⚛️ phenomenology

Decay constants of the two-pole $D_0^*(2300)$

This paper calculates the decay constants of the two-pole structure of the scalar charmed meson $D_0^*(2300)$ using an effective Lagrangian approach, finding values significantly smaller than conventional quark-model predictions to propose decay constants as a discriminative probe for its internal structure, and subsequently predicts branching fractions for related $B$ and $\Lambda_b$ decays to experimentally validate this two-pole interpretation.

Original authors: Qi-Wei Yuan, Jia-Ting Zhang, Ming-Zhu Liu

Published 2026-07-28

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CC BY 4.0

Original authors: Qi-Wei Yuan, Jia-Ting Zhang, Ming-Zhu Liu

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

Imagine the universe is built from a giant, invisible Lego set. Most of the time, the pieces snap together in predictable ways: two pieces make a simple molecule, three make a tiny atom, and so on. But in the world of particle physics, specifically inside the "strong force" that holds the universe's smallest building blocks together, things get weird. Sometimes, the Lego pieces don't just snap; they swirl around each other, creating temporary, ghostly shapes that look like particles but act more like a cloud of interacting friends. These are called "exotic states," and they are the universe's way of showing us that the rules of the strong force are far more complex and dynamic than we thought. One of the most puzzling characters in this story is a particle called $D^*_0(2300)$ . Scientists have been arguing about what it really is: is it a solid, traditional particle made of a specific pair of quarks (like a standard Lego brick), or is it a fleeting, molecular dance between two other particles? Figuring this out is like trying to identify a shadow—is it a person standing still, or just two people passing each other quickly? The answer matters because it tells us how the fundamental forces of nature actually work when they get really crowded.

This paper dives into that mystery by treating the $D^*_0(2300)$ not as a single solid brick, but as a "two-pole" structure. Imagine a double-decker bus where the lower deck and the upper deck are actually two different vehicles that happen to be driving in the exact same lane at the same time. In this scenario, the "lower pole" is a vehicle mostly made of a $D$ meson and a pion ( $D\pi$ ), while the "higher pole" is a vehicle mostly made of a $D_s$ meson and an antikaon ( $D_s\bar{K}$ ). The authors of this study used a mathematical toolkit called "effective Lagrangian" to calculate a specific property of these two ghostly vehicles: their "decay constant." Think of the decay constant as a measure of how "tight" or "loose" the particle is, or how easily it can be created from the vacuum of space.

The results are quite surprising. The team calculated that the decay constant for the lower pole is about $64.6^{+0.9}_{-1.0}$ MeV, and for the higher pole, it is $80.8^{+9.6}_{-5.3}$ MeV. When they compared these numbers to what we would expect if $D^*_0(2300)$ were a standard, solid particle (a "conventional excited state"), they found a huge mismatch. The standard models predicted values much higher, around $100$ to $373$ MeV. This suggests that the decay constant is a very sensitive "sniffer dog" that can tell the difference between a tight, solid particle and a loose, molecular dance. Because the numbers they found are so much smaller, it strongly hints that the $D^*_0(2300)$ is indeed this weird, two-pole molecular structure rather than a simple brick.

To make sure this idea holds water, the authors didn't just stop at the math; they predicted what would happen if we tried to create these particles in real experiments. They looked at how heavy particles called $B_s$ , $\Lambda_b$ , and $\Xi_b$ decay into these $D^*_0$ states. Using their new, smaller decay constants, they predicted that these decays would happen about $0.48 \times 10^{-4}$ to $0.94 \times 10^{-4}$ of the time. This is roughly ten times less frequent than creating the standard, ground-state particles. The paper suggests that if future experiments at particle colliders measure these rates and find them to be this low, it would be a "smoking gun" confirming that the $D^*_0(2300)$ is indeed this complex, two-pole molecular structure. While the paper doesn't claim to have solved the mystery with absolute, unshakeable proof, it provides a very strong, testable prediction that could finally settle the debate on what this elusive particle really is.

Technical Summary: Decay Constants of the Two-Pole $D^*_0(2300)$

Problem Statement
The nature of the scalar charmed meson $D^*_0(2300)$ remains a subject of debate in hadron spectroscopy. While conventional quark models treat it as a $c\bar{q}$ excited state, an alternative and prominent interpretation posits that it is a dynamically generated two-pole structure arising from coupled-channel interactions involving $D\pi$ , $D\eta$ , $D_s\bar{K}$ , and $D\eta'$ . In this scenario, the lower pole couples primarily to the $D\pi$ channel, while the higher pole couples dominantly to the $D_s\bar{K}$ channel. A critical challenge is identifying observables capable of distinguishing between these internal structures (compact quark model vs. hadronic molecule). The decay constant, a key quantity characterizing hadron production in vacuum, is proposed as a sensitive probe for this discrimination.

Methodology
The authors employ an effective Lagrangian approach within the framework of Chiral Effective Field Theory (ChEFT) to calculate the decay constants of the two poles. The methodology proceeds in three main stages:

Unitarized Coupled-Channel Amplitude: The two-pole structure is generated by solving the Lippmann-Schwinger (LS) equation using a potential derived from ChEFT up to next-to-leading order (NLO). The potential respects $SU(3)$-flavor symmetry and includes Weinberg-Tomozawa interactions. The loop function is evaluated using dimensional regularization. Pole positions and residues (couplings to constituent mesons) are extracted from the unitarized amplitude.
Decay Constant Calculation: The decay constants ( $f_{D^*_0}$ ) are computed by evaluating the vector-current matrix element $\langle D^*_0(p)|\bar{q}\gamma_\mu c|0\rangle = f_{D^*_0}p_\mu$ . This is modeled as a loop diagram where the $D^*_0$ is formed from its constituent mesons ( $D^{(*)}$ and pseudoscalars $P$ ), which subsequently transition to a $W$ boson. The calculation utilizes effective Lagrangians for the $D^{(*)}P$ transition and the $D^*_0$ formation. The resulting loop integrals are regularized dimensionally, and the decay constant is expressed as a sum of contributions from each channel ( $D\pi, D\eta, D_s\bar{K}, D\eta'$ ), weighted by the pole residues and semileptonic form factors at $q^2=0$ .
Phenomenological Application: Using the calculated decay constants, the authors predict branching fractions for Cabibbo-favored decays of $b$ -flavored hadrons: $B_s \to D_s D^*_0$ , $\Lambda_b \to \Lambda_c D^*_0$ , and $\Xi_b \to \Xi_c D^*_0$ . These processes are analyzed using the naive factorization approach, assuming non-factorizable corrections are small.

Key Results

Pole Positions and Couplings: The calculation confirms the existence of two poles. The lower pole is located at $\sqrt{s} = (2102.8^{+4.2}_{-3.6}) - i(92.6^{+3.9}_{-3.5})$ MeV and couples most strongly to $D\pi$ . The higher pole is at $\sqrt{s} = (2437.3^{+25.1}_{-21.0}) - i(150.7^{+4.3}_{-9.9})$ MeV and is dominated by the $D_s\bar{K}$ channel. The calculated $I=1/2$ $D\pi$ scattering length ( $0.387^{+0.011}_{-0.011}$ fm) is consistent with previous lattice QCD and ChEFT studies, validating the amplitude.
Decay Constants: The computed decay constants are:
- Lower pole: $f^{(\text{lower})}_{D^*_0} = 64.6^{+0.9}_{-1.0}$ MeV.
- Higher pole: $f^{(\text{higher})}_{D^*_0} = 80.8^{+9.6}_{-5.3}$ MeV.
  These values are substantially smaller than those predicted by conventional $c\bar{q}$ excited-state scenarios (which range from $\sim 100$ to $\sim 370$ MeV in various models like QCD sum rules and quark models).
Branching Fractions: The predicted branching fractions for the Cabibbo-favored decays are on the order of $10^{-5}$ (specifically $0.48$ to $0.94 \times 10^{-4}$ depending on the pole and decay mode). These are approximately one order of magnitude smaller than the corresponding ground-state meson decays. The higher pole consistently yields larger branching fractions than the lower pole due to its larger decay constant.

Significance and Claims
The paper claims that the decay constant serves as a sensitive discriminator between the molecular (two-pole) and compact quark model interpretations of the $D^*_0(2300)$ . The significantly smaller values obtained in the molecular picture compared to conventional models suggest that measuring this quantity could validate the two-pole structure. Furthermore, the authors note that the two-pole framework results in the smallest $SU(3)$-flavor symmetry breaking for the decay constants (approx. 10%) compared to conventional models (ranging from 11% to 45%).

As a phenomenological application, the paper asserts that the predicted branching fractions for $B_s$ , $\Lambda_b$ , and $\Xi_b$ decays provide crucial tests for the two-pole interpretation. Future experimental measurements of these rates, particularly the ratios between the two poles and ground-state mesons, are presented as a necessary step to validate the molecular scenario for the $D^*_0(2300)$ .

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