Gravitational Effects On The Vacuum Stability Bound For Higgs Boson

The Standard Model of particle physics is a theory to describe the basic articles and the basic interactions of nature. The theory agrees well with experiments. In 2012, LHC and CMS declared that they found Higgs boson, which proved the Standard Model is the right theory to describe the nature.Among the four kinds of interactions, gravitation can not be renormalized.So we can’t unit gravitation with other three interactions.While by the way of effective field theory, the quantum effect were important at low energy so we can study the gravitation[2].But it is problematic to extend the validity of the Standard Model to Planck scale.Standard Model is still a effective theory at low energy.there may be new physics at high energy.One way to detect new physics is the vacuum stability[18, 19].If we include the loop corrections to the Higgs potential in Standard Model,the couplingλ will run with the energy scale.At planck scale λ will vanish.This will lead to a new vacuum in the potential.The quantum tunneling effect make the electromagnetic-weak vacuum decay,called vacuum instability[6].In this paper,I studied the graviton one-loop correction to the top Yukawa coupling with the frame of Standard Model and gravitation effective theory. From the action we derive the Feynman rules and calculate the Feynman graphs. Then we found that the results relies on the gauge parameter,which is coincident with the conclusion of Pietrykowski.We will make ζ = 1 and do the calculations.We include the gravitation corrections to gauge coupling which was finished by Wilczeck and the corrections to λ. Then we get the new renormalization group equations.finally the numerical calculation were done and we get the gravitational corrections to the RGE running at Planck scale. Then we compare the lower bound of Higgs mass with and without the gravitational correction. And the result shows that the vacuum stability become more serious.