Someone argues: “The top-loop correction to the Higgs mass-squared at a cutoff is

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

Someone argues: “The top-loop correction to the Higgs mass-squared at a cutoff Λ=1016 GeV\Lambda = 10^{16}\,\mathrm{GeV} is ∣δmH2∣≈(3yt2/8π2)Λ2≈4×1030 GeV2|\delta m_H^2| \approx (3y_t^2/8\pi^2)\Lambda^2 \approx 4\times10^{30}\,\mathrm{GeV^2}, using yt=0.99y_t = 0.99. The measured Higgs mass gives mH2=(125.2 GeV)2≈1.6×104 GeV2m_H^2 = (125.2\,\mathrm{GeV})^2 \approx 1.6\times10^4\,\mathrm{GeV^2}, twenty-six orders of magnitude smaller. Since a quantum-field-theory calculation gives a result twenty-six orders of magnitude too big, the Standard Model prediction for mHm_H is internally inconsistent and must be wrong.” Find the error in this reasoning, and state, with a number, what the calculation actually establishes.

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