# “Pure” Yang-Mills and the absence of light matter

I am researching various models of Neutral Naturalness which involve the addition of an additional gauge group whose matter content is uncharged under SM color. Many of these theories state that their low energy dynamics are controlled by a "pure" Yang-Mills theory and then go on to say that this means there can be no light matter (and thus the lightest states are glueballs). I have yet to find an explanation of why this is the case. I am further confused because these theories all have a top partner to cancel the quadratic divergences in the Higgs mass, so they do in fact have matter content. My question is two fold:

1) What exactly is a "pure" Yang-Mills theory, and

2) why does it forbid the existence of light matter, despite the existence of a top partner?

Refs:

Pure Yang-Mills theory just means a nonabelian gauge theory without any extra matter fields charged under it. Suppose you have such a theory with confinement scale $$\Lambda$$. Then essentially by dimensional analysis, the lightest states are glueballs with mass around $$\Lambda$$.

If you did have matter charged under the gauge field, you could have much lighter states. For example, in QCD, the lightest bound states are pions, which have mass substantially less than $$\Lambda_{\text{QCD}}$$. This evades the dimensional analysis argument because the pions are pseudo-Nambu Goldstone bosons of $$SU(2)_A$$, as explained further here.

Therefore the lightest new states in the model would be glueballs. You would also have the top partner, but it would be much heavier than the glueballs (must be, by experimental constraints) and hence doesn't figure into this discussion.

• ok, so that is why there is the caveat that only the "low energy dynamics" are controlled by a pure Yang-Mills theory? Because at that scale the top partner does not have an effect so effectively there is no matter that is charged? I think I was confused and thinking that i.e. an extra SU(3) implied an extra QCD – Jackson Burzynski Apr 5 '19 at 15:14
• @JacksonBurzynski Yeah, the top partner is too heavy to matter. – knzhou Apr 5 '19 at 15:16