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Signatures of Invisible Fermions in $\Lambda_b^0 \to \Lambda_c^+ \ell^- \bar{X}_{\rm inv}$ Decays

This paper demonstrates that a model-independent angular analysis of $\Lambda_b^0 \to \Lambda_c^+ \ell^- \bar{X}_{\rm inv}$ decays can distinguish between massless and massive invisible fermions while simultaneously discriminating among various interaction types and chiral structures.

Original authors: Shantanu Sahoo, Soumitra Nandi

Published 2026-09-11

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Shantanu Sahoo, Soumitra Nandi

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, matter is built from a small family of fundamental particles that interact through invisible forces. Among these, the bottom quark is a heavy, unstable particle that rarely exists on its own, usually bound inside larger particles called baryons. When these heavy baryons decay, they transform into lighter particles, often releasing energy in the form of other particles that fly away. Physicists study these transformations with extreme precision because they act as a sensitive test for the Standard Model, the current best theory describing how the universe works at its smallest scales. Usually, when a heavy particle decays into a lighter one and a charged particle like an electron, a third particle must be created to carry away missing energy and momentum. In the standard version of this process, that third particle is a neutrino, a ghostly particle so light and elusive that it passes through almost everything without a trace. However, the possibility exists that this missing particle is not a standard neutrino at all, but something entirely new and heavier, perhaps a member of a hidden "dark sector" that interacts with our world only through gravity or very weak forces.

A team of researchers has now mapped out how to spot these heavier, invisible particles if they are hiding in the decay of a specific heavy baryon known as the Lambda-b. By analyzing the angles at which the visible particles fly apart, the scientists demonstrated that the mass of the invisible partner leaves a distinct fingerprint on the data. If the invisible particle were massless, like a standard neutrino, the visible debris would scatter in a predictable pattern. But if that invisible particle has even a small amount of mass, the available space for the decay changes, forcing the visible particles to arrange themselves differently. The researchers used a flexible mathematical framework to simulate these decays, testing various scenarios where the invisible particle could be a heavy version of a neutrino or a dark matter candidate. They found that by carefully measuring the direction of the electron and the resulting lighter baryon, it is possible to distinguish between a massless ghost and a heavy, invisible traveler.

The study goes further by showing that these angular measurements can reveal the specific nature of the force causing the decay. In the subatomic realm, particles have a property called "handedness," which describes how they spin relative to their direction of motion. The standard model only allows for left-handed interactions in this type of decay, but new physics could introduce right-handed forces or other exotic types of interactions. The researchers showed that different types of invisible particles and different force structures produce unique patterns in the data. For instance, certain types of interactions would cause the particles to cluster in specific directions, while others would push them apart in a different way. By looking at the full picture of how the particles are distributed, scientists can tell not just if a new particle exists, but also whether it interacts through a vector force, a scalar force, or a tensor force, and whether it prefers left-handed or right-handed partners.

This work is particularly powerful because it does not rely on guessing exactly what the new particle is. Instead, it provides a set of tools to identify the particle's mass and its interaction style based on the shape of the data. The researchers identified specific observables that are highly sensitive to the mass of the invisible particle, allowing them to separate the signal of a heavy dark fermion from the background of standard neutrinos. They also found that some of these measurements are uniquely good at distinguishing between left-handed and right-handed currents, which is crucial for ruling out or confirming theories about sterile neutrinos or dark matter. While the paper presents these findings through detailed simulations rather than direct experimental observation, the results offer a clear roadmap for future experiments. If detectors can measure these angular distributions with enough precision, they will be able to determine if the invisible particle in these decays is the familiar, nearly massless neutrino or a heavier, exotic cousin from a hidden part of the universe.

Technical Summary: Signatures of Invisible Fermions in $\Lambda^0_b \to \Lambda^+_c \ell^- \bar{X}_{inv}$ Decays

Problem Statement
Semileptonic decays of the $\Lambda^0_b$ baryon, specifically $\Lambda^0_b \to \Lambda^+_c \ell^- \bar{X}_{inv}$ , serve as a critical testing ground for the Standard Model (SM) and the determination of the CKM matrix element $|V_{cb}|$ . In the SM, the invisible particle $X_{inv}$ is a nearly massless neutrino. However, missing-energy signatures in these decays also offer a unique opportunity to probe non-standard invisible states, such as light sterile neutrinos or dark-sector fermions. While current measurements of missing-mass-squared distributions show a peak near zero with finite spread, there is motivation to explore scenarios where the invisible particle possesses a non-zero mass ( $m_\chi$ ). The presence of such massive invisible fermions can significantly alter the phase space and angular observables of these decays, yet a comprehensive analysis distinguishing these effects from various Beyond-the-Standard-Model (BSM) interaction structures is required.

Methodology
The authors investigate the decay $\Lambda_b \to \Lambda_c \ell \chi$ (where $\chi$ is a massive invisible fermion) using a model-independent weak effective field theory (EFT) framework.

Effective Hamiltonian: The study retains relevant vector, scalar, and tensor operators, allowing for both left- and right-handed interactions for both quark and lepton currents. The effective Hamiltonian includes the SM operator $O^{\ell,SM}_{V1L}$ and additional operators involving the dark fermion $\chi$ with chiralities $L$ and $R$ . The analysis assumes real Wilson coefficients (WCs) and focuses on light leptons ( $\ell = e, \mu$ ).
Kinematics and Phase Space: A key distinction in this framework is the kinematic range of the dilepton invariant mass-squared, $q^2$ . For a massless neutrino, $q^2 \in [m_\ell^2, (m_{\Lambda_b} - m_{\Lambda_c})^2]$ . For a massive invisible particle, the range shifts to $[(m_\ell + m_\chi)^2, (m_{\Lambda_b} - m_{\Lambda_c})^2]$ , modifying the available phase space.
Angular Analysis: The authors perform a comprehensive angular analysis of the four-fold differential decay distribution for $\Lambda_b \to \Lambda_c(\to \Lambda \pi) \ell \chi$ . This involves calculating helicity amplitudes for hadronic and leptonic currents, utilizing lattice QCD form factors parameterized via the $z$ -expansion (BCL parameterization).
Observables: The study defines and analyzes normalized angular coefficients ( $\hat{K}_i$ ) and forward-backward asymmetries ( $A_{FB}$ ) for the lepton, the $\Lambda_c$ baryon, and their combined system. These observables are constructed to cancel systematic uncertainties in ratios.

Key Contributions and Results
The paper demonstrates that a non-zero invisible-particle mass leaves characteristic imprints on angular observables, enabling the discrimination between massless and massive invisible states. The primary contributions include:

Mass Sensitivity: Several angular observables exhibit enhanced sensitivity to the mass $m_\chi$ . The shift in the $q^2$ range and the modification of decay distributions allow for the identification of massive invisible states distinct from the SM neutrino scenario.
Lorentz Structure Discrimination: The analysis identifies specific observables capable of distinguishing between different Lorentz structures:
- Tensor vs. Vector/Axial-Vector: Observables such as $A^{\Lambda_c}_{FB}(q^2)$ , $\hat{K}_{2ss}(q^2)$ , and $\hat{K}_{3sc}(q^2)$ show distinctive behaviors. Tensor interactions produce negative shifts (potentially rendering these observables negative), whereas vector and axial-vector interactions generally keep them positive or near zero. The differential decay rate $d\Gamma/dq^2$ shows stronger sensitivity to tensor couplings than to vector/axial-vector operators.
- Scalar/Pseudoscalar vs. Others: Scalar and pseudoscalar interactions significantly affect $\hat{K}_{1c}(q^2)$ and $\hat{K}_{1cc}(q^2)$ . While scalar and pseudoscalar scenarios produce qualitatively similar effects in these specific observables, they are clearly distinguished from tensor and vector patterns.
Chiral Structure Discrimination:
- Lepton Current Chirality: The study highlights that specific combinations of angular observables can distinguish between left- and right-handed lepton currents. This is crucial for differentiating scenarios involving dark-sector fermions with both chiralities from models like sterile neutrinos or right-handed neutrino models, which typically have restricted chiral structures.
- Quark Current Chirality: Observables such as $\hat{K}_{2cc}(q^2)$ and $\hat{K}_{2ss}(q^2)$ (particularly at low $q^2$ ) allow for the separation of left- and right-handed scalar/pseudoscalar interactions based on the chirality of the quark current.
- Vector/Axial-Vector Separation: The differential decay rate $d\Gamma/dq^2$ shows sizeable deviations for $C_{V1L,R}$ but remains largely indistinguishable from the SM for $C_{V2L,R}$ . Conversely, $A^{\Lambda_c}_{FB}(q^2)$ , $\hat{K}_{2ss}(q^2)$ , and $\hat{K}_{2cc}(q^2)$ show observable deviations only for $C_{V2L,R}$ , providing a clean separation between $V_1$ and $V_2$ operators. Further discrimination between $C_{V1L}$ , $C_{V1R}$ , and $C_{V2L}$ is achieved via $A^\mu_{FB}(q^2)$ and $\hat{K}_{1c}(q^2)$ .

Significance
The authors claim that a combined analysis of the differential decay rate and angular observables in semileptonic $\Lambda_b$ decays provides a powerful framework for determining the Lorentz and chiral structure of possible new-physics interactions. The work establishes that:

Specific observables can cleanly discriminate between tensor, scalar/pseudoscalar, and vector/axial-vector contributions based on their characteristic deviation patterns from SM predictions.
The sensitivity of certain observables to the chirality of the lepton current offers a unique opportunity to distinguish scenarios mediated by dark-sector fermions (with both left- and right-chiral couplings) from those involving only standard left-handed weak interactions or restricted chiral models.
Future precision measurements of $q^2$ distributions and angular observables in $\Lambda_b$ decays can not only reveal the presence of new physics but also determine its specific Lorentz structure and chiral origin.

The paper concludes that these findings offer a promising probe for light invisible fermions and dark-sector scenarios in flavor physics, provided that future experimental data can achieve the necessary precision to resolve these angular distributions.

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