1-loop corrections

[xiekeping]

Hi Florian, I am Keping Xie. I am still a little confused about the SPheno to calculate 1-loop mass. As we know, the mass is the pole of propagator. So in paper 1709.03501, [eig M(p^2=mi^2)]=mi^2 give the right pole. But when I loop at the code, I am not sure whether the code does it correctly.

Such as
mat2 = mat2a - Real(PiSf(i1,:,:),dp)
Call Eigensystem(mat2,mi2,RS,kont,test)
The matrix "mat2a" is the tree level mass. while the PiSf(i1,:,:) gives the self energy. However, this 2 matrices are in 2 different basis. mat2a is in the gauge basis (i.e. fields in the Lagrangian), while PiSf(i1,:,:) is calculate in the mass basis. To my understanding, we can work either in gauge basis or mass basis, but we have to unify them to work in the same basis. Here
eig [mat2a - PiSf]=eig[ZH M2 ZH^dag -PiSf]=eig[M2- ZH^dag PiSf ZH], while M2=ZH^dag mat2a ZH= diag(...mi^2...). Is this treatment correct?

Another question is the rotation matrix. In 1-loop level, the mass matrix receives corrections, so does the rotation matrix. However, SPheno code only update the tadpole equations and correspondingly update the solutions. And every other part keep in the same frame, such as the 1-loop mass of W/Z bosons, and gauge couplings. Similar as above, I am not sure whether the code rotates the tadpole loop diagrams back to the gauge basis in order to update the tadpole equations.

I want to do a simple cross check, with all the tree-level couplings, and do the 1-loop calculations, without update the Tadpole solution or the eigenvalues of squared mass matrices. It seems SPheno only do this case for the 1-loop induced decay (such as triangle diagrams H->gamma gamma) or the low energy observables (such as Delta_rho). For the 1-loop mass spectrum, it seems 1 little complicated, which leave it difficult to cross check.

Best regards,
Keping

[FStaub]

The matrix "mat2a" is the tree level mass. while the PiSf(i1,:,:) gives the self energy. However, this 2 matrices are in 2 different basis. mat2a is in the gauge basis (i.e. fields in the Lagrangian), while PiSf(i1,:,:) is calculate in the mass basis.

No, the self-energies are calculated for external gauge eigenstates, see e.g. http://stauby.de/sarah_wiki/index.php?t ... d_Tadpoles

Another question is the rotation matrix. In 1-loop level, the mass matrix receives corrections, so does the rotation matrix. However, SPheno code only update the tadpole equations and correspondingly update the solutions. And every other part keep in the same frame, such as the 1-loop mass of W/Z bosons, and gauge couplings.

That's correct. If you would use one-loop rotation matrices in one-loop corrections this is a two-loop effect. The two-loop corrections take care of that.

Similar as above, I am not sure whether the code rotates the tadpole loop diagrams back to the gauge basis in order to update the tadpole equations.

See above

I want to do a simple cross check, with all the tree-level couplings, and do the 1-loop calculations, without update the Tadpole solution or the eigenvalues of squared mass matrices.

I don't understand that. You need the one-loop tadpoles even if you work with the effective potential approach. Of course, the iteration to find p^2=m^2 would not be necessary then.

You find many details about the mass calculation for scalars in these papers:
1706.05372
1503.03098
1411.0675
They focus in the two-loop part but explain also the one-loop calculations to some extent for consistency.

Cheers,
Florian