  We analyze the energy spectra of $single$ b-jets and B-hadrons resulting from
the production and decay of top quarks within the SM at the LHC at the NLO QCD.
For both hadrons and jets, we calculate the correlation of the peak of the
spectrum with the top quark mass, considering the "energy-peak" as an
observable to determine the top quark mass. Such a method is motivated by our
previous work where we argued that this approach can have reduced sensitivity
to the details of the production mechanism of the top quark, whether it is
higher-order QCD effects or new physics contributions. As part of the NLO
improvement over the original proposal, we assess the residual sensitivity of
the extracted top quark mass to perturbative effects both in top quark
production and decay. For a 1% jet energy scale uncertainty (and assuming
negligible statistical error), the top quark mass can then be extracted using
the energy-peak of b-jets with an error +- (1.2 (exp) + 0.6(th)) GeV. We note
that recently the CMS collaboration reported a top quark mass measurement based
on the original proposal (with b-jets) so that our result contributes to a
precise evaluation of the associated theory uncertainty. In view of the
dominant jet energy scale uncertainty in the measurement using b-jets, we also
investigate the extraction of the top quark mass from the energy-peak of the
corresponding B-hadrons which, in principle, can be measured without this
uncertainty. The calculation of the B-hadron energy spectrum is carried out
using fragmentation functions at NLO. The dependence on the fragmentation scale
turns out to be the largest theoretical uncertainty in this extraction of top
quark mass. Future improvement of the treatment of bottom quark hadronization
can reduce this uncertainty, rendering methods based on the B-hadron
energy-peak competitive for the top quark mass measurement.
