The Standard Model one-loop coefficients give pairwise crossing scales between and

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

The Standard Model one-loop coefficients give pairwise crossing scales between 101310^{13} and 1017 GeV10^{17}\,\mathrm{GeV}. A supersymmetric extension is asserted to change the coefficients to (b1,b2,b3)=(335,1,−3)(b_1, b_2, b_3) = (\tfrac{33}{5}, 1, -3), with no supporting particle yet found. Using α2−1(MZ)=29.6\alpha_2^{-1}(M_Z) = 29.6, α3−1(MZ)=8.47\alpha_3^{-1}(M_Z) = 8.47 and MZ=91.19 GeVM_Z = 91.19\,\mathrm{GeV}, calculate the scale μ\mu at which α2=α3\alpha_2 = \alpha_3 under these supersymmetric coefficients.

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