# A How to get these Equations?

1. Apr 25, 2016

### Monaliza Smile

Hi all,

Do any one know how from the mass eigenvalues:

$M_{H,h}^2 = \frac{1}{2} [\lambda_1 v_1^2 + \lambda_2 v_2^2 \mp \sqrt{(\lambda_1 v_1^2 - \lambda_2 v_2^2)^2 + 4 \lambda^2 v_1^2 v_2^2} ],$

and $\tan 2\alpha =\frac{2 \lambda v_1 v_2}{\lambda_1 v_1^2 - \lambda_2 v_2^2}$

To get the couplings $\lambda_{1,2}$ as in Equs. (6) in [arXiv:1508.00702v2[hep-ph]]
or Equs. (9) in [arXiv:1303.5098v1 [hep-ph]], Note that I'd like to put $m_{12} =0$.

PS. The angle $\alpha$ is the angle which diagnolize the mass matrix of the two cp- even Higgs scalars of the two Higgs doublets $\Phi_1$ and $\Phi_2$ in the 2HD potential (2), [arXiv:1508.00702v2[hep-ph]] to get the physical states: h, H, so it's Eigenvalues problem. But now after getting mh and mH, how to get the couplings $\lambda_{1,2,3}$ in terms of them ?

You can see in [arXiv:1508.00702v2[hep-ph]] that $\lambda_{4,5}$ can be driven easily from the charged and the cp- odd Higgs masses (5) .

Any help ?

2. Apr 30, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Jul 10, 2016

### malawi_glenn

You just have to do algebra

Mathematica or Maple helps for sure