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Mixing effects in radiative decays of heavy-strange axial-vector mesons within light-cone QCD sum rules

This paper utilizes light-cone QCD sum rules to calculate the radiative decay widths of heavy-strange axial-vector mesons, demonstrating that the significant difference in decay patterns between the lower and higher states arises from the constructive and destructive interference of $^{1}P_{1}$ - $^{3}P_{1}$ mixing, respectively.

Original authors: T. M. Aliev, S. Bilmis, M. Savci

Published 2026-08-27

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CC BY 4.0

Original authors: T. M. Aliev, S. Bilmis, M. Savci

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

Deep within the heart of matter, protons and neutrons are built from smaller particles called quarks. These quarks are bound together by a powerful force, but they can also pair up with other quarks to form heavier, short-lived particles known as mesons. Some of these mesons are made of a heavy quark, like a charm or bottom quark, paired with a lighter strange quark. Physicists study these heavy-light mesons because they act as a unique laboratory. By watching how they behave and how they change, scientists can test the fundamental rules that govern the strong force, the invisible glue holding the atomic nucleus together. Among these particles, a specific family called axial-vector mesons is particularly intriguing. Unlike simpler particles, these have a complex internal structure where the spins of the two quarks can align in different ways. Because the heavy quark is not infinitely heavy, these different spin arrangements mix together, creating physical particles that are a blend of two distinct theoretical states. Understanding exactly how they mix is crucial, because this mixing determines how the particles interact with light and how they decay.

A team of researchers has now taken a closer look at how these mixed mesons emit light, a process known as a radiative decay. Using a sophisticated theoretical tool called light-cone QCD sum rules, they calculated the rates at which four specific mesons—two containing charm quarks and two containing bottom quarks—should transform into a lighter version of themselves by releasing a photon. The study focused on the charm-strange mesons named Ds1(2460) and Ds1(2536), as well as the bottom-strange mesons Bs1(5750) and Bs1(5830). While the Ds1(2460) and Bs1(5830) have been observed in experiments, the Ds1(2536) has never been seen emitting light, and the Bs1(5750) remains a theoretical prediction that has not yet been spotted. The researchers wanted to see if their calculations could explain why some of these particles seem to avoid emitting light while others do so readily.

The calculations revealed a striking difference between the two charm-strange mesons. The lower-mass particle, Ds1(2460), was predicted to decay into a photon with a width of approximately 45.9 keV, a measure of how quickly the decay happens. In sharp contrast, the higher-mass partner, Ds1(2536), was found to have a decay width of only about 0.55 keV. This massive difference arises from the way the internal spin configurations of the quarks interfere with one another. Inside the Ds1(2460), the two possible spin states work together, reinforcing each other to make the decay happen easily. Inside the Ds1(2536), however, these same states work against each other, effectively canceling out the ability to emit light. This destructive interference makes the Ds1(2536) extremely reluctant to release a photon, which explains why this decay has been so difficult to observe in experiments.

The situation is different for the bottom-strange mesons. For the predicted lower state, Bs1(5750), the team calculated a decay width of about 12.0 keV, while the observed Bs1(5830) was predicted to decay at a rate of roughly 8.9 keV. Unlike the charm system, these two rates are comparable, meaning both particles should emit light at similar speeds, even though the higher state still experiences some cancellation effects. The researchers noted that the results for the bottom sector are sensitive to the exact angle at which the spin states mix, but within the uncertainties of their calculation, the two widths are close enough to be considered similar. This suggests that the dramatic suppression seen in the charm sector does not necessarily repeat in the bottom sector.

These findings provide a clear explanation for the experimental difficulty in spotting the light emission from the Ds1(2536). The study predicts that the chance of this particle decaying into a photon is incredibly small, roughly one in a thousand of its total decays. This tiny probability aligns with the fact that no such event has been definitively recorded yet. The work also offers a new prediction for the Bs1(5830), a particle whose light-emitting behavior has not been measured. By showing how the mixing of internal states dictates the outcome, the research highlights that the way these heavy particles interact with light is a sensitive probe of their internal quantum structure. If future experiments can measure these decays, they will be able to test these predictions and refine our understanding of how quarks combine to form the matter around us.

Technical Summary: Mixing Effects in Radiative Decays of Heavy-Strange Axial-Vector Mesons

Problem Statement
The internal structure of heavy-light mesons, particularly axial-vector states ( $J^P = 1^+$ ), is complicated by the mixing of two basis configurations: $^1P_1$ and $^3P_1$ . In the heavy-quark limit, physical states are classified by the total angular momentum of the light degrees of freedom ( $j_\ell$ ), but for finite heavy-quark masses, spin-dependent interactions induce mixing between these basis states. This mixing significantly influences radiative transition amplitudes, as the contributions from the two basis currents can interfere constructively or destructively. While this interference mechanism has been discussed in quark models (specifically by Bondar and Milstein), it remains an open question whether this cancellation pattern emerges within the Light-Cone QCD Sum Rules (LCSRs) framework, where effects arise from correlation functions of independent interpolating currents rather than explicit wave function components. Furthermore, while the radiative decay of the lower charm-strange state $D_{s1}(2460)$ has been observed, the decay of the higher state $D_{s1}(2536)$ remains unobserved, and the radiative properties of the bottom-strange sector (including the experimentally observed $B_{s1}(5830)$ and the theoretically predicted lower state $B_{s1}(5750)$ ) require theoretical investigation.

Methodology
The authors calculate the radiative decay widths for four transitions: $D_{s1}(2460) \to D_s\gamma$ , $D_{s1}(2536) \to D_s\gamma$ , $B_{s1}(5750) \to B_s\gamma$ , and $B_{s1}(5830) \to B_s\gamma$ . The analysis is performed within the LCSR framework using the following key steps:

Interpolating Currents and Mixing: Two independent interpolating currents are employed to represent the $^3P_1$ ( $J^A_\mu$ ) and $^1P_1$ ( $J^B_\mu$ ) basis states. The physical axial-vector states are constructed as linear combinations of these currents using a mixing angle $\theta$ , consistent with the heavy-quark limit classification.
Correlation Functions: The transition form factors are extracted from the vacuum correlation function involving the interpolating current for the axial-vector meson, the electromagnetic current, and the pseudoscalar current.
OPE and Distribution Amplitudes: The correlation function is evaluated on the QCD side using the Operator Product Expansion (OPE) in the presence of an external electromagnetic field (background-field method). The calculation includes:
- Perturbative contributions (photon emission from quark propagators).
- Non-perturbative contributions parameterized by photon light-cone distribution amplitudes (DAs) up to twist four.
- Contributions from two-particle and three-particle (quark-antiquark-gluon and quark-antiquark-photon) operators.
- Retention of finite strange-quark mass effects throughout the calculation.
Sum Rule Construction: The hadronic representation (in terms of physical states and decay constants) is equated to the QCD representation. Double Borel transformations are applied to suppress higher resonance contributions, and continuum subtraction is implemented via quark-hadron duality.
Numerical Analysis: The transition form factors are determined using input parameters including quark masses, meson masses, decay constants, condensates, and mixing angles derived from previous studies ( $\theta_{Ds} \approx 26.6^\circ$ , $\theta_{Bs} \approx 38.5^\circ$ ). Uncertainties are propagated by varying QCD inputs, Borel parameters, continuum thresholds, and mixing angles.

Key Contributions and Results
The primary contribution of this work is the first application of the LCSR framework to study the $D_{s1}(2536) \to D_s\gamma$ transition and the radiative decays of the bottom-strange axial-vector mesons, explicitly incorporating $^1P_1$ – $^3P_1$ mixing.

The calculated radiative decay widths are:

$\Gamma[D_{s1}(2460) \to D_s\gamma] = 45.9^{+10.1}_{-8.5}$ keV
$\Gamma[D_{s1}(2536) \to D_s\gamma] = 0.55^{+1.73}_{-0.48}$ keV
$\Gamma[B_{s1}(5750) \to B_s\gamma] = 12.0^{+2.9}_{-2.3}$ keV
$\Gamma[B_{s1}(5830) \to B_s\gamma] = 8.9^{+2.4}_{-2.0}$ keV

Key Findings:

Charm-Strange Sector: There is a substantial difference between the decay widths of the lower and higher charm-strange states. The $D_{s1}(2460)$ width is significantly larger than that of $D_{s1}(2536)$ . This suppression in the higher state arises from destructive interference between the $^1P_1$ and $^3P_1$ basis-current contributions, whereas the lower state exhibits constructive interference. This result reproduces the interference mechanism previously discussed in quark models but confirms its validity within the LCSR formalism.
Bottom-Strange Sector: The predicted widths for $B_{s1}(5750)$ and $B_{s1}(5830)$ are comparable within their uncertainties. While the higher state ( $B_{s1}(5830)$ ) still exhibits destructive interference, the specific mixing angle used ( $\theta_{Bs} \approx 38.5^\circ$ ) places the system away from the region of strongest cancellation, resulting in comparable magnitudes for both states.
Branching Fraction: The calculated width for $D_{s1}(2536) \to D_s\gamma$ corresponds to a branching fraction of approximately $0.60 \times 10^{-3}$ , which explains the experimental difficulty in observing this mode given the narrow total width of the state.

Significance
The paper demonstrates that the radiative decay pattern of heavy-strange axial-vector mesons is highly sensitive to the mixing of the $^1P_1$ and $^3P_1$ spin configurations. The LCSR framework successfully captures the interference effects that lead to the strong suppression of the $D_{s1}(2536) \to D_s\gamma$ decay, providing an independent theoretical confirmation of mechanisms proposed in quark models. The authors note that the wide spread in existing theoretical predictions for these decays (ranging from sub-keV to hundreds of keV) reflects different treatments of mixing and transition amplitudes. Consequently, future experimental measurements of these radiative modes, particularly the elusive $D_{s1}(2536) \to D_s\gamma$ and the $B_{s1}(5830) \to B_s\gamma$ , could provide crucial constraints on the mixing angles and help discriminate between different theoretical descriptions of heavy-light meson structure. The inclusion of the theoretically predicted $B_{s1}(5750)$ serves as a benchmark for future searches for the lower bottom-strange $1^+$ state.

Technical Summary: Mixing Effects in Radiative Decays of Heavy-Strange Axial-Vector Mesons

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