  In this paper we propose a new reconstruction method to explore the low mass
region in the associated production of top-quark pairs ($t\bar{t}$) with a
generic scalar boson ($\phi$) at the LHC. The new method of mass reconstruction
shows an improved resolution of at least a factor of two in the low mass region
when compared to previous methods, without the loss of sensitivity of previous
analyses. It turns out that it also leads to an improvement of the mass
reconstruction of the 125 GeV Higgs for the same production process. We use an
effective Lagrangian to describe a scalar with a generic Yukawa coupling to the
top quarks. A full phenomenological analysis was performed, using Standard
Model background and signal events generated with MadGraph5\_aMC@NLO and
reconstructed using a kinematic fit. The use of CP-sensitive variables allows
then to maximize the distinction between CP-even and CP-odd components of the
Yukawa couplings. Confidence Levels (CLs) for the exclusion of $\phi$ bosons
with mixed CP (both CP-even and CP-odd components) were determined as a
function of the top Yukawa couplings to the $\phi$ boson. The mass range
analysed starts slightly above the $\Upsilon$ mass up to 40 GeV, although the
analysis can be used for an arbitrary mass. %We focus on dileptonic final
states of the $t\bar{t}\phi$ system, with $\phi\rightarrow b\bar{b}$. If no new
light scalar is found, exclusion limits at 95\% CL for the absolute value of
the CP-even and CP-odd Yukawa are derived. %couplings are expected to be,
approximately, as low as 0.10 and 0.50, respectively, at the end of the High
Luminosity phase of the LHC (HL-LHC). Finally, we analyse how these limits
constrain the parameter space of the complex two-Higgs doublet model (C2HDM).
