Insights into the exotic charged states $Z_b(10610)$ and $Z_b(10650)$ from their photoproduction off nuclei

This paper investigates the photoproduction of the exotic charged states $Z_b(10610)$ and $Z_b(10650)$ off nuclei using a collision model based on the nuclear spectral function, demonstrating that absolute and relative observables calculated for various internal structure scenarios (compact tetraquarks, molecules, and mixtures) are sensitive enough to distinguish their nature in future high-luminosity electron-ion collider experiments.

The Gist

Imagine the atomic nucleus as a bustling city, and inside that city, there are tiny, exotic particles called Zb(10610) and Zb(10650). These particles are famous in the world of physics because they are "charged" and look like they are made of four quarks stuck together, rather than the usual two or three. But here's the big mystery: What exactly are they made of?

Are they tight, compact balls of four quarks (like a solid marble)?
Are they loose, fluffy clouds of two mesons orbiting each other (like a double-star system)?
Or are they a mix of both?

This paper is like a detective story. The author, E. Ya. Paryev, proposes a way to solve this mystery by shining a high-energy "flashlight" (a photon) at different nuclear "cities" (like Carbon and Tungsten) and seeing how these exotic particles are created and how they survive the journey through the city.

The Detective's Toolkit: The "Flashlight" Experiment

The author suggests using a powerful beam of light (photons) to hit a target nucleus. When the light hits a proton or neutron inside the nucleus, it can create one of these exotic Zb particles.

Think of the nucleus as a crowded room. If you throw a ball (the photon) into the room to create a new object (the Zb particle), that new object has to try to get out of the room.

• If the object is small and compact (a tetraquark), it might slip through the crowd easily without bumping into anyone.
• If the object is big and fluffy (a molecule), it's more likely to bump into people, get stuck, or be absorbed before it can escape.

By measuring how many of these particles make it out of different-sized rooms (nuclei), the scientists can guess what shape the particle actually is.

The Four Suspects (The Scenarios)

The paper tests four different "suspects" or theories about what these particles look like:

1. The Compact Tetraquark: A tight, hard ball of four quarks.
2. The Molecule: A loose pair of heavy mesons holding hands.
3. The Hybrid (50/50): A mix where the particle is half-tight-ball and half-loose-pair.
4. The Hybrid (25/75): A mix where it's mostly a loose pair but has a little bit of a tight ball inside.

The Results: What the Numbers Say

The author ran complex computer simulations to see what would happen if these particles were created in two different "cities": a small one (Carbon-12) and a very large, crowded one (Tungsten-184).

• The "Absorption" Test: The simulations showed that if the particles are "molecules" (big and fluffy), they get absorbed (stopped) much more easily in the crowded Tungsten city than if they are "compact tetraquarks" (small and hard).
• The Difference: The difference in how many particles escape is significant. For the heavy Tungsten target, the difference between the "molecule" theory and the "hybrid" theory is huge (up to 70% difference in results). For the lighter Carbon target, the difference is smaller, but still noticeable.
• The Ratios: The author also calculated "transparency ratios." Imagine this as a score: if the nucleus is very transparent, the score is high (the particle got through easily). If it's opaque, the score is low. The paper shows that these scores change dramatically depending on whether the particle is a molecule or a compact ball.

The Future: Where to Look

The paper concludes that we can't solve this mystery with current data alone. We need a new, super-powerful microscope. The author points to upcoming Electron-Ion Colliders (specifically the EIC in the US and EicC in China).

These machines will be able to shine the "flashlight" with enough precision to count exactly how many of these exotic particles are produced and how they behave. By comparing the real-world data from these future machines with the author's predictions, scientists should finally be able to say: "Aha! It's a molecule!" or "No, it's a compact tetraquark!"

Summary in a Nutshell

This paper doesn't discover a new particle; it discovers a new way to measure the shape of an existing one. It argues that by shooting high-energy light at heavy nuclei and counting the survivors, we can tell if these mysterious Zb particles are tight little balls or loose, floppy clouds. The math says the difference is big enough to be seen, provided we have the right tools (the future colliders) to look.

Technical Summary

Technical Summary: Insights into the Exotic Charged States $Z_b(10610)$ and $Z_b(10650)$ from Their Photoproduction off Nuclei

Problem Statement
The intrinsic nature of the exotic charged bottomonium-like states $Z_b(10610)^\pm$ and $Z_b(10650)^\pm$ remains an open question in heavy quarkonium physics. While their existence is confirmed by the Belle Collaboration, their internal structure is debated. Proposed interpretations include compact tetraquarks, loosely bound $B\bar{B}^*$ and $B^*\bar{B}^*$ hadronic molecules, and various mixtures of these configurations. Distinguishing between these scenarios is crucial for understanding the dynamics of exotic hadrons. The paper addresses the challenge of determining these structures by investigating the inclusive photoproduction of these states off nuclei near the kinematic threshold, a process proposed for future high-luminosity electron-ion colliders (EIC and EicC).

Methodology
The study employs a collision model based on the nuclear spectral function to calculate the production of $Z_b(10610)^\pm$ and $Z_b(10650)^\pm$ mesons off target nuclei ($^{12}\text{C}$ and $^{184}\text{W}$) in the photon energy range of 61–90 GeV.

1. Production Mechanism: The model considers direct photon-nucleon interactions ($\gamma p \to Z_b^+ n$ and $\gamma n \to Z_b^- p$) as the primary production channel. The incident photon is treated as undistorted, while the produced mesons undergo absorption within the nuclear medium.
2. Internal Structure Scenarios: Four distinct scenarios for the intrinsic configurations of the $Z_b$ states are evaluated:
   • Compact Tetraquark (4q): Tightly bound diquark-antidiquark states with a radius of $\sim 0.65$ fm.
   • Hadronic Molecules: $S$-wave $B\bar{B}^*$ and $B^*\bar{B}^*$ molecular states.
   • Hybrid States (50/50): A linear superposition of 50% compact tetraquark and 50% molecular components.
   • Hybrid States (25/75): A linear superposition of 25% compact tetraquark and 75% molecular components.
3. Absorption Cross Sections: The model calculates effective absorption cross sections ($\sigma_{Z_b N}$) for each scenario. Compact tetraquarks are assigned a geometric cross section of $\sim 13.3$ mb. Molecular states are treated via a quasi-free approximation where constituent mesons scatter off nucleons, yielding larger cross sections ($\sim 30\text{--}54$ mb depending on charge and target nucleon). Hybrid cross sections are derived as incoherent probability-weighted sums of the pure components.
4. Observables: The study calculates:
   • Absolute and relative excitation functions (cross sections vs. photon energy).
   • Absolute momentum differential cross sections ($d\sigma/dp$) at laboratory polar angles of $0^\circ\text{--}5^\circ$.
   • Transparency ratios ($S_A$ and $T_A$), defined as the ratio of nuclear cross sections to free nucleon cross sections (normalized by nucleon number or a light nucleus like $^{12}\text{C}$), which are sensitive to absorption effects.

Key Results

• Sensitivity to Structure: The calculated observables exhibit distinct sensitivity to the assumed internal structure of the $Z_b$ states. The absorption cross sections vary significantly between the compact tetraquark and molecular scenarios, leading to measurable differences in the final yields.
• Target Dependence: The sensitivity to the internal structure is strongly dependent on the target nucleus. For the heavy nucleus $^{184}\text{W}$, the differences in production yields between the various structural scenarios are substantial (ranging from $\sim 15\%$ to $70\%$ depending on the specific comparison and charge state). For the light nucleus $^{12}\text{C}$, these differences are smaller ($\sim 10\text{--}27\%$) but still potentially measurable with high-precision experiments.
• Excitation Functions: At photon energies of 80–85 GeV, the predicted cross sections are approximately 10 nb for $Z_b(10610)^\pm$ and 2 nb for $Z_b(10650)^\pm$ on Carbon, scaling to $\sim 100$ nb and $\sim 20$ nb respectively on Tungsten.
• Transparency Ratios: The transparency ratios $S_A$ and $T_A$ show a strong dependence on the nuclear mass number $A$ and the structural scenario. For heavy nuclei in the molecular scenario, $S_A$ drops to $\sim 0.1$, a significant deviation from unity. The ratios $T_A$ (normalized to $^{12}\text{C}$) are less sensitive to the absolute production cross sections but still distinguishable between compact and molecular/hybrid configurations.
• Event Rates: Estimates for future facilities suggest that observing these states is feasible. For a one-year run at EicC with a $^{12}\text{C}$ target, approximately 2,000 $Z_b(10610)^+$ events are expected; for $^{184}\text{W}$, this rises to $\sim 20,000$. At the EIC with higher luminosity, event counts could reach $\sim 10^4$ and $\sim 10^5$ respectively.

Significance and Claims
The paper claims that the absolute and relative observables calculated (excitation functions, momentum distributions, and transparency ratios) provide a viable method to discriminate between the competing theoretical models for the $Z_b(10610)^\pm$ and $Z_b(10650)^\pm$ internal structures.

The authors emphasize that while absolute cross sections depend on the uncertain elementary production cross sections on free nucleons, the relative observables (particularly transparency ratios) are less sensitive to these theoretical uncertainties due to cancellation effects. Consequently, the study concludes that future high-precision photoproduction experiments at planned electron-ion colliders (EIC in the US and EicC in China) could utilize these observables to determine whether these exotic states are compact tetraquarks, hadronic molecules, or mixtures thereof. The work serves as a theoretical guide for these upcoming experimental efforts.