With the Standard Model coefficients ,

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Loops, renormalisation and the renormalisation group · Beyond the Standard Model

Symmetry and Flavour, Ch Grand unification: running couplings, SU(5), proton decay and the hierarchy problem

Problem

With the Standard Model coefficients b2=−196b_2 = -\tfrac{19}{6}, b3=−7b_3 = -7, α2−1(MZ)=29.6\alpha_2^{-1}(M_Z) = 29.6 and αs(MZ)=0.118\alpha_s(M_Z) = 0.118 (so α3−1(MZ)=8.47\alpha_3^{-1}(M_Z) = 8.47), the α2=α3\alpha_2 = \alpha_3 crossing scale comes out at μ≈1.0×1017 GeV\mu \approx 1.0\times10^{17}\,\mathrm{GeV}. Suppose instead the measured value were αs(MZ)=0.121\alpha_s(M_Z) = 0.121, about three standard deviations above the world average, as a deliberate stress test, with everything else unchanged. Calculate the new α2=α3\alpha_2 = \alpha_3 crossing scale, and state by what factor it has moved.

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