Gravitational Corrections to Yukawa and ${\phi }^4$ Interactions

We consider the lowest order quantum gravitational corrections to Yukawa and ${\phi }^4$ interactions. Our results show that quantum gravity leads to contributions to the running coupling constants if the particles are massive and therefore alters the scaling behavior of the standard model. Furthermore, we find that the gravitational contributions to the running of the masses vanish.

Figure 1

Order ${\kappa }^2$ corrections to the two-point functions.

Figure 2

Order $\lambda {\kappa }^2$ corrections to the ${\phi }^4$ interaction.

Figure 3

Order $g{\kappa }^2$ corrections to the Yukawa interaction.