NLO EW and QCD dimension-6 SMEFT results for Higgs and gauge boson decays in POPxf format

This paper presents next-to-leading-order QCD and electroweak results for dimension-6 SMEFT corrections to Higgs and gauge boson decays, as well as the Higgstrahlung process, providing total widths, differential distributions, and precision observables in the user-friendly POPxf format.

The Gist

Imagine the Standard Model of particle physics as a highly detailed, perfect instruction manual for how the universe's tiniest building blocks behave. Scientists at the Large Hadron Collider (LHC) and future facilities are trying to find tiny typos or missing pages in this manual that might hint at "new physics" hiding just beyond our current view.

This paper is essentially a massive calculator update for scientists trying to find those typos. Here is a breakdown of what the authors did, using everyday analogies:

1. The "SMEFT" Recipe Book

The authors are using a tool called SMEFT (Standard Model Effective Field Theory). Think of the Standard Model as a perfect cake recipe. SMEFT is like adding a "what-if" section to that recipe book. It asks: "What if there were invisible ingredients (new physics) at a very high scale that we can't see directly, but which slightly change how the cake rises?"

They are looking specifically at "dimension-6" ingredients. In their math, these are like specific spices that might be added to the mix. The paper calculates exactly how much these invisible spices would change the taste of the final product.

2. The "High-Definition" Upgrade (NLO)

In the past, scientists calculated these changes using a "low-resolution" map (Leading Order). It was good, but a bit blurry.

This paper provides a High-Definition (NLO) map.

• The Analogy: Imagine trying to measure the distance between two cities. A "low-res" calculation might just look at a straight line on a flat map. A "high-res" calculation (NLO) accounts for the curves of the road, the hills, and the traffic.
• The authors calculated these "traffic and hills" (quantum corrections) for two types of forces: the strong force (QCD) and the electromagnetic/weak force (EW). This makes their predictions much more precise, allowing scientists to spot even the tiniest deviations from the standard recipe.

3. The "Universal Translator" (POPxf)

One of the biggest headaches in physics is that different scientists use different formats to share their numbers, making it hard to combine their work.

The authors packaged all their results into a format called POPxf.

• The Analogy: Think of this as converting a bunch of handwritten recipes written in different languages and handwriting styles into a single, standardized digital file (like a JSON file).
• This "Universal Translator" allows experimentalists (the people building the machines) and theorists (the people doing the math) to easily swap data. If an experiment at the LHC sees a weird result, they can instantly plug it into these files to see if it matches the "invisible spice" theory.

4. What Did They Calculate?

They didn't just look at one thing; they calculated the behavior of the Higgs boson (the "God particle" that gives mass to others) and the Z and W bosons (force carriers) in great detail:

• Higgs Decay: They calculated how the Higgs boson breaks apart into other particles (like pairs of photons, gluons, or fermions). They looked at both simple breaks (2-body) and complex breaks (4-body).
  • Key Detail: They found that for some calculations, it matters how you define the mass of the particles (like using a "pole" definition vs. a "running" definition). They provided results for both methods so scientists can choose the one that fits their specific experiment.
• Precision Observables: They calculated how these invisible spices affect the "Z-pole" (a specific energy level where Z bosons are created). This is like checking the calibration of a scale to see if it's off by a fraction of a gram.
• Higgstrahlung: They also calculated the process where an electron and positron collide to create a Z boson and a Higgs boson (like a "Higgs-strahlung" or "Higgs shower"). They did this for three different energy levels (240, 365, and 500 GeV), which are the target energies for future electron-positron colliders.

5. The "Total Width"

A major highlight of the paper is the calculation of the Total Higgs Width.

• The Analogy: If the Higgs boson is a spinning top, the "width" is how fast it wobbles and falls apart. The authors calculated the total wobble, including every possible way it can fall apart, including the subtle effects of the invisible spices. This is crucial because if the total wobble is different from the standard prediction, it's a huge clue that new physics is present.

Summary

In short, this paper is a comprehensive, high-precision data package. It takes the complex math of "what if new physics exists?" and turns it into a clean, standardized, and highly accurate set of numbers. These numbers are now ready for experimentalists to use as a ruler to measure the real universe and see if it matches the standard model or if there are hidden secrets waiting to be found.

The authors have made these results available in a digital repository (GitLab) so that anyone working on these experiments can download and use them immediately.

Technical Summary

Technical Summary: NLO EW and QCD Dimension-6 SMEFT Results for Higgs and Gauge Boson Decays

Problem and Context
The primary objective of the High-Luminosity LHC (HL-LHC) and future facilities like FCC-ee is to precisely constrain or observe deviations from Standard Model (SM) predictions. The Standard Model Effective Field Theory (SMEFT) serves as a framework for searching for high-scale new physics, assuming no unobserved light particles and preserving the SM gauge symmetry. While tree-level (Leading Order, LO) calculations for dimension-6 operators are readily available via automated tools, the anticipated experimental precision requires predictions beyond LO. Specifically, Next-to-Leading Order (NLO) corrections in both Quantum Chromodynamics (QCD) and Electroweak (EW) sectors are necessary. A significant challenge in NLO EW corrections is their dependence on dozens of Wilson coefficients that do not contribute at tree level, with results historically scattered across the literature. Furthermore, achieving consistent accuracy at $O(1/\Lambda^2)$ requires careful handling of renormalization schemes and input parameters.

Methodology
This work compiles and presents NLO QCD and EW results for dimension-6 SMEFT operators across a broad spectrum of processes. The calculations are accurate to $O(1/16\pi^2 \Lambda^2)$, retaining terms up to linear order in $1/\Lambda^2$ to ensure consistent power counting without requiring dimension-8 operators or double insertions of dimension-6 operators.

The results are formatted using POPxf, a data exchange format designed to standardize arbitrary polynomial dependences of observables on model parameters. This format facilitates the sharing and reproduction of theoretical predictions in Effective Field Theory (EFT) analyses by storing observables as functions of polynomials of Wilson coefficients, along with necessary metadata (renormalization scales, parameter inputs, basis choices).

The study covers:

1. Higgs Decays: All 2-body and 4-body decays ($H \to \gamma\gamma, \gamma Z, gg, f\bar{f}$, and $H \to 4\ell$).
2. Gauge Boson Decays: $Z$ and $W$ boson decays and associated Electroweak Precision Observables (EWPOs).
3. Higgstrahlung: The process $e^+e^- \to ZH$ at center-of-mass energies of 240, 365, and 500 GeV.

The calculations utilize specific input schemes, primarily $\{M_W, M_Z, G_F\}$ and $\{\alpha(0), M_Z, G_F\}$. For Higgs decays, the authors investigate the impact of quark mass renormalization schemes (On-Shell vs. $\overline{\text{MS}}$) on the results. The narrow width approximation is employed for NLO corrections in 4-body decays, while full 4-body final states are computed at LO.

Key Contributions and Results
The paper provides a comprehensive set of numerical results in JSON files via a GitLab repository, enabling users to replicate the findings. Key technical outputs include:

• Higgs Decay Widths and Branching Ratios: Inclusive decay widths and branching ratios for all 2- and 4-body Higgs decays are presented. The authors parameterize deviations from SM predictions as linear functions of Wilson coefficients.
  • Scheme Dependence: The study highlights that the choice between On-Shell (OS) and $\overline{\text{MS}}$ renormalization schemes for quark masses can have a sizable impact on numerical results, particularly for operators like $C_{\phi D}$ and $C_{d\phi}$. This dependence propagates to all branching ratios due to the expansion of the total width in the denominator.
  • Differential Distributions: For $H \to 4\ell$ decays, the paper provides differential distributions ($d\Gamma/dm_{Z^*}$) and results with a kinematic cut ($M_{Z^*} > 12$ GeV), motivated by experimental analyses.
• Electroweak Precision Observables (EWPOs): NLO QCD and EW results for $Z$ and $W$ decays are provided for both input schemes. The results cover total widths ($\Gamma_W, \Gamma_Z$), hadronic cross-sections, and various asymmetry parameters ($A_{FB}, A_{\ell}, R_{\ell}$, etc.).
  • Input Scheme Sensitivity: The authors demonstrate that input scheme dependence is significant for certain operators (e.g., $C_{\phi D}, C_{\phi W B}$) even at NLO, while it is smaller for others (e.g., $C_{lq}^{(3)}$).
• Higgstrahlung ($e^+e^- \to ZH$): Total cross-sections are provided for polarized and unpolarized beams at $\sqrt{s} = 240, 365, 500$ GeV, including full LO and NLO SMEFT contributions with QCD and EW corrections.

Significance and Claims
The authors position this work as an essential component for future global fits to SMEFT parameters. They claim that:

1. Completeness: The compilation offers the first unified set of NLO QCD/EW dimension-6 results for Higgs decays, $Z/W$ decays, and Higgstrahlung in a standardized format.
2. Utility for Global Fits: The results are designed to be straightforwardly implemented into global fits and experimental codes. The inclusion of NLO EW corrections is crucial for LHC fits aiming for complete dimension-6 accuracy, as most current production process predictions lack full NLO EW precision.
3. Future Readiness: For future $e^+e^-$ colliders (like FCC-ee), these results allow for consistent NLO QCD/EW fits by combining Higgs decay data with Higgstrahlung and precision Z-pole observables.
4. Standardization: The use of the POPxf format is highlighted as a critical step toward providing a common interface for the implementation and exchange of precision SMEFT predictions, simplifying the combination of results from different calculations within global analyses.

The paper does not propose new experimental strategies or claim the observation of new physics; rather, it provides the theoretical infrastructure required to interpret high-precision data within the SMEFT framework at the next order of accuracy.