Physics Asked by Stefano Barone on January 21, 2021
Considering the one-loop running coupling constant in QCD:
$$alpha_s(mu) = frac{a_s(mu_0)}{1 + frac{33-2f}{6 pi}lnleft( frac{mu}{mu_0}right)}$$
where f is the number of quarks flavours with mass $2m_q leq mu $
I’d like to compute the formula for the energy $mu=2m_c = 2.8$ GeV where $m_c$ is the upper limit on the charm quark mass.
Knowing that $alpha_s(m_z)=0.12$ where $m_z = 91$GeV I considered $mu_0 = m_z$ but I this way I obtain $alpha_s(mu)= – 0.057$ where I put f = 4 to include up-down-strange and charm quarks.
This definitely makes no sense. Where am I wrong? Do I need to change $mu_0$ and $alpha(mu_0)$?
In this last case what values do I need to consider?
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