At the SU(2) coupling has

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

At MZ=91.19 GeVM_Z = 91.19\,\mathrm{GeV} the SU(2) coupling has α2−1(MZ)=29.6\alpha_2^{-1}(M_Z) = 29.6, and its one-loop coefficient is b2=−196b_2 = -\tfrac{19}{6}. Using the one-loop running equation dα2−1dln⁡μ=−b22π,\frac{\mathrm{d}\alpha_2^{-1}}{\mathrm{d}\ln\mu} = -\frac{b_2}{2\pi}, calculate α2\alpha_2 at μ=10 TeV\mu = 10\,\mathrm{TeV}.

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