ImplementVacuumConditions
ImplementVacuumConditions[lagrangian]
simplifies a broken phase Lagrangian, with assumptions based on the vacuum being true and the broken phase fields being properly identified as eigenstates.
Details and Options
- ImplementVacuumConditions must be called on a full broken-phase Lagrangian w/ masses, kinetic terms, etc. for all fields (e.g. directly on the return from ToBrokenPhase).
- ImplementVacuumConditions simplifies a broken-phase Lagrangian under the assumptions that it is expanded around the minimum of the potential, i.e., assuming that all conditions identified by GetVacuumConditions are simultaneously satisfied: 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.
- N.b. ImplementVacuumConditions, will simplify the Lagrangian even if the conditions are mutually contradictory. It is up to the user to verify that a true vacuum can be obtained with the specified symmetry-breaking pattern and field decomposition. The user can always get information about the underlying conditions with GetVacuumConditions.
- The following options can be given to ImplementVacuumConditions:
-
SubstituteMasses True specifies whether to substitute the mass terms of the heavy vectors and radial scalar modes, in terms of their canonical mass labels (also for the GB-vector kinetic mixing terms).
Examples
open allclose allBasic Examples (1)
The broken-phase of the SM can be loaded with the broken SM model file and using ToBrokenPhase (here removing the fermionic sector for simplicity):
To get to the true vacuum one then calls
Notice the absence of a Higgs boson () tadpole term and would-be GB (χ and χ0) masses. These are removed with ImplementVacuumConditions.
The formulas for the substituted masses (M, M, M) in terms of the underlying parameters can also be referenced with
Options (1)
SubstituteMasses (1)
The SubstituteMasses option indicates that the resulting Lagrangian should directly substitute the mass terms for the heavy vector and radial scalar mode masses as well as the GB-vector kinetic mixing terms for the canonical mass labels associated with the fields (those specified in DefineField during field definition).
Turning this of for the bosonic SM, with Lagrangian leaves the mass expressions in terms of other theory parameters, dictated by the symmetric phase parameters and the parameter substitutions specified in SetSSBReplacements.