Why should we care about the top quark Yukawa coupling?
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In the cosmological context, for the Standard Model to be valid up to the scale of inflation, the top quark Yukawa coupling $y_t$ should not exceed the critical value $y_t^{crit}$, coinciding with good precision (about 0.02%) with the requirement of the stability of the electroweak vacuum. So, the exact measurements of $y_t$ may give an insight on the possible existence and the energy scale of new physics above 100 GeV, which is extremely sensitive to $y_t$. We overview the most recent theoretical computations of $y_t^{crit}$ and the experimental measurements of $y_t$. Within the theoretical and experimental uncertainties in $y_t$ the required scale of new physics varies from $10^7$ GeV to the Planck scale, urging for precise determination of the top quark Yukawa coupling.
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Fixed points of the renormalisation group running of quark and fermion mixing matrices in the Standard Model and beyond
Six fixed points exist for the massless one-loop RG running of three-generation fermion mixing matrices, remaining fixed points to all orders via geometric properties of vector fields on the space of mixing matrices.
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