Probing Large Extra Dimension at DUNE using beam tunes

The Deep Underground Neutrino Experiment (DUNE) is a leading experiment in neutrino physics which is presently under construction. DUNE aims to measure the yet unknown parameters in the three flavor oscillation case which includes discovery of leptonic CP violation, determination of the neutrino mass hierarchy and measuring the octant of $\theta_{23}$. Additionally, the ancillary goals of DUNE include probing the subdominant effects induced by possible physics beyond the Standard Model (BSM). One such new physics scenario is the possible presence of Large Extra Dimension (LED) which can naturally give rise to tiny neutrino masses. LED impacts neutrino oscillation through two new parameters, - namely the lightest Dirac mass $m_{0}$ and the radius of the extra dimension $R_{\text{ED}}$ ($< 2$ $\mu$m). At the DUNE baseline of 1300 km, the probability seems to be modified more at the higher energy ($\gtrsim 4-5$ GeV) in presence of LED. In this work, we attempt to constrain the parameter space of $m_{0}$ and $R_{\text{ED}}$ by performing a statistical analysis of neutrino data simulated at DUNE far detector (FD). We illustrate how a combination of the standard low energy (LE) neutrino beam and a medium energy (ME) neutrino beam can take advantage of the relatively large impact of LED at higher energy and improve the constraints. In the analysis we also show the role of the individual oscillation channels ($\nu_{\mu} \to \nu_{e}, \nu_{\mu} \to \nu_{\mu}, \nu_{\mu} \to \nu_{\tau}$), as well as the two neutrino mass hierarchies.