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The present work is the second part of a series of computations for theself-mass-squared of the conformally coupled (CC) scalar interacting withgravitons. This work includes the kinetic-kinetic and kinetic-conformal parts,and thus completes the full scalar self-mass squared at one loop order in deSitter background when combined with the conformal-conformal part previouslyevaluated. We use dimensional regularization and renormalize the results bysubtracting appropriate counterterms. The self-mass squared is finally ready toquantum-correct the CC scalar field equation so that one can study the effectof inflationary produced gravitons on the CC scalar and its observationalconsequences.

Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms