Understand
Heavy quark fragmenting jet functions describe the fragmentation of a parton into a jet containing a heavy quark, carrying a fraction of the jet momentum.
- They are two-scale objects, sensitive to the heavy quark mass, $m_Q$, and to a jet resolution variable, $\tau_N$.
- We discuss how cross sections for heavy flavor production at high transverse momentum can be expressed in terms of heavy quark fragmenting jet functions, and how the properties of these functions can be used to achieve a simultaneous resummation of logarithms of the jet resolution variable, and logarithms of the quark mass.
- We calculate the heavy quark fragmenting jet function $\mathcal G_Q^Q$ at $\mathcal O(\alpha_s)$, and the gluon and light quark fragmenting jet functions into a heavy quark, $\mathcal G_g^Q$ and $\mathcal G_l^Q$, at $\mathcal O(\alpha_s^2)$.