LHC di-dijet excesses as signals of fourth-generation tetraquarks

This paper proposes that LHC di-dijet excesses observed at various invariant masses are signals of fourth-generation tetraquarks composed of four $b'$ quarks, where resonant and non-resonant production mechanisms involving color-octet bound states explain the data as a TeV-scale analog of fully charmed tetraquark searches.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Scientists smash protons together at incredible speeds to see what tiny fragments fly out. Usually, these fragments follow a predictable pattern, like raindrops falling in a steady rhythm. But recently, the detectors at the LHC (specifically the ATLAS and CMS experiments) noticed something strange: unexpected "clumps" of energy.

These clumps appeared as groups of four jets (sprays of particles) with specific masses. Some clumps were huge (around 8 TeV), some were medium-sized (around 3.6 TeV), and they kept showing up more often than the standard rules of physics predicted. It was like hearing a specific, unusual note played on a piano in a room full of random noise.

This paper, written by physicist Hsiang-nan Li, proposes a bold explanation for these strange notes: They are the sound of a new, heavy family of particles forming a "tetraquark" (a four-particle molecule).

Here is the breakdown of the idea, using simple analogies:

1. The Missing Family Member: The "Fourth-Generation" Quark

In our standard understanding of the universe, matter is built from three "generations" of quarks (like up, down, charm, strange, top, and bottom). Think of these as three floors of an apartment building.

• The Idea: The author suggests there is a fourth floor we haven't seen yet. On this floor lives a super-heavy quark called $b'$ (b-prime).
• The Weight: This $b'$ quark is incredibly heavy—about 2,000 times heavier than a proton (2 TeV). Because it's so heavy, it's hard to create, but when the LHC smashes protons hard enough, it might pop into existence.

2. The "Molecular" Formation: The Tetraquark

When the LHC creates these heavy $b'$ quarks, they don't just float away alone. They are attracted to each other by a force similar to how magnets stick together, but in this case, it's a force mediated by the Higgs boson (the particle that gives other particles mass).

• The Analogy: Imagine four heavy magnets ($b'$ quarks) thrown into a room. Instead of bouncing off each other, they snap together to form a tight, four-magnet cluster.
• The Result: This cluster is called a tetraquark ($b'b'\bar{b}'\bar{b}'$). It's a "super-molecule" made of four heavy quarks.

3. The Two Types of "Clumps" (Resonances)

The paper explains the different sizes of the energy clumps seen at the LHC by looking at how these tetraquarks are formed and how they break apart.

The "Big Boom" (8 TeV Signal)

• What happened: The LHC created a massive tetraquark resonance (a vibrating, excited state of the four-quark molecule).
• The Breakup: This heavy molecule didn't just fall apart randomly. It split into two smaller pairs.
• The Analogy: Imagine a large, heavy drum (the 8 TeV tetraquark) being hit. It doesn't just shatter; it splits cleanly into two smaller, heavy drums (each about 2 TeV).
• The Physics: These smaller drums are "excited states" of a $b'$ and an anti-$b'$ pair. They are like a guitar string vibrating at a high pitch (the first excited state). These smaller drums then decay into jets of particles, creating the "di-dijet" signal (two pairs of jets).

The "Smaller Clump" (3.6 TeV Signal)

• What happened: Here, the four quarks were produced, but not as a single, tight, vibrating resonance. They were produced more loosely.
• The Breakup: They formed two pairs of $b'$ and anti-$b'$, but these were in their lowest energy state (the "ground state").
• The Analogy: Instead of a vibrating drum, imagine two heavy bowling balls rolling together gently. They are still a pair, but they aren't "excited" or vibrating wildly.
• The Physics: These ground-state pairs are lighter (about 0.95 TeV). When they decay, they create the 3.6 TeV signal.

4. The "Tea-Scale" vs. "GeV-Scale" Connection

The author makes a fascinating comparison to help us understand this.

• The GeV Scale (The Small Version): Recently, scientists found a particle called X(6900). This is a tetraquark made of four charm quarks (which are much lighter). It was found by looking at four muons (a type of particle) produced when the X(6900) decayed.
• The TeV Scale (The Big Version): The author is saying, "What we are seeing at the LHC with the heavy $b'$ quarks is just the heavy, giant version of that X(6900) discovery."
  • If X(6900) is a small toy car, the new $b'$ tetraquark is a massive semi-truck. They are built the same way, just with much heavier parts.

5. Why This Matters (The "No Free Parameters" Rule)

In physics, it's easy to make up a theory by adding new numbers (parameters) until the math fits the data. This is like trying to tune a radio by guessing every single frequency.

• The Author's Claim: This theory is special because it doesn't need to guess any numbers. The mass of the $b'$ quark and how it interacts are already predicted by a specific mathematical framework (the "Sequential Fourth Generation" model).
• The Result: When the author plugged these known numbers into the equations, the predicted signals matched the weird clumps the LHC saw perfectly. It's as if the theory predicted the exact notes the piano would play before anyone even heard them.

Summary

The paper suggests that the strange, unexplained energy spikes at the LHC are actually the fingerprints of a new, super-heavy family of particles (fourth-generation quarks) forming four-particle molecules (tetraquarks).

• The 8 TeV signal is a heavy, vibrating molecule breaking into two excited pairs.
• The 3.6 TeV signal is a looser collection of molecules breaking into two calm, ground-state pairs.

It's a "Tea-scale" (heavy) version of a discovery already made at the "Ge-scale" (light), suggesting that the universe might have a hidden, heavier floor of matter waiting for us to find it.

Technical Summary

1. Problem Statement

The paper addresses several anomalous excesses of di-dijet events (events with four jets) observed by the ATLAS and CMS collaborations at the Large Hadron Collider (LHC). These excesses appear at specific invariant mass scales that current Standard Model (SM) backgrounds cannot explain:

• Resonant Excesses:
  • A four-jet mass ($m_{4j}$) of $\approx 8$ TeV with two dijet resonances ($m_{2j}$) of $\approx 2$ TeV (observed by CMS).
  • Events at $m_{4j} = 6.6$ TeV and $5.8$ TeV with $m_{2j} \approx 2$ TeV (observed by ATLAS and CMS).
• Non-Resonant Excess:
  • A four-jet mass of $\approx 3.6$ TeV with dijet resonances of $\approx 0.95$ TeV (observed by CMS).

Existing theoretical models (e.g., color-sextet diquarks, supersymmetry, heavy gluons) have failed to provide a comprehensive explanation that accommodates all these resonance masses simultaneously. The author proposes that these excesses are signatures of fourth-generation quarks ($b'$) forming bound states (tetraquarks and mesons) mediated by a Yukawa potential generated by Higgs boson exchanges.

2. Methodology

The author employs a multi-faceted theoretical approach combining the Sequential Fourth Generation Model (SM4) with Effective Field Theory (EFT) matching:

• SM4 Framework: The study assumes a fourth generation of quarks where the $b'$ quark has a mass $m_{b'} \approx 2.0$ TeV at the TeV scale. This mass is derived from renormalization group (RG) evolution of Yukawa couplings.
• Bound State Spectrum Calculation:
  • The $b'\bar{b}'$ system is modeled using a Yukawa potential $V(r) = -\alpha_Y \frac{e^{-m_H^* r}}{r}$, where $\alpha_Y$ is determined by the $b'$ Yukawa coupling and $m_H^*$ is the Higgs mass.
  • Unlike previous non-relativistic Schrödinger approaches (which suffer from Thomas collapse for heavy fermions), the author uses a relativistic formalism based on the Dirac equation to calculate the mass spectrum of $b'\bar{b}'$ bound states.
  • A spin-symmetry parameter ($C_s$) is tuned to match the observed dijet masses, predicting a ground state and an excited state.
• Effective Theory Matching:
  • To avoid complex multi-loop simulations of the full SM4, the author maps the full theory (involving four $b'$ quarks) to effective theories containing color-octet scalars ($\Theta$) and color-octet vectors (colorons, $Y$).
  • Resonant Channel ($m_{4j} \approx 8$ TeV): The process $q\bar{q} \to Y \to \Theta\Theta \to (jj)(jj)$ is matched to the full theory diagram involving virtual gluons and Higgs bosons splitting into $b'$ pairs.
  • Non-Resonant Channel ($m_{4j} \approx 3.6$ TeV): The process is interpreted as non-resonant production via a virtual coloron, matched to the same full theory diagrams but with different kinematic configurations.
• Cross-Section Scaling: The effective couplings derived from the matching are used to scale existing literature results (e.g., from Dobrescu et al.) to predict event rates consistent with LHC luminosity.

3. Key Contributions

• Unified Interpretation: The paper provides a single theoretical framework (SM4 with $b'$ tetraquarks) that explains both the high-mass resonant excesses ($\approx 8$ TeV) and the lower-mass non-resonant excess ($\approx 3.6$ TeV).
• Relativistic Bound State Spectrum: It demonstrates that a $b'\bar{b}'$ system in a Yukawa potential naturally generates the required mass spectrum:
  • Ground State ($n=1$): A color-octet vector with mass $\approx 0.94$ TeV (matching the $0.95$ TeV dijet resonance).
  • First Excited State ($n=2$): A color-octet scalar with mass $\approx 2.1$ TeV (matching the $2$ TeV dijet resonance).
• Analogy to X(6900): The author draws a compelling parallel between these TeV-scale $b'$ tetraquarks and the GeV-scale fully charmed tetraquark $X(6900)$ observed by LHCb, suggesting a universal mechanism for heavy fermion bound states across energy scales.
• Rejection of Di-quark Models: The paper argues that di-quark scalar models are disfavored in this context because the required $u \to b'$ transition is heavily suppressed by the small CKM matrix element $V_{ub'}$.

4. Results

• Mass Spectrum Verification: Solving the relativistic Dirac equation with the Yukawa potential yields:
  • Ground state mass ($m_1$): 0.94 TeV (Color-octet vector).
  • First excited state mass ($m_2$): 2.1 TeV (Color-octet scalar).
  • These values align precisely with the dijet masses observed in the LHC excesses.
• Effective Coupling Determination:
  • For the resonant channel ($8$ TeV), the matching yields an effective coupling $g' \approx 2.8 g_s$ (where $g_s$ is the strong coupling). This amplifies the cross-section by a factor of $\approx 60$, bringing the predicted event count ($\approx 1.3$ events in $138 \text{ fb}^{-1}$) in line with the CMS observation.
  • For the non-resonant channel ($3.6$ TeV), the matching suggests an effective coupling $g'' \approx 0.31$. The paper posits that the mediator is a virtual (off-shell) coloron of mass $8$ TeV. The suppression from the off-shell propagator ($3.6^2/8^2 \approx 0.2$) compensates for the coupling enhancement, resulting in a cross-section consistent with the observed excess.
• Event Interpretation:
  • $m_{4j} \approx 8$ TeV: Resonant production of a $b'b'\bar{b}'\bar{b}'$ tetraquark decaying into two excited $b'\bar{b}'$ states (scalars).
  • $m_{4j} \approx 3.6$ TeV: Non-resonant production of a $b'b'\bar{b}'\bar{b}'$ system decaying into two ground-state $b'\bar{b}'$ pairs (vectors).
  • $m_{4j} \approx 6.6/5.8$ TeV: Likely lower-lying tetraquark states decaying into mixed ground/excited states.

5. Significance

• New Physics Evidence: If confirmed, this would be the first evidence of a fourth generation of quarks and the existence of stable or long-lived tetraquarks composed of superheavy quarks.
• Theoretical Economy: The SM4 model is presented as the "most economical" extension of the Standard Model, requiring no new free parameters (masses and couplings are fixed by dispersion relations and RG evolution).
• Resolution of Anomalies: It offers a coherent solution to multiple disparate LHC anomalies that have previously been explained by disjointed models.
• Phenomenological Bridge: The work bridges the gap between high-energy collider physics and the spectroscopy of heavy bound states, suggesting that the search for tetraquarks should extend from the GeV scale (charm/bottom) to the TeV scale (fourth generation).

In conclusion, the paper proposes that the LHC di-dijet excesses are not statistical flukes or artifacts of specific BSM models like SUSY, but rather the resonant and non-resonant signatures of a fourth-generation quark sector forming bound states via Higgs-mediated Yukawa interactions.