Can I use non-analytical effective potential in WallGo?

[nayuta-psiomega]

Hi,
I have a little question regarding the implementation of the effective potential.
I'd like to implement the NNLO effective potential obtained via DRalgo, but the analytical expressions are too complicated, so I found it'd be less intractable to implement the numerical values of Veff instead. For this purpose, I need to sample Veff at each temperature, but WallGo.EffectivePotential.evaluate() uses an internal temperature profile that I cannot directly control. I'm considering to pre-computing Veff by fine-sampling it over the relevant temperature range and interpolating it, but I'm wondering whether there is a more straightforward or recommended method for this.

Thanks in advance.

[jorindevandevis]

Hi,
Thank you for the question!
I am afraid that we currently do not have a simpler method implemented for your problem.
But can't you take the DRalgo expressions to Python before substituting them? That should give you a manageable function of phi and T.

Let me also point out that we briefly discussed the use of the NNLO effective potential in section 4 of https://arxiv.org/pdf/2510.27691 . There, we stress that there is no physical argument why the NNLO effective potential would give a more accurate value for the wall velocity than the one-loop one. Of course, I don't know your physical set-up, so maybe our arguments don't apply to what you are computing.

Cheers,
Jorinde

[nayuta-psiomega]

Thanks a lot for the reply.

But can't you take the DRalgo expressions to Python before substituting them? That should give you a manageable function of phi and T.

In principle it'd be doable, but I'm afraid the expressions would be terribly lengthy if I substitute every effective coupling in terms of 4d couplings.

I'm considering the U(1) Higgs model without fermions. At this stage, I've obtained the NNLO Veff at the ultrasoft scale, as well as the nucleation temperature calculated using BubbleDet which would be inserted in WallGo.
In the toy example of real scalar yukawa model (Sec. 4 of 2108.04377), there's only a single scale hierarchy. Since the tree-level potential already has a barrier, it's straightforward to implement Veff as demonstrated in BubbleDet and WallGo example.
In the U(1) case, the things become a bit nontrivial due to two scale hierarchies. Moreover, because the barrier is generated radiatively, I need to consider full NNLO potential at the nucleation scale which I assumed to be ultrasoft scale.
If I understood your comment correctly, there does not appear to be a strong consensus on which Veff (4d daisy or 3d NNLO) should be used to compute the wall velocity. Is there a consistent way to combine the 3d EFT approach with WallGo?

Edit : I found that the tree-level potential at nucleation scale should be used in scale-shifting scheme.