⚛️ phenomenology

Radiative Higgs decay to $\psi\left(4230\right)$

This paper calculates the branching ratio for the radiative Higgs decay into a $\psi(4230)$ meson and a photon, predicting a Standard Model value of approximately $4.88 \times 10^{-7}$ that could increase to $10^{-6}$ if the charm quark's Higgs-Yukawa coupling is modified.

Original authors: Ahmed Ali, Muhammad Jamil Aslam

Published 2026-10-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ahmed Ali, Muhammad Jamil Aslam

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 subatomic world, particles known as quarks bind together to form the protons and neutrons that make up our physical reality. Among these, the charm quark is a heavier, unstable cousin that rarely appears on its own, usually hiding inside short-lived particles called mesons. For decades, physicists have studied how these particles interact, but a newer, more mysterious class of matter has emerged: exotic tetraquarks. These are not simple pairs of quarks but complex structures containing four quarks bound together, behaving like a single particle. One such candidate, named ψ(4230), has puzzled scientists because its internal structure remains unclear—it might be a loose molecule of two other particles or a tightly packed cluster of four. Understanding exactly what this particle is, and how it is made, offers a rare window into the fundamental forces that hold the universe together.

At the heart of this mystery lies the Higgs boson, a particle discovered in 2012 that gives mass to other particles. Physicists are constantly looking for ways the Higgs interacts with different types of matter, particularly the charm quark. When a Higgs boson decays, it can sometimes transform into a photon, a particle of light, and a heavy quark-antiquark pair. If that pair immediately forms a known particle like the J/ψ meson, scientists can measure the process to learn about the strength of the Higgs' connection to charm. However, the ψ(4230) is different. Because it is an exotic tetraquark, the standard rules for how a Higgs creates it are not fully understood. This uncertainty makes the decay of the Higgs into a ψ(4230) and a photon a difficult but potentially rewarding puzzle to solve.

In a recent study, researchers set out to calculate how often this specific event happens: a Higgs boson turning into a ψ(4230) and a photon. The team, working with data from particle accelerators, faced a significant challenge. While they knew how the Higgs creates a simple charm-anticharm pair, they did not know how that pair rearranges itself to become the complex ψ(4230). To bridge this gap, the scientists proposed a practical method. Instead of trying to model the complex internal dynamics of the tetraquark from scratch, they used a measurable property of the ψ(4230) itself: how often it decays into electrons and positrons. This "leptonic coupling" acts as a data-driven probe, allowing them to estimate the likelihood of the Higgs successfully creating the exotic state. It is a way of using what is known about the particle's behavior to guess how it is born.

The calculations revealed that this decay is extremely rare. In the standard model of particle physics, the chance of a Higgs boson decaying into a ψ(4230) and a photon is roughly five in ten million. The researchers found that the process is dominated by an "indirect" mechanism, where the Higgs first turns into two photons, one of which then transforms into the ψ(4230). A second, "direct" mechanism, where the Higgs creates the charm quarks directly, plays a smaller role but is sensitive to the specific strength of the Higgs' interaction with charm. Because the measurement of the ψ(4230)'s decay into electrons currently has a large margin of error, the final prediction for the Higgs decay rate also carries a wide range of uncertainty. The team estimates the rate could be as low as zero or as high as nearly ten in ten million, depending on the precise value of that electron decay measurement.

The study also explored what would happen if the laws of physics were slightly different from our current understanding. If the Higgs' connection to the charm quark were stronger or had a different sign than predicted, the rate of this decay could change dramatically. The researchers showed that if the interaction strength were three times the standard value but with a reversed sign, the decay rate could double. This sensitivity means that if future experiments at the Large Hadron Collider can measure this rare event, they could either confirm the standard model or reveal new physics. Currently, no such decay has been observed, and the limits set by existing experiments are still far above the predicted rates. However, with the upcoming High-Luminosity upgrade to the collider, which will produce billions of Higgs bosons, the statistical power to detect such rare events will increase significantly.

Ultimately, this work provides a roadmap for how to search for the Higgs boson's interaction with exotic matter. By using the known properties of the ψ(4230) to estimate the unknown, the researchers have created a practical tool for future discovery. While the current uncertainty in the data prevents a definitive prediction, the method itself is robust. As experiments at facilities like BESIII and Belle II refine the measurements of the ψ(4230)'s properties, the uncertainty will shrink, and the prediction will become sharper. Until then, the search continues, relying on the massive data sets of the next generation of colliders to catch a glimpse of the Higgs transforming into one of nature's most enigmatic particles.

Technical Summary: Radiative Higgs Decay to $\psi(4230)$

Problem Statement
The paper addresses the calculation of the radiative Higgs decay rate $H \to \psi(4230) + \gamma$ within the Standard Model (SM) and Beyond the Standard Model (BSM) scenarios. While radiative decays to conventional vector quarkonia like $J/\psi$ and $\Upsilon(nS)$ have been proposed as probes of Higgs Yukawa couplings ( $y_Q$ ), the $\psi(4230)$ presents a unique challenge. The $\psi(4230)$ is a candidate exotic tetraquark state ( $c\bar{c}q\bar{q}$ ) with quantum numbers $I^G(J^{PC}) = 0^-(1^{--})$ , rather than a conventional charmonium state. Consequently, standard theoretical tools used for $J/\psi$ , such as Non-Relativistic QCD (NRQCD) factorization or Light-Cone Distribution Amplitudes (LCDA), are not directly applicable because the short-distance overlap between a locally produced $c\bar{c}$ pair and the exotic $\psi(4230)$ wavefunction is unknown.

Methodology
The authors calculate the decay amplitude by considering two competing mechanisms:

Direct Amplitude: The Higgs boson couples directly to a short-distance $c\bar{c}$ pair via the Yukawa interaction, which then radiates a photon and transitions into the $\psi(4230)$ .
Indirect Amplitude: The Higgs decays into a real and a virtual photon ( $H \to \gamma\gamma^*$ ), where the virtual photon transitions into the $\psi(4230)$ via the electromagnetic current.

The paper evaluates two theoretical frameworks for the $\psi(4230)$ structure:

Molecular Interpretation: A superposition of a compact $c\bar{c}$ component and a $D_1\bar{D} + \bar{D}_1D$ molecular component.
Compact Tetraquark Interpretation: A state built from diquark-antidiquark pairs ( $[cq][\bar{c}\bar{q}]$ ).

Key Innovation: Data-Driven Parametrization
Recognizing that the non-perturbative overlap factor $M(c\bar{c} \to \psi(4230))$ in the direct amplitude cannot be calculated from first principles for an exotic state, the authors propose a practical, data-driven parametrization. They utilize the measured leptonic decay width $\Gamma_{ee}[\psi(4230)]$ to estimate the coupling of the $\psi(4230)$ to a local charm vector current.

They assume the dominance of the charm vector current in the electronic width extraction.
This coupling is used to normalize the short-distance contribution to the direct amplitude, effectively bypassing the need for a detailed model of the tetraquark's internal dynamics.
The calculation is performed at leading order in the strong coupling constant $\alpha_s$ and heavy-quark velocity.

Results
Using input parameters from the Particle Data Group (PDG) and recent experimental measurements, the authors derive the following results:

Standard Model Branching Ratio: The calculated branching ratio is:
$\mathcal{B}_{SM}(H \to \psi(4230)\gamma) = 4.88^{+4.71}_{-4.52} \times 10^{-7}$
The uncertainty is dominated by the large experimental error in the leptonic decay width of the $\psi(4230)$ ( $\Gamma_{ee} = 1.53 \pm 0.26 \pm 0.54$ keV).
Amplitude Contributions:
- The indirect amplitude is numerically dominant, contributing approximately $6.69 \times 10^{-7}$ to the branching ratio.
- The direct amplitude is significantly smaller but non-negligible.
- The interference between the two amplitudes is destructive in the SM configuration (assuming a specific phase convention), reducing the total rate.
BSM Sensitivity: The decay rate is sensitive to the charm Yukawa coupling modifier $y_c$ (where $y_c=1$ in the SM). The branching ratio depends on the magnitude and sign of $y_c$ due to the interference term.
- For $y_c = -3$ , the branching ratio increases to approximately $10^{-6}$ (a factor of 2 increase).
- The paper notes that current LHC limits on $H \to J/\psi\gamma$ allow for a wide range of $y_c$ , meaning the $H \to \psi(4230)\gamma$ channel remains a viable probe for deviations in the charm Yukawa coupling.

Significance and Claims
The paper claims to extend the study of exclusive radiative Higgs decays to include exotic tetraquark states. Its primary significance lies in:

Practical Estimation: Providing a method to estimate the decay rate for an exotic state without a complete theoretical understanding of its wavefunction, by anchoring the calculation to the experimentally measured leptonic width.
Phenomenological Prediction: Establishing a baseline SM prediction ( $\sim 5 \times 10^{-7}$ ) that is roughly two orders of magnitude below current LHC experimental upper limits, indicating that future high-luminosity runs (HL-LHC) or future colliders (HE-LHC, FCC-hh) are required for observation.
Model Independence: The authors explicitly state that their predictions are estimates based on a phenomenological prescription rather than model-independent results, acknowledging that non-perturbative effects and relative phases between amplitudes could modify the outcome.

The work suggests that once the leptonic width of the $\psi(4230)$ is measured with higher precision (e.g., by BESIII or Belle II), the theoretical uncertainty will decrease, making this channel a more precise probe of the charm Yukawa coupling and potential BSM physics.

Technical Summary: Radiative Higgs Decay to ψ(4230)\psi(4230)ψ(4230)

More like this

Technical Summary: Radiative Higgs Decay to $\psi(4230)$