Heavy Quark $\bar{q}q$ Matrix Elements in the Nucleon from Perturbative QCD

Abstract

The scalar heavy quark content of the nucleon, ${\cal M}_q = \bra{N} m_q \bar q q \ket{N},$ is relevant for computing the interaction of dark matter candidates with ordinary matter, while ${\cal M}_s$ is important for predicting the properties of dense matter. We compute ${\cal M}_q$ in perturbative QCD to ${\cal{O}}{(α^3)}.$ As one goes from ${\cal M}_t$ to ${\cal M}_c$ the leading order contribution decreases as the number of light quarks is dropping, while the radiative corrections grow and are all positive. The leading source of uncertainty in the calculation is due to the poorly known value of ${\cal M}_s.$ A related calculation suggests that a large value for ${\cal M}_s$ may be reasonable.