Advances in High Energy Physics

Volume 2015, Article ID 820941, 13 pages

http://dx.doi.org/10.1155/2015/820941

**Constraints on the Nonstandard Interaction in Propagation from Atmospheric Neutrinos**

Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan

Received 3 May 2015; Accepted 5 August 2015

Academic Editor: Vincenzo Flaminio

Copyright © 2015 Shinya Fukasawa and Osamu Yasuda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The sensitivity of the atmospheric neutrino experiments to the nonstandard flavor-dependent interaction in neutrino propagation is studied under the assumption that only nonvanishing components of the nonstandard matter effect are the electron and tau neutrino components , and , and that the tau-tau component satisfies the constraint which is suggested from the high energy behavior for atmospheric neutrino data. It is shown that the Super-Kamiokande (SK) data for 4438 days constrains at 2.5 (98.8%) CL whereas the future Hyper-Kamiokande experiment for the same period of time as SK will constrain as at 2.5CL from the energy rate analysis and the energy spectrum analysis will give even tighter bounds on and .

#### 1. Introduction

From the experiments with solar, atmospheric, reactor, and accelerator neutrinos it is now established that neutrinos have masses and mixing [1]. Neutrino oscillations in the standard three-flavor scheme are described by three mixing angles, , , and , one CP phase , and two independent mass-squared differences, and . The sets of the parameters (, ) and (, ) were determined by the solar neutrino experiments and the KamLAND experiment and by atmospheric and long baseline neutrino experiments, respectively. was determined by the reactor experiments and the long baseline experiments [1]. The only oscillation parameters which are still undetermined are the value of the CP phase and the sign of (the mass hierarchy). In the future neutrino long-baseline experiments with intense neutrino beams the signs of and are expected to be determined [2, 3]. As in the case of B factories [4, 5], such high precision measurements will enable us to search for deviation from the standard three-flavor oscillations (see, e.g., [6]). Among such possibilities, in this paper, we will discuss the effective nonstandard neutral current flavor-dependent neutrino interaction with matter [7–9], given by where and stand for fermions (the only relevant ones are electrons, and quarks), is the Fermi coupling constant, and stands for a projection operator that is either or . If the interaction (1) exists, then the standard matter effect [7, 10] is modified. We will discuss atmospheric neutrinos which go through the Earth, so we make an approximation that the number densities of electrons (), protons, and neutrons are equal (this assumption is not valid in other environments, e.g., in the Sun.). Defining , the Hermitian matrix of the matter potential becomes where stands for the matter effect due to the charged current interaction in the standard case. With this matter potential, the Dirac equation for neutrinos in matter becomes where is the leptonic mixing matrix defined by and , , and .

Constraints on have been discussed by many authors, from atmospheric neutrinos [11–15], from colliders [16], from the compilation of various neutrino data [17], from solar neutrinos [18–20], from or scatterings [21, 22], from solar and reactor neutrinos [23], and from solar, reactor, and accelerator neutrinos [24]. Since the coefficients in (2) are given by , considering the constraints in these references, we have the following limits [25] at 90%CL: From (5) we observe that the bounds on , , and are much weaker than those on .

On the other hand, the nonstandard interaction (NSI) with components must be consistent with the high-energy atmospheric neutrino data. It was pointed out in [26, 27] that the relation should hold for the matter potential (2) to be consistent with the high-energy atmospheric neutrino data, which suggest the behavior of the disappearance oscillation probability where and are the oscillation parameters in the two-flavor formalism. In [28] it was shown that, in the high-energy behavior of the disappearance oscillation probability in the presence of the matter potential (2), and imply and .

Taking into account the various constraints described above, in the present paper we take the ansatz and analyze the sensitivity to the parameters of the atmospheric neutrino experiment at Super-Kamiokande and the future Hyper-Kamiokande (HK) facility [29] (as far as is concerned, the ansatz (9) is believed to be the best fit of the high energy atmospheric neutrino data at present. So as long as the true value of satisfies the relation (6), even if we analyze the data assuming that is a free parameter, the allowed region in (, ) and the sensitivity to NSI are not expected to change very much, because the region of , which does not satisfy (6), gets an additional contribution of and is not supposed to contribute to enlarge the allowed region or to increase the sensitivity to NSI).

The constraints on and from the atmospheric neutrino have been discussed in [30] along with those from the long-baseline experiments, in [31] by the Super-Kamiokande Collaboration, in [32–34] on the future extension of the IceCube experiment, and in [35] in the global analysis, with the ansatz different from ours.

The sensitivity of the ongoing accelerator experiments to the nonstandard interaction in propagation was studied by various authors. The constraints have been obtained from the MINOS experiment in [36], from the MINOS data using the same ansatz as the present paper in [37, 38], from the MINOS data from the viewpoint of degeneracy of and NSI in [39], from appearance in MINOS and T2K in [40], from the OPERA experiment in [41, 42], and from the LHC experiment in [43]. As for the future long-baseline experiments, the sensitivity of the INO experiment was discussed in [44], that of the reactor and superbeam experiments was discussed in [45], that of the T2KK experiment was studied in [28, 46], and that of the LBNE experiment was discussed in [43, 47]. The sensitivity of neutrino factories [6] was studied in various contexts: the sensitivity to NSI [48–50], the confusion with the effect of [51], the optimization [52], resolving degeneracy with two baselines [53, 54], and the relation with nonunitary mixing [55].

The paper is organized as follows. In Section 2, we analyze the SK atmospheric neutrino data and give the constraints on the parameters from the SK atmospheric neutrino data. In Section 3, we discuss the sensitivity to of the future Hyper-Kamiokande atmospheric neutrino experiment. In Section 4, we draw our conclusions.

#### 2. The Constraint of the Super-Kamiokande Atmospheric Neutrino Experiment on and

In this section we discuss the constraint of the SK atmospheric neutrino experiment on the nonstandard interaction in propagation with the ansatz (9). The independent degrees of freedom in addition to those in the standard oscillation scenario are , and .

The SK atmospheric neutrino data we analyze here is those in [56] for 4438 days. In [56], the contained events, the partially contained events, and the upward going events are divided into a few categories. Since we have been unable to reproduce all their results of the Monte Carlo simulation, we have combined the two sub-GeV -like data set in one, the two multi-GeV -like in one, the two partially contained event data set and the multi-GeV -like in one, and the three upward going in one. Reference [56] gives information on the ten zenith angle bins, while that on the energy bins is not given, so we perform analysis with the ten zenith angle bins and one energy bin; that is, we perform the rate analysis as far as the energy is concerned.

The analysis was performed with the codes which were used in [57–59]. is defined as In (10) for the sub-GeV, multi-GeV, and upward going events are defined by The summation on runs over the ten zenith angle bins for each , ; ) stands for the neutrino and antineutrino data of the numbers of the sub-GeV, multi-GeV, and upward going events, () stands for the theoretical prediction for the number of -like events () which is produced from () that originates from () through the oscillation process (), and it is expressed as the product of the oscillation probability (), the flux (), the cross section, the number of the targets, and the detection efficiency. stands for the uncertainty in the overall flux normalization for the sub-GeV, multi-GeV, and upward going events and () stands for the uncertainty in the relative normalization between flux ( flux) for the sub-GeV () and multi-GeV () events, respectively. It is understood that is minimized with respect to , (), , (), and . We have put the systematic errors and we have assumed that and for the contained events are free parameters as in [60]. We have omitted the other uncertainties, like the spectral index, the relative normalization between PC and FC and up-down correlation, and so forth, for simplicity. In (10) the sum of each is optimized with respect to the mixing angle , the mass squared difference , the Dirac CP phase , and the phase of the parameter . The other oscillation parameters give little effect on , so we have fixed them as , , and .

The result for the Super-Kamiokande data for 4438 days is given in Figure 1. The best-fit point for the normal (inverted) hierarchy is (, ) = (−1.0, 0.0) ((3.0, 1.7)) and the value of at this point is 79.0 (78.6) for 50 degrees of freedom, and goodness of fit is 2.8 (2.7) CL, respectively. The best-fit point is different from the standard case (, ) = (0, 0), and this may be not only because we have been unable to reproduce the Monte Carlo simulation by the Super-Kamiokande group, but also because we use only the information on the energy rate and the sensitivity to NSI is lost due to the destructive phenomena between the lower and higher energy bins (see the discussions in Section 3.1). The difference of the value of for the standard case and that for the best-fit point for the normal (inverted) hierarchy is (3.4) for 2 degrees of freedom (1.1CL (1.3CL)), respectively, and the standard case is certainly acceptable for the both mass hierarchies in our analysis. From Figure 1 we can read off the allowed region for , and we conclude that the allowed region for is approximately