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The leading term in the gauge coupling beta function comes due to interaction of gauge field with gravitons.
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C. Ford, I. Jack and D. R. T. Jones, “The Standard model effective potential at two loops,” Nucl. Phys. B 387
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J. F. Donoghue, “Introduction to the effective field theory description of gravity,” gr-qc/9512024
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D. J. Toms, “Quadratic divergences and quantum gravitational contributions to gauge coupling constants,” Phys. Rev. D 84
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2011
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2012
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