Evidence for BSM spin 0 and spin 2 resonances at LHC Possible Interpretations

This paper interprets nine statistically significant LHC decay channels around 650 GeV as evidence for a sequence of spin-2 Kaluza-Klein graviton resonances (specifically T690) and potential spin-0 scalars within a composite or Randall-Sundrum framework, suggesting that these findings support the case for future high-luminosity $e^+e^-$ colliders to produce and study these new particles.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed particle smasher. Scientists have been throwing protons together for years, looking for "new physics"—particles that don't fit into our current rulebook (the Standard Model).

This paper, written by physicists Alain Le Yaouanc and François Richard, is like a detective story. They are saying: "We think we've found a whole new neighborhood of particles hiding in the data, but we've been looking for them with the wrong magnifying glass."

Here is the story of their discovery, broken down into simple concepts and analogies.

1. The "Ghost" at 650 GeV

For a long time, the LHC has been seeing strange "bumps" or excesses of energy around 650 GeV (a unit of mass). It's like hearing a faint hum in a noisy room. Sometimes it's there, sometimes it's not.

The authors argue that this isn't just random noise. They believe there are actually two distinct particles living right next to each other in this energy zone:

• H650: A "heavy scalar" particle (think of it as a standard, round ball).
• T690: A "spin-2 tensor" particle. This is the star of the show. Think of it not as a ball, but as a spinning, wobbling top or a complex geometric shape that behaves very differently from a ball.

2. The "Spin-2" Mystery: Why the Signal Disappears

The biggest clue that T690 is a "spin-2" particle (a type of particle predicted by theories involving extra dimensions) comes from a game of "hide and seek."

• The Setup: The LHC experiments (ATLAS and CMS) usually look for new particles by filtering out background noise. They use specific "cuts" (rules) designed to catch standard, round particles (scalars).
• The Trick: When the scientists applied these standard rules to the 650 GeV data, the signal vanished.
• The Analogy: Imagine you are looking for a soccer ball (scalar) in a field. You use a net with round holes. If you throw a spinning top (spin-2) at the net, it might slip right through the holes because of how it's shaped and moving.
• The Discovery: The authors realized that the signal only appears when they stop looking for soccer balls and start looking for spinning tops. When they changed their search criteria to match the "wobble" of a spin-2 particle, the signal popped back up, especially in a production method called VBF (Vector Boson Fusion).

3. The "Kaluza-Klein" Graviton: A Particle from Another Dimension

The authors propose that T690 is a Kaluza-Klein (KK) Graviton.

• The Analogy: Imagine our universe is a 3D sheet of paper. The theory of Randall-Sundrum (RS) suggests there is a hidden 5th dimension, like a thick book.
• The Resonance: Just as a guitar string can vibrate at different notes (fundamental, octave, etc.), particles moving in this extra dimension can vibrate at different "frequencies" or masses.
• The Sequence: The authors found evidence for a whole family of these particles, like a musical scale:
  • T376: The low note (376 GeV).
  • T690: The middle note (690 GeV).
  • T1000: The high note (1000 GeV).
    The fact that these three masses fit the mathematical pattern of a vibrating string in extra dimensions is their strongest evidence.

4. The "Composite" Twist: Why It's Not a Standard Graviton

Standard theory says these gravitons should love to interact with gluons (the glue holding atoms together). If they did, we would have seen them easily years ago. But we didn't.

• The Puzzle: T690 seems to ignore gluons completely but loves to talk to electrons and photons.
• The Solution: The authors suggest these aren't "elementary" particles (like a single point). Instead, they might be composite particles—like a molecule made of smaller parts.
• The Analogy: Imagine a ghost made of "invisible" parts. If the parts are "colorless" (they don't interact with the strong nuclear force/gluons), the ghost can pass right through the "glue" of the atom. But because the parts are "charged," the ghost can still interact with light and electricity. This explains why the particle is hard to find but shows up in electron/positron collisions.

5. The "Deficit" vs. The "Bump"

Usually, when scientists look for new particles, they look for a "bump" in the data (a spike where there shouldn't be one).

• The Problem: For heavy particles decaying into Top Quarks (the heaviest known particles), the math gets weird. The new particle interferes with the background noise in a way that creates a dip or a deficit instead of a bump.
• The Analogy: Imagine you are trying to hear a new singer in a choir. Instead of the singer making the sound louder, their voice cancels out the choir's sound in a specific spot, making that spot quieter.
• The Insight: The authors argue that previous searches missed these particles because they were only looking for "louder" spots (bumps), not "quieter" spots (deficits). They found evidence of this "quiet spot" around 490 GeV and 650 GeV.

6. The Future: Building a "Factory"

The paper concludes with a bold proposal for the future.

• The Problem: The LHC is messy. It's like trying to find a specific needle in a haystack while the hay is on fire.
• The Solution: Build a Future Electron-Positron Collider (a "GigaFactory").
• Why? If we tune a collider to exactly 690 GeV, we wouldn't just find one T690 particle. Because of the high precision and the particle's specific coupling to electrons, we could produce billions of them.
• The Payoff: This would allow us to study these "extra-dimensional gravitons" in perfect detail, confirming if they are indeed the keys to understanding gravity, dark matter, and the structure of the universe.

Summary

The authors are saying: "We think we've found a family of heavy, spinning particles from extra dimensions hiding in the LHC data. They are tricky because they don't look like the particles we usually search for, and they hide by making the data look 'quieter' rather than 'louder.' If we build a cleaner, more precise machine tuned to their specific frequency, we can finally catch them and prove that our universe has hidden extra dimensions."

Technical Summary

1. Problem Statement

The paper addresses the challenge of interpreting a cluster of statistically significant excesses observed in LHC data (ATLAS and CMS) around the 650 GeV mass region. Standard searches for Beyond the Standard Model (BSM) physics often rely on "bump hunting" (looking for local excesses over a smooth background). However, the authors argue that:

• Standard interpretations (e.g., heavy scalars in 2HDM or standard Randall-Sundrum (RS) gravitons) fail to explain the specific combination of decay channels, production mechanisms, and angular distributions observed.
• Conventional search strategies for heavy resonances decaying to top pairs ($t\bar{t}$) are flawed because they ignore interference effects between the signal and the QCD background, which can turn a resonance "bump" into a "deficit."
• There is a lack of a unified framework that accommodates the observed tensor (spin-2) and scalar (spin-0) candidates, their specific couplings (e.g., to $e^+e^-$ but suppressed to gluons), and the perturbative unitarity requirements of the $WW/ZZ$ sector.

2. Methodology

The authors employ a multi-faceted approach combining phenomenological analysis, model re-interpretation, and statistical combination:

• Data Re-analysis: They re-examine existing LHC results (Run 2 and early Run 3) across nine specific decay channels: $ZZ \to 4\ell$, $WW \to \ell\nu\ell\nu$, $e^+e^-$, $\gamma\gamma$, $hh$, $t\bar{t}$, and dijet resonances.
• Angular Distribution Analysis: They utilize the angular distributions of final states to distinguish between spin-0 (scalar) and spin-2 (tensor) hypotheses. Specifically, they analyze how signals behave under Vector Boson Fusion (VBF) versus Gluon-Gluon Fusion (ggF) selections.
• Interference Modeling: For the $t\bar{t}$ channel, they incorporate the complex interference between the BSM signal (via top loops) and the QCD continuum, explaining why standard "bump" searches fail to see heavy scalars/tensors in this channel.
• Model Construction:
  • Randall-Sundrum (RS) Extension: They propose a modified RS model where the Kaluza-Klein (KK) gravitons are composite particles made of colorless partons. This explains the suppression of the $gg$ coupling and the enhancement of the $e^+e^-$ coupling.
  • Three-Higgs-Doublet Model (3HDM): They integrate the scalar sector using a Weinberg-inspired 3HDM to explain the scalar candidates ($H_{650}$, $A_{490}$).
  • Perturbative Unitarity: They invoke the existence of charged tensor resonances ($T^+, T^{++}$) forming an Isospin $I=2$ multiplet to satisfy unitarity sum rules in the $WW/ZZ$ scattering sector.

3. Key Contributions

A. Identification of Two Nearby Resonances

The authors argue that the "650 GeV" region actually contains two distinct resonances:

1. $T_{690}$ (Spin-2 Tensor): A KK graviton-like resonance with mass $\approx 690$ GeV and width $\Gamma \approx 20$ GeV.
   • Key Feature: It is primarily produced via VBF, not ggF. This explains why the signal disappears when ATLAS/CMS apply scalar-optimized angular cuts (which suppress VBF).
   • Couplings: It has a significant branching ratio to $e^+e^-$ ($\sim 0.25\%$) and $ZZ/WW$, but a negligible coupling to gluons (contradicting standard RS predictions).
2. $H_{650}$ (Spin-0 Scalar): A wide scalar resonance contributing to channels with poor mass resolution (e.g., $t\bar{t}$, $hh$). It decouples from $WW/ZZ$ but couples to top pairs.

B. Resolution of the $t\bar{t}$ Search Paradox

The paper explains why heavy resonances ($A_{490}$, $H_{650}$) are not seen as bumps in $t\bar{t}$ mass distributions.

• Mechanism: The top-loop contribution to ggF production introduces a large imaginary part in the amplitude. When interfering with the real QCD background, this creates a destructive interference (deficit) rather than an excess near the resonance mass.
• Result: This explains the "deficits" observed by ATLAS and CMS in the 700–850 GeV region, which are actually signatures of $H_{650}$ and $A_{490}$.

C. The "Composite" KK Graviton Hypothesis

To reconcile the RS mass predictions with the observed lack of $gg$ coupling, the authors propose that $T_{690}$ is a composite state of colorless, charged partons.

• This explains the suppression of the $gg$ mode (no colored partons).
• It explains the enhanced $e^+e^-$ coupling (charged partons).
• It allows the particle to fit within the RS mass spectrum ($T_{376}, T_{690}, T_{1000}$) while evading standard exclusion limits.

D. Prediction of Charged Tensor Multiplets

To satisfy perturbative unitarity in $WW/ZZ$ scattering, the model predicts an Isospin $I=2$ multiplet including charged tensors $T^+$ and $T^{++}$.

• Evidence is cited for $T^{++}$ in $W^+W^+$ channels and $T^+$ in $ZW$ channels.
• These states are necessary to cancel amplitude growth at high energies, a feature not present in standard scalar models.

4. Key Results

• Statistical Significance: Combining nine independent channels (including $ZZ$, $WW$, $e^+e^-$, $\gamma\gamma$, $t\bar{t}$, etc.), the authors estimate a local significance of 6.3$\sigma$ and a global significance of ~6$\sigma$ for the presence of new physics in the 600–750 GeV range.
• Mass Spectrum Consistency: The observed masses fit the RS prediction for KK graviton recurrences:
  • $T_{376}$ (predicted 376 GeV, observed in $hh$, $ZZ$, $T_{690} \to T_{376}h$).
  • $T_{690}$ (observed 690 GeV).
  • $T_{1000}$ (predicted 1000 GeV, hinted in $hh$ channel).
• RS Parameters: The data yields consistent RS parameters: $k/M_{Pl} \approx 0.90$ and $kR \approx 11.98$, matching theoretical stabilization requirements.
• Top Loop Effects: The analysis confirms that $A_{490}$ and $H_{650}$ are likely present in $t\bar{t}$ data but obscured by interference, requiring a re-interpretation of exclusion limits on $g_{Htt}$ and $g_{Att}$.
• Dark Matter Connection: The $T_{1000}$ resonance is proposed as a mediator for Dark Matter annihilation ($\chi\chi \to T_{1000} \to ZZ/WW$), potentially explaining the Fermi-LAT 20 GeV gamma-ray excess.

5. Significance and Future Prospects

• Paradigm Shift: The paper challenges the standard "bump hunting" methodology for heavy resonances, emphasizing the critical role of interference effects and angular analysis (VBF vs. ggF).
• Collider Strategy:
  • LHC (Run 3/HL-LHC): Needs to re-analyze $t\bar{t}$ and $ZZ$ data with spin-2 hypotheses and VBF selections. Confirmation of the $T^{++}$ and $T^+$ charged states is crucial.
  • Future Lepton Colliders ($e^+e^-$): The authors argue that a 1.5 TeV $e^+e^-$ collider is the "smoking gun" for this scenario.
    • The large $e^+e^-$ coupling of $T_{690}$ ($BR \sim 0.25\%$) implies a massive production cross-section ($\sim 150$ pb at resonance).
    • A "Gigafactory" at 690 GeV could produce $10^9$ events, allowing precise measurement of the KK sequence ($T_{376}, T_{690}, T_{1000}$) and confirming the RS/composite nature.
• Theoretical Synthesis: The work suggests a "Theory of Everything" (TOE) approach where SUSY (explaining the scalar sector and Higgs mass), Extra Dimensions (RS model for gravitons), and Compositeness (explaining the coupling hierarchy) are not mutually exclusive but complementary.

Conclusion: The authors present a coherent, albeit non-standard, interpretation of LHC anomalies suggesting a rich BSM spectrum dominated by a composite KK graviton ($T_{690}$) and associated scalars. They posit that the absence of standard RS signatures (like strong $gg$ coupling) is due to the composite nature of the graviton, and that future high-energy lepton colliders are essential to definitively prove this hypothesis.