The Irony of the Higgs Mechanism: Giving Mass to the Massless?

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The Higgs mechanism provides mass to fermions and bosons through the Higgs field, which couples to these particles via a Higgs vacuum expectation value (vev). The discussion highlights the irony that the Higgs particle itself has mass, raising questions about the relationship between the Higgs field and its particle. It is noted that if the Higgs vev is zero, the Higgs mass also becomes zero, suggesting a deeper connection. Additionally, there is a request for clarification on the concept of first order as used in a referenced arXiv paper, specifically regarding its application to obtain a particular equation. This conversation emphasizes the complexities and nuances of the Higgs mechanism in particle physics.
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Forgive if I'm being sarcastic, but I just read on the Higgs mechanism, giving mass to the fermions and bosons. But at the same time, Higgs itself has mass? Isn't that abit irony?
 
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There are two separate concepts:: Higgs field (the mechanism) and Higgs particle.
 
arivero said:
There are two separate concepts:: Higgs field (the mechanism) and Higgs particle.

I meant the Higgs mechanism itself used the Higgs field to couple to the bosons to give them their masses, via a Higgs vev. But at this point, I guess I should have read the arxiv paper more properly. Now I notice that had if the Higgs vev = 0, so too will the Higgs mass. I think I can say that, not only does the Higgs mechanism gives mass to the fermions and bosons, but also to the Higgs particle itself ?
Also, in the same arxiv paper: http://www.arxiv.org/abs/hep-ph/0503172
what is first order and how did the author use it to obtain equation 1.33 ?
 

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