  Dirac electrons in graphene in the presence of Coulomb interactions of
strength $\beta$ have been shown to display power law behavior with $\beta$
dependent exponents in certain correlation functions, which we call the mass
susceptibilities of the system. In this work, we first discuss how this
phenomenon is intimately related to the excitonic insulator transition, showing
the explicit relation between the gap equation and response function approaches
to this problem. We then provide a general computation of these mass
susceptibilities in the ladder approximation, and present an analytical
computation of the static exponent within a simplified kernel model, obtaining
$\eta_0 =\sqrt{1-\beta/\beta_c}$ . Finally we emphasize that the behavior of
these susceptibilities provides new experimental signatures of interactions,
such as power law Kohn anomalies in the dispersion of several phonons, which
could potentially be used as a measurement of $\beta$.
