⚛️ phenomenology

Probing new $C\!P$ -violating sources in $\Lambda_b\to\Lambda_c\ell^-\bar\nu_\ell$

This paper demonstrates that analyzing the angular distributions of the baryonic decay $\Lambda_b\to\Lambda_c\ell^-\bar\nu_\ell$ , in conjunction with mesonic decays and lattice-QCD inputs, provides unique sensitivity to new $CP$ -violating sources and Wilson coefficient combinations inaccessible through mesonic channels alone.

Original authors: Dong-Hao Li, Meng-Chao Gao, Qin Qin, Meng-Han Wu, Fu-Sheng Yu, Xing-Bo Yuan

Published 2026-10-28

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CC BY 4.0

Original authors: Dong-Hao Li, Meng-Chao Gao, Qin Qin, Meng-Han Wu, Fu-Sheng Yu, Xing-Bo Yuan

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 called baryons and mesons are the building blocks of matter, yet they behave in ways that sometimes defy our deepest expectations. Among these, a phenomenon known as CP violation acts as a subtle asymmetry, a tiny tilt in the laws of physics that distinguishes matter from antimatter. While scientists have long observed this tilt in the decay of mesons, a different class of particles called baryons has remained a mystery. The question driving recent research is whether these baryons hold a secret key to understanding new, undiscovered forces that lie beyond our current theories. To find the answer, researchers must look at how these particles decay, specifically focusing on the angles at which their fragments fly apart. These angles are not random; they carry a hidden signature of the weak nuclear force, the interaction responsible for radioactive decay. If the angles reveal a pattern that cannot be explained by the standard model of physics, it would signal the presence of a new particle or force, potentially solving one of the universe's greatest puzzles regarding why we exist at all.

A team of physicists has now taken a significant step toward unlocking this mystery by comparing two specific types of particle decay: one involving a meson and the other involving a baryon. They focused on a process where a heavy particle transforms into a lighter one, emitting a lepton and a neutrino in the process. In the first scenario, a meson decays into another meson that quickly breaks apart into a pion and a D meson. In the second, a baryon decays into a lighter baryon that subsequently splits into a proton and a pion. While these events might sound similar, the researchers discovered that the baryon decay offers a unique window into the physics that the meson decay simply cannot provide. By using powerful computer simulations based on the theory of quantum chromodynamics to calculate the internal structure of these particles, the team mapped out exactly how the angles of the decay products relate to the underlying forces at play.

The study reveals a crucial difference in what these two decay modes can measure. The meson decay, which has been studied extensively, is sensitive to certain combinations of forces but is completely blind to a specific type of interaction involving scalar currents. In plain terms, the meson decay cannot "see" a particular way that new physics might be interfering with the standard forces. The baryon decay, however, is sensitive to this missing piece. Because the baryon has a different internal structure and spin, its decay produces a distinct angular pattern that includes interference terms absent in the meson case. The researchers found that by measuring the specific angles of the particles emerging from the baryon decay, they could isolate a signal that would remain invisible in the meson decay, even if the new physics were present. This makes the baryon decay an essential, complementary tool for identifying new sources of CP violation.

To test this idea, the authors performed a detailed numerical analysis, simulating how these decays would behave if new, unknown forces were influencing them. They adjusted the theoretical parameters to match existing experimental data on how often these decays occur and how the particles are polarized. Within these allowed ranges, they calculated the expected angular signals. The results showed that in scenarios where new physics involves a scalar interaction, the meson decay angles would show no deviation from the standard model, while the baryon decay angles would display a clear, measurable shift. Specifically, the team identified a particular angular moment, a weighted average of the decay angles, that would be zero for the meson but non-zero for the baryon. This difference provides a clean way to distinguish between different types of new physics, effectively ruling out the possibility that the meson data alone is sufficient to uncover these hidden forces.

The researchers also looked ahead to future experiments, estimating how many events would be needed to detect this subtle signal. They calculated that with the high luminosity expected from the next generation of particle accelerators, such as the LHCb Upgrade II, it would be possible to gather enough data to measure this baryon-specific angle with high statistical significance. While the current data is not yet sufficient to confirm the presence of new physics, the study establishes a clear roadmap. It demonstrates that by combining the well-understood meson decays with the newly accessible baryon decays, scientists can probe combinations of forces that were previously inaccessible. This work does not claim to have found new physics yet, but it provides the precise theoretical framework and the specific observables needed to find it, turning the baryon decay into a powerful new probe for the secrets of the subatomic world.

Technical Summary: Probing New CP-Violating Sources in $\Lambda_b \to \Lambda_c \ell^- \bar{\nu}_\ell$

Problem Statement
While CP violation has been observed in baryonic decays (specifically $\Lambda_b^0 \to p K^- \pi^+ \pi^-$ ), the extent to which baryonic decays can reveal new physics (NP) beyond the sensitivity of mesonic decays remains an open question. Standard Model (SM) predictions for semileptonic $b \to c \ell \bar{\nu}_\ell$ transitions contain a single weak phase; thus, any non-zero CP-odd angular signal would indicate NP. Current constraints on NP Wilson coefficients rely heavily on CP-even observables (such as $R(D^{(*)})$ and polarization measurements), which often leave the sign of a weak phase unresolved. Furthermore, mesonic angular distributions (e.g., in $\bar{B} \to D^* \ell^- \bar{\nu}_\ell$ ) lack sensitivity to specific interference terms, particularly those involving scalar currents, due to the vanishing scalar matrix element $\langle D^* | \bar{c} b | \bar{B} \rangle = 0$ . This paper investigates whether the baryonic decay $\Lambda_b \to \Lambda_c (\to \Lambda \pi) \ell^- \bar{\nu}_\ell$ offers complementary sensitivity to these "blind spots" in mesonic channels.

Methodology
The authors employ a unified effective Hamiltonian framework for $b \to c \ell \bar{\nu}_\ell$ transitions, incorporating dimension-six operators in both chiral and parity bases. The analysis proceeds through the following steps:

Form Factor Inputs:
- Baryonic Channel ( $\Lambda_b \to \Lambda_c$ ): Utilizes state-of-the-art lattice-QCD results (RBC/UKQCD) providing correlated vector, axial-vector, and tensor form factors. The analysis implements a full set of ten helicity form factors using a first-order $z$ -expansion, with correlations propagated from the global fit.
- Mesonic Channel ( $\bar{B} \to D^*$ ): Adopts HPQCD lattice form factors parameterized via a Boyd-Grinstein-Lebed (BGL) expansion. These are subjected to weak unitarity bounds to constrain the parameter space, ensuring a consistent treatment of hadronic uncertainties across both channels.
Global Fits:
- The authors perform global fits to CP-even observables ( $R(D)$ , $R(D^*)$ , $P_\tau(D^*)$ , $F_L(D^*)$ , $R(J/\psi)$ ) to constrain the allowed parameter space for one complex Wilson coefficient at a time (in both chiral and parity bases).
- NP is restricted to the tau channel for these benchmarks.
Angular Distribution Analysis:
- Using the allowed Wilson coefficient ranges from the CP-even fits and the lattice form factors, the authors compute CP-odd angular moments for both channels.
- For $\bar{B} \to D^*$ , they analyze moments $I_7, I_8, I_9$ .
- For $\Lambda_b \to \Lambda_c$ , they analyze the moment $K_{3s}$ , which arises from the interference of vector/scalar and axial-vector/pseudoscalar amplitudes, mediated by the parity-violating secondary decay $\Lambda_c \to \Lambda \pi$ .

Key Contributions and Results

Complementary Sensitivity: The study demonstrates that the baryonic decay mode probes combinations of Wilson coefficients inaccessible to mesonic angular distributions. Specifically:
- The mesonic coefficients $I_7, I_8, I_9$ are independent of the scalar current ( $C_S$ ) because the scalar matrix element vanishes in the mesonic channel.
- The baryonic coefficient $K_{3s}$ contains interference terms involving the scalar current, specifically $\text{Im}(C_V C_S^*)$ and, in the presence of tensor couplings, $\text{Im}(C_S C_T^*)$ .
- Conversely, the mesonic channel retains sensitivity to the vector-pseudoscalar interference ( $\text{Im}(C_V C_P^*)$ ) which is absent in the specific baryonic moment analyzed.
Resolving Degeneracies: The analysis shows that CP-odd angular moments can distinguish between complex-conjugate solutions of Wilson coefficients that remain degenerate in CP-even rate fits. Since CP-even observables depend on modulus squares and real interference terms, they are invariant under complex conjugation of the coefficients. In contrast, CP-odd angular moments are linear in imaginary bilinears ( $\text{Im}(C_i C_j^*)$ ) and change sign under conjugation, thereby breaking the degeneracy.
Scalar Phase Sensitivity: In a pure-scalar NP benchmark, the mesonic angular moments ( $I_7, I_8, I_9$ ) vanish entirely within the allowed parameter space. However, the baryonic moment $\langle K_{3s} \rangle$ spans a non-zero range (approximately $\pm 2.67 \times 10^{-2}$ at 68.3% confidence). This indicates that $\Lambda_b \to \Lambda_c$ provides critical supplementary information regarding the scalar weak phase, which is otherwise unconstrained by $D^*$ angular distributions.
Experimental Prospects: The authors estimate the statistical reach for measuring these asymmetries. For the LHCb Upgrade II scenario (300 fb $^{-1}$ ), a 5 $\sigma$ sensitivity to the scalar-induced asymmetry requires an effective efficiency of at least 73% relative to the Run 1 yield reference. For Belle II, the projected sensitivity for vector and tensor benchmarks suggests ideal 5 $\sigma$ thresholds of approximately 60 ab $^{-1}$ and 570 ab $^{-1}$ , respectively, before accounting for angular information loss.

Significance
The paper claims that baryonic decays offer a unique and necessary probe for new CP-violating sources that are invisible to mesonic angular analyses. By accessing scalar-current interference terms and breaking degeneracies between complex-conjugate Wilson coefficient solutions, the $\Lambda_b \to \Lambda_c$ channel provides vital, complementary constraints on the nature of potential New Physics. The study establishes a consistent phenomenological framework using correlated lattice inputs, demonstrating that baryonic angular distributions are not merely redundant but essential for a complete characterization of the $b \to c$ transition in the presence of NP.

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