Determination of the first-generation quark couplings at the Z-pole

TL;DR

This work presents a method to determine the Z boson couplings to first-generation quarks by comparing radiative and non-radiative hadronic decays at the Z-pole. It combines detailed event simulation (Whizard for matrix elements with hard photons, ISR/FSR matching, Pythia hadronisation, and Delphes detector effects) with a maximum-likelihood framework across jet-flavour categories to extract $c_u$ and $c_d$, including systematic uncertainties. The study finds that heavy-flavour tagging systematics dominate the error budget, requiring sub-permille tagging to fully exploit future high-luminosity colliders and potentially improving LEP constraints by an order of magnitude. The approach generalizes to all five flavours (2-flavour and 5-flavour fits) and shows promising prospects for sub-percent precision on light-quark couplings, with substantial gains for $b$ and $c$ couplings as well.

Abstract

Electroweak Precision Measurements are stringent tests of the Standard Model and sensitive probes to New Physics. Accurate studies of the $Z$-boson couplings to the first-generation quarks, which are currently constrained from LEP data to a few percent, could reveal potential discrepancies from the theory predictions. Future $e^+e^-$ colliders running at the $Z$-pole would be an excellent tool for an analysis based on a comparison of radiative and non-radiative $Z$ boson decays. In this paper, we present a method to extract the values of the $Z$ couplings to light quarks and discuss the uncertainty of the measurement, including contributions from various systematic effects. We show that systematic uncertainty in the heavy-flavour tagging performance is the key factor in the analysis and reducing it to a sub-permille level might be crucial to fully profit from the high luminosity of future $e^+e^-$ machines. The measurement could improve the LEP results by at least an order of magnitude.

Figures (8)

• Figure 1: The fraction of events from the sample with no photons generated at the ME level rejected by the matching procedure for different quark flavours (normalised to the cross section per flavour) for ISR (aquamarine upwards) and FSR (purple downwards).
• Figure 2: Left: the distribution of measurable photons (normalised to an integrated luminosity of 100 fb$^{-1}$) as a function of $q^T$. The thick gray line stands for the sum of all the samples, the solid aquamarine line for the 0-ME-photon sample, the purple dashed one for the 1-ME-photon sample and the blue dotted one -- for the 2-ME-photon sample. Fast detector simulation is included in the results. Right: the signal efficiency (left axis, black solid line) and the signal purity (right axis, pink dashed line) for different values of $y_{cut}$, starting at a minimal value of 2 GeV considered in the study. Note that the distributions are defined at the event level, i.e. they relate to the number of those events in which exactly one photon was tagged.
• Figure 3: The uncertainty of the $d$ (aquamarine) and $u$ (purple) coupling measurement as a function of $y_{cut}$ (left) and the integrated luminosity (right). Dashed lines indicate statistical uncertainty only, solid lines with points -- statistical and systematic uncertainties of 0.1% combined, dash-dotted lines -- statistical and systematic uncertainties of 1% combined. The luminosity uncertainty was fixed at 10$^{-4}$. For the left plot, we assume collecting 100 fb$^{-1}$ of data and for the right plot, we set the value of $y_{cut}$ to 10 GeV.
• Figure 4: The uncertainty of the $d$ (aquamarine) and $u$ (purple) coupling measurement as a function of $y_{cut}$ (left) and the integrated luminosity (right). Dashed lines indicate statistical uncertainty only, solid lines with points -- statistical and systematic uncertainties for the 5-flavour fit, and dash-dotted lines -- statistical and systematic uncertainties for the 2-flavour fit. We assume 0.1% uncertainty for all the contributions, except for the luminosity uncertainty (fixed at 10$^{-4}$). For the left plot, the luminosity was fixed at 100 fb$^{-1}$ and for the right plot, the value of $y_{cut}$ was set to 10 GeV.
• Figure 5: The uncertainty of the $d$ (aquamarine), $u$ (purple), $s$ (pink), $c$ (blue) and $b$ (gray) coupling measurement as a function of $y_{cut}$ (left) and the integrated luminosity (right). Dashed lines indicate statistical uncertainty only, the two other lines -- statistical and systematic uncertainties combined for two cases: solid lines with points for $u$- and $d$-tagging uncertainties uncorrelated, dash-dotted lines for $u$- and $d$-tagging uncertainties fully correlated. We assume 0.1% uncertainty for all the contributions, except for the luminosity (fixed at 10$^{-4}$). For the left plot, the luminosity was fixed at 100 fb$^{-1}$ and for the right plot, the value of $y_{cut}$ was set to 10 GeV. Data for heavy quarks (correlated $u$- and $d$-tagging uncertainties) are skipped in the right (left) plot to improve readability.