Hunting for QCD Instantons

Imagine the universe's most fundamental building blocks (quarks and gluons) are like a vast, churning ocean. Most of the time, we understand this ocean using standard waves and currents (what physicists call "perturbative" physics). But deep down, there are hidden, swirling whirlpools that don't follow the usual rules. These are called Instantons.

This paper is a "treasure hunt" guide. The authors, M. G. Ryskin and V. A. Khoze, are trying to figure out how to find these invisible whirlpools in the massive particle colliders we have today, like the Large Hadron Collider (LHC) and the NICA facility.

Here is the story of their hunt, broken down into simple concepts:

1. What is an Instanton?

Think of the vacuum of space (empty space) not as a blank canvas, but as a room with different "settings" or "modes."

The Tunnel Analogy: Usually, to get from one side of a hill to the other, you have to climb over it. In quantum physics, particles can sometimes "tunnel" through the hill. An instanton is the mathematical description of that tunnel.
The Sphaleron: If you have enough energy, you don't need to tunnel anymore; you can just jump over the hill. In the paper, they call this high-energy version a "sphaleron," but they mostly stick to the word "instanton" for simplicity.
The Signature: When an instanton happens, it's like a tiny, sudden explosion in the middle of the ocean. It doesn't shoot particles in a straight line (like a laser); instead, it sprays them out in a perfect sphere, like a dandelion seed puffing out in all directions.

2. The Problem: The "Noise" of the Party

The authors explain that finding these instantons is incredibly hard because the universe is very "noisy."

The Background Noise: In a particle collider, protons smash together constantly. Most of the time, they just create standard jets of particles that look like two streams of water shooting out in opposite directions (back-to-back).
The "Fireball" Confusion: Sometimes, multiple small collisions happen at once (called Multiple Parton Interactions). These can accidentally look like a sphere of particles, mimicking the instanton signal. It's like trying to hear a specific whisper in a crowded stadium; the crowd (background noise) is too loud.

3. How to Find the "Whirlpool" (The Signatures)

The authors propose two main ways to spot the instanton amidst the noise, using specific "clues."

Clue A: The Shape of the Explosion (Sphericity)

Normal Collisions: Usually, particles fly out in two opposite directions (like a dumbbell).
Instanton Collisions: Particles fly out in a ball (like a beach ball).
The Test: The authors suggest measuring the "sphericity" of the event. If the particles form a round ball rather than a dumbbell, it's a good sign.
The "Fireball" Trick: They also look for events with a huge number of small particles (high multiplicity) packed into a small area, but without any single giant, high-energy jet. It's like finding a room full of confetti rather than a few large rocks.

Clue B: The "Ghost" Gap (Diffractive Events)

The Strategy: They suggest looking for collisions where there is a huge empty space (a "rapidity gap") between the two sides of the explosion.
Why it works: In normal messy collisions, the "noise" (other particles) fills up the empty space. But instantons are special; they can happen without filling that gap. It's like finding a quiet room in a noisy house because the door was closed. This helps filter out the "multiple collision" noise.

Clue C: The Spin Dance (Spin-Spin Correlations)

The Spin: Particles have a property called "spin" (like a spinning top). In normal physics, if you start with a left-spinning particle, you usually end with a left-spinning one.
The Instanton Magic: Instantons break this rule. They can take a left-spinning particle and turn it into a right-spinning one.
The Experiment: At the NICA facility, they propose smashing polarized protons (protons spinning in a specific direction) together. If they see specific types of particles (hyperons like Sigma or Lambda) that have "flipped" their spin in a way that shouldn't happen normally, it's a strong hint that an instanton was there. It's like seeing a coin land on its edge when it should have landed heads or tails.

4. The Verdict

The paper concludes that while instantons have never been seen directly, they are theoretically crucial for understanding how the universe works (like why protons have mass).

At the LHC: They propose looking for "perfectly round" explosions of many small particles in empty gaps between other collisions.
At NICA: They propose looking for particles that have "flipped" their spin in a way that only an instanton could cause.

The Bottom Line: The authors are saying, "We know these invisible whirlpools exist in the math. We have a map (the signatures) and a strategy (filtering out the noise). Now we just need to look in the right place with the right tools to catch a glimpse of them."

Technical Summary: Hunting for QCD Instantons

Problem Statement
QCD instantons are non-perturbative classical solutions to Euclidean equations of motion in non-abelian gauge theories. They describe quantum tunneling between different vacuum sectors and are theoretically responsible for key aspects of low-energy strong interaction dynamics, including the breaking of $U(1)_A$ symmetry, spontaneous chiral symmetry breaking, and the formation of quark and gluon condensates. Despite their theoretical importance, instantons (or their high-energy counterparts, sphalerons) have never been experimentally observed. The primary challenge in detection is the suppression of the production cross-section for small-size instantons by the factor $\exp(-2\pi/\alpha_s)$ , while large-size instantons, though having larger cross-sections, emit few low-energy minijets that are difficult to distinguish from standard soft QCD processes.

Methodology and Signatures
The paper proposes identifying instanton production through specific event topologies that distinguish them from perturbative QCD (pQCD) backgrounds. The authors outline the following theoretical signatures and selection criteria:

Event Topology and Sphericity: Instanton production is modeled as the creation of a "fireball" emitting a large number of isotropically distributed minijets ( $N_{jet} \sim 1/\alpha_s$ ) and light quark-antiquark pairs ( $q\bar{q}$ ). Unlike pQCD dijet events which are back-to-back (low sphericity, $S \approx 0$ ), instanton events are expected to exhibit high sphericity ( $S \to 1$ ). The sphericity $S$ is calculated using the eigenvalues of the momentum tensor $S_{\alpha\beta}$ .
Chirality Violation and Spin Correlations: Instanton processes violate light quark helicity conservation due to the chiral anomaly. The process $g + g \to n_g \times g + \sum (q_R + \bar{q}_L)$ produces correlated chiralities ( $q_R$ and $\bar{q}_L$ ). This is distinct from pQCD where helicity is generally conserved.
Displaced Vertices: The production of additional heavy quark pairs (specifically $c\bar{c}$ if $m_c < 1/\rho$ ) leads to displaced vertices from charmed hadron decays.
Diffractive Selection (LRG): To suppress the dominant background from Multiple Parton Interactions (MPI) which mimic the "fireball" topology, the authors propose searching in diffractive events characterized by Large Rapidity Gaps (LRG). MPI processes involve color flow that fills rapidity gaps, whereas instanton production in a diffractive channel (via Pomeron exchange) preserves the gap.
Spin-Spin Correlations at NICA: For low-mass (large-size) instantons, the paper suggests studying spin-spin correlations in polarized proton collisions ( $p^\uparrow + p \to \Sigma + X$ ) at the NICA facility. The instanton mechanism is predicted to double the incoming polarization and produce specific hyperon polarization states (e.g., right-handed $\Lambda$ and left-handed $\bar{\Lambda}$ ) that differ from standard pQCD expectations.

Key Contributions and Results

Background Suppression Strategy: The authors demonstrate that while MPI backgrounds produce high sphericity, they can be effectively suppressed by selecting events with Large Rapidity Gaps. The survival probability of the gap ( $S^2 \le 0.1$ ) suppresses the probability of observing $n$ additional MPI branches by $(S^2)^n$ .
Selection Criteria for LHC: A specific selection strategy for the LHC ( $\sqrt{s} = 13$ $s = 13$ TeV) is proposed:
- Charged particle multiplicity $N_{ch} > 20$ .
- Total transverse energy $\sum E_{Ti} > 15$ GeV within the rapidity interval $0 < \eta < 2$ .
- Exclusion of high- $E_T$ jets ( $p_{Ti} > 2$ GeV) to ensure the event is not a standard hard scattering.
- Under these conditions, the instanton signal (predicted elementary cross-section $\sim 1 \mu$ b) is expected to exceed the background by a significant margin, resulting in a signal cross-section of approximately 1 nb.
Sphericity Analysis: Simulations indicate that for instanton masses $M_I = 20-40$ GeV, there is an expected $\sim 75\%$ excess of events with sphericity $S > 0.85$ compared to the background (modeled by PYTHIA8).
Hyperon Polarization: At NICA, the paper estimates a cross-section of $\sim 1 \mu$ b for large-size instanton production leading to hyperon pairs. The observation of specific spin correlations (e.g., in $\Sigma$ hyperons containing vector diquarks) could serve as a unique signature.

Significance and Claims
The paper asserts that observing QCD instantons is crucial to confirming the existence of multiple equivalent vacuum sectors in QCD. If instantons do not exist, the theory must be restricted to fields decreasing faster than $1/x$ at infinity, forbidding the instanton solution.

The authors maintain a modest tone regarding the experimental feasibility:

They acknowledge that previous searches at HERA were unsuccessful and that distinguishing small-size instantons from soft QCD processes remains "challenging."
They note that the sphericity excess observed in sphaleron models is "within the uncertainty of the model" because general-purpose Monte Carlo generators are not tuned for such exotic events.
They emphasize that to be certain of an instanton observation, at least two signatures (e.g., high sphericity combined with displaced vertices or spin correlations) must be used simultaneously.
The paper concludes that while the signal cross-section after selection is small (1 nb at LHC), the unique topological and spin properties offer a viable, albeit difficult, path to discovery, potentially aided by future facilities like the Electron-Ion Collider or NICA.