We consider the decay of a polarized top quark into a stable $W^{+}$ boson and charmed-flavored (D) or bottom-flavored (B) hadrons via $t(\uparrow )\to W^{+}+D/B+X$. We study the angular distribution of the scaled energy of B/D hadrons at next-to-leading order, considering the contribution of bottom and gluon fragmentations into the heavy mesons B and D. To obtain the energy spectrum of B/D hadrons, we present our analytical expressions for the parton-level differential decay widths of $t(\uparrow )\to b+W^{+}(+g)$ at next-to-leading order. A comparison of our predictions with data at the LHC enables us to test the universality and scaling violations of the B- and D-hadron fragmentation functions. These can also be used to determine the polarization states of top quarks, and since the energy distributions depend on the ratio $m_W/m_t$, we advocate the use of such angular decay measurements for the determination of the top quark’s mass.

• Received 2 October 2013

DOI:https://doi.org/10.1103/PhysRevD.88.094011