Matchete`
Matchete`

SetSSBReplacements

SetSSBReplacements[rules]

sets coupling substitutions to be applied during symmetry breaking.

Details and Options

  • rules can be a single Rule/RuleDelayed or a list of such rules.
  • The open indices on must agree on both sides of the substitution rules. Dummy summation indices on the RHS of the rules are made unique during substitution to prevent accidental repeated indices.
  • The LHS of the rules must be couplings. Open indices on the LHS are automatically made into patterns, so that the substitutions are applied regardless of the dummy indices appearing in the original Lagrangian.
  • Each use of SetSSBReplacements overwrites the previous substitution rules. All rules to be applied in the symmetry breaking should be included as a single list.

Examples

open allclose all

Basic Examples  (1)

In the SM EWSB one will typically write the broken phase interactions in terms of the EM coupling and weak angle rather than the gauge couplings of the symmetric phase:

Scope  (1)

It is conventional to write the broken phase SM in terms of fermion masses and the CKM matrix rather than the Yukawa-coupling matrices:

Here the mass indices are Diagonal, so they are not counted for the purposes of dummy index summation convention.

Tech Notes
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  • SM Electroweak Symmetry Breaking