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wilson-eft / wilson

A Python package for the running and matching of Wilson coefficients above and below the electroweak scale
https://wilson-eft.github.io
MIT License
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The case of lambda < 0 and m2 < 0 (and Cphi < 0) #66

Closed JoseEliel closed 3 years ago

JoseEliel commented 3 years ago

Thanks for the recent updates on the lambda and m2 routines. It has been very helpful. I wanted to raise an issue related to https://github.com/wilson-eft/wilson/pull/62 (I saw it was closed).

When solving the minimization conditions, one gets two solutions, v2 = ( Lambda - sqrt(sqrt_arg) )/( 3 Cphi ) or v2 = ( Lambda + sqrt(sqrt_arg) )/( 3 Cphi ).

The code takes the first one. However, for Lambda < 0 and m2 < 0 (and Cphi<0) both solutions are positive and different.

That region of the parameter space is relevant for people thinking about phase transitions, as it is one of the cases where one has a wall at tree-level.

JoseEliel commented 3 years ago

Ignore the message above. While both solutions are positive, only one corresponds to a minimum and it turns out to be the one with -. The one with + is the top of the tree-level barrier, of course.