  We investigate the effect on neutrino oscillations generated by
beyond-the-standard-model interactions between neutrinos and matter.
Specifically, we focus on scalar-mediated non-standard interactions (NSI) whose
impact fundamentally differs from that of vector-mediated NSI. Scalar NSI
contribute as corrections to the neutrino mass matrix rather than the matter
potential and thereby predict distinct phenomenology from the vector-mediated
ones. Similar to vector-type NSI, the presence of scalar-mediated neutrino NSI
can influence measurements of oscillation parameters in long-baseline neutrino
oscillation experiments, with a notable impact on CP measurement in the case of
DUNE. Our study focuses on the effect of scalar NSI on neutrino oscillations,
using DUNE as an example. We introduce a model-independent parameterization
procedure that enables the examination of the impact of all non-zero scalar NSI
parameters simultaneously. Subsequently, we convert DUNE's sensitivity to the
NSI parameters into projected sensitivity concerning the parameters of a light
scalar model. We compare these results with existing non-oscillation probes.
Our findings reveal that the region of the light scalar parameter space
sensitive to DUNE is predominantly excluded by non-oscillation probes, except
for scenarios with very light mediator mass.
