⚛️ high-energy experiments

Revisiting two-body charmed anti-charmed baryonic $B$ decays

This paper revisits two-body charmed anti-charmed baryonic $\overline B$ decays by incorporating $b\to u\bar u q$ contributions alongside $b\to c\bar c q$ terms, demonstrating that these CKM-suppressed amplitudes are significantly enhanced in $\Delta S=0$ transitions and can substantially increase decay rates for specific channels like $B^-\to \Xi_c^0 \bar \Xi_c^{-}$ .

Original authors: Chun-Khiang Chua

Published 2026-09-09

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Chun-Khiang Chua

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 handful of fundamental particles that combine in specific ways to form the protons and neutrons inside atoms. Among these building blocks are quarks, which come in different "flavors," including the heavy charm quark. When a heavy particle called a B meson decays, it often breaks apart into other particles, sometimes creating a pair of charmed baryons—particles made of three quarks, one of which is a charm quark. Scientists have long studied these decays to understand the fundamental forces that govern how matter transforms. For decades, the prevailing view was that a specific type of transformation, where a bottom quark turns into a charm quark and an anti-charm quark, was the dominant driver of these events. This process is well understood and has been the focus of many theoretical models. However, there is another, less obvious pathway where the bottom quark transforms into an up quark and an anti-up quark. Because of the way the universe's fundamental mixing rules work, this second pathway was thought to be so rare in certain types of decays that it could be safely ignored.

A recent study by physicist Chun-Khiang Chua revisits this assumption, asking whether that ignored pathway might actually play a much larger role than previously thought, particularly in a specific class of decays where the total number of strange particles remains unchanged. The researcher used a method called topological amplitude analysis, which is essentially a way of mapping out all the possible ways these particles can rearrange themselves during a decay, to include this previously overlooked contribution. By updating the mathematical framework to account for both the dominant charm-producing path and the suppressed up-quark path, the study reveals that while the up-quark contribution remains tiny in decays involving a change in strangeness, its influence is dramatically amplified in decays where strangeness does not change. In these specific cases, the relative importance of the up-quark path is boosted by a factor of roughly twenty compared to the other type of decay. This amplification means that the up-quark contribution is no longer negligible; in fact, current experimental data slightly favors the idea that this contribution is present and significant.

The study finds that when this up-quark contribution is included, the predicted rates for several specific decay processes change noticeably. For instance, the model suggests that the decay of a negatively charged B meson into a neutral charmed cascade baryon and an anti-charmed cascade baryon could occur much more frequently than models that ignore the up-quark path would predict. Similarly, the rates for a neutral B meson decaying into a charmed lambda baryon and an anti-charmed cascade baryon, and for a neutral B meson decaying into a charmed cascade baryon and an anti-charmed cascade baryon, are also predicted to be significantly higher. These three specific reactions are unique because they are not subject to the same internal cancellations that suppress other decay modes, making them ideal places to look for the up-quark effect. The data currently available for other decay modes, such as the decay of a B meson into a charmed lambda and an anti-charmed lambda, remains consistent with the new model, but the small size of that rate does not rule out the presence of the up-quark contribution; rather, it suggests that different parts of the process are canceling each other out.

The implications of these findings are that the scientific community should not dismiss the up-quark contribution as a minor detail. While it does not alter the results for decays where the number of strange particles changes, it offers a compelling explanation for why certain other decays might be more common than expected. The study does not claim to have definitively proven that these contributions are large, but it demonstrates that the current experimental data allows for them and even slightly prefers a scenario where they are present. This opens a new avenue for experimentalists at facilities like the Large Hadron Collider and Belle II to search for these specific decay patterns. By measuring the rates of these three highlighted decays, scientists can determine whether the up-quark pathway is indeed a major player in the subatomic world of charmed baryons. If future measurements confirm these higher rates, it will provide a clearer picture of the complex interplay of forces that govern particle decay, refining our understanding of the fundamental rules that shape the universe.

Technical Summary: Revisiting Two-Body Charmed Anti-Charmed Baryonic B Decays

Problem Statement
Experimental progress in investigating two-body charmed anti-charmed baryonic $B$ decays ( $B \to B_c \bar{B}_c$ ) has accelerated, with recent measurements by LHCb and Belle II for modes such as $\bar{B}^0 \to \Lambda_c^+ \bar{\Lambda}_c^-$ and $B^- \to \Xi_c^+ \bar{\Sigma}_c(2455)^{--}$ . While theoretical studies utilizing the topological amplitude approach have been conducted (e.g., Refs. [13, 16]), these prior analyses typically considered only $b \to c\bar{c}q$ transitions. A potential gap exists in the systematic treatment of $b \to u\bar{u}q$ contributions. Specifically, in $\Delta S = -1$ transitions, these $b \to u\bar{u}q$ diagrams are Cabibbo-Kobayashi-Maskawa (CKM) suppressed and often neglected. However, the paper argues that in $\Delta S = 0$ transitions, the relative suppression of $b \to u\bar{u}q$ compared to $b \to c\bar{c}q$ is significantly reduced (by a factor of roughly $\lambda^{-2} \approx 20$ ), potentially making these contributions non-negligible. Furthermore, existing data on $B^- \to \Xi_c^0 \bar{\Lambda}_c^-$ and $\bar{B}^0 \to \Xi_c^+ \bar{\Lambda}_c^-$ show central values pointing in the opposite direction to the identical rates expected in the SU(2) limit, leaving room for contributions from SU(2) breaking effects arising from these previously unconsidered transitions.

Methodology
The author employs the topological amplitude approach to decompose the decay amplitudes of $B \to B_c \bar{B}_c$ processes. The study updates the formalism to include both $b \to c\bar{c}q$ and $b \to u\bar{u}q$ transitions.

Hamiltonian Construction: The effective Hamiltonians for $\Delta S = -1$ and $\Delta S = 0$ transitions are constructed using $SU(3)$ flavor symmetry. The $b \to c\bar{c}q$ contributions are governed by operators of the form $(\bar{c}b)(\bar{s}c)$ , while the new $b \to u\bar{u}q$ contributions are governed by $(\bar{u}b)(\bar{s}u)$ .
Topological Decomposition: The decay amplitudes are decomposed into topological diagrams:
- $b \to c\bar{c}q$ : Internal W-tree ( $C$ ) and W-exchange ( $E$ ) amplitudes.
- $b \to u\bar{u}q$ : Internal W-tree ( $D$ ), W-exchange ( $F$ ), and annihilation ( $A$ ) amplitudes. These diagrams (Figs. 2c–2e) are identified as new additions to the analysis.
SU(3) Breaking: The formalism incorporates $SU(3)$ flavor breaking effects arising from the strange quark mass, parameterized by $\delta$ coefficients acting on the weak vertex, spectator lines, and pair creation lines (Figs. 3 and 4).
CKM Scaling: The relationship between $\Delta S = -1$ and $\Delta S = 0$ amplitudes is established via CKM matrix elements. The paper highlights that the ratio of $b \to u\bar{u}q$ to $b \to c\bar{c}q$ amplitudes in $\Delta S = 0$ is enhanced by a factor of $\approx 20$ compared to $\Delta S = -1$ (Eq. 2).
Numerical Analysis: The author performs a $\chi^2$ $χ^{2}$ fit using experimental data for four low-lying $\Delta S = -1$ $Δ S = - 1$ and $\Delta S = 0$ $Δ S = 0$ decay rates ( $B^- \to \Xi_c^0 \bar{\Lambda}_c^-$ $B^{-} \to Ξ_{c}^{0} \overset{ˉ}{Λ}_{c}^{-}$ , $\bar{B}^0 \to \Xi_c^+ \bar{\Lambda}_c^-$ $\overset{ˉ}{B}^{0} \to Ξ_{c}^{+} \overset{ˉ}{Λ}_{c}^{-}$ , $\bar{B}_s^0 \to \Lambda_c^+ \bar{\Lambda}_c^-$ $\overset{ˉ}{B}_{s}^{0} \to Λ_{c}^{+} \overset{ˉ}{Λ}_{c}^{-}$ , and $\bar{B}^0 \to \Lambda_c^+ \bar{\Lambda}_c^-$ $\overset{ˉ}{B}^{0} \to Λ_{c}^{+} \overset{ˉ}{Λ}_{c}^{-}$ ). Two scenarios are tested:
- Case 1: Uses central values of $b \to c\bar{c}q$ parameters from Ref. [16] as fixed inputs, fitting only the $b \to u\bar{u}q$ parameters ( $d_1, f_1, a_{1,v}$ ).
- Case 2: Allows slight modifications to the $b \to c\bar{c}q$ input parameters to achieve a perfect fit ( $\chi^2_{min} = 0$ ).

Key Contributions

Updated Amplitude Decomposition: The paper provides the complete topological decomposition for $B \to B_c(\bar{3}_f)B_c(3_f)$ , $B_c(6_f)B_c(3_f)$ , $B_c(\bar{3}_f)B_c(\bar{6}_f)$ , and $B_c(6_f)B_c(\bar{6}_f)$ decays, explicitly including the $b \to u\bar{u}q$ contributions (Tables III–VI).
Quantification of CKM Enhancement: It rigorously demonstrates that while $b \to u\bar{u}q$ contributions are sub-leading in $\Delta S = -1$ modes, they are significantly amplified in $\Delta S = 0$ modes due to the specific structure of CKM factors.
Re-evaluation of Data Fit: The analysis shows that current experimental data allow for, and in the case of a perfect fit slightly prefer, non-negligible $b \to u\bar{u}q$ contributions. Specifically, the small branching ratio of $\bar{B}^0 \to \Lambda_c^+ \bar{\Lambda}_c^-$ is shown to be consistent with large $b \to u\bar{u}q$ contributions due to destructive interference between the $D'$ and $F'$ amplitudes.

Results

$\Delta S = -1$ Transitions: The inclusion of $b \to u\bar{u}q$ contributions does not significantly alter the predicted rates for $\Delta S = -1$ modes compared to previous studies (Ref. [16]), as these contributions remain CKM suppressed. However, the fit improves the agreement for $B^- \to \Xi_c^0 \bar{\Lambda}_c^-$ and $\bar{B}^0 \to \Xi_c^+ \bar{\Lambda}_c^-$ by adjusting the relative phases and magnitudes of the amplitudes.
$\Delta S = 0$ Transitions: The impact is substantial. The paper predicts that modes dominated by single topological amplitudes from $b \to u\bar{u}d$ $b \to u \overset{u}{ˉ} d$ (without destructive interference) will exhibit significantly enhanced branching ratios compared to predictions considering only $b \to c\bar{c}d$ $b \to c \overset{c}{ˉ} d$ .
- Specifically, the branching ratios for $B^- \to \Xi_c^0 \bar{\Xi}_c^-$ , $\bar{B}_s^0 \to \Lambda_c^+ \bar{\Xi}_c^-$ , and $\bar{B}^0 \to \Xi_c^+ \bar{\Xi}_c^-$ are predicted to be much larger in Case 2 (where $b \to u\bar{u}q$ is non-vanishing) than in Case 1 or previous literature. For instance, the predicted rate for $B^- \to \Xi_c^0 \bar{\Xi}_c^-$ jumps from $\sim 0.24 \times 10^{-4}$ (Ref. [16]) to $\sim 11.86 \times 10^{-4}$ in Case 2 (Table IX).
Other Modes: Predictions for $B \to B_c(6_f)B_c(\bar{6}_f)$ modes are provided, noting that modes with $E_4$ contributions remain unpredictable.

Significance
The paper claims that the systematic inclusion of $b \to u\bar{u}q$ contributions is necessary for a complete theoretical description of two-body charmed anti-charmed baryonic $B$ decays. While the author does not advocate for "huge" contributions, they emphasize that these terms were previously overlooked and that current data permits their existence. The primary significance lies in identifying specific $\Delta S = 0$ decay channels ( $B^- \to \Xi_c^0 \bar{\Xi}_c^-$ , $\bar{B}_s^0 \to \Lambda_c^+ \bar{\Xi}_c^-$ , and $\bar{B}^0 \to \Xi_c^+ \bar{\Xi}_c^-$ ) where the effects of $b \to u\bar{u}q$ are maximized. Measuring these decays is presented as a crucial experimental test to clarify the role of these contributions and resolve potential discrepancies in the understanding of SU(2) breaking and topological amplitudes in heavy baryon decays.

More like this