Corrigendum to: “Complete electroweak chiral Lagrangian with a light Higgs at NLO” [Nucl. Phys. B 880 (2014) 552–573]

The matching of the Higgs-portal example to the chiral Lagrangian in Section 7.2 is corrected to properly account for the systematics of the relevant strong-coupling limit. The text of Section 7.2 given below supersedes the previous version. The main conclusions of Section 7.2 and the rest of the paper are not affected by this correction. The Higgs-portal model discussed here is equivalent to the Standard Model extended by a heavy scalar singlet. The chiral Lagrangian as the low-energy effective field theory of this model in the strong-coupling regime is further elaborated on in [1].

The matching of the Higgs-portal example to the chiral Lagrangian in Section 7.2 is corrected to properly account for the systematics of the relevant strong-coupling limit. The text of Section 7.2 given below supersedes the previous version. The main conclusions of Section 7.2 and the rest of the paper are not affected by this correction.
The Higgs-portal model discussed here is equivalent to the Standard Model extended by a heavy scalar singlet. The chiral Lagrangian as the low-energy effective field theory of this model in the strong-coupling regime is further elaborated on in [1].

Higgs portal
As a specific model for a UV completion we consider the Higgs portal (see [2][3][4][5] and references therein). This model postulates the existence of a new, Standard-Model singlet scalar particle, which has allowed dimension-4 couplings to the Higgs field. This interaction modifies the scalar potential of Eq. (4) to where φ s refers to the standard scalar doublet and φ h denotes the hidden scalar. Both of them acquire a vacuum expectation value, which can be written as Expanding both scalars around their vacuum expectation value, i.e. |φ i | = 1 √ 2 (v i + h i ), leads to a potential of the form The transformation diagonalizes the mass matrix. The rotation angle χ is defined as The masses of the physical states H 1 and H 2 are given by The Lagrangian relevant for the two scalars then reads where The couplings λ i and z i depend on μ s , μ h , λ s , λ h and η. With the parameters of the Higgs-portal model the theory is renormalizable and unitary. The scalar H 1 is now identified with the light scalar h that was found at the LHC. H 2 is assumed to be heavy such that it can be integrated out. In doing so, we take its mass M 2 to be larger than all other energy scales in the model, M 2 v h , v s , M 1 .
In this limit the couplings λ s , λ h and η become large. We will assume, however, that they still remain in a regime where perturbation theory is a sufficiently reliable approximation. H 2 can then be integrated out at tree level by solving its equation of motion and inserting the solution into the Lagrangian (7). The H 2 -part of this Lagrangian can be written as where the J i can be read off from (7) and (8). Making the dependence on M 2 explicit, the J i take the form where J 0 i is a pure polynomial in H 1 ≡ h. The equation of motion for H 2 reads It can be solved order by order in powers of 1/M 2 2 by expanding Extending the derivation to the NLO terms of O(1/M 2 2 ) one finds where (H The effective Lagrangian L NLO contains operators that modify the leading-order Lagrangian (4) as well as a subset of the next-to-leading operators of Section 4. In particular, we have the hermitean conjugates of the O ψSi in (18), and 4-fermion operators coming from the square of the Yukawa bilinears contained in J 1 . The 4-fermion operators that are generated have the same structure as those in the heavy-Higgs model discussed in [6], which are 1 and their hermitean conjugates, but they are now dressed with functions F i (h/v).
This discussion shows explicitly how a subset of our NLO operators is generated in the Higgs-portal scenario. After integrating out the heavy scalar H 2 in the non-decoupling limit M 2 v h , v s , M 1 the effective theory takes the form of a chiral Lagrangian. In particular, even for F i (h/v) → 1, it is seen that operators of canonical dimension 4 (O D1 ), 5 (O ψSi ) and 6 (4-fermion terms) contribute at the same (next-to-leading) order 1/M 2 2 . This shows that the effective Lagrangian is not simply organized in terms of canonical dimension.