Probing QCD instantons using jet correlation observables in proton-proton collisions at the LHC

This paper proposes jet correlation observables to unambiguously distinguish instanton-induced processes from perturbative QCD events in proton-proton collisions at the LHC, utilizing constraints derived from 2+1 flavor QCD calculations to guide future searches at the Electron-Ion Collider.

The Gist

The Big Picture: Hunting for "Quantum Ghosts"

Imagine the vacuum of space (the empty space between atoms) isn't actually empty. According to the theory of Quantum Chromodynamics (QCD)—which explains how the "glue" holds atoms together—this empty space is actually a bubbling, chaotic ocean of energy.

In this ocean, there are tiny, fleeting disturbances called Instantons. You can think of them as quantum ghosts or brief whirlpools that pop in and out of existence. They are special because they carry a "topological charge," meaning they twist the fabric of space in a way that normal physics doesn't usually allow.

The Problem: Scientists have been trying to catch a glimpse of these ghosts for decades. We know they should exist, but they are incredibly hard to spot because they look a lot like the "noise" of normal particle collisions. It's like trying to hear a specific whisper in a crowded stadium; the background noise drowns it out.

The New Strategy: Looking at the "Shape" of the Explosion

The authors of this paper propose a new way to find these ghosts at the Large Hadron Collider (LHC), where protons smash into each other at near-light speed.

Instead of just looking at how much energy is released, they propose looking at the shape of the debris (the "jets" of particles) flying out after the crash.

The Analogy: The Billiard Ball vs. The Firework

To understand their idea, imagine two different ways to break a pool table:

1. The Normal Crash (Perturbative QCD):
   Imagine hitting a billiard ball with a cue stick. The ball flies off in one direction, and the cue stick recoils in the exact opposite direction. If you smash two protons together normally, they usually spit out two jets of particles that fly back-to-back (180 degrees apart). It's a clean, predictable, two-way street.

2. The Instanton Crash:
   Now, imagine setting off a firework in the middle of the room. The explosion doesn't send things flying in just two directions; it sends sparks flying everywhere in a sphere. It's chaotic, round, and isotropic (the same in all directions).

The Hypothesis: The authors believe that when a "quantum ghost" (an instanton) is involved in a collision, it creates a firework-like explosion (isotropic spray of particles) rather than a billiard-ball recoil (back-to-back jets).

How They Tested It: The "Lattice" and the "Simulator"

To prove this, they did two main things:

1. The "Lattice" (Checking the Theory):
First, they used a supercomputer to simulate the QCD vacuum. Think of this as building a giant 3D grid (a lattice) of space and calculating exactly how big these "ghost whirlpools" are and how far apart they usually sit.

• The Result: They found that the ghosts are small and usually far enough apart that they don't interfere with each other too much. This confirmed that the "firework" theory is mathematically sound.

2. The "Simulator" (The Crash Test):
Next, they used a computer program (called SHERPA) to simulate millions of proton collisions at the LHC.

• Group A: They simulated normal collisions (the billiard balls).
• Group B: They simulated collisions where a "ghost" (instanton) was involved (the fireworks).

Then, they looked at the angle between the two biggest sprays of particles (jets) in each crash.

• Normal Collisions: The two big sprays were almost always pointing in opposite directions (180 degrees apart).
• Ghost Collisions: The two big sprays were scattered all over the place. There was no "opposite" direction.

The "Acoplanarity" Test: Measuring the Angle

The authors invented a specific measurement called Jet Acoplanarity.

• If the angle between the two jets is close to 180 degrees, it's a normal collision.
• If the angle is random and scattered, it's a candidate for an instanton collision.

They found that the "ghost" collisions looked completely different from the "normal" ones. The difference was so big that it wasn't just a fluke of the computer simulation; it was a clear signal.

Why This Matters

1. A New Way to Look: Previous searches for instantons failed because they were looking for the wrong things or the background noise was too loud. This paper suggests that looking at the geometry (the angles) of the debris is a much cleaner way to spot them.
2. Future Experiments: The authors say this method will work even better at the future Electron-Ion Collider (EIC). Imagine the LHC is a noisy, crowded party where it's hard to hear anything. The EIC will be a quiet library. If you can't find the ghost in the noisy party, you definitely have a better chance in the quiet library.
3. Understanding the Universe: Finding instantons would prove that the vacuum of space has these weird, twisted properties. It would help us understand why matter has mass and why the universe behaves the way it does.

Summary in One Sentence

The authors propose that instead of looking for a specific "sound" in the chaotic noise of particle collisions, we should look for a round, firework-like explosion of particles, which would be the unique signature of a mysterious "quantum ghost" (instanton) hiding in the vacuum of space.

Technical Summary

1. Problem Statement

The discovery of QCD instantons in collider experiments remains one of the most significant unfulfilled goals in high-energy physics. Instantons are non-perturbative, topological field configurations responsible for phenomena like chiral symmetry breaking and color confinement. While indirect evidence exists, direct observation has been elusive due to two main challenges:

• Theoretical Uncertainty: Previous searches (e.g., at HERA) relied on event generators using the "valley method," which assumes a dilute gas of instantons. However, the validity of this approximation in dynamical QCD with physical quark masses was not rigorously established.
• Experimental Background: Instanton-induced events are difficult to distinguish from the overwhelming background of standard perturbative Deep Inelastic Scattering (DIS) and multi-parton interactions (MPI). Existing search strategies relied on identifying high-multiplicity hadronic final states, but the signal-to-background ratio was poor.

The authors aim to propose a robust method to discriminate instanton-induced processes from perturbative QCD (pQCD) dijet events in $pp$ collisions at the LHC, utilizing specific jet correlation observables.

2. Methodology

The study employs a two-pronged approach combining first-principles Lattice QCD calculations with phenomenological event simulations.

A. Lattice QCD Constraints (Theoretical Foundation)

To validate the theoretical inputs required for event generators, the authors performed ab-initio lattice simulations:

• Setup: Simulations were conducted in 2+1 flavor QCD with physical quark masses (pion mass $\approx 135$ MeV, kaon mass $\approx 435$ MeV) on a $32^3 \times 8$ lattice at a temperature of 149 MeV (mimicking the hadronic phase).
• Technique: They utilized Overlap Fermions to preserve exact chiral symmetry on the lattice, allowing for the precise identification of topological charge via the Atiyah-Singer index theorem.
• Measurements:
  1. Instanton Size Distribution ($\rho$): Extracted by fitting the density of Dirac zero eigenmodes.
  2. Separation Distribution ($R$): Calculated by analyzing the distances between identified instanton ($I$) and anti-instanton ($\bar{I}$) peaks in the eigenmode spectrum.

B. Event Simulation and Observable Definition

Using the lattice-derived constraints, the authors simulated $pp$ collisions at $\sqrt{s} = 13$ TeV:

• Generators:
  • SHERPA: Used to simulate both instanton-induced processes (via the 't Hooft interaction vertex) and perturbative dijet backgrounds.
  • PYTHIA8: Used as a cross-check for perturbative dijet modeling (Detroit tune).
• Kinematic Cuts: Events were selected with a leading jet $p_T > 25$ GeV and a sub-leading jet $10 < p_T < p_{T,lead}$ GeV.
• Proposed Observables:
  1. Jet Acoplanarity ($\Delta\phi$): The azimuthal angle difference between the leading and sub-leading jets ($\Delta\phi = |\phi_L - \phi_{SL}|$).
  2. Harmonic Moment ($\langle \cos(2\Delta\phi) \rangle$): A quantitative measure of the back-to-back correlation strength.

3. Key Contributions

1. First Lattice Calculation with Physical Masses: The paper provides the first determination of instanton size and separation distributions in 2+1 flavor QCD with physical quark masses. This validates the "dilute gas" approximation for small instantons ($\rho \lesssim 0.5$ fm) even in the hadronic phase, confirming the theoretical basis for instanton perturbation theory in this regime.
2. Novel Discriminator: The authors propose jet acoplanarity and its harmonic moments as the primary discriminators. Unlike previous searches focusing on multiplicity, this method exploits the topological difference:
   • pQCD Dijets: Characterized by a $2 \to 2$ scattering topology, resulting in back-to-back jets ($\Delta\phi \approx \pi$).
   • Instanton Events: Characterized by an isotropic, multi-parton final state (fireball) lacking a preferred recoil axis, leading to a broad $\Delta\phi$ distribution.
3. Robustness Check: The study demonstrates that the signal separation is significantly larger than the systematic differences between different event generators (PYTHIA8 vs. SHERPA) and standard underlying event effects.

4. Results

• Lattice Findings:
  • The average instanton size is $\langle \rho \rangle \approx 0.65$ fm.
  • The distribution peaks at $\sim 0.65$ fm and drops rapidly for larger sizes.
  • The average separation between instanton-anti-instanton pairs is $\langle R \rangle \approx 2.43 \langle \rho \rangle$, confirming that for the relevant energy scales ($\sqrt{s'} = 50-100$ GeV), instantons are sufficiently separated to be treated perturbatively.
• Simulation Results:
  • Acoplanarity ($\Delta\phi$): Perturbative dijet events show a sharp peak near $\pi$ (back-to-back). In contrast, instanton-induced events exhibit a broad, flat distribution with a suppressed peak at $\pi$.
  • Harmonic Moment ($\langle \cos(2\Delta\phi) \rangle$): For pQCD dijets, this value approaches 1 as $p_T$ increases, indicating strong correlation. For instanton events, the value remains significantly suppressed (near 0) across the entire $p_T$ range, indicating an isotropic distribution.
  • Energy Dependence: The suppression of correlations is even more pronounced for $\sqrt{s'} = 100$ GeV compared to 50 GeV, consistent with the contribution of smaller, more numerous instantons.

5. Significance

• Experimental Feasibility: The proposed observables are directly measurable at the LHC using standard jet reconstruction algorithms (e.g., anti-$k_t$ with $R=0.3$). The method offers a "cleaner" probe than previous multiplicity-based searches because it targets the fundamental topological difference in event shape rather than just particle count.
• Future Applications: The strategy is explicitly highlighted as highly suitable for the Electron-Ion Collider (EIC). The cleaner lepton-hadron environment at the EIC, with reduced underlying events, would allow for an even more precise isolation of instanton-induced topologies.
• Theoretical Validation: By linking lattice QCD results directly to collider observables, the paper bridges the gap between non-perturbative vacuum structure and experimental high-energy physics, providing a concrete roadmap for the first potential discovery of QCD instantons in $pp$ collisions.