triangular parametrization in the remainder of this work. As we will see in section 6, the dependence on the diagonal non-unitarity parameters is particularly interesting. Indeed, when the normalization accounting for the new physics e ects at the near detector is considered, it e ectively cancels any leading order in disappearance channels in vacuum. This can be easily understood 3Note that, apart from correcting the PMNS mixing angles and CP-phase CP at order , phase rede nitions of the three charged leptons as well as corrections to the two neutrino Majorana phases are necessary at the same order. by introducing the triangular parameterization in eq. (2.7). Expanding in = (1 + the dependence on cancels out. This illustrates how relevant the role of the near detectors is regarding the sensitivity to the new physics parameters. Both types of new physics e ects in neutrino oscillations discussed above can be described through the Non-Standard Interaction (NSI) formalism, which parametrizes the new physics e ects in neutrino production, detection, and propagation processes in a completely model-independent way. Let us rst focus on NSI a ecting neutrino production and detection. When these e ects are included, the oscillation probability is given by (1 + d)U S0U y(1 + s where s and d are general 3 3 complex matrices which represent the NSI modi cations to the production and detection diagrams, respectively. S0 is de ned in eq. (2.4) with the Hamiltonian H given in eq. (2.2). The non-unitarity (eq. (2.5)) and averaged-out sterile neutrino (eq. (2.10)) e ects at production and detection can be mapped to the NSI formalism (eq. (4.1)) with the identi cation = d This mapping can be easily obtained just considering the triangular parameterization, which can be applied in both the non-unitarity and averaged-out sterile neutrino cases, in eqs. (2.5) or (2.10) and comparing the result to eq. (4.1). On the other hand, NSI a ecting neutrino propagation are usually described through H = C + VCC U y B in the mass basis, where U is the standard unitary PMNS matrix, and are complex and real parameters respectively. In order to understand how the nonunitarity/averaged-out sterile neutrino corrected matter e ects can be translated to this parametrization, we introduce the triangular parameterization of N into eq. (2.2), obtaining the following Hamiltonian at leading order in H = where approximately equal densities of electrons ne and neutrons nn (for the neutral current contribution) in the Earth have been assumed (see also ref. [30]). Comparing eqs. (4.4) and (4.3) we nd the mapping between the NSI parametrization and the lower triangular parametrization of the non-unitarity and sterile neutrino scenarios ee = e = e = which apply for neutrino oscillation experiments in the Earth with constant matter. Note that, in presence of production and detection NSI, the same normalization as for the nonunitarity case discussed in section 2 needs to be taken into account. Present constraints on deviations from unitarity The mapping to NSI described above works both for the non-unitarity and the averaged out sterile neutrino contributions to neutrino oscillations. However, the present constraints on each of these contributions from other observables are very di erent. Indeed, PMNS nonunitarity from very heavy extra neutrinos induces modi cations of the W and Z couplings that impact precision electroweak and avour observables [14, 30{44]. These modi cation translate into very strong upper limits on the parameters. These have been taken from ref. [44] and are listed in the left column in table 1. The second number quoted in parenthesis for the e element includes the ! e observable, which can in principle be evaded [45] for heavy neutrino masses close to MW and some ne-tuning of the parameters. In this case, the quoted bound is derived from the constraints on the diagonal parameters, through eq. (3.5). However, for sterile neutrinos with masses below the electroweak scale these stringent constraints are lost, since all mass eigenstates are kinematically available in the observables used to derive the constraints and unitarity is therefore restored. If the masses of the extra states are in the MeV or GeV range, even stronger constraints can be derived from direct searches at beam-dump experiments as well as from meson and beta decays [51{53]. On the other hand, for masses below the keV scale even the beta decay searches are no longer sensitive, and the only applicable bounds are the much milder constraints stemming from the non-observation of their e ects in neutrino oscillation experiments [19, 54, 55]. The sensitivity, or lack thereof, of oscillation experiments to sterile neutrino mixing will depend on the actual value of the sterile neutrino mass, which determines if the corresponding m2 leads to oscillations for the energy and baseline that characterize the experimental m2 increases, there will be a point at which the sterile neutrino oscillations enter the averaged-out regime. Once oscillations are averaged-out, the constraints derived will become independent of m2 and apply to arbitrarily large values of derived in this regime are summarized in in the middle column of table 1 and apply as m2 > 100 eV2. They are thus relevant when the sterile neutrino oscillations are in the averaged out regime for both the near and far detectors of the DUNE experiment. Some of these constraints also apply for values of m2 smaller than 100 eV2. For a more parameters in the scenarios considered in this work. The limits are shown at 2 and 95% C.L. (1 d.o.f.) for the non-unitarity and light sterile neutrino scenarios. The bounds in the middle column apply for m2 & 100 eV2 and will thus be relevant when the sterile neutrino oscillations are in the averaged-out regimes for both the near and far detectors of most long-baseline experiments. The bounds in the right column apply for 1 eV2 and will thus be relevant when the sterile neutrino oscillations are in the averaged-out regime for the far detector, but not for the near detector. The second number quoted in parenthesis for the e element includes the ! e observable, which can in principle be evaded [45], see main text for details. The numbers for the o -diagonal parameters without a reference are obtained indirectly from constraints on the diagonal parameters via for further details. (see eq. (3.5)). See appendix A comprehensive breakdown of the available constraints and their ranges of applicability, we refer the interested reader to appendix A. Even though the case in which the sterile neutrino oscillations are undeveloped at the near detector, but averaged-out at the far, applies to a signi cantly smaller fraction of the parameter space, we nd it instructive to analyze this scenario as well, since it leads to very di erent phenomenology and sensitivities, as will be discussed in section 6. For the case of DUNE, this scenario requires 0:1{1 eV2 and the corresponding constraints have been compiled in the right column of table 1. Notice that in this range of constraints come from experiments that would not have reached the averaged-out regime but would rather have oscillations well-matched to their energies and baselines. Thus, the corresponding constraints in this regime oscillate signi cantly and the value quoted in the table is the most conservative available in that range. DUNE sensitivities In this section we present, as an example, the sensitivities that the proposed DUNE experiment would have to PMNS non-unitarity or, equivalently, to averaged-out sterile neutrino oscillations as discussed in section 2. For this analysis we choose the triangular parametrization of the new physics e ects since, as argued in section 3, its unitary part can be more directly mapped to the \standard" PMNS matrix as determined by present experiments through neutrino oscillation disappearance channels. Indeed, production and detection new physics e ects in a given channel P only depend on the elements such that ; when the avour indices are ordered as e < [27]. Furthermore, when the new physics a ects the near and far detectors in the same manner, the normalization of the oscillation probabilities presented in eq. (2.7) has to be applied, which e ectively cancels any leading order dependence on the new physics parameters in disappearance channels in vacuum (see eq. (3.13)). The choice of the facility under study is motivated by the strong matter e ects that characterize the DUNE setup and that allow to probe not only the source and detector e ects induced by the new physics, but also the matter e ects which now provide sensitivity to other parameters not necessarily satisfying ; The simulation of the DUNE setup was performed with the GLoBES software [56, 57] using the DUNE CDR con guration presented in ref. [58]. The new physics e ects have been implemented in GLoBES via the MonteCUBES [59]4 plug-in, which has also been used to perform a Markov chain Monte Carlo (MCMC) scan of the 15-dimensional parameter space (the 6 standard oscillation parameters plus the 6 moduli of the and the 3 phases of the o -diagonal elements). In the t, the assumed true values for the standard oscillation parameters are set according to their current best- ts from ref. [60]. The mixing angles and squared-mass splittings are allowed to vary in the simulations, using a Gaussian prior corresponding to their current experimental uncertainties from ref. [60] centered around their true values. In the case of 13 and 23 the Gaussian priors are implemented on sin2 2 , which is a more accurate description of the present situation and, in the case of 23, allows to properly account for the octant degeneracy: sin2 2 23 = 0:991 m231 = (2:457 0:049) 10 3 eV2, 12 = 33:48 0:77 , sin2 2 13 = 0:085 0:02. Notice that, as described in section 3, the use of the triangular m221 = (7:50 parametrization allows a direct mapping of the present measurements to the elements of the U matrix. Nevertheless, the present uncertainties adopted in this analysis are still large enough that any correction due to non-unitarity is negligible. The CP-violating phase is a 2% uncertainty in the PREM matter density pro le [61] has also been considered. The nal 2 implemented in our simulations reads: ch i=1 2 = min 2 X X Ncthe;sit(f ; g) Ncthru;ie +Ncthru;ie log where we are summing over di erent oscillation channels (ch) and energy bins (i). Here, N test and N true are the predicted and observed event rates, respectively, and f g denotes the standard and non-unitarity oscillation parameters. The nal 2 is obtained after minimization over all nuisance parameters f g, where j are the corresponding priors. Note that in eq. (6.1) only the far detector event rates are considered, while the values of the systematic errors from ref. [58] assume the presence of a near detector in order to reduce the uncertainties on the ux and the cross section relevant for the far detector. In presence of non-unitarity or averaged steriles, there might be already new physics e ects at the near detector and thus, ideally, both detectors should be simulated together with correlated systematics. However, the exact design and technology for the DUNE near detector is still in discussion within the collaboration and a full simulation of the two detectors with 4A new version of the MonteCUBES software implementing the triangular parametrization is available. correlated systematic errors is beyond the scope of this work. We nevertheless take into account the impact that new physics would have on the near detector by normalizing our probability according to eq. (2.7) and the discussion in section 2. We have performed simulations for two distinct new physics scenarios. In the rst case (ND averaged) we normalize the oscillation probabilities according to eq. (2.7). Indeed, as discussed in section 2, at leading order in the new physics parameters this scenario accurately describes both the e ects of PMNS non-unitarity from very heavy neutrinos as well as sterile neutrino oscillations that have been averaged out both at the near detector (ND) and far detector. For the DUNE setup, the requirement for having averaged-out oscillations at the near detector translates to the condition m2 > few 100 eV2. The second scenario (ND undeveloped) would correspond to the case where sterile neutrino oscillations are averaged out at the far detector but have not yet developed at the near detector. In this case, no extra normalization is needed and the oscillation probability is directly given by eq. (2.5). Note that, for the energies and baseline characterizing the DUNE setup, only values of the sterile neutrino masses around 0:1{1 eV2 roughly satisfy these conditions. However, we nd it instructive to study also this regime in order to remark the di erences between the two scenarios and the importance of the normalization in eq. (2.7) that will generally apply in most of the parameter space. Figures 1 and 2 show the expected sensitivities to the new physics parameters. These have been obtained by assuming that the true values of all entries are zero to obtain the corresponding expected number of events, and tting for the corresponding parameters while marginalizing over all other standard and new physics parameters. The resulting frequentist allowed regions are shown at at 1 , 90%, and 2 C.L. The sensitivities obtained for all parameters fall at least one order of magnitude short of the current bounds on the non-unitarity from heavy neutrino scenario presented in table 1. Thus, the standard three-family oscillations explored at DUNE (and the other present and near-future oscillation facilities) will be free from the possible ambiguities that could otherwise be induced by this type of new physics [62{65]. While these bounds on nonunitarity are too strong for these e ects to be probed at present and near-future facilities a Neutrino Factory [66, 67] could be precise enough to explore these e ects [24, 29, 68]. The situation is slightly di erent if the results are interpreted in terms of an averaged-out sterile neutrino, since present constraints are weaker in this case. We will therefore focus on this scenario for the rest of our discussion and also study the case in which DUNE data is complemented by our present prior constraints on the sterile neutrino mixing (middle and right columns of table 1 for the ND averaged and undeveloped scenarios respectively), since synergies between the data sets may be present. This case is depicted with dashed gures 1 and 2. As an example of such synergy, the sensitivity to the real part improves for the ND undeveloped scenario through the combination of DUNE data and the present priors with respect to both datasets independently. Indeed, the prior on its own would give the same bound for the real an imaginary parts (as for the ND averaged case in the left panel) and its value roughly corresponds to the constraint obtained for the the imaginary part of , while the sensitivity to the real part does improve through the combination with DUNE. physics parameters are assumed to be zero so as to obtain the expected sensitivities. The left panels (ND averaged) correspond to the non-unitarity case, or to the sterile case when the lightheavy oscillations are averaged out in the near and far detectors. The right panels (ND undeveloped) give the sensitivity for the sterile case when the light-heavy oscillations have not yet developed in the near detector, but are averaged out in the far. The solid lines correspond to the analysis of DUNE data alone, while the dashed lines include the present constraints on sterile neutrino mixing from the middle and right columns in table 1 for the NS averaged and ND undeveloped scenarios Another conclusion that can be drawn from gure 1 is that the sensitivities to the diagonal parameters ee and are signi cantly stronger for the ND undeveloped (right panels) as compared to the ND averaged scenario (left panels). This was to be expected since the source and detection e ects that provide a leading order sensitivity to the diagonal parameters are totally or partially cancelled once the normalization of eq. (2.7) is included (see eq. (3.13)). In the disappearance channel both e ects cancel in the ratio, while for the appearance channel there is a partial cancellation that only allows the experiment to be sensitive to the combination . This leads to a pronounced correlation among ee , seen in the upper left panel of gure 1. From a phenomenological point of view we observe that, if both near and far detectors are a ected by the new physics in the same way (as is the case when the sterile neutrino oscillations are averaged out at both detectors, or in the non-unitarity scenario) their e ects are more di cult to observe since they cannot be disentangled from the cross section determination at the near detector. Conversely, in the case in which sterile neutrino oscillations have not yet developed at the near detector but are averaged out at the far, the ux determined by both detectors will have a di erent normalization. Thus, a strong linear sensitivity to is obtained from detector and source e ects respectively, although there is no improvement over present constraints. Figure 1 also shows strong correlations in the middle left panel, involving ee. Indeed, sensitivity to comes through the matter e ects, which only depend on the diagonal entries through their di erences , since a global term of the form I does not a ect neutrino oscillations at leading order in . In these panels we also observe a large di erence between the allowed regions for once prior constraints on the parameters are included in the analysis, by comparing the solid and dashed lines. This is due to the lifting of degeneracies involving 23 and the combination be discussed in more detail below. Interesting correlations and degeneracies among the standard and new physics parameters can indeed take place in the averaged-out sterile neutrino scenario [55, 69{71]. In our results, even though the true values of the parameters were set to zero, some very interesting correlations and degeneracies among 23 and the new physics parameters have been recovered. These are shown in gure 2, and have been noticed in the context of NSI5 in refs. [72{75] (for other works on degeneracies among standard and non-standard parameters in DUNE see e.g., refs. [76{79]). The rst degeneracy appears for the wrong octant of 23, which would otherwise be correctly determined by the interplay between the appearance and disappearance channels at DUNE (see e.g., ref. [80]). We have checked that this degeneracy is characterized by non zero values of e with a non-trivial phase around . At the same time, positive values of are slightly preferred. From ref. [75] this degeneracy was expected for the phase of e = arg( since CP = =2 and strong correlations between these two parameters are required in order to reproduce this degeneracy. Note that this degeneracy is partially lifted in the ND undeveloped scenario (right panels). Indeed, the strong sensitivity that this scenario presents to into very stringent bounds that do not allow the preferred positive values of in the left panels for the ND averaged case since the diagonal elements of are positive (see eq. (3.5)). Upon the inclusion of prior constraints this degeneracy is lifted in both scenarios. Interestingly, the second degeneracy involves values of 23 =4, so that it could potentially compromise the capabilities of DUNE to determine the maximality of this 5Note the correspondence between NSI, steriles, and non-unitarity presented in section 4. -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.02 0.04 0.06 0.08 0.02 0.04 0.06 0.08 physics parameters are assumed to be zero so as to obtain the expected sensitivities. The left panels (ND averaged) correspond to the non-unitarity case, or to the sterile case when the lightheavy oscillations are averaged out in the near and far detectors. The right panels (ND undeveloped) give the sensitivity for the sterile case when the light-heavy oscillations have not yet developed in the near detector, but are averaged out in the far. The solid lines correspond to the analysis of DUNE data alone, while the dashed lines include the present constraints on sterile neutrino mixing from the middle and right columns in table 1 for the ND averaged and ND undeveloped scenarios mixing angle. This degeneracy takes place for 0:6, and large values of e are also needed. Fortunately, present constraints on these parameters are already strong enough to also rule out this possibility (see table 1), so that a clean determination of the maximality of 23 should be possible at DUNE. Moreover, when the current bound on e from the right column in table 1 is added as prior to the simulations, the sensitivity to e is increased slightly beyond the present prior and the allowed region around 23 ruled out. This example shows explicitly the complementarity between current constraints and DUNE sensitivities. All in all, we nd that, upon solving the degeneracies through the inclusion of present priors, DUNE's sensitivity would slightly improve upon the present constraints on the ND averaged case as well as the real part of for the ND undeveloped scenario. While the potential improvement over present bounds is marginal, this also implies that, at the con dence levels studied in this work, the sensitivities to the standard three neutrino oscillations are rather robust and not signi cantly compromised by the new physics The simplest and most natural extension of the Standard Model that can account for our present evidence for neutrino masses and mixings is the addition of right-handed neutrinos to the Standard Model (SM) particle content. Gauge and Lorentz invariance then imply the possible existence of a Majorana mass for these new particles at a scale to be determined by observations. In this work we have studied the impact that two limiting regimes for this new physics scale can have in neutrino oscillation experiments. For very high Majorana masses, beyond the kinematic reach of our experiments, the imprint of these new degrees of freedom at low energies takes the form of unitarity deviations of the PMNS mixing matrix. In the opposite limit, for small Majorana masses, these extra sterile neutrinos are produced and can participate in neutrino oscillations. However, it should be kept in mind that the neutrino oscillation phenomenology discussed here applies also to other types of new physics that could induce unitarity deviations for the PMNS mixing matrix. This includes any model in which heavy fermions mix with the SM neutrinos or charged leptons, as for instance the type-I/type-III seesaw, Left-Right symmetric models, and models with kinematically accessible sterile neutrinos in the averaged-out regime. Despite being sourced by di erent underlying physics, we have seen that, when the sterile neutrino oscillations are averaged out (and at leading order in the small heavy-active mixing angles) both limits lead to the same modi cations in the neutrino oscillation probabilities. Namely, a modi cation of the interactions in the source and detector which implies short-distance e ects as well as modi ed matter e ects which, contrary to the standard scenario, also involve neutral current interactions. However, the present constraints that apply to these two scenarios are very di erent. Indeed, PMNS non-unitarity is bounded at the per mille level, or even better for some elements, through precision electroweak and avour observables, while sterile neutrino mixing in the averaged-out regime is allowed at the percent level since it can only be probed via oscillation experiments themselves. Thus, PMNS non-unitarity can have no impact in present or near-future oscillation facilities while sterile neutrino mixing could potentially be discovered by them. We have also noted apparently con icting results depending on the parametrization used to encode these new physics e ects. The source of this apparent inconsistency was found to be the di erent quantities that are commonly identi ed with the standard PMNS matrix in each parametrization. The con ict was solved by providing a mapping between the two sets of parameters and by identifying the parametrization for which these PMNS parameters correspond to what is determined experimentally. The role of the near detector was also explored in depth. Indeed, since present and near future oscillation experiments constrain their uxes and detection cross sections using near detector data it is important to consider if the new physics a ects the near and far detector measurements in the same way. If this is the case, the source and detector short-distance e ects cancel to a large extent, since there is no additional handle to separate them from ux and cross-section uncertainties. This is always the case in the non-unitarity scenario and when sterile neutrino oscillations are averaged out both at the near and far detectors. Conversely, if sterile neutrino oscillations have not developed yet at the near detector, the determination of the ux and cross section is free from new physics ambiguities and, when compared with the far detector data, a greater sensitivity to the avour-conserving new physics e ects is obtained. This crucial di erence is sometimes overlooked in the present literature. Finally we also provided a mapping of these new physics e ects in the popular non-standard interaction (NSI) formalism. These e ects were exempli ed through numerical simulations of the proposed DUNE neutrino oscillation experiment. Our simulations con rm that PMNS non-unitarity is indeed beyond the reach of high precision experiments such as DUNE, but that sterile neutrino oscillations could manifest in several possible interesting ways. Indeed, degeneracies between 23 and the new physics parameters, previously identi ed in the context of NSI, have been found in our simulations. These degeneracies could potentially compromise the capability of DUNE to determine the maximality of 23 as well as its ability to discern its correct octant. We nd that current bounds on the new physics parameters are able to lift the degeneracies around 23 Through these simulations the importance of correctly accounting for the impact of the near detector was made evident. Indeed, a very signi cant increase in the sensitivity to the new physics parameters was found for the case in which the near detector is not a ected in the same way as the far. This would be the case of sterile neutrino oscillations that are undeveloped at the near detector but averaged out at the far. However, the parameter space for this situation to take place is rather small (for 0:1{1 eV2). The most common situation would rather be that in which sterile neutrino oscillations are averaged out at both near and far detectors. However, this fact has been usually overlooked in previous literature. The origin of neutrino masses remains one of our best windows to explore the new physics underlying the open problems of the SM. Its simplest extension to accommodate neutrino masses and mixings o ers a multitude of phenomenological consequences that vary depending of the new physics scale introduced and that should be thoroughly explored by future searches. In this work, we have explored the impact of these new physics in neutrino oscillation phenomena. We have found that neutrino oscillation facilities are best suited to probe the lightest new physics scales, i.e., kinematically accessible sterile neutrinos. Acknowledgments We warmly thank Joachim Kopp and Rafael Torres for useful discussions. We also thank Mariam Tortola for her useful input pointing out competitive bounds for the sterile neutrino mixings. We acknowledge support from the EU through grants H2020-MSCA-ITN2015/674896-Elusives and H2020-MSCA-RISE-2015/690575-InvisiblesPlus. This work was supported by the Goran Gustafsson Foundation (MB). EFM and JHG also acknowledge support from the EU FP7 Marie Curie Actions CIG NeuProbes (PCIG11-GA-2012-321582) and the Spanish MINECO through the \Ramon y Cajal" programme (RYC2011-07710), the project FPA2012-31880, through the Centro de Excelencia Severo Ochoa Program under grant SEV-2012-0249 and the HPC-Hydra cluster at IFT. Fermilab is operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy. EFM and JHG also warmly thank Fermilab for its hospitality during their InvisiblesPlus secondment where this project was initiated. Current constraints on sterile neutrinos In this appendix we summarize and explain in more detail the current constraints on sterile neutrinos that arise from oscillation searches in the averaged out regime and thus apply for arbitrarily large values of m2 as well as those stemming from electroweak and avour precision observables. Notice that, for the latter, some of the observables only apply above the electroweak scale [44]. Nevertheless, below this scale, stronger constraints from direct searches are available [51{53]. Regarding the oscillation searches, the validity of these constraints will depend on the particular con guration of the experiment used to derive it, which determines when the averaged-out regime is reached. These constraints together with their range of validity are listed in table 2. The strongest constraints on the mixing with electrons ( ee) stem from the BUGEY3 experiment [46]. At this experiment, oscillations enter the averaged-out regime for m2 & 4 eV2. Recent competitive constraints on this parameter by the Daya Bay experiment [83] tend to dominate for smaller m2 values and are comparable to the bounds from BUGEY-3 [46] around m2 & 0:1 eV2. In the range m2 & 0:1{1 eV2 the bound oscillates signi cantly between 3:0 10 3 and 1:0 10 2: therefore, we quote the latter more conservative bound in the rightmost column of table 1. Current limits on the elements are dominated by the bounds derived from the SK analysis of atmospheric neutrino oscillations [47]. These are derived in the averagedout regime, which in this case corresponds to stronger constraints for lower values of m2 & 0:1 eV2. For , MINOS [48] sets m2. Again, these oscillate between 4:4 10 3 and 1:4 10 2 in the range m2 & 0:1{1 eV2. Thus, we quote the more conservative bound in the rightmost column of table 1. Regarding , MINOS [84] has similar constraints to the ones from SK atmospherics. Stronger limits are obtained in the global t in ref. [85] but m2 = 6 eV2 and not in the averaged-out limit. For the o -diagonal elements, the strongest limit for e stems from the null results of appearance searches by NuTeV [82] j e j < 2:3 10 2, valid once they enter the m2 & 1000 eV2 [2] P. Minkowski, to sterile neutrinos above a certain mass range. The bounds on the o -diagonal elements which do not have a reference have been obtained indirectly from the bounds on the diagonal elements at that scale, using (see eq. (3.5)). averaged-out regime for m2 & 1000 eV2. Nevertheless, similar bounds from NOMAD [49] j e j < 2:5 10 2 and KARMEN [81] j e j < 2:8 10 2 apply for m2 & 100 eV2 and m2 & 10 eV2 respectively. NOMAD [50] also gives the most stringent constraints for m2 & 100 eV2. For e, the strongest bounds are derived from those on the diagonal elements through (see eq. (3.5)). Finally, for very light sterile neutrinos, 0:1 eV2, all the direct constraints on the o -diagonal elements from NuTeV, NOMAD and KARMEN fade away. In this case, the strongest bounds are obtained indirectly from the diagonal elements via Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [1] M. Fukugita and T. Yanagida, Baryogenesis without grand uni cation, Phys. Lett. B 174 (1986) 45 [INSPIRE]. ! e at a rate of one out of 109 muon decays?, Phys. Lett. B 67 (1977) 421 Phys. Rev. Lett. 44 (1980) 912 [INSPIRE]. [4] T. Yanagida, Horizontal symmetry and masses of neutrinos, in Proceedings of the Workshop on the Baryon Number of the Universe and Uni ed Theories, Tsukuba Japan, 13{14 Feb 1979 [INSPIRE]. PRINT-80-0576 [arXiv:1306.4669] [INSPIRE]. arguments. 1. Application to SUSY and seesaw cases, JHEP 11 (2004) 057 [hep-ph/0410298] [INSPIRE]. superstring models, Phys. Rev. D 34 (1986) 1642 [INSPIRE]. nonconservation at high-energies in a superstring inspired standard model, Phys. Lett. B 187 (1987) 303 [INSPIRE]. conserved lepton number, Nucl. Phys. B 312 (1989) 492 [INSPIRE]. Phys. Lett. B 249 (1990) 458 [INSPIRE]. standard model with Majorana elds, Z. Phys. C 55 (1992) 275 [hep-ph/9901206] [INSPIRE]. neutrino mass generation, Phys. Rev. D 76 (2007) 073005 [arXiv:0705.3221] [INSPIRE]. masses, JHEP 12 (2007) 061 [arXiv:0707.4058] [INSPIRE]. of the leptonic mixing matrix, JHEP 10 (2006) 084 [hep-ph/0607020] [INSPIRE]. beam, Phys. Rev. D 64 (2001) 112007 [18] P. Huber, On the determination of anti-neutrino spectra from nuclear reactors, Phys. Rev. C 84 (2011) 024617 [Erratum ibid. C 85 (2012) 029901] [arXiv:1106.0687] global picture, JHEP 05 (2013) 050 [arXiv:1303.3011] [INSPIRE]. observation of e appearance in a [hep-ex/0104049] [INSPIRE]. [arXiv:1303.2588] [INSPIRE]. [arXiv:1101.2755] [INSPIRE]. [16] MiniBooNE collaboration, A.A. Aguilar-Arevalo et al., Improved search for oscillations in the MiniBooNE experiment, Phys. Rev. Lett. 110 (2013) 161801 [arXiv:1512.04758] [INSPIRE]. baseline data, Nucl. Phys. B 908 (2016) 354 [arXiv:1602.00671] [INSPIRE]. A proposal for a three detector short-baseline neutrino oscillation program in the Fermilab booster neutrino beam, arXiv:1503.01520 [INSPIRE]. 6 avor mixing matrix in the presence of three [arXiv:1503.08879] [INSPIRE]. description of nonunitary neutrino mixing, Phys. Rev. D 92 (2015) 053009 unitarity violation in the lepton mixing matrix, Phys. Rev. D 93 (2016) 033008 [arXiv:1508.00052] [INSPIRE]. mixing and CP-violation at a neutrino factory, Phys. Rev. D 80 (2009) 033002 [arXiv:0903.3986] [INSPIRE]. with matter from physics beyond the standard model, Nucl. Phys. B 810 (2009) 369 [arXiv:0807.1003] [INSPIRE]. Phys. Lett. B 96 (1980) 159 [INSPIRE]. Phys. Rev. D 22 (1980) 2227 [INSPIRE]. [31] R.E. Shrock, New tests for and bounds on, neutrino masses and lepton mixing, pseudoscalar-meson decays, with associated tests for, and bounds on, neutrino masses and lepton mixing, Phys. Rev. D 24 (1981) 1232 [INSPIRE]. Phys. Rev. D 24 (1981) 1275 [INSPIRE]. Phys. Rev. D 38 (1988) 886 [INSPIRE]. [35] P. Langacker and D. London, Mixing between ordinary and exotic fermions, [36] S.M. Bilenky and C. Giunti, See-saw type mixing and Phys. Lett. B 300 (1993) 137 [hep-ph/9211269] [INSPIRE]. Phys. Lett. B 327 (1994) 319 [hep-ph/9402224] [INSPIRE]. neutrinos and lepton avor violation, Nucl. Phys. B 444 (1995) 451 [hep-ph/9503228] leptons, Phys. Lett. B 668 (2008) 378 [arXiv:0806.2558] [INSPIRE]. type-I seesaw models, JHEP 01 (2013) 118 [arXiv:1209.2679] [INSPIRE]. future sensitivities, JHEP 10 (2014) 094 [arXiv:1407.6607] [INSPIRE]. JHEP 02 (2016) 174 [arXiv:1511.03265] [INSPIRE]. JHEP 08 (2016) 079 [arXiv:1605.07643] [INSPIRE]. heavy neutrino mixing, JHEP 08 (2016) 033 [arXiv:1605.08774] [INSPIRE]. avor violation and non-unitary lepton mixing in low-scale type-I seesaw, JHEP 09 (2011) 142 [arXiv:1107.6009] [INSPIRE]. from a nuclear power reactor at Bugey, Nucl. Phys. B 434 (1995) 503 [INSPIRE]. [arXiv:1410.2008] [INSPIRE]. neutrinos in MINOS, Phys. Rev. Lett. 117 (2016) 151803 [arXiv:1607.01176] [INSPIRE]. ! e oscillations in the NOMAD experiment, Phys. Lett. B 570 (2003) 19 [hep-ex/0306037] [INSPIRE]. [50] NOMAD collaboration, P. Astier et al., Final NOMAD results on oscillations including a new search for appearance using hadronic Nucl. Phys. B 611 (2001) 3 [hep-ex/0106102] [INSPIRE]. JHEP 05 (2009) 030 [arXiv:0901.3589] [INSPIRE]. JHEP 06 (2012) 100 [arXiv:1112.3319] [INSPIRE]. arXiv:1502.00477 [INSPIRE]. [52] O. Ruchayskiy and A. Ivashko, Experimental bounds on sterile neutrino mixing angles, [53] M. Drewes and B. Garbrecht, Experimental and cosmological constraints on heavy neutrinos, [54] S. Parke and M. Ross-Lonergan, Unitarity and the three avor neutrino mixing matrix, Phys. Rev. D 93 (2016) 113009 [arXiv:1508.05095] [INSPIRE]. experiments in the presence of a sterile neutrino, JHEP 11 (2016) 122 [arXiv:1607.02152] experiments with GLoBES (General Long Baseline Experiment Simulator), Comput. Phys. Commun. 167 (2005) 195 [hep-ph/0407333] [INSPIRE]. of neutrino oscillation experiments with GLoBES 3.0: General Long Baseline Experiment Simulator, Comput. Phys. Commun. 177 (2007) 432 [hep-ph/0701187] [INSPIRE]. CDR, arXiv:1606.09550 [INSPIRE]. MonteCUBES, Comput. Phys. Commun. 181 (2010) 227 [arXiv:0903.3985] [INSPIRE]. status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE]. [64] S. Verma and S. Bhardwaj, Probing non-unitary CP violation e ects in neutrino oscillation experiments, arXiv:1609.06412 [INSPIRE]. determination at DUNE, NO A and T2K, arXiv:1609.07094 [INSPIRE]. [66] S. Geer, Neutrino beams from muon storage rings: characteristics and physics potential, factory, Nucl. Phys. B 547 (1999) 21 [hep-ph/9811390] [INSPIRE]. avor mixing at a neutrino factory, JHEP 04 (2010) 041 [69] J.M. Berryman, A. de Gouv^ea, K.J. Kelly and A. Kobach, Sterile neutrino at the Deep [70] S.K. Agarwalla, S.S. Chatterjee and A. Palazzo, Physics reach of DUNE with a light sterile neutrino, JHEP 09 (2016) 016 [arXiv:1603.03759] [INSPIRE]. neutrino, Phys. Rev. Lett. 118 (2017) 031804 [arXiv:1605.04299] [INSPIRE]. [73] A. de Gouv^ea and K.J. Kelly, Non-standard neutrino interactions at DUNE, Nucl. Phys. B 908 (2016) 318 [arXiv:1511.05562] [INSPIRE]. source, detector and matter non-standard neutrino interactions at DUNE, JHEP 08 (2016) 090 [arXiv:1606.08851] [INSPIRE]. full con guration of the Daya Bay experiment, Phys. Rev. Lett. 117 (2016) 151802 [84] MINOS collaboration, P. Adamson et al., Active to sterile neutrino mixing limits from neutral-current interactions in MINOS, Phys. Rev. Lett. 107 (2011) 011802 complete neutrino mixing matrix with a sterile neutrino, Phys. Rev. Lett. 117 (2016) 221801 [5] M. Gell-Mann , P. Ramond and R. Slansky , Complex spinors and uni ed theories , in Proceedings of the Supergravity Workshop , New York U.S.A., 27 { 28 Sep 1979 , [6] J.A. Casas , J.R. Espinosa and I. Hidalgo , Implications for new physics from ne-tuning [7] R.N. Mohapatra and J.W.F. Valle , Neutrino mass and baryon number nonconservation in [8] J. Bernabeu , A. Santamaria , J. Vidal , A. Mendez and J.W.F. Valle , Lepton avor [9] G.C. Branco , W. Grimus and L. Lavoura , The seesaw mechanism in the presence of a [10] W. Buchmu ller and D. Wyler , Dilatons and Majorana neutrinos, [11] A. Pilaftsis , Radiatively induced neutrino masses and large Higgs neutrino couplings in the [12] J. Kersten and A.Y . Smirnov , Right-handed neutrinos at CERN LHC and the mechanism of [13] A. Abada , C. Biggio , F. Bonnet , M.B. Gavela and T. Hambye , Low energy e ects of neutrino [14] S. Antusch , C. Biggio , E. Fernandez-Martinez , M.B. Gavela and J. Lopez-Pavon , Unitarity [15] LSND collaboration, A. Aguilar-Arevalo et al., Evidence for neutrino oscillations from the [19] J. Kopp , P.A.N. Machado , M. Maltoni and T. Schwetz , Sterile neutrino oscillations: the [17] G. Mention et al., The reactor antineutrino anomaly , Phys. Rev. D 83 ( 2011 ) 073006 [22] LAr1-ND, ICARUS-WA104 and MicroBooNE collaborations , M. Antonello et al., [23] A. Broncano , M.B. Gavela and E.E. Jenkins , The e ective Lagrangian for the seesaw model of neutrino mass and leptogenesis , Phys. Lett . B 552 ( 2003 ) 177 [Erratum ibid . B 636 ( 2006 ) 332] [hep-ph/0210271] [INSPIRE]. [24] E. Fernandez-Martinez , M.B. Gavela , J. Lopez-Pavon and O. Yasuda , CP-violation from non-unitary leptonic mixing , Phys. Lett . B 649 ( 2007 ) 427 [hep-ph/0703098] [INSPIRE]. [25] Z.-z. Xing, Correlation between the charged current interactions of light and heavy Majorana neutrinos , Phys. Lett . B 660 ( 2008 ) 515 [arXiv:0709.2220] [INSPIRE]. [26] Z.-z. Xing, A full parametrization of the 6 light or heavy sterile neutrinos, Phys. Rev. D 85 (2012) 013008 [arXiv:1110.0083] [27] F.J. Escrihuela, D.V. Forero, O.G. Miranda, M. Tortola and J.W.F. Valle, On the [28] Y.-F. Li and S. Luo, Neutrino oscillation probabilities in matter with direct and indirect [29] S. Antusch, M. Blennow, E. Fernandez-Martinez and J. Lopez-Pavon, Probing non-unitary [30] S. Antusch, J.P. Baumann and E. Fernandez-Martinez, Non-standard neutrino interactions [32] J. Schechter and J.W.F. Valle, Neutrino masses in SU(2) [33] R.E. Shrock, General theory of weak processes involving neutrinos. I. Leptonic [34] R.E. Shrock, General theory of weak processes involving neutrinos. II. Pure leptonic decays, [42] A. Abada and T. Toma, Electric dipole moments of charged leptons with sterile fermions, [43] A. Abada and T. Toma, Electron electric dipole moment in inverse seesaw models, [44] E. Fernandez-Martinez, J. Hernandez-Garcia and J. Lopez-Pavon, Global constraints on [45] D.V. Forero, S. Morisi, M. Tortola and J.W.F. Valle, Lepton [46] Y. Declais et al., Search for neutrino oscillations at 15-meters, 40-meters and 95-meters [47] Super-Kamiokande collaboration, K. Abe et al., Limits on sterile neutrino mixing using atmospheric neutrinos in Super-Kamiokande, Phys. Rev. D 91 (2015) 052019 [48] MINOS collaboration, P. Adamson et al., Search for sterile neutrinos mixing with muon [49] NOMAD collaboration, P. Astier et al., Search for [51] A. Atre, T. Han, S. Pascoli and B. Zhang, The search for heavy Majorana neutrinos, [55] D. Dutta, R. Gandhi, B. Kayser, M. Masud and S. Prakash, Capabilities of long-baseline [56] P. Huber, M. Lindner and W. Winter, Simulation of long-baseline neutrino oscillation [57] P. Huber, J. Kopp, M. Lindner, M. Rolinec and W. Winter, New features in the simulation [58] DUNE collaboration, T. Alion et al., Experiment simulation con gurations used in DUNE [59] M. Blennow and E. Fernandez-Martinez, Neutrino oscillation parameter sampling with [60] M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated t to three neutrino mixing: [61] A.M. Dziewonski and D.L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Interiors 25 (1981) 297 [INSPIRE]. [62] O.G. Miranda , M. Tortola and J.W.F. Valle , New ambiguity in probing CP-violation in neutrino oscillations , Phys. Rev. Lett . 117 ( 2016 ) 061804 [arXiv:1604.05690] [INSPIRE]. [63] S.-F. Ge , P. Pasquini , M. Tortola and J.W.F. Valle , Measuring the leptonic CP phase in neutrino oscillations with nonunitary mixing , Phys. Rev. D 95 (2017) 033005 [65] D. Dutta , P. Ghoshal and S. Roy , E ect of non unitarity on neutrino mass hierarchy [67] A. De Rujula , M.B. Gavela and P. Hernandez , Neutrino oscillation physics with a neutrino [68] D. Meloni , T. Ohlsson , W. Winter and H. Zhang , Non-standard interactions versus [71] S.K. Agarwalla , S.S. Chatterjee and A. Palazzo , Octant of 23 in danger with a light sterile [72] P. Coloma, Non-standard interactions in propagation at the Deep Underground Neutrino DUNE and other long baseline experiments , Phys. Rev. D 94 (2016) 013014 [77] M. Masud and P. Mehta , Nonstandard interactions spoiling the CP violation sensitivity at [74] M. Blennow , S. Choubey , T. Ohlsson , D. Pramanik and S.K. Raut , A combined study of [75] S.K. Agarwalla , S.S. Chatterjee and A. Palazzo , Degeneracy between 23 octant and neutrino non-standard interactions at DUNE , Phys. Lett . B 762 ( 2016 ) 64 [arXiv:1607.01745] [76] M. Masud and P. Mehta , Nonstandard interactions and resolving the ordering of neutrino masses at DUNE and other long baseline experiments , Phys. Rev. D 94 (2016) 053007 [78] M. Masud , A. Chatterjee and P. Mehta , Probing CP-violation signal at DUNE in presence of non-standard neutrino interactions , J. Phys. G 43 ( 2016 ) 095005 [arXiv:1510.08261] [79] P. Coloma and T. Schwetz , Generalized mass ordering degeneracy in neutrino oscillation experiments , Phys. Rev. D 94 ( 2016 ) 055005 [arXiv:1604.05772] [INSPIRE]. [80] V. De Romeri , E. Fernandez-Martinez and M. Sorel , Neutrino oscillations at DUNE with improved energy reconstruction , JHEP 09 ( 2016 ) 030 [arXiv:1607.00293] [INSPIRE]. [81] KARMEN collaboration, B. Armbruster et al., Upper limits for neutrino oscillations ! e from muon decay at rest , Phys. Rev. D 65 ( 2002 ) 112001 [hep-ex /0203021] [82] NuTeV collaboration , S. Avvakumov et al., Search for [83] Daya Bay collaboration , F.P. An et al ., Improved search for a light sterile neutrino with the [ 85] G.H. Collin , C.A. Arguelles , J.M. Conrad and M.H. Shaevitz , First constraints on the


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Mattias Blennow, Pilar Coloma, Enrique Fernandez-Martinez, Josu Hernandez-Garcia, Jacobo Lopez-Pavon. Non-unitarity, sterile neutrinos, and non-standard neutrino interactions, Journal of High Energy Physics, 2017, 153, DOI: 10.1007/JHEP04(2017)153