⚛️ phenomenology

Angular Observables in the $\Lambda_{b}\to \Lambda \nu \bar{\nu}$ Decay

This paper demonstrates that angular observables in the rare decay of polarized $\Lambda_b$ baryons to $\Lambda \nu \bar{\nu}$ provide unique access to orthogonal Wilson coefficient combinations and CP-violating phases, thereby resolving parameter degeneracies and enabling a complete characterization of new physics in $b \rightarrow s \nu \bar{\nu}$ transitions that is inaccessible in mesonic decays.

Original authors: Wolfgang Altmannshofer, Shibasis Roy

Published 2026-10-06

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Wolfgang Altmannshofer, Shibasis Roy

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, nature plays by a set of rules that are often hidden from view. One of the most reliable ways to test these rules is to watch for rare events where particles change their identity in ways that the standard model of physics predicts should happen, but only very rarely. A prime example is a process where a heavy particle containing a bottom quark transforms into a lighter particle containing a strange quark, while simultaneously emitting a pair of invisible neutrinos. Because neutrinos are so elusive and interact so weakly with matter, they escape detection, leaving behind a puzzle: scientists can see the heavy particle disappear and the lighter one appear, but they cannot see the neutrinos that carried away the missing energy. This makes the event difficult to study, yet it is also a powerful tool. Because the standard model predicts these events with high precision, any deviation in how often they happen or how the visible particles fly apart could signal the presence of entirely new forces or particles that have never been seen before.

For years, physicists have focused on these rare transformations using mesons, which are particles made of a quark and an antiquark. These mesons are produced in vast numbers in modern particle accelerators, making them the primary targets for discovery. However, a new study suggests that looking at a different kind of particle, the baryon, could unlock secrets that mesons simply cannot reveal. Baryons are heavier cousins of mesons, made of three quarks, and they behave differently when they decay. Specifically, researchers have turned their attention to the decay of the Lambda-b baryon, a heavy particle that can transform into a lighter Lambda baryon and a pair of neutrinos. The unique feature of this study is that it focuses on Lambda-b particles produced at a specific type of future machine called the FCC-ee, where these particles are born with spin pointing in a particular direction (parallel to its momentum), much like a spinning top. This spin is not just a detail; it acts as a compass that allows scientists to see angles and directions in the decay that are completely invisible in other experiments.

The researchers, working with the theoretical tools of quantum mechanics, mapped out exactly how the decay products of this spinning Lambda-b particle should be distributed in space. They found that the pattern of the decay is not random but is described by five distinct numbers, or observables, that capture the geometry of the event. Four of these numbers rely entirely on the fact that the initial particle was spinning. By analyzing these patterns, the team discovered that they can extract information about the fundamental forces driving the decay that is completely orthogonal to, or independent of, what is learned from meson decays. While meson experiments can tell scientists the combined strength of two types of forces, they cannot tell if those forces are balanced or if one is stronger than the other, nor can they easily detect a specific type of symmetry breaking related to time and charge. The new angular observables in the Lambda-b decay, however, act as a key that opens these locked doors, allowing physicists to separate the different forces and measure their individual strengths and phases.

One of the most striking findings is the identification of a specific pattern in the decay that acts as a direct probe for a violation of charge-parity symmetry, a phenomenon where the laws of physics treat matter and antimatter slightly differently. In the standard model, this effect is expected to be zero for this particular decay, but if new physics exists, it could create a measurable imbalance. The study shows that by measuring the angles at which the decay products emerge, scientists can detect this imbalance directly, without needing the complex and difficult techniques required for other types of particles. The team calculated what the standard model predicts for all five observables, using the most advanced computer simulations available to describe the internal structure of the baryons. They found that while some of the numbers are very small, others are large and distinct, providing a clear baseline against which to compare future experimental data.

The paper then looked ahead to the capabilities of the proposed FCC-ee facility, which is expected to produce billions of these particles. The researchers simulated how well these future machines could measure the five observables, assuming different levels of experimental precision. They found that even with modest measurement accuracy, the new data would be powerful enough to rule out many popular theories of new physics that try to explain anomalies seen in other experiments. More importantly, the combination of the meson data and the new baryon data would allow physicists to completely determine the nature of the forces involved. If the standard model is correct, the measurements will align with the predicted values. If new particles or forces are at play, the angular patterns will shift in a way that reveals exactly how the new physics is structured, distinguishing between different theoretical possibilities that have so far remained indistinguishable.

This work does not claim to have discovered new physics; rather, it provides a detailed roadmap for how to find it. The authors emphasize that the beauty of this approach lies in its ability to resolve a long-standing ambiguity in the field. Just as looking at a three-dimensional object from a single angle can make it impossible to tell its true shape, looking at particle decays through the limited lens of mesons leaves a gap in our understanding. By adding the perspective of the spinning baryon, the study shows that we can finally see the full picture. The results suggest that including these baryonic decays in the global search for new physics is not just a nice addition, but an essential step. Without them, scientists might measure a deviation from the standard model but remain unable to explain what is causing it. With them, the path forward becomes clear, offering a definitive way to characterize the chiral nature and the symmetry properties of any new interactions that might be hiding in the data.

Technical Summary: Angular Observables in the $\Lambda_b \to \Lambda \nu \bar{\nu}$ Decay

Problem Statement
The rare flavor-changing neutral current (FCNC) transition $b \to s \nu \bar{\nu}$ is a theoretically clean probe for physics beyond the Standard Model (SM). While mesonic decays such as $B \to K^{(*)} \nu \bar{\nu}$ and $B_s \to \phi \nu \bar{\nu}$ are the primary experimental targets, they suffer from a fundamental limitation in characterizing new physics (NP). The observables in these mesonic channels depend only on two combinations of the short-distance Wilson coefficients, $|C_L + C_R|$ and $|C_L - C_R|$ . Consequently, even with precise measurements, a continuous degeneracy remains regarding the third physical parameter: the relative phase between $C_L$ and $C_R$ . Furthermore, standard mesonic observables cannot directly access CP-violating phases or distinguish certain chiral structures without time-dependent flavor-tagging, which is experimentally challenging. The paper investigates whether the baryonic decay $\Lambda_b \to \Lambda (\to p \pi^-) \nu \bar{\nu}$ can resolve these degeneracies and provide complementary information.

Methodology
The authors analyze the cascade decay of polarized $\Lambda_b$ baryons produced at the $Z$ pole, specifically at the proposed Future Circular Collider (FCC-ee). The methodology involves:

Formalism Development: Deriving the full six-dimensional angular distribution for the cascade decay $\Lambda_b \to \Lambda (\to p \pi^-) \nu \bar{\nu}$ using the helicity formalism. The analysis accounts for the longitudinal polarization of the initial $\Lambda_b$ inherited from the parity-violating $Z \to b \bar{b}$ decay.
Observable Definition: Identifying five independent angular observables ( $S_1, S_2, S_3, S_4, A_5$ ) from the differential decay distribution. The analysis distinguishes between observables accessible with unpolarized samples and those requiring initial polarization.
Theoretical Prediction: Calculating Standard Model (SM) predictions for the branching ratio and angular observables using lattice QCD form factors for the $\Lambda_b \to \Lambda$ transition. The authors update previous calculations with current values for the top quark mass and CKM matrix elements.
New Physics Scenarios: Evaluating the sensitivity of these observables to various benchmark NP scenarios, including cases with pure right-handed currents, complex Wilson coefficients, and CP-violating phases.
Sensitivity Projections: Estimating the projected sensitivity at FCC-ee by combining theoretical uncertainties (dominated by form factors) with assumed experimental precisions (10% for the branching ratio and varying levels for angular observables). The analysis compares the constraining power of baryonic observables against projected mesonic measurements.

Key Contributions

Identification of Orthogonal Probes: The paper demonstrates that the angular observables in $\Lambda_b \to \Lambda \nu \bar{\nu}$ provide access to orthogonal combinations of Wilson coefficients, specifically $|C_R|^2 - |C_L|^2$ and $\text{Im}(C_L C_R^*)$ , which are inaccessible in mesonic decays.
Discovery of a T-odd CP Asymmetry: The authors identify a T-odd CP asymmetry, $A_5$ , which is directly proportional to $\text{Im}(C_L C_R^*)$ . This observable offers a direct probe of CP-violating phases in the short-distance effective Hamiltonian without requiring flavor tagging or time-dependent measurements.
Resolution of Parameter Degeneracies: The study shows that while mesonic observables constrain Wilson coefficients to a ring-shaped region in the parameter space, the inclusion of baryonic angular observables ( $S_1, S_2, A_5$ ) allows for the complete determination of the three physical parameters ( $|C_L|, |C_R|, \text{Arg}(C_R/C_L)$ ), effectively breaking the discrete and continuous degeneracies.
Zero Crossings as Form Factor Tests: The paper notes that the zero crossings of observables $S_2, S_3,$ and $S_4$ in the $q^2$ distribution are determined by form factors. Specifically, the zero crossing of $S_2$ is independent of Wilson coefficients, providing a potential clean test of hadronic form factor calculations.

Results

SM Predictions: The SM predicts a branching ratio of $\langle \text{BR} \rangle = (7.59 \pm 1.03) \times 10^{-6}$ . The integrated angular observables are predicted to be $\langle S_1 \rangle = -0.926 \pm 0.018$ , $\langle S_2 \rangle = -0.053 \pm 0.068$ , $\langle S_3 \rangle = 0.025 \pm 0.069$ , and $\langle S_4 \rangle = 0.029 \pm 0.047$ . The asymmetry $A_5$ vanishes in the SM.
Sensitivity to Right-Handed Currents: Observables $S_1$ and $S_2$ are governed by $|C_R|^2 - |C_L|^2$ . In scenarios with pure right-handed currents (e.g., $C_L=0, C_R=C_L^{SM}$ ), these observables reverse sign relative to the SM, providing a clear signal.
CP Violation: The asymmetry $A_5$ reaches maximal magnitude in scenarios with complex Wilson coefficients (e.g., $C_L = C_L^{SM}/\sqrt{2}, C_R = i C_L^{SM}/\sqrt{2}$ ), demonstrating high sensitivity to CP-violating new physics.
Projected Sensitivity: Even with moderate experimental uncertainties ( $\pm 0.5$ on angular observables), the baryonic observables can break parameter degeneracies that mesonic observables cannot. With improved precision ( $\pm 0.1$ ), the combined fit can distinguish specific benchmark NP scenarios from the SM. Splitting the $q^2$ region into bins further improves sensitivity, though the qualitative conclusions remain robust without binning.

Significance
The paper argues that baryonic angular observables are essential for a comprehensive characterization of $b \to s \nu \bar{\nu}$ transitions. While mesonic modes will remain the flagship measurements due to larger event samples, they are insufficient for a complete determination of the chiral and CP structure of potential new physics. The $\Lambda_b \to \Lambda \nu \bar{\nu}$ decay, accessible at the $Z$ pole with polarized $\Lambda_b$ samples, provides the necessary complementary information to resolve parameter degeneracies and directly probe CP violation. The authors conclude that including this decay in the global $b \to s \nu \bar{\nu}$ program is compelling, particularly for future facilities like FCC-ee, to fully resolve the nature of any deviations from the Standard Model.

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