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We know that the beta function for QCD is $$ \beta = -\left(11 - \dfrac{2N_f}{3}\right), $$ where $N_f$ is the number of fermions in the theory. We have $\beta_{\text{SM}} = -7$.

Now, my question is, how would this result be affected if we had a new fermion doublet at an insanely high energy? Let's say we have a new quark doublet with mass $1000\, \text{TeV}$, so that it cannot be a final state in our current particle colliders. Would this impact the beta function measured in the LHC, so that $\beta_{\text{SM}} = -17/3$? Or is this a high energy problem, that would have no effects in the measured $\beta$?

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    $\begingroup$ Indeed, the loop effect may be visible below the production threshold of the "insane" particles. Charm was anticipated from its loops. $\endgroup$
    – Cosmas Zachos
    Commented May 30 at 20:35
  • $\begingroup$ Thank you Professor Zachos! $\endgroup$
    – Gabriel Ybarra Marcaida
    Commented May 30 at 23:00

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