EFT at JADE: a case study

TL;DR

The paper assesses what can be learned about new physics from low-energy EFT data by applying the low-energy effective field theory (LEFT) to JADE’s e+e- → μ+μ- data below the Z pole. A Bayesian fit shows QED alone is strongly disfavored and LEFT provides a better description of the angular cross sections through the Wilson coefficients of four dimension-6 operators, with the differential cross section given by $\frac{d\sigma}{d\cos\theta} = \left[\frac{\alpha}{16} \frac{1}{\Lambda^2} \Re(C^{LL}+C^{RR}+C^{LR}+C^{RL}) + \frac{\pi \alpha^2}{2s}\right](1+\cos^2\theta) + \left[\frac{\alpha}{16} \frac{1}{\Lambda^2} \Re(C^{LL}+C^{RR}-C^{LR}-C^{RL})\right] 2\cos\theta$. By matching these LEFT coefficients to the electroweak theory, the study links them to $G_F$ and $\sin^2\theta_W$ via $\frac{1}{\Lambda^2}\Re(C^{LL}+C^{RR}) = -8\sqrt{2}G_F(g_V^2+g_A^2)$ and $\frac{1}{\Lambda^2}\Re(C^{LR}+C^{RL}) = -8\sqrt{2}G_F(g_V^2-g_A^2)$ with $g_V=\sin^2\theta_W-1/4$, $g_A=-1/4$. Propagating these through the LO relations $M_W^2 = \frac{\pi\alpha}{\sqrt{2}G_F\sin^2\theta_W}$ and $M_Z^2 = \frac{\pi\alpha}{\sqrt{2}G_F(1-\sin^2\theta_W)\sin^2\theta_W}$ yields posterior distributions for the weak-boson masses, showing that EFT data can inform UV-complete model parameters and potentially guide future collider design. The work highlights both the promise and limitations of EFT in discovering and characterizing new physics when higher-order corrections and additional data are not included.

Abstract

As we use the standard model effective field theory to search for signs of new physics beyond the direct reach of the LHC, we often wonder what we may learn from the effective field theory, and what it would look like to make a discovery via effective field theory. This article presents a case study that provides some answers to these questions. We apply the low-energy effective field theory to $e^+e^- \to μ^+μ^-$ data below the Z boson mass from the JADE experiment at DESY. The low-energy effective field theory allows the observation of physics beyond QED in the JADE data and furthermore, by matching the Wilson coefficients to the electroweak theory, a rough measurement of the masses of the W and Z bosons is possible. The ability to make this rough measurement challenges the conventional wisdom that an observation of new physics via EFT tells us nothing about the nature of that new physics. A measurement of this quality would have been sufficient to guide the construction of colliders such as the super proton-antiproton synchrotron or the large electron-positron collider, and so we anticipate that a discovery of new physics via effective field theory at the LHC would be similarly sufficient to guide the construction of future colliders.

Figures (6)

• Figure 1: The five tree-level Feynman diagrams resulting from the LEFT operators under consideration and from QED.
• Figure 2: Posterior probability density for the LEFT Wilson coefficients. The green, yellow, and red regions contain 68, 95, and 99.7% of the posterior probability, respectively. The black square shows the location of the maximum posterior probability density. The red dot shows the values of the LEFT Wilson coefficients predicted by QED alone. QED alone is very strongly disfavored.
• Figure 3: The JADE data (dots with error bars), compared to the prediction from QED alone (dashed line) and to the predictions resulting from the fit to the LEFT (solid line, with 68 and 95% credible intervals shown in green and yellow, respectively). The JADE data is inconsistent with QED alone, especially at higher center-of-mass energies, but it is consistent with the LEFT predictions.
• Figure 4: The tree-level Z boson exchange Feynman diagram from the electroweak theory.
• Figure 5: Posterior probability density for the LEFT Wilson coefficients, with contours of constant $G_F$ and contours of constant $\sin^2 \theta_W$ overlaid.