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I am slightly confused about the coupling constants of the fundamental forces and would really appreciate some help in clearing up this confusion.

Some sources(like this one: http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/couple.html) seem to convey that $\alpha_W= 10^{-6}$ while some other sources like the text by Griffiths on particle physics suggest that $\alpha_W\sim1/30$.

My guess is that this has something to do with running coupling but I am not really sure. Any reference to how $\alpha_W$ changes with energy would be helpful too.

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  • $\begingroup$ Perhaps this answer might reduce your puzzlement. The running of dimensionless gauge couplings is a mere distraction in your question. The differences are definitional and methodological. $\endgroup$
    – Cosmas Zachos
    Commented Oct 2, 2020 at 14:07
  • $\begingroup$ Page 4 of the PDG, the standard go-to reference in particle physics, confirms that the actual running is quite small; from the macroscopic/asymptotic $1/137 \to 1/133.5$ at the Z mass. $\endgroup$
    – Cosmas Zachos
    Commented Oct 2, 2020 at 14:29
  • $\begingroup$ Thanks @CosmasZachos , I think that answer really helped clear the confusion. Just to confirm: The relation $\alpha_W*(sin(\theta_W))^2=\alpha$ is always valid. The low energy(~0.1 GeV) values of $\alpha_W$ and $\alpha$ are 1/30 and 1/137 respectively. As the energy is increased, both of them have a running value(which is small change as per PDG). The 10^-6/10^13 are actually talking about the effective coupling in different energy regimes and not talking about the coupling constants as such. Is this correct? $\endgroup$
    – lifelong_student
    Commented Oct 2, 2020 at 16:09
  • $\begingroup$ Also, the linked answer states that "EM cross sections decrease like 1/s, while weak ones increase like s" Could you help me see why? $\endgroup$
    – lifelong_student
    Commented Oct 2, 2020 at 16:13
  • $\begingroup$ Yes, your comment understanding is basically sound. The answer to your 2nd comment is essentially dimensional analysis. In natural units, σ goes like inverse energy squared, so EM which has no significant scale must go like 1/s. By contrast, EW at "lower" energies goes like $G_F^2 \propto 1/M_W^4$ so needs s upstairs for dimensional consistency, very crudely. $\endgroup$
    – Cosmas Zachos
    Commented Oct 2, 2020 at 16:47

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