  The present work is the second part of a series of computations for the
self-mass-squared of the conformally coupled (CC) scalar interacting with
gravitons. This work includes the kinetic-kinetic and kinetic-conformal parts,
and thus completes the full scalar self-mass squared at one loop order in de
Sitter background when combined with the conformal-conformal part previously
evaluated. We use dimensional regularization and renormalize the results by
subtracting appropriate counterterms. The self-mass squared is finally ready to
quantum-correct the CC scalar field equation so that one can study the effect
of inflationary produced gravitons on the CC scalar and its observational
consequences.
