NLO Inspired Effective Lagrangians for Higgs Physics

TL;DR

The paper advocates a bottom-up effective-field-theory program for Higgs physics, augmenting the Standard Model with $d=6$ operators $\mathcal{O}_i^{(6)}$ and small Wilson coefficients $a_i$, to capture precision deviations in Higgs couplings at the LHC within a UV-consistent framework.It develops the formalism for renormalization and S-matrix mapping in the presence of EFT insertions, classifies dimension-6 operators by their ultraviolet origin (tree-level $T$ vs loop $L$), and analyzes both decoupling and non-decoupling scenarios with explicit Higgs-decay and production calculations including loops and four-fermion final states.The work also discusses MSSM and other BSM Lagrangians as ultraviolet completions that generate the EFT operators, examines perturbative unitarity bounds, and stresses the range of validity of the EFT, highlighting how large deviations could point to the need for higher-dimension operators or a UV-complete theory.

Abstract

Either late autumn this year or latest early next year LHC should have results with 2-3 times the current data which migth give first clues on the couplings of the light narrow resonance. A strategy for measuring deviations from the Standard Model can be based on using the "full" Standard Model, including all available QCD and electroweak higher-order corrections, and supplement it with d= 6 local operators. Their Wilson coefficients are assumed to be small enough that they can be treated at leading order. Examples of the connection of local operators with BSM Lagrangians are presented as well as a discussion of Lagrangians with/without decoupling of heavy degrees of freedom. The whole strategy is critically reviewed in the light of internal consistency.

Figures (5)

• Figure 1: Example of Ward-Salvnov-Taylor identity; the grey circle denotes insertion of $d = 6$ operators, black circles denote the replacement of the polarization vector by $i$ times the momentum flowing inwards. $\HepAntiParticle{\HepParticle{Z}{}{}\xspace}{}{}\xspace$ and $\HepAntiParticle{\upphi}{}{\,0}\xspace$ lines represent Dyson resummed propagators.
• Figure 2: The three-point function $\HepParticle{H}{}{}\xspace^3$ with the insertion of the ${\cal O}_{{\partial\HepParticle{K}{}{}\xspace}}$ operator (left) and the same contribution in the full Lagrangian of Eq.(\ref{['NPL']}).
• Figure 3: The three families of diagrams contributing to the bosonic amplitude for $\HepParticle{H}{}{}\xspace \to \HepParticle{\upgamma}{}{}\xspace\HepParticle{\upgamma}{}{}\xspace$; $\HepParticle{W}{}{}\xspace/\upphi$ denotes a $\HepParticle{W}{}{}\xspace\,$-line or a $\upphi\,$-line. $\HepParticle{\HepParticle{X}{}{}\xspace}{}{\pm}\xspace$ denotes a FP-ghost line
• Figure 4: Example of diagram giving a contribution to the $d= 6$ operator of type $L$. Solid lines represent colored scalar fields, e.g. transforming in the $\left( 8\,,\,2\,,\,\frac{1}{2}\right)$ representation of $SU(3)\,\otimes\,SU(2)\,\otimes\,U(1)$.
• Figure 5: Amplitude for a two-body decay of the Higgs boson (dash line) including LO+NLO SM contributions with a sum over all one-loop diagrams (i); SM diagrams are eventually multiplied by a universal scaling from $d = 6$ operators (black circle); the grey circle represents a contact term.