A Study of Invisible Neutrino Decay at DUNE and its Effects on $\theta_{23}$ Measurement.

We study the consequences of invisible decay of neutrinos in the context of the DUNE experiment. We assume that the third mass eigenstate is unstable and decays to a light sterile neutrino and a scalar or a pseudo-scalar. We consider DUNE running in 5 years neutrino and 5 years antineutrino mode and a detector volume of 40 kt. We obtain the bounds on the rest frame life time $\tau_3$ normalized to the mass $m_3$ as $\tau_3/m_3 > 4.50\times 10^{-11}$ s/eV at 90\% C.L. for a normal hierarchical mass spectrum. We also find that DUNE can discover neutrino decay for $\tau_3/m_3 > 4.27\times 10^{-11}$ s/eV at 90\% C.L. In addition, for an unstable $\nu_3$ with an illustrative value of $\tau_3/m_3$ = $1.2 \times 10^{-11}$ s/eV, the no decay case gets disfavoured at the $3\sigma$ C.L. At 90\% C.L. the allowed range for this true value is obtained as $1.71 \times 10^{-11} > \tau_3/m_3 > 9.29\times 10^{-12}$ in units of s/eV. We also study the correlation between a non-zero $\tau_3/m_3$ and standard oscillation parameters and find an interesting correlation in the appearance channel probability with the mixing angle $\theta_{23}$. This alters the octant sensitvity of DUNE, favorably (unfavorably) for true $\theta_{23}$ in the lower (higher) octant. The effect of a decaying neutrino does not alter the hierarchy or CP discovery sensitivity of DUNE in a discernible way.