⚛️ phenomenology

Disentangling $V_{ud}$ from New Physics in Beta Decays with the FCC-ee

This paper demonstrates that while current and future high-energy collider data (HL-LHC) only partially resolve the degeneracy between the CKM element $V_{ud}$ and New Physics in superallowed $\beta$ -decays, the FCC-ee will fully disentangle them, restoring SM-level precision for $V_{ud}$ and significantly tightening constraints on SMEFT Wilson coefficients.

Original authors: Lemonia Gialidi, Elie Hammou, Kamil Laurent, Vaisakh Plakkot, Juan Rojo, Jordy de Vries

Published 2026-09-29

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CC BY 4.0

Original authors: Lemonia Gialidi, Elie Hammou, Kamil Laurent, Vaisakh Plakkot, Juan Rojo, Jordy de Vries

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, particles interact through forces that are described by a grand theory called the Standard Model. This theory acts like a rulebook, predicting how particles behave and how they transform into one another. One of the most important numbers in this rulebook is a value that tells us how likely a specific type of particle, called an up quark, is to turn into a down quark. This probability is crucial because it governs how atoms in our universe are built and how they decay. Scientists have measured this number with incredible precision for decades, using experiments that observe the decay of atomic nuclei. However, a recent puzzle has emerged: when scientists combine this number with other similar measurements, the math doesn't quite add up. The numbers suggest a tiny gap, a discrepancy that hints either that our measurements are slightly off, or that there is a hidden force or particle influencing the process that we have not yet discovered. This mystery is known as the Cabibbo angle anomaly, and it has left physicists wondering if the rulebook needs a new chapter.

To solve this, a team of researchers has developed a new way to look at the data, combining the smallest experiments with the largest machines ever built. They focused on a specific type of radioactive decay called superallowed beta decay, where a nucleus transforms by emitting an electron. These events are incredibly clean and predictable, making them perfect for measuring the fundamental probability of quark transformation. The problem is that these low-energy experiments cannot tell the difference between a simple shift in the probability value and the influence of a new, unknown force. It is like trying to hear a whisper in a quiet room; if the room is silent, you know the whisper is there, but you cannot tell if the sound is coming from a person or a machine. To distinguish between the two, the researchers needed to bring in data from the highest energy collisions in the universe.

The team, working with a sophisticated computer framework, combined the precise data from nuclear decays with projections for future experiments at the Large Hadron Collider and a proposed next-generation machine called the FCC-ee. They ran simulations to see what would happen if they treated the probability value and the potential influence of new physics as two separate things to be measured at the same time. Their results show that the current data from the world's largest colliders, even with planned future upgrades, is not enough to fully separate the two. The uncertainty remains too high, and the two possibilities still blur together. However, when they added the projected data from the FCC-ee, a future electron-positron collider, the picture changed completely. The new data acts like a powerful lens that brings the two possibilities into sharp focus, allowing scientists to measure the probability value with its original precision while simultaneously pinning down the influence of any new physics.

The study demonstrates that the FCC-ee is essential for resolving this specific mystery. Without it, the uncertainty in the probability value would remain inflated, leaving the Cabibbo angle anomaly unresolved. With the FCC-ee, the researchers found they could recover the same level of precision seen in the Standard Model, but now with the added confidence that no hidden forces are distorting the result. This conclusion holds true even when the researchers tested different assumptions about how new physics might behave or when they considered that their calculations of nuclear effects might be slightly uncertain. The findings highlight a beautiful synergy in modern science: the most precise measurements of the very small require the most powerful probes of the very large. By combining the quiet precision of nuclear decay with the high-energy reach of future colliders, physicists can finally disentangle the known from the unknown, ensuring that the rulebook of the universe is read correctly.

Technical Summary: Disentangling $V_{ud}$ from New Physics in Beta Decays with the FCC-ee

Problem Statement
Superallowed nuclear $\beta$ -decays currently provide the most precise determination of the CKM matrix element $V_{ud}$ . However, these low-energy observables are sensitive only to an effective combination of $V_{ud}$ and potential New Physics (NP) contributions to left-handed charged currents. Within the Standard Model Effective Field Theory (SMEFT), the presence of non-zero Wilson coefficients (WCs) modifies the charged-current interactions, making the extraction of $V_{ud}$ from $\beta$ -decay data alone theoretically inconsistent if $V_{ud}$ is treated as a fixed external input. This degeneracy prevents a robust test of the first-row CKM unitarity and obscures the interpretation of the "Cabibbo Angle Anomaly" (CAA), a $\sim 3\sigma$ tension in CKM unitarity. While high-energy collider data constrains SMEFT operators, current datasets (LEP, LHC) and even High-Luminosity LHC (HL-LHC) projections are insufficient to fully break the degeneracy between $V_{ud}$ and the relevant SMEFT Wilson coefficients.

Methodology
The authors extend the SMEFiT framework to perform a simultaneous global fit of the CKM element $V_{ud}$ and the relevant SMEFT Wilson coefficients. The analysis integrates:

Low-Energy Likelihood: A dedicated likelihood for superallowed $0^+ \to 0^+$ nuclear transitions, incorporating the most precise experimental lifetimes, phase-space corrections, and theoretical uncertainties (radiative corrections $\Delta^V_R$ , isospin-breaking $\delta_C$ , and nuclear-structure effects $\delta_{NS}$ ). This likelihood includes nuisance parameters to account for correlated theoretical uncertainties.
High-Energy Likelihoods: Existing world data from LEP and LHC, combined with projections for the HL-LHC and the Future Circular Collider (FCC-ee) across energy ranges $\sqrt{s} = 91$ GeV to $365$ GeV (Tera-Z, $W^+W^-$ , $ZH$ , and $t\bar{t}$ thresholds).
EFT Framework: The analysis operates within the SMEFT, matching operators at the New Physics scale ( $\mu_0 = 10$ TeV) to the Low-Energy Effective Field Theory (LEFT) at $\mu \sim 2$ GeV via Renormalization Group Evolution (RGE). The matching connects collider observables to the LEFT coefficients governing $\beta$ -decays.
Flavor Assumptions: Two flavor structures are considered: the universal $U(3)^5$ symmetry and the less restrictive $G_F = U(2)_{qL} \otimes U(2)_{uR} \otimes U(3)_{dR} \otimes U(3)_{\ell} \otimes U(3)_{e}$ . In both cases, the analysis focuses on the four (or six) Wilson coefficients relevant to the matching of the LEFT vector current.

Key Contributions

Simultaneous Determination: This work presents the first implementation within SMEFiT that treats $V_{ud}$ as an independent degree of freedom to be determined simultaneously with SMEFT Wilson coefficients, rather than fixing it as an external SM parameter.
Unified Likelihood: The paper constructs a consistent pipeline linking low-energy $\beta$ -decay data with high-energy collider constraints through RGE running and LEFT matching, ensuring a model-independent interpretation of the CAA.
Fisher Information Analysis: The authors utilize the Fisher information matrix to quantify the sensitivity of different datasets (LEP, LHC, HL-LHC, FCC-ee, $\beta$ -decays) to the specific Wilson coefficients and $V_{ud}$ , demonstrating the complementary nature of these probes.

Results

SM Validation: In a Standard Model-only fit using only low-energy data, the extracted value $V_{ud} = 0.97366 \pm 0.00029$ agrees with the PDG 2026 average, validating the implementation of the low-energy likelihood.
Degeneracy with Current/HL-LHC Data: When combining low-energy data with LEP, LHC, and HL-LHC projections, the degeneracy between $V_{ud}$ and the effective Wilson coefficient combination $L'$ is only partially lifted. The uncertainty on $V_{ud}$ increases significantly ( $\delta V_{ud} \sim 6 \times 10^{-4}$ ) compared to the SM fit, indicating that HL-LHC data alone cannot fully disentangle NP effects from the CKM parameter.
FCC-ee Breakthrough: The inclusion of FCC-ee projections fully decouples $V_{ud}$ from New Physics contributions. The FCC-ee constraints on the semileptonic operator $c^{(3)}_{q\ell}$ (via fermion-pair production above the Z pole) and vertex corrections ( $c^{(3)}_{\phi q}, c^{(3)}_{\phi \ell}, c'_{\ell\ell}$ ) are an order of magnitude tighter than HL-LHC projections. Consequently, the simultaneous fit recovers the SM-level precision for $V_{ud}$ ( $\delta V_{ud} \approx 2.9 \times 10^{-4}$ ) while significantly tightening constraints on the Wilson coefficients.
Robustness: The results are stable against variations in flavor assumptions ( $U(3)^5$ vs. $G_F$ ) and different scenarios for theoretical uncertainties (conservative vs. optimistic estimates of radiative corrections and FCC-ee theory errors). Even in optimistic scenarios where theory uncertainties are reduced, the FCC-ee remains necessary to maintain precision in the presence of NP.

Significance
The paper concludes that future lepton colliders, specifically the FCC-ee, are essential for a SMEFT-consistent interpretation of first-row CKM unitarity tests. While low-energy experiments provide the highest precision for $\beta$ -decay rates, they cannot distinguish between shifts in $V_{ud}$ and New Physics without high-energy constraints. The FCC-ee provides the necessary complementary information to "disentangle" $V_{ud}$ from New Physics, allowing for a clean determination of the CKM element and a rigorous assessment of the Cabibbo Angle Anomaly. The authors emphasize that this synergy between low-energy precision and high-energy collider reach is critical for probing the nature of potential New Physics without losing precision on fundamental SM parameters.

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