[Paper Review] Truncation, validity, uncertainties

Ilaria Brivio, S. Dawson+20 more|arXiv (Cornell University)|Jan 12, 2022

Superconducting Materials and Applications8 citations

TL;DR

This paper summarizes ongoing debates within the LHC EFT Working Group on handling truncation uncertainties in the Standard Model Effective Field Theory (SMEFT), focusing on dimension-six and dimension-eight operator contributions. It evaluates four proposals for improving EFT validity assessment, emphasizing the use of squared dimension-six amplitudes as a gauge-invariant proxy for $1/\Lambda^4$ corrections, advocating for full likelihood reporting and careful clipping of simulations and data to avoid biases in constraints.

ABSTRACT

The truncation of the standard-model effective field theory, its validity and the associated uncertainties have been discussed in meetings of the LHC EFT WG. Proposals were made by participants to address these issues. No consensus was reached and no formal recommendation is therefore put forward at this time. None of the proposals has been approved or validated and further work is needed to establish a prescription. This note aims at summarizing the proposals and points of debate.

Motivation & Objective

• Address the lack of consensus on how to consistently estimate and report truncation uncertainties in SMEFT analyses.
• Improve the reliability of EFT constraints by assessing the validity of truncating at dimension-six operators.
• Provide a framework for comparing linear and quadratic SMEFT approximations to detect potential breakdowns in EFT validity.
• Ensure that EFT constraints remain robust and model-independent by minimizing biases from improper clipping of data or simulations.
• Establish best practices for publishing EFT results, including full likelihoods and covariance matrices, to support future model-independent interpretations.

Proposed method

• Propose using the square of the linear dimension-six amplitude, $|A_6|^2/\Lambda^4$, as a well-defined and gauge-invariant proxy for $1/\Lambda^4$ corrections.
• Advocate for publishing full likelihoods or covariance matrices instead of only marginalized constraints to preserve information on parameter correlations.
• Introduce the concept of clipping EFT simulations at the truth level and data at the reconstructed level to study sensitivity to kinematic variables.
• Highlight that clipping on unmeasured variables can introduce pathologies due to phase space mismatches between data and predictions.
• Suggest using quantiles of the SM distribution in energy variables as a flexible, model-informed clipping strategy.
• Stress that data and simulation clipping are equivalent only when applied to measured variables, and that mismatched clipping leads to biased constraints.

Experimental results

Research questions

• RQ1 How can truncation uncertainties in SMEFT be consistently estimated when higher-dimensional operators (e.g., dimension-eight) are neglected?
• RQ2 What is the most robust and unambiguous way to estimate $1/\Lambda^4$ corrections in EFT amplitudes?
• RQ3 To what extent do correlations between operator coefficients affect the validity of linear SMEFT approximations?
• RQ4 How does clipping EFT simulations on unmeasured variables impact the reliability of extracted operator constraints?
• RQ5 What criteria should guide the choice of clipping variables in EFT analyses to minimize model-dependent biases?

Key findings

• The square of the linear dimension-six amplitude, $|A_6|^2/\Lambda^4$, is gauge invariant and basis-independent, making it a well-defined proxy for $1/\Lambda^4$ corrections.
• Publishing full likelihoods or covariance matrices is essential for proper interpretation of EFT constraints and for assessing EFT validity across different new-physics scenarios.
• Clipping EFT simulations on unmeasured variables can lead to biased operator constraints due to phase space mismatches with data.
• Clipping data and simulation on the same measured variable yields equivalent results up to finite resolution effects, but mismatched clipping introduces systematic biases.
• No consensus emerged among the LHC EFT Working Group on a single prescription for handling truncation uncertainties, and no formal recommendation was adopted.
• The benchmarking of different proposals on the working-group fitting exercise is recommended as a path toward establishing a standardized, robust method.