Can we measure $\theta_{23}$ octant in 3+1 scheme?

TL;DR

This paper investigates how the presence of a light sterile neutrino in the 3+1 scheme could hinder the ability of DUNE to determine the octant of the mixing angle θ23, due to new interference effects.

Contribution

It analyzes the impact of a light sterile neutrino on θ23 octant measurement prospects in DUNE, revealing potential complete loss of octant sensitivity.

Findings

Sterile neutrino introduces a new interference term in oscillation probability.

This interference can completely obscure θ23 octant determination in DUNE.

The effect challenges the standard three-neutrino paradigm for octant measurement.

Abstract

Current 3$\nu$ global fits predict two degenerate solutions for $\theta_{23}$: one lies in lower octant ($\theta_{23} <\pi/4$), and the other belongs to higher octant ($\theta_{23} >\pi/4$). Here, we study how the measurement of $\theta_{23}$ octant would be affected in the upcoming Deep Underground Neutrino Experiment (DUNE) if there exist a light eV-scale sterile neutrino. We show that in 3+1 scheme, a new interference term in $\nu_\mu \to \nu_e$ oscillation probability can spoil the chances of measuring $\theta_{23}$ octant completely.

Equations

$$U={\tilde{R}}_{34}{R}_{24}{\tilde{R}}_{14}{R}_{23}{\tilde{R}}_{13}{R}_{12},$$

$$P_0$$

$$P_1$$

$$P_2$$

$$\Delta P\equiv P_{\mu e}^{\mathrm{HO}}({\delta }_{13}^{\mathrm{HO}},{\delta }_{14}^{\mathrm{HO}})-P_{\mu e}^{\mathrm{LO}}({\delta }_{13}^{\mathrm{LO}},{\delta }_{14}^{\mathrm{LO}})\ne 0,$$

$$\Delta P_0$$

$$\Delta P_1$$

$$\Delta P_2$$

Full text

Introduction: The resolution of octant111According to the present 3$\nu$ best-fit [5], $\theta_{23}$ can have two solutions: one $<$ $\pi/4$, labelled as lower octant (LO), and other $>$ $\pi/4$, known as higher octant (HO). [1] of $\theta_{23}$ is one of the fundamental problems in neutrino oscillation. Long-baseline (LBL) experiments [2] can resolve this octant ambiguity of $\theta_{23}$ with the help of $\nu_{\mu}\rightarrow\nu_{e}$ appearance channel, and the vital information coming from $\nu_{\mu}\rightarrow\nu_{\mu}$ disappearance channel also play an important role. Interestingly, at present, there are short-baseline anomalies which hint towards the existence of light eV-scale sterile neutrino [3]. Here, we expound in detail the capability of proposed LBL experiment DUNE to measure $\theta_{23}$ octant considering one light eV-scale sterile neutrino along with three active neutrinos.

Theoretical framework: In the 3+1 scheme, a new a mass eigenstate $\nu_{4}$ appears on top of 3$\nu$ framework whose mixing is parametrized as

[TABLE]

where $R_{ij}$ ($\tilde{R}_{ij}$) is a real (complex) rotation in the ($i,j$) plane. The details of the parametrization of U can be seen in [4].

In [4], it was shown that the 4-flavor appearance probability can be approximately expressed as the sum of three terms $P^{4\nu}_{\mu e}\simeq P_{\rm{0}}+P_{\rm{1}}+P_{\rm{2}}$,  which in vacuum appears as

[TABLE]

where $\Delta\equiv\Delta m^{2}_{31}L/4E$ and $\alpha\equiv\Delta m^{2}_{21}/\Delta m^{2}_{31}$. In the double sign, the upper (lower) sign corresponds to neutrinos (antineutrinos). The new interference term $P_{\rm{2}}$ is governed by the interference between the atmospheric frequency and the large frequency related to the new mass eigenstate [4] which gets averaged out by the finite energy resolution of the detector. Recent global fits [5, 6, 7] suggests $s_{13}\sim s_{14}\sim s_{24}\sim 0.15\,(\sim\epsilon)$ and $\alpha\,=\,0.03\,(\sim\epsilon^{2})$ implying $P_{\rm{0}}\sim\epsilon^{2},\,\;P_{\rm{1}}\sim\epsilon^{3},\,\;P_{\rm{2}}\sim\epsilon^{3}$. An experiment can measure the octant of $\theta_{23}$ even in the presence of unknown CP-phases, if there is a difference between the probabilities corresponding to the different octants, i.e.

[TABLE]

where one of the two octants should be considered to generate data and the other octant should be used to simulate the theoretical model. From the expression of $P^{4\nu}_{\mu e}$, $\Delta P$ can be written as,    $\Delta P=\Delta P_{\rm{0}}+\Delta P_{\rm{1}}+\Delta P_{\rm{2}}$.

$\Delta P_{\rm{0}}$ is positive-definite. $\Delta P_{\rm{1}}$ and $\Delta P_{\rm{2}}$ depends on the CP-phases and can be both positive or negative. These terms can be expressed as

[TABLE]

In above, $\phi\,=\,\delta_{13}$ and $\psi\,=\,\delta_{13}-\delta_{14}$ with the appropriate superscripts LO or HO. The term $\eta$ is a positive definite angle and dictates the deviation from maximal mixing as $\theta_{23}=\frac{\pi}{4}\pm\eta$, where +(-) corresponds to HO (LO). If we need to measure the octant of $\theta_{23}$, the contribution coming from $\Delta P_{\rm{0}}$ must not get cancelled completely in cases where the sum of $\Delta P_{\rm{1}}$ and $\Delta P_{\rm{2}}$ gives a negative contribution.

Results and discussion: Simulations for DUNE have been performed considering a total 248 kt.MW.yr of exposure, divided equally between $\nu$ and $\bar{\nu}$ mode. In fig.1, we show the bi-event plot. The ellipses (colored blobs) correspond to the 3$\nu$ (3+1 scheme) where, $\sin^{2}\theta_{23}=0.42\,(0.58)$ has been assumed as a benchmark value for the LO (HO). Since mass hierarchy can be measured relatively easily222In fig.1, we notice an small overlap between normal hierarchy (NH) and inverted hierarchy (IH) blobs which can be eliminated using the spectral information available in DUNE (see [8]). in DUNE, we can only concentrate on one of the two hierarchies, say normal hierachy. While going from 3$\nu$ to 3+1 scheme, the ellipses becomes blobs because of the convolution of different combinations of $\delta_{13}$ & $\delta_{14}$ (see [8, 9]). In this figure, we see a substantial overlap between LO and HO blobs due to the presence of the term $\Delta P_{2}$, which depends on the new CP-phase $\delta_{14}$. For detailed discussion, see [10].

Fig.2 depicts the discovery reach of $\theta_{23}$ octant in $\left[\sin^{2}\theta_{23},\delta_{13}\right]$(true) plane assuming NH as true choice. Left (right) panel shows the results for 3$\nu$ (3+1) scheme. In 3$\nu$ case, a minimum 2$\sigma$ sensitivity can be achieved if $\sin^{2}\theta_{23}(\rm true)\,\lesssim\,0.47$ and $\sin^{2}\theta_{23}(\rm true)\,\gtrsim\,0.55$ irrespective of the choice of $\delta_{13}$(true). But, in 3+1 case we hardly have any octant sensitivity in the entire $\left[\sin^{2}\theta_{23},\delta_{13}\right]$(true) plane.

Conclusions: In this work, we have studied the impact of a light eV-scale sterile neutrino in measuring the octant of $\theta_{23}$ at DUNE. The sensitivity towards $\theta_{23}$ octant can be completely lost if there is active- sterile oscillations.

Acknowledgments: S.S.C. would like to thank the organizers of XXII DAE-BRNS HEP Symposium 2016 for giving an opportunity to present this work. S.K.A. is supported by the DST/INSPIRE Research Grant [IFA-PH-12], Department of Science & Technology, India. A.P. is supported by the grant “Future In Research” Beyond three neutrino families, Fondo di Sviluppo e Coesione 2007-2013, APQ Ricerca Regione Puglia, Italy, ÒProgramma regionale a sostegno della specializzazione intelligente e della sostenibilità sociale ed ambientale. A.P. acknowledges partial support by the research project TAsP funded by the Instituto Nazionale di Fisica Nucleare (INFN).