⚛️ phenomenology

New molecular bonds existing in the strong interaction

This paper extends the concept of hadronic covalent bonds induced by shared quarks to explain exotic hadrons like $Z_c(3900)$ and $X(3872)$ by establishing a logical framework where molecular existence depends on wave function overlap and Pauli principle satisfaction, while incorporating both the creation and annihilation of sea quark-antiquark pairs as unique strong interaction mechanisms for studying QCD confinement.

Original authors: Hua-Xing Chen

Published 2026-03-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hua-Xing Chen

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 as a giant, bustling construction site. For decades, physicists have been trying to understand how the smallest building blocks of matter—quarks—stick together to form protons, neutrons, and the exotic particles we call "hadrons."

Usually, we think of these particles as being held together by a single, unbreakable glue (the strong force). But recently, scientists have discovered some very strange, "exotic" particles that don't fit the standard blueprint. They seem to be made of two or more particles loosely hugging each other, like a molecular handshake rather than a solid block.

This paper, written by physicist Hua-Xing Chen, proposes a new way to understand these exotic hugs. He suggests that just as atoms in chemistry share electrons to form molecules, these subatomic particles share quarks in three distinct, magical ways.

Here is the breakdown of his three new "bonds," explained with everyday analogies:

1. The "Covalent Bond" (The Shared Handshake)

The Concept: In chemistry, two hydrogen atoms share a pair of electrons to form a hydrogen molecule. They hold hands so tightly that they become one unit.
The Analogy: Imagine two people (particles) who each have a spare umbrella (a quark). They decide to share these umbrellas. Because they are sharing, they are forced to stand very close together.
The Paper's Twist: Chen suggests that in the subatomic world, particles like the Tcc(3875) and the Deuteron (a nucleus of hydrogen) are held together because they are sharing "light quarks."

The Catch: Just like people holding hands, they have to follow strict rules (the Pauli Exclusion Principle). They can only hold hands if their "spins" (a quantum property like a spinning top) are arranged correctly. If they are arranged right, they get a strong grip. If not, they push each other away.
Result: This explains why some particles stick together tightly, while others (like two identical D-mesons) simply refuse to hold hands at all.

2. The "Creation Bond" (The Magic Vacuum Pop-Up)

The Concept: Sometimes, particles that shouldn't stick together (like a particle and its anti-particle) are found hugging anyway. How?
The Analogy: Imagine two strangers on a park bench who don't know each other. Suddenly, the ground beneath them (the vacuum) opens up and spits out two extra pairs of friends (sea quark-antiquark pairs). These new friends grab onto the strangers, linking them all together in a big, chaotic group hug.
The Paper's Twist: This explains the Zc(3900).

In this scenario, the two main particles aren't just sharing their own quarks. They are borrowing "ghost" quarks that pop out of the empty space (the vacuum) around them.
These ghost particles act as a bridge. The main particles share a light quark-antiquark pair, but they also share the "sea" of extra particles popping in and out of existence.
The Result: This creates a "Confined Molecule." It's a bit wobbly and often exists as a "resonance" (a short-lived vibration) rather than a stable, permanent object. It's like a group hug that forms spontaneously because the room is so crowded with energy.

3. The "Annihilation Bond" (The Vanishing Act)

The Concept: If you create something from the vacuum, you can also destroy it back into the vacuum.
The Analogy: Imagine the group hug from the previous example. If the two strangers in the middle decide to cancel each other out (annihilate), they disappear, but their energy doesn't vanish—it transforms. It might turn into a flash of light or a different type of particle.
The Paper's Twist: This explains the X(3872).

Chen suggests that for this specific particle, the shared quark and anti-quark don't just hold hands; they occasionally look at each other and say, "Let's disappear!"
When they annihilate, they mix with a "charmonium" state (a heavy particle made of a charm quark and its anti-quark).
The Result: This "annihilation" acts like a glue that lowers the energy of the system, making the particle lighter and more stable. It's a delicate balance: the particle is held together by the possibility of the two parts destroying each other and re-emerging as something else.

Why Does This Matter?

Think of the strong force (which holds atoms together) as a mysterious, invisible ocean. We know the waves exist, but we don't fully understand the currents.

Covalent Bonds are like the steady, predictable currents we can map.
Creation and Annihilation Bonds are like the whirlpools and eddies created by the ocean's interaction with the air (the vacuum).

Chen argues that these "Creation" and "Annihilation" bonds are unique to the strong force. You won't find them in electricity or magnetism. They provide a special, low-energy laboratory where we can study QCD Confinement—the rule that says quarks can never be found alone, they must always be trapped inside a group.

The Big Picture

This paper is essentially a new instruction manual for building exotic matter.

If you share light quarks carefully: You get a stable molecule (like the Deuteron).
If you borrow ghost particles from the vacuum: You get a wobbly, short-lived molecule (like the Zc).
If you let particles vanish and reappear: You get a unique, mixed-state particle (like the X(3872)).

By understanding these three "bonds," physicists can finally predict where to look for new, strange particles in the universe and understand the deep, hidden rules of how matter is stitched together. It turns the chaotic subatomic world into a structured, albeit very complex, dance of sharing, borrowing, and vanishing.

1. Problem Statement

The paper addresses the theoretical challenge of explaining the binding mechanisms of exotic hadrons, specifically hadronic molecules, which cannot be fully described by the standard constituent quark model or simple residual strong interactions.

Context: While the $T_{cc}(3875)$ (a doubly charmed tetraquark) and the deuteron were previously explained via a "hadronic covalent bond" induced by shared light quarks (analogous to chemical covalent bonds), this mechanism fails to explain molecules composed of a meson and an anti-meson (e.g., $D\bar{D}^*$ ).
Specific Gap: The existence of states like $Z_c(3900)$ (an isovector $D\bar{D}^*$ molecule) and $X(3872)$ (an isoscalar $D\bar{D}^*$ molecule) requires a different binding mechanism, as the simple exchange of light quarks between a meson and an anti-meson does not yield sufficient attraction or the correct quantum numbers under the Pauli exclusion principle alone.
Goal: To propose and validate new binding mechanisms within Quantum Chromodynamics (QCD) that account for the role of the vacuum (sea quarks) and quark-antiquark annihilation, thereby explaining the $Z_c(3900)$ and $X(3872)$ and providing a unified framework for QCD confinement at low energies.

2. Methodology

The author employs a forward and backward reasoning approach based on the Pauli exclusion principle and wave function overlap, extending the previous "hadronic covalent bond" model.

Theoretical Framework:
- Hadronic Covalent Bond (Refined): Re-examined for systems like $T_{cc}$ and the deuteron. The core hypothesis is that attraction occurs when shared light quarks are totally antisymmetric in their combined color, flavor, spin, and orbital wave functions.
- Hadronic Creation Bond (New): Proposed for $D^{(*)}\bar{D}^{(*)}$ systems. This mechanism incorporates not only the valence light quark-antiquark pair ( $q\bar{q}$ ) from the mesons but also two sea quark-antiquark pairs ( $q\bar{q}$ ) generated from the QCD vacuum.
- Hadronic Annihilation Bond (New): Proposed for isoscalar systems. It considers the annihilation of the shared light quark-antiquark pair back into the vacuum, treating creation and annihilation as symmetric processes in the strong interaction.
Quantum Number Analysis:
- The author systematically analyzes the symmetry properties (Color, Flavor, Spin, Orbital) of multi-quark configurations.
- Specific attention is paid to the quantum numbers of the sea pairs, assuming they form $^3S_1$ states ( $I=0, S=1$ ) or recombine into color-singlet/pseudoscalar states ( $\pi$ -like) to provide long-range attraction.
Toy Model for Binding Energy:
- An updated semi-empirical formula is used to estimate binding energies ( $B$ ):
  $B = N_{SS}S + N_{WW}W + N_{\Lambda\Lambda}\Lambda - N_{RR}R - N\epsilon$
  Where $S, W, \Lambda, R$ represent energies of strong/weak bonds, strange-quark bonds, and repulsive bonds, respectively, and $\epsilon$ is the residual energy of components.
- Parameters are fitted based on known states ( $T_{cc}$ , deuteron, $P_c$ ).

3. Key Contributions

The paper introduces three distinct types of "molecular bonds" existing solely in the strong interaction:

Hadronic Covalent Bond (Refined):
- Induced by shared light quarks between two hadrons.
- Requires total antisymmetry of shared quarks to satisfy the Pauli principle, generating attraction.
- Successfully explains $T_{cc}(3875)$ and the deuteron.
Hadronic Creation Bond:
- Induced by the shared light quark-antiquark pair from the mesons plus two sea quark-antiquark pairs from the vacuum.
- The sea pairs facilitate the formation of a "confined" structure where four strong bonds and two weak bonds can form between the components.
- This mechanism explains the existence of $Z_c(3900)$ ( $I^G J^{PC} = 1^+ 1^{+-}$ ) as a $D\bar{D}^*/D^*\bar{D}$ molecule.
Hadronic Annihilation Bond:
- Accounts for the annihilation of the shared light quark-antiquark pair.
- Crucial for understanding the $X(3872)$ ( $I^G J^{PC} = 0^+ 1^{++}$ ). The paper argues that the $X(3872)$ is a mixture of a $D\bar{D}^*$ molecule and a charmonium state ( $\chi_{c1}(2P)$ ).
- The annihilation bond lowers the mass of the isoscalar state (via mixing), explaining why $X(3872)$ is lighter than the isovector $Z_c(3900)$ .

4. Key Results

Explanation of $Z_c(3900)$ : The paper demonstrates that the $D\bar{D}^*$ system can form a bound state (resonance) via the creation bond. The configuration involves the valence $q\bar{q}$ pair and two sea pairs, allowing for a stable isovector ( $I=1$ ) state with $J^{PC}=1^{+-}$ .
Explanation of $X(3872)$ : The annihilation bond is identified as the mechanism that stabilizes the isoscalar ( $I=0$ ) $D\bar{D}^*$ state. The mixing with the charmonium state reduces its mass, making it a narrow resonance just below the $D^0\bar{D}^{*0}$ threshold.
Predictions for New States:
- $D^*\bar{D}^*$ Molecules: The model predicts the existence of $D^*\bar{D}^*$ confined molecules with quantum numbers $0^{++}$ , $1^{+-}$ , and $2^{++}$ .
- Hidden-Charm Baryonium: The framework is extended to baryon-antibaryon systems, predicting possible confined molecules like $\bar{\Lambda}_c \Sigma_c$ , $\bar{\Sigma}_c \Sigma_c$ , and $\bar{\Xi}'_c \Xi'_c$ .
- Binding Energies: Table I provides estimated binding energies for various covalent and confined molecules (e.g., $D^*\bar{B}^{(*)}$ estimated at ~15 MeV, complex multi-hadron systems up to ~90 MeV).
Distinction between Covalent and Confined Molecules:
- Covalent molecules (shared quarks) tend to be bound states below threshold.
- Confined molecules (creation/annihilation bonds involving sea quarks) often behave as resonances lying above the threshold.

5. Significance

Unified Framework: The paper provides a unified theoretical language ("covalent," "creation," and "annihilation" bonds) to describe diverse exotic hadrons, bridging the gap between conventional quark models and molecular interpretations.
QCD Confinement Platform: These bonds are described as a "quasi-static low-energy platform" for studying QCD confinement. They highlight how the non-perturbative vacuum (sea quarks) plays a direct role in binding hadrons, distinct from electromagnetic interactions.
Mass Hierarchy Explanation: The mechanism successfully explains the mass difference between the isovector $Z_c(3900)$ and the isoscalar $X(3872)$ , attributing the lower mass of $X(3872)$ to the energy-lowering effect of the annihilation bond and charmonium mixing.
Experimental Guidance: The predictions for specific quantum numbers ( $J^{PC}$ ) and binding energies for $D^*\bar{D}^*$ and hidden-charm baryonium states offer concrete targets for future experiments at facilities like LHCb, Belle II, and BESIII.

In conclusion, Chen proposes that the strong interaction possesses unique binding mechanisms driven by the dynamic creation and annihilation of sea quark pairs, which are essential for understanding the spectrum and nature of exotic hadronic molecules.