GetVacuumConditions
GetVacuumConditions[lagrangian]
returns an association containing all the conditions on the parameter of a broken-phase Lagrangian to be at the true vacuum and in mass basis, attempts to derive a solution for the resulting set of conditions, and identifies masses.
Details and Options
- GetVacuumConditions must be called on a full broken-phase Lagrangian w/ masses, kinetic terms, etc. for all fields (e.g., the direct output from ToBrokenPhase).
- GetVacuumConditions returns an association with three keys: "Conditions" indexes into an association collecting all conditions on the parameters for the Lagrangian to be in the true vacuum; "Solution" gives a substitution rule for parameters, which satisfy all conditions simultaneously; and "MassSubstitutions" which is a list of all heavy vector masses and radial scalar mode masses in terms of the Lagrangian parameters.
- GetVacuumConditions collects the conditions needed for the Lagrangian to satisfy the following conditions: tadpole terms must vanish; there should not be mass terms for the would-be Goldstone bosons; the Lagrangian should be in a mass basis (no mass mixings); there should not be any kinetic mixing between massive vectors and non-GB scalar fields; and all kinetic terms should be canonically normalized.
- GetVacuumConditions runs a method attempting to find a non-trivial solution for the couplings that satisfies all conditions simultaneously. If one is found, it can be found under the key "Solution" in the output association. A solution might not be found even if it exists; if "Solution" False is returned, the user ought to manually verify that the system is consistent.
- The following options can be given:
-
TimeConstraint 60 sets the time limit (in seconds) to find a solution satisfying all constraint. Variables Automatic specifies which coupling parameters to solve for.
Examples
open allclose allBasic Examples (1)
The broken-phase SM is loaded from the model data-base:
It is however not in the true vacuum because no condition has been put on the VEV of the Higgs relative to the symmetric-phase parameters. GetVacuumConditions identifies a tadpole for the Higgs boson and mass terms for the GBs χ and χ0.
All conditions can be simultaneously satisfied with the "Solution" for the parameters, in this case solving for the Higgs mass parameter μ2. The key "MassSubstitutions" contains formulas for the masses of the Higgs boson, the W and the Z boson masses in terms of the underlying parameters.
Options (1)
Variables (1)
If no other option is chosen, GetVacuumConditions will try to find a solution to the conditions in terms of couplings entering linearly in the equations (the Higgs mass parameter μ2 in the case of the SM). Using the option Variables, one can specify a (list of) couplings that should be solved for, here in terms of the Higgs VEV v.