# What would be the masses of the elemental particles if the Higgs field had a different value?

Afaik there is some function, for example, for the mass of the electron $m_e(\phi_1, \phi_2, \phi_3, \phi_4)= ...$, and similarly to the other elemental particles. (Here the $\phi_{1..4}$ are the components of the Higgs field.)

What is this function?

## 1 Answer

Look around page 700 of Peskin and Schroeder. Now change the variable they call v.

You get things like $m_e = \frac{1}{\sqrt{2}} \lambda_e v$ at least at first. You then have to do the whole renormalization of bare parameters rigamarole.

• Thank you very much the answer! At least it is something to begin the research. Your answer is very important and useful in this sense. But, I suggest to put in at least the essence of this page, simple "look here" answers are mostly removed here (not by me, your answer is far too important to be handled on such a way, I will edit it to SE-compatible form). It would be even okay if you would copy-paste the text or upload a scanned photo from the required page here (it is also not SE-conform, but so I will be able to edit it). Thank you again! Commented Jun 25, 2016 at 2:33
• To the mods / VtDs: as you can see in the previous comment, a significant extension is on the way, please don't do irrecoverable things yet. Thanks! Commented Jun 25, 2016 at 2:36
• Ok. My layman intuition says the result will have the form $m_e={c_1}{\phi}_1^2+{c_2}{\phi}_2^2+{c_3}{\phi}_3^2+{c_4}{\phi}_4^2$, where $c_{1..4}$ are constants specific to a given particle. Am I right? Commented Jun 25, 2016 at 7:01
• What are $\phi$? Commented Jun 25, 2016 at 7:21
• The 4 components of the Higgs field. Commented Jun 25, 2016 at 8:04