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SMEFT effects on spin correlations and entanglement at NLO QCD in di-boson production at hadron colliders

Giovanni Pelliccioli, Emanuele Re

TL;DR

This work addresses the problem of quantifying spin correlations in inclusive WZ production at the LHC by performing full quantum-state tomography of the di-boson system and linking the resulting spin-density matrix to purity and entanglement markers. It combines NLO QCD accuracy with a dimension-six SMEFT operator that shifts electroweak triple-gauge couplings, introducing the EFT expansion parameter $\xi = C_W/\Lambda^2$ and extracting angular coefficients $\alpha_{lm}$ that map to the spin structure. A key finding is that NLO QCD corrections markedly modify polarization and spin-correlation coefficients and tend to decohere the di-boson spin state; more importantly, truncating the SMEFT expansion at linear order can yield non-physical results (e.g. ${\rm Tr}[\rho^2]>1$), whereas including quadratic EFT terms ($\text{SMEFT8}$) yields well-defined, unit-trace, semi-positive density matrices. The study shows that SMEFT effects are modest in inclusive kinematics but can be sizeable in boosted regimes, underscoring the necessity of higher-order QCD and careful EFT truncation for reliable spin-tomography-based EFT analyses.

Abstract

We perform for the first time a full study of spin correlations in inclusive WZ production at the LHC with leptonic decays in the presence of NLO QCD corrections and of effects from a dimension-six operator in the SMEFT modifying the electroweak triple-gauge coupling. We carry out the complete quantum-state tomography of the di-boson system and relate its results to common purity and spin-entanglement markers, highlighting the sizeable impact of both QCD corrections and SMEFT insertions. Additionally, we show how a naive truncation at dimension-six in the SMEFT expansion of the spin-density matrix can lead to a cumbersome spin interpretation of the quantum-tomography results.

SMEFT effects on spin correlations and entanglement at NLO QCD in di-boson production at hadron colliders

TL;DR

This work addresses the problem of quantifying spin correlations in inclusive WZ production at the LHC by performing full quantum-state tomography of the di-boson system and linking the resulting spin-density matrix to purity and entanglement markers. It combines NLO QCD accuracy with a dimension-six SMEFT operator that shifts electroweak triple-gauge couplings, introducing the EFT expansion parameter and extracting angular coefficients that map to the spin structure. A key finding is that NLO QCD corrections markedly modify polarization and spin-correlation coefficients and tend to decohere the di-boson spin state; more importantly, truncating the SMEFT expansion at linear order can yield non-physical results (e.g. ), whereas including quadratic EFT terms () yields well-defined, unit-trace, semi-positive density matrices. The study shows that SMEFT effects are modest in inclusive kinematics but can be sizeable in boosted regimes, underscoring the necessity of higher-order QCD and careful EFT truncation for reliable spin-tomography-based EFT analyses.

Abstract

We perform for the first time a full study of spin correlations in inclusive WZ production at the LHC with leptonic decays in the presence of NLO QCD corrections and of effects from a dimension-six operator in the SMEFT modifying the electroweak triple-gauge coupling. We carry out the complete quantum-state tomography of the di-boson system and relate its results to common purity and spin-entanglement markers, highlighting the sizeable impact of both QCD corrections and SMEFT insertions. Additionally, we show how a naive truncation at dimension-six in the SMEFT expansion of the spin-density matrix can lead to a cumbersome spin interpretation of the quantum-tomography results.
Paper Structure (5 sections, 27 equations, 1 figure, 1 table)

This paper contains 5 sections, 27 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Generalities
  3. SMEFT effects
  4. Numerical results
  5. Conclusion

Figures (1)

  • Figure 1: Dependence of purity and concurrence markers on the Wilson coefficient $C_W$ for inclusive $\text{W}\xspace\text{Z}\xspace$ production at the LHC: the trace of the squared single-boson ($\text{W}\xspace$) spin-density matrix (upper panels), the trace of the squared $\rho$ matrix associated to the overall $\text{W}\xspace\text{Z}\xspace$ system (middle panels), and the concurrence lower and upper bounds for the $\text{W}\xspace\text{Z}\xspace$ system (lower panels). Results have been computed at both LO and NLO QCD accuracy, including SMEFT effects up to linear (SMEFT6) and quadratic (SMEFT8) level. The inclusive (boosted) setup described in Eq. \ref{['eq:incS']} (Eq. \ref{['eq:booS']}) is considered in the left (right) plot. In the upper and middle panels, the gray bands correspond to allowed values for generic hermitian, semi-positive definite, unit-trace spin-density matrices.