Loop correction for quartic Higgs coupling

[Safinaz]

Hi all,

Has anyone an idea about the loop correction for quartic Higss coupling?

In [arXiv:1507.03618v2 [hep-ph]], equ. (13) it's pointed out that the perturbativity constrains on the quartic couplings in the Higgs potential is $\lambda^2 < 16 \pi^2$
Which means that loop factor is $\frac{\lambda^2}{(4 \pi)^2}$, but actually I don't why?

Any explanation or refernce about that ?

 

[Hepth]

Is it something more than the fact that every order in the perturbative series goes like $\left(\frac{\lambda^2}{16 \pi^2}\right)^n$, and so to be perturbative at all (for the series to converge or at minimum to have higher orders smaller than the previous) this requires that this factor must be less than one?

Or are you looking for an actual analytic explanation of how the calculation is done?

 

[Safinaz]

Yes please, I want some good and clear reference for QFT notes explain the calculations of the loop correction for a quaric vertex ..

Ok, is it the 4 point Green function ?

Thanx.

 

[Hepth]

Check out http://www.physics.mcgill.ca/~jcline/qft1b.pdf

starting at the top of page 10, maybe this will help with the full calculation, and i think some results around page 25.

 

[Safinaz]

Yes, I think the calculations in equs. ( 47 ) and the result in (96), what I was looking for.