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This research aims to derive two-loop beta coefficients and establish a self-consistent GUT scale using foam geometry.

March 19, 2026Open Access

Two-Loop Beta Functions and the Self-Consistent GUT Scale from Foam Geometry

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The study derives self-consistent GUT scale from foam geometry, highlighting significant shifts in couplings.

This research aims to derive two-loop beta coefficients and establish a self-consistent GUT scale using foam geometry.
Derivation of beta coefficients from foam Casimir operators without free parameters.
Calculation of GUT scale by running three SM couplings simultaneously at two loops from M_Z.
Analysis of corrections to GUT scale compared to one-loop results.
Self-consistent GUT scale identified at M_GUT=1.50×10¹⁶ GeV.
The two-loop correction results in a 6.4-fold shift from the one-loop GUT scale.
Exact value of α_s(M_Z)=0.1179 is achieved from the GUT chain.

Luke Alexander Martin (2026) studied this question.

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March 19, 2026Open Access

View Full Paper

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Authors

The study derives self-consistent GUT scale from foam geometry, highlighting significant shifts in couplings.

This research aims to derive two-loop beta coefficients and establish a self-consistent GUT scale using foam geometry.
Derivation of beta coefficients from foam Casimir operators without free parameters.
Calculation of GUT scale by running three SM couplings simultaneously at two loops from M_Z.
Analysis of corrections to GUT scale compared to one-loop results.
Self-consistent GUT scale identified at M_GUT=1.50×10¹⁶ GeV.
The two-loop correction results in a 6.4-fold shift from the one-loop GUT scale.
Exact value of α_s(M_Z)=0.1179 is achieved from the GUT chain.

Luke Alexander Martin (2026) studied this question.

View Full Paper

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