Advances in High Energy Physics

Volume 2019, Article ID 8464535, 13 pages

https://doi.org/10.1155/2019/8464535

## Nonstandard Interactions and Prospects for Studying Standard Parameter Degeneracies in DUNE and T2HKK

Department of Physics and Astronomical Science, Central University of Himachal Pradesh, Dharamshala 176215, India

Correspondence should be addressed to Surender Verma; ni.oc.oohay@amrev7_s

Received 26 January 2019; Revised 3 April 2019; Accepted 28 April 2019; Published 13 May 2019

Academic Editor: Sally Seidel

Copyright © 2019 Surender Verma and Shankita Bhardwaj. 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 future long baseline experiments such as DUNE and T2HKK have promising prospects to determine the neutrino mass hierarchy and measuring standard phase . However, presence of possible nonstandard interactions of neutrinos with matter may intricate this picture and is the subject matter of the present work. We have studied the standard parameter degeneracies in presence of nonstandard interactions (NSI) with DUNE and T2HKK experiments. We examine the mass hierarchy degeneracy assuming (i) all NSI parameters to be nonzero and (ii) one NSI parameter () and its corresponding phase () to be nonzero. We find that the latter case is more appropriate to resolve mass hierarchy degeneracy with DUNE and T2HKK experiments due to relatively small uncertainties emanating from the NSI sector. We have, also, investigated the octant degeneracy with neutrino () and antineutrino () mode separately. We find that to resolve this degeneracy the long baseline experiment with combination of neutrino and antineutrino mode is essential. Furthermore, we have considered DUNE in conjunction with T2HKK experiment to study phase degeneracy due to standard () and nonstandard () phases. We find that DUNE and T2HKK, in conjunction, have more sensitivity for violation effects (10 for true NH and 8.2 for true IH).

#### 1. Introduction

The discovery of nonzero neutrino masses and lepton flavor mixing by the reactor [1], accelerator [2], atmospheric [3], and solar [4] neutrino oscillation experiments have revealed the values of oscillation parameters such as mass squared differences and mixing angles [5], to an unprecedented accuracy. At present, there are some unknown quantities in standard three-neutrino framework, namely, sign of , the octant of , and the -phase , the determination of which is the prime objective of current and future neutrino oscillation experiments. The difficulty in the determination of these unknowns is the existence of degeneracies in neutrino oscillation parameters. To overcome these degeneracies, one of the methods is to combine data from different neutrino oscillation experiments. Recently, this procedure has been adopted by various studies [6–8], where the synergy between current and future experiments has been considered. In principle, future neutrino oscillation experiments have sensitivity reach to perform precision test of standard neutrino oscillation paradigm and to probe new physics beyond standard model (SM). In neutrino oscillation experiments, one model-independent way to study new physics (NP) is given by the framework of nonstandard interactions (NSI) [9, 10].

An alternative phenomenon to explain neutrino flavor transitions, on the basis of NSI, was first proposed by Wolfenstein [11]. Although we know that they will show their effect in neutrino oscillation experiments at subleading level, they are important, with the emergence of next generation experiments like Tokai-to-Hyper-Kamiokande (T2HK) [12], Deep Underground Neutrino Experiment (DUNE) [13], Tokai-to-Hyper-Kamiokande-and-Korea (T2HKK) [14], etc., where such type of interactions can be probed. In general, the NSIs may manifest itself in propagation of neutrino through matter and the processes involved in its creation and detection. The possible manifestations of NSIs have been widely studied in the literature and bounds on NSI parameters have been derived from various experiments [9, 10, 15, 16]. Furthermore, the model-independent bounds on NSI in production and detection regions are an order of magnitude stronger than the matter NSI [15]. In this work, we focus on matter NSI which can be defined by dimension-six four-fermion operators given by [11, 17]where , , , and are dimensionless parameters indicating the strength of the new interaction having units of . To probe matter NSI long baseline neutrino experiments (LBNE) are ideal and the neutral current (NC) interactions which affect the neutrino propagation coherently can also be studied at far detectors. The next generation LBNE such as DUNE, T2HK, and T2HKK may reach the sensitivity to reveal NSI in neutrino sector.

In the leptonic sector, the violation can render leptogenesis mechanism which in turn may shed light on baryogenesis [19, 20]. It is very difficult to measure leptonic -violation in presence of NSI as it will get bewildered by the existence of possible -violation generated by NSI itself. Undoubtedly, the existence of NSI has opened an entirely new window to explore NP beyond standard model.

Previously, the authors of [6] have explored the ability to disentangle the violating effects due to standard and nonstandard contributions under the assumption that only one NSI parameter or is present. In [7], the parameter degeneracies in LBNE originating from nonstandard interactions have been studied and [21] has focused on NSI at DUNE, T2HK, and T2HKK and has concluded that overall DUNE has the best sensitivity to the magnitude of the NSI parameters, while T2HKK has the best violation sensitivity with or without NSI. Furthermore, in [22], the authors have studied the impact of nonzero NSI on the precision of DUNE. The authors of [23–25] have explored the effects of NSI on violation sensitivity and hierarchy sensitivity at DUNE, respectively. In [8] the authors have studied the sensitivity to mass hierarchy, the octant of , and phase in the future long baseline experiments T2HK and DUNE assuming standard interactions (SI) only. In general, earlier studies on standard parameters degeneracies with SI or matter NSI have mostly focused on DUNE [23–26]. Motivated by the long baseline of T2HKK experiment, it is imperative to study physics potential of T2HKK and DUNE+T2HKK, in resolving standard parameter degeneracies in presence of NSI. In the present work, we have investigated prospects for lifting mass hierarchy degeneracy (sign degeneracy), -octant degeneracy, and -phase degeneracy in DUNE, T2HKK, and DUNE+T2HKK with matter NSIs.

T2HKK is a long baseline experiment proposed to enhance the hierarchy sensitivity of T2HK by setting one of the two tanks of HK detector at a site in Korea. This multidetector setup is advantageous as it gives access to a longer baseline of 1100 km and simultaneously boosts the data at the T2HK with baseline of 295 km [27]. The neutrino oscillation probabilities are strongly affected by the matter effects in long baseline experiments. These matter effects can be beneficial in lifting up the standard parameter degeneracies. Therefore, we have considered the T2HKK setup with larger baseline of 1100 km in the analysis. In present work, we have studied the standard parameter degeneracies, i.e., mass hierarchy degeneracy and octant degeneracy in presence of matter NSI with DUNE and T2HKK experiment. We have assumed all NSI parameters to be nonzero in one case and only one off-diagonal NSI parameter to be nonzero, in another case. We find that the latter case is better at resolving standard parameter degeneracies in case of both DUNE and T2HKK experiments. Due to the larger baseline, T2HKK is found to have similar sensitivity as DUNE experiment to resolve standard parameter degeneracies including NSI. Furthermore, we have investigated the phase degeneracy occurring due to the contribution from standard and nonstandard phases. We observe that it is difficult to disentangle the effects due to SI phase from NSI phase at DUNE+T2HKK experiment as this conjunction is more sensitive to study violation effects [27].

We organize the paper as follows: in Section 2, we present the formalism to write oscillation probability in presence of matter NSIs. We discuss about the long baseline experiments DUNE, T2HKK, and corresponding simulation details in Section 3. In Section 4, we discuss the prospects to resolve standard parameter degeneracies in these LBNEs. We have presented our results and, subsequent, discussion in Section 5. Finally, we conclude in Section 6.

#### 2. Formalism: Oscillation Probabilities

The Hamiltonian for the neutrino propagation in presence of matter NSI can be written aswhere is the PMNS mixing matrix containing three mixing angles and one phase , . is the matter potential due to interaction of neutrino with matter, viz.,where . The unit contribution in the first element of the matrix is due to the matter term contribution from standard charged-current interactions. The diagonal element of is real, i.e., (where ) for and . The oscillation probability for channel can be written as [7]where , . Similar expression can be obtained for inverted hierarchy (IH) by replacing (i.e., and ). The expression for antineutrino oscillation probability can be written by replacing and in (4).

#### 3. Experimental Setups

Considering the sensitivity reach of the present and future long baseline neutrino oscillation experiments (for example, DUNE and T2HKK), it is very important to study the individual and collective effects of NSI parameters on parameter degeneracies. We have used GLoBES package [28, 29] with best-fit values and ranges of the standard neutrino mixing parameters, as given in [30] to simulate the DUNE and T2HKK. The current bounds on NSI parameters used in present analysis are [15]. The phases of the off-diagonal NSI parameters are still unconstrained and can lie in the range .

The experimental configurations, energy resolutions, and systematic uncertainties considered in the present work are as follows.

##### 3.1. DUNE

The DUNE experiment [13], situated in the USA, is a globally synchronized endeavor of neutrino physicists around the world. Out of many others, the neutrino physics goals of the experiment are to unravel the sign of neutrino mass hierarchy and to measure the phase(s). The experiment is planned to direct neutrino beam from Fermilab to Homestake mine in South Dakota providing an optimum baseline of 1300 km for manifestation of matter effects in neutrino oscillations. Unlike Hyper-K, DUNE is an on-axis experiment. We have used DUNE CDR [13, 31] with 35 kt LAr far detector. The optimized beam design that employs 80 GeV beam of protons having 1.0 MW power has been used to simulate the experiment. We have considered 5(+5) years of run in neutrino (antineutrino) mode resulting in an exposure of 350 kt.MW.years. The appearance efficiency () and energy resolutions () taken in the present analysis are 80% (, ), respectively. The normalization and energy calibration uncertainty for signal ()/background () is taken to be , %, %, and %. For signal ()/background () the values are %, %, %, and %.

##### 3.2. T2HKK

The T2HKK experiment [14], an extension T2HK [12], is proposed to be stretched over Japan and Korea. The neutrino beam will be directed from J-PARC facility in Japan to two water-Cherenkov detectors: (i) first detector at Kamioka mine in Japan with a baseline of 295 km; (ii) second detector to be built in Korea providing a baseline of 1100 km. In the present work, we have considered 1100 km baseline (also, referred to as T2HKK), with detector at off-axis with respect to the neutrino beam, where matter effects will be large. We choose 13 MW.years beam power which is similar to that of T2HK. The running time, in ratio 1:3 for neutrino and antineutrino mode, is 10 years amounting to total exposure of protons on target (POT). The appearance efficiency () and energy resolutions () taken in the present analysis are 50% (0.085, 0.085), respectively. The normalization and energy calibration uncertainty for signal)/background are taken to be , , , and . For signal)/background) the values are , , , and .

#### 4. Parameter Degeneracies

In general, different set of oscillation parameters may give identical predictions for oscillation probability resulting in parameter degeneracies and making it difficult to uniquely determine these parameters. The biprobability plots are well known constructions to study parameter degeneracies in presence of NSI parameters and phases. In presence of off-diagonal NSI the neutrino/antineutrino oscillation probability exhibits degeneracy between SI and NSI phase when and , where is Dirac phase in a model with NSI. If we presume that mixing angles and mass squared differences are known from some other experiment, then for every value of SI phase there will be three unknowns (, , and the phase ) which generate an off-diagonal NSI degeneracy. Accordingly, a measurement of and in an experiment provides two constraints; for each value of , a solution for and will exist for any value of resulting in parameter degeneracy. As a representative plot to depict standard parameter degeneracies we have shown, in Figure 1, mass hierarchy and octant degeneracy assuming NSI parameters and varying from to for DUNE experiment. All other NSI parameters are assumed to be zero. The solid and dashed ellipses correspond to higher octant (HO) and lower octant (LO) of , respectively, for normal hierarchy (NH). Similarly, the dotted and dash-dotted ellipses correspond to higher octant (HO) and lower octant (LO) of , respectively, for inverted hierarchy (IH). The significant overlapping of the ellipses shows fourfold octant and mass hierarchy degeneracy. For example, points of intersection of solid (dotted) and dashed (dash-dotted) ellipses exhibit octant degeneracy as neutrino and antineutrino oscillation probabilities are the same in both cases for normal (inverted) hierarchy.