Fingerprints of heavy scales in electroweak effective Lagrangians

Abstract

The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking $SU(2{)}_L\otimes SU(2{)}_R\to SU(2{)}_{L+R}$, which couples the known particle fields to heavier states with bosonic quantum numbers $J^P=0^{\pm }$ and $1^{\pm }$. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.

Comments: 57 pages, 1 pdf figure. Version published at JHEP