  We study the Monte Carlo uncertainties due to modeling of hadronization and
showering in the extraction of the top-quark mass from observables that use
exclusive hadronic final states in top decays, such as $t \rightarrow
\text{anything+J/}\psi$ or $t\rightarrow \text{anything}+(B\rightarrow
\text{charged tracks})$, where $B$ is a $B$-hadron. To this end, we investigate
the sensitivity of the top-quark mass, determined by means of a few observables
already proposed in the literature as well as some new proposals, to the
relevant parameters of event generators, such as HERWIG 6 and PYTHIA 8. We find
that constraining those parameters at $\mathcal{O}(1\%-10\%)$ is required to
avoid a Monte Carlo uncertainty on $m_t$ greater than 500 MeV. For the sake of
achieving the needed accuracy on such parameters, we examine the sensitivity of
the top-quark mass measured from spectral features, such as peaks, endpoints
and distributions of $E_{B}$, $m_{B\ell}$, and some $m_{T2}$-like variables. We
find that restricting oneself to regions sufficiently close to the endpoints
enables one to substantially decrease the dependence on the Monte Carlo
parameters, but at the price of inflating significantly the statistical
uncertainties. To ameliorate this situation we study how well the data on
top-quark production and decay at the LHC can be utilized to constrain the
showering and hadronization variables. We find that a global exploration of
several calibration observables, sensitive to the Monte Carlo parameters but
very mildly to $m_{t}$, can offer useful constraints on the parameters, as long
as such quantities are measured with a 1% precision.
