Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO

Abstract

We consider the Standard Model, including a light scalar boson $h$, as an effective theory at the weak scale $v=246\mathrm{GeV}$ of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with $h$ emerging as a pseudo-Goldstone boson. The symmetry breaking scale $\Lambda$ is taken to be at $4\pi v$ or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, $\mathcal{O}(v^2/{\Lambda }^2)$. This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.

Comments: 25 pages, no figures; v2: references added, matches published version; v3: corrected matching of Higgs-portal example to chiral Lagrangian in sec. 7.2