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Baryon-Number Violating $Λ_c$ Decays from Light-Cone Sum Rules

This paper employs light-cone sum rules to calculate the branching fractions for baryon-number-violating $\Lambda_c$ decays into a meson and an invisible fermion, predicting rates potentially accessible to future experiments like STCF, Belle II, and FCC-ee.

Original authors: Ali Mohamed

Published 2026-10-30

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CC BY 4.0

Original authors: Ali Mohamed

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

The universe we see around us is built from matter, but the laws of physics that govern the subatomic world contain a deep mystery: why is there more matter than antimatter? In the early moments of the cosmos, matter and antimatter should have been created in equal amounts, only to annihilate each other and leave behind a void of pure energy. Yet, we exist. This suggests that a subtle imbalance occurred, a process where the rules of nature allowed matter to slightly outnumber its mirror image. One of the necessary conditions for this imbalance to happen is the violation of "baryon number," a bookkeeping rule that usually ensures the total number of heavy particles like protons and neutrons remains constant. While the standard model of physics treats this rule as unbreakable, many theories suggest it can be bent, perhaps by interactions involving invisible particles that carry away the missing balance.

Scientists have long searched for signs of this violation, traditionally looking for a proton to spontaneously decay or a neutron to transform into an antineutron. However, there is another possibility: that baryon number is not lost, but shared. Imagine a heavy particle decaying into a visible piece of matter and an invisible partner that escapes detection. If this invisible partner carries a specific type of "charge" related to matter, the total amount of matter in the universe remains conserved, even though the visible part of the experiment appears to have lost some. This scenario creates a unique signature: a particle disappearing and leaving behind a visible remnant with missing energy. To find this, researchers must look at heavy particles that are unstable and decay quickly, such as the Lambda-c baryon, which is a heavy cousin of the proton containing a charm quark.

In a new study, a researcher at the University of Siegen has calculated how likely it is for a Lambda-c baryon to decay into a common meson, like a pion or a kaon, and an invisible particle. The goal was to predict the rate of this rare event with enough precision to guide future experiments. The challenge lies in the fact that the Lambda-c is a complex object made of three quarks held together by the strong nuclear force. To predict how it breaks apart, one must understand the intricate dance of these quarks as they rearrange themselves into a lighter meson. The researcher used a sophisticated mathematical tool called light-cone sum rules, which allows physicists to calculate these complex interactions by treating the meson as a collection of probability waves rather than a solid object. This method accounts for the messy, non-linear behavior of the strong force that cannot be solved with simple equations.

The study focused on two specific decay paths: one where the Lambda-c turns into a pion and an invisible particle, and another where it becomes a kaon and an invisible particle. By running detailed calculations that included various levels of complexity in the quark interactions, the researcher determined the probability of these events occurring. The results suggest that if the invisible particle exists and interacts in the way the theory predicts, these decays should happen roughly once in every ten million Lambda-c baryons. In some specific scenarios, the rate could be as high as one in a million. These numbers are small, but they are large enough to be potentially detectable by modern particle detectors.

The researcher also compared their findings with previous estimates made using different theoretical approaches. While earlier methods suggested different rates, this new calculation provides a fresh and independent perspective, helping to narrow down the range of possibilities. The study explicitly notes that these are estimates based on current theoretical models and that the actual rates depend on the mass of the invisible particle, which remains unknown. The calculations show that the uncertainty in the prediction is significant, but the central values point toward a region that is within reach of upcoming experiments.

Looking ahead, the paper highlights that future facilities like the Super Tau-Charm Factory in China and the upgraded Belle II experiment in Japan will produce enough Lambda-c baryons to test these predictions. If these experiments can detect even a handful of these decays, it would provide strong evidence for new physics that connects the visible world to a hidden sector of invisible particles. The Large Hadron Collider at CERN has already set limits on how strong these interactions can be, and this new work translates those limits into concrete predictions for what we should see in a laboratory. If the invisible particle is light enough, the next generation of detectors could finally catch a glimpse of this hidden exchange, offering a new clue to why the universe is filled with matter at all.

Technical Summary: Baryon-Number Violating $\Lambda_c$ Decays from Light-Cone Sum Rules

Problem and Motivation
Baryon number violation (BNV) is a generic feature of many Standard Model (SM) extensions and a necessary condition for the dynamical generation of the matter–antimatter asymmetry. While traditional searches focus on proton decay or neutron–antineutron oscillations, recent theoretical frameworks (such as $B$ -mesogenesis) suggest that baryon number may be shared between the visible sector and a light, feebly interacting SM-singlet fermion $\chi$ . In such scenarios, dimension-six operators of the form $qqq\chi$ conserve total baryon number but induce apparent BNV in the visible sector, manifesting as decays with missing energy.

This work extends the study of such decays to the charm sector, specifically investigating the exclusive two-body decays $\Lambda_c \to \pi \bar{\chi}$ and $\Lambda_c \to K \bar{\chi}$ . Predicting the branching fractions for these processes requires non-perturbative matrix elements of three-quark operators between the $\Lambda_c$ baryon and a light meson. Previous estimates using QCD factorisation (QCDF) or baryon chiral perturbation theory (BChPT) suffer from significant hadronic uncertainties due to the application of heavy-quark expansions at the charm scale or the extrapolation of light-baryon matrix elements to the charmed sector. This paper aims to provide an independent determination of the relevant transition form factors using QCD light-cone sum rules (LCSRs) to better assess these uncertainties.

Methodology
The author calculates the transition form factors for $\Lambda_c \to \pi(K)$ using LCSRs with light-meson distribution amplitudes (DAs). The core of the calculation involves the correlation function:
$\Pi^{(J)}_{I,X}(P, q) = -i \int d^4x e^{-iP\cdot x} \langle M(p) | T\{ \bar{j}^{(J)}_{\Lambda_c}(x), \tilde{O}_{I,X}(0) \} | 0 \rangle$
where $j^{(J)}_{\Lambda_c}$ is an interpolating current for the $\Lambda_c$ and $\tilde{O}_{I,X}$ represents the relevant three-quark effective operators.

Key methodological features include:

Interpolating Currents: To assess current dependence, two local three-quark currents are employed: a pseudoscalar ( $P$ ) current and an axial-vector ( $A$ ) current.
Light-Cone OPE: The correlation function is expanded near the light cone at leading order in $\alpha_s$ $α_{s}$ . The calculation retains:
- Leading-order (LO) two-particle contributions involving pion/kaon DAs up to twist four.
- Factorisable four-particle contributions expressed through the quark condensate $\langle \bar{q}q \rangle$ and two-particle DAs.
Hadronic Representation: The sum rules include the positive-parity ground state $\Lambda_c$ and the lowest negative-parity state $\Lambda_c^*$ . The contribution of the $\Lambda_c^*$ is explicitly eliminated by constructing specific linear combinations of invariant amplitudes that cancel the negative-parity pole.
Extrapolation: Since LCSRs are valid in the spacelike region ( $q^2 < 0$ ), the results are extrapolated to the physical timelike region ( $0 \le q^2 \le (m_{\Lambda_c} - m_M)^2$ ) using conformal mapping variables ( $z$ -expansions). For the pion channel, a quadratic expansion is used; for the kaon channel, a single-pole parametrisation factoring out the nearest subthreshold $\Xi_c$ resonance is employed.

Key Contributions and Results

Form Factor Determination: The paper provides the first LCSR determination of the complete set of form factors for the dimension-six operators relevant to $\Lambda_c \to \pi(K) \bar{\chi}$ . The results at $q^2=0$ are presented for both $P$ and $A$ currents. For most form factors, the two current determinations are compatible within uncertainties, though specific cases (e.g., $F_{2,R}$ and $F_{1,L}$ ) show discrepancies that guide the selection of the more reliable current for phenomenological analysis.
Twist Analysis: The study highlights that the choice of interpolating current dictates which subset of DAs contributes at leading order. For instance, the $P$ current selects twist-2 and twist-4 DAs for certain operators, while the $A$ current selects twist-3 DAs. The factorisable four-particle terms (twist-5, -6, or -7) are found to be sizeable in some scenarios, sometimes exceeding the LO two-particle contributions, emphasizing the importance of including higher-twist effects.
Branching Fractions: Combining the calculated form factors with single-operator benchmarks derived from LHC missing-energy searches, the author estimates the branching fractions.
- The predicted branching fractions are of the order of $10^{-7}$ over sizeable parts of the physical region (as a function of the invisible fermion mass $m_\chi$ ).
- Uncertainty envelopes can reach $10^{-6}$ in certain scenarios, driven by input parameters, sum-rule parameters, and scale variations.
Comparison with Other Methods: The results are compared with existing ChPT and QCDF estimates. The LCSR predictions yield branching fractions compatible with ChPT scales but are generally larger than QCDF estimates. The author notes that QCDF results are restricted to hard-scattering contributions, whereas LCSR captures the full non-perturbative dynamics.

Significance and Outlook
The paper establishes that $\Lambda_c \to \pi(K) \bar{\chi}$ decays are theoretically accessible and experimentally promising probes of BNV interactions involving charm quarks. The calculated branching fractions ( $10^{-7}$ to $10^{-6}$ ) fall within the potential reach of current and future flavour factories.

The author concludes that:

Experimental Prospects: Experiments such as STCF and Belle II could probe part of the predicted range, particularly if signal efficiencies can be improved. The FCC-ee is projected to reach sensitivities down to a few times $10^{-8}$ .
Theoretical Status: The results represent indicative estimates within the retained light-cone expansion. The author acknowledges that a more complete assessment of theoretical uncertainties would require the inclusion of three-particle DAs, radiative corrections, and a rigorous check of the factorisation approximation for four-particle terms.
Motivation: The work motivates dedicated experimental searches for $\Lambda_c \to \pi(K) + \text{invisible}$ , noting that establishing realistic efficiencies and backgrounds is a necessary next step.

In summary, this work provides a robust, independent theoretical framework for evaluating BNV in the charm sector, offering crucial hadronic inputs that complement existing effective field theory approaches and guiding future experimental efforts at high-luminosity colliders.

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