  We develop a method for the determination of the top quark mass using the
distribution of the decay length of the $B$-hadrons originating from its decay.
This technique is based on our earlier observation regarding the location of
the peak of the $b$ quark energy distribution. Such "energy-peak" methods enjoy
a greater degree of model-independence with respect to the kinematics of top
quark production compared to earlier proposals. The CMS experiment has
implemented the energy-peak method using associated $b$-jet energy as an
approximation for $b$ quark energy. The new method uses $B$-hadron decay
lengths, which are related to $b$ quark energies by convolution. The advantage
of the new decay length method is that it can be applied in a way that evades
jet-energy scale (JES) uncertainties. Indeed, CMS has measured the top quark
mass using $B$-hadron decay lengths, but they did not incorporate the
energy-peak method. Therefore, mismodeling of top quark transverse momentum
remains a large uncertainty in their result. We demonstrate that, using
energy-peak methods, this systematic uncertainty can become negligible. We show
that with the current LHC data set, a sub-GeV statistical uncertainty on the
top quark mass can be attained with this method. To achieve a comparable
systematic uncertainty as is true for many methods based on exclusive or
semi-inclusive observables using hadrons, we find that the quark-hadron
transition needs to be described significantly better than is the case with
current fragmentation functions and hadronization models.

High Energy Physics - Phenomenology;High Energy Physics - Experiment