QCD energy scale $\Lambda_{\rm MS} $, $\Lambda_{\rm QCD}$, ...?

Question

Why there seems to be different conventions of QCD energy scales? Is that due to the running coupling?

For example in Wikipedia https://en.wikipedia.org/wiki/Coupling_constant#QCD_scale: $$ \Lambda_{\rm MS} = 218\pm24\text{ MeV} $$ and also some search of the article https://inspirehep.net/literature/296684: $$ \Lambda_{\rm MS} = 254\text{ MeV}. $$

However, from Lubos and others What is the significance of the QCD scale parameter $\Lambda$?, it seems that people also set $$ \Lambda_{\rm QCD} = 150\text{ MeV}. $$

So what exactly defines the QCD energy scale? $$\Lambda_{\rm MS} \text{ vs } \Lambda_{\rm QCD}?$$

How do they relate to confinement and pion mass?

This post imported from StackExchange Physics at 2020-12-03 13:05 (UTC), posted by SE-user annie marie heart

Comments

I think this all depends on what you mean by QCD scale. Often people mean define this as the Landau pole of QCD, the scale at which the QCD beta function blows up. I think if you just use the 1-loop QCD beta function you get like $\Lambda_{\rm QCD}\sim 90$ MeV, but using higher order corrections gives $\Lambda_{\rm QCD}\sim 213$ MeV.

This post imported from StackExchange Physics at 2020-12-03 13:05 (UTC), posted by SE-user 4xion

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This also depends on the measured value of the QCD coupling (at a specific scale), and possibly also on the RG scheme

This post imported from StackExchange Physics at 2020-12-03 13:05 (UTC), posted by SE-user 4xion