arXiv subjects

Sebastian Schuhmacher

Publications and source records attributed to Sebastian Schuhmacher.

3 recordsLinked to original sources

arXiv2026

Integrating out a heavy Higgs singlet: on the edge between SMEFT and HEFT

We use a functional approach based on the background-field formalism and the expansion by regions to integrate out the heavy Higgs field (associated with the mass eigenstate H) at the one-loop level in a singlet extension of the SM, which features an additional real scalar singlet and a spontaneously broken $Z_2$ symmetry. We obtain an effective Lagrangian to $O(1/M_H^2)$ in the limit of large Higgs mass ($M_H\gg M_h=125$GeV) providing a consistent treatment of effects from Higgs mixing and the renormalization of the underlying model. The scaling behaviour of the model parameters in the large-$M_H$ limit determines whether the effective Lagrangian can be accommodated in the SM Effective Field Theory (SMEFT) or involves non-SMEFT operators within the more general Higgs Effective Field Theory (HEFT) framework. We choose a limit that ensures decoupling of beyond-SM (BSM) effects at $O(M_H^0)$ by demanding that the Higgs mixing angle $α$ is of $O(M_h/M_H)$ and putting minimal constraints on the other input parameters. The considered model is restricted to massless fermions. Bottom-up (diagrammatic) matching with only bosonic SMEFT operators at $O(1/M_H^2)$ necessarily fails, although the BSM sector does not directly couple to massless fermions. However, it is possible to match SMEFT with bosonic and fermionic operators to the SESM in the considered large-$M_H$ limit. For the emerging Effective Field Theory (EFT) we give two alternative Lagrangians: one that includes only bosonic BSM EFT operators, but necessarily involves operators of non-SMEFT type, and another one that is of SMEFT form, but involves also fermionic EFT operators. We validate our results for the effective Lagrangians at NLO in the coupling expansion by verifying that the difference between EFT and full-theory predictions vanishes faster than $1/M_H^2$ for several electroweak observables in the large-$M_H$ limit.

hep-ph↗

arXiv2026

Effective Lagrangians from functional matching

We briefly review a variant of functional matching to derive an Effective Field Theory (EFT) for heavy particles at the one-loop level in the top-down approach. The method integrates out heavy fields that correspond to mass eigenstates, i.e. after removing mixing effects by diagonalizing mass matrices. Tree- and loop-level effects are separated by employing the background-field method, hard and soft modes are separated with the use of the expansion by regions. The method is exemplified for the Higgs Singlet Extension of the Standard Model where the mass $M_\mathrm{H}$ of the additional Higgs boson is considered large, and the Higgs mixing angle $α$ is assumed to scale like $1/M_\mathrm{H}$, in order to guarantee decoupling in the large-$M_\mathrm{H}$ limit. Our calculation is agnostic w.r.t. the type (SMEFT vs. HEFT) of the emerging EFT. Eventually the emerging EFT Lagrangian can be transformed into SMEFT form, but only at the cost of introducing fermionic EFT operators, although no such operators are directly generated upon solving the functional integral over the heavy Higgs field.

hep-ph↗

arXiv2021

Integrating out heavy fields in the path integral using the background-field method: general formalism

Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding effective Lagrangian including the one-loop contributions of the heavy particle(s) is particularly transparent, flexible, and algorithmic. The background-field formalism allows for a clear separation of tree-level and one-loop effects involving the heavy fields. Using expansion by regions the one-loop effects are further split into contributions from large and small momentum modes. The former are contained in Wilson coefficients of effective operators, the latter are reproduced by one-loop diagrams involving effective tree-level couplings. The method is illustrated by calculating potential non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of the Standard Model. In particular, we work in a field basis corresponding to mass eigenstates and properly take into account non-vanishing mixing between the two Higgs fields of the model. We also show that a proper choice of renormalization scheme for the non-standard sector of the underlying full theory is crucial for the construction of a consistent effective field theory.

hep-ph↗