Diffractive structure functions from JIMWLK evolution

This paper computes diffractive structure functions using JIMWLK evolution constrained by HERA vector meson data, comparing results to existing measurements and providing predictions for nuclear modification factors and diffractive-to-total cross-section ratios at the future Electron-Ion Collider (EIC).

The Gist

The Big Picture: Smashing Particles to See the Invisible

Imagine you are trying to figure out what a complex, invisible machine looks like. You can't open it up, so instead, you shoot tiny, high-speed marbles (electrons) at it. When the marbles hit the machine, they bounce off, and sometimes they knock a piece of the machine loose. By studying how the marbles bounce and what pieces fly off, you can build a mental map of the machine's interior.

In this paper, the "machine" is a proton (a building block of atoms) or a heavy gold nucleus. The "marbles" are electrons fired at incredibly high speeds. The scientists are specifically looking at a rare event called diffractive scattering.

The "Ghostly" Collision

Usually, when you smash two things together, they shatter into a chaotic mess of debris. But in diffractive scattering, something magical happens: the target (the proton or nucleus) stays completely intact, like a ghost passing through a wall, while a new, separate cloud of particles is created.

• The Analogy: Imagine throwing a tennis ball at a solid brick wall. In a normal crash, the wall crumbles. In this "diffractive" event, the ball hits the wall, and a small, separate cloud of dust appears in front of the wall, but the wall itself remains perfectly standing and doesn't even shake.
• The "Gap": Because the wall stays intact and the dust cloud flies off in a different direction, there is a huge empty space (a "rapidity gap") between the wall and the dust. This empty space is the signature that tells scientists, "Hey, this was a special, ghostly collision!"

The Tool: JIMWLK and the "Traffic Jam"

To predict how these collisions happen, the authors use a mathematical framework called JIMWLK evolution.

• The Analogy: Think of the inside of a proton not as a solid ball, but as a crowded dance floor filled with tiny, energetic dancers (gluons and quarks).
• The Problem: As you look at the proton with higher and higher energy (like zooming in with a super-microscope), you see more and more dancers. It gets so crowded that they start bumping into each other, creating a "traffic jam" or a "condensate."
• The Solution: The JIMWLK equation is like a sophisticated traffic control algorithm. It simulates how this crowd of dancers rearranges itself as the energy changes. The authors used this algorithm to simulate the proton's interior and predict what would happen when an electron hits it.

What They Did: Testing the Map

The team first tested their simulation against real data from the HERA lab in Germany, which ran similar experiments years ago.

• The Result: They compared their computer-generated "ghostly collisions" with the actual photos taken at HERA.
• The Verdict: The simulation matched the real data very well, especially for protons. This proved their "traffic control algorithm" (JIMWLK) was working correctly. They also looked at how the "size" of the interaction changed, finding that as the energy increased, the effective size of the proton's "dance floor" grew slightly, just as their math predicted.

The New Prediction: The Gold Nucleus

Once they were sure their map was accurate for a single proton, they applied it to something much bigger: a Gold nucleus (which is like a proton's massive cousin, packed with many more particles).

• The Prediction: They calculated what would happen if they shot electrons at a Gold nucleus at a future facility called the EIC (Electron-Ion Collider).
• The Finding: They predicted a strong suppression.
  • The Analogy: If hitting a single proton is like throwing a ball at a single dancer, hitting a Gold nucleus is like throwing a ball at a packed stadium of dancers. The authors found that the "ghostly" effect (the intact nucleus with a dust cloud) happens much less often in the Gold nucleus than you would expect if the dancers were just sitting there quietly.
  • Why? Because the "traffic jam" (saturation) is so dense in the Gold nucleus that the incoming electron gets blocked or scattered by multiple dancers at once before it can create that clean, ghostly separation. It's like trying to sneak a secret message through a crowded room; in a small room (proton), it's easy. In a packed stadium (Gold nucleus), the crowd swallows the message.

Summary

In short, this paper says:

1. We built a high-tech simulation (using JIMWLK) to understand how protons and nuclei behave when hit by electrons in a "ghostly" way where the target stays intact.
2. We checked our simulation against old data from HERA, and it worked perfectly.
3. We used this successful simulation to predict what will happen at the future EIC when they smash electrons into Gold nuclei.
4. The main takeaway: We predict that the "ghostly" collisions will be significantly weaker in Gold nuclei than in protons because the Gold nucleus is so crowded with particles that it disrupts the process. This gives scientists a specific target to look for when the EIC starts operating.

Technical Summary

Technical Summary: Diffractive Structure Functions from JIMWLK Evolution

Problem and Motivation
The primary objective of this work is to predict the dependence of diffractive structure functions on the momentum fraction carried by the pomeron ($x_{\mathbb{P}}$) using the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, and Kovner (JIMWLK) evolution equation. The authors aim to establish a baseline by comparing their results for the proton against combined HERA reduced cross-section data. The central goal is to extend these calculations to heavy nuclei, specifically providing predictions for the nuclear modification of diffractive structure functions for gold nuclei within the kinematic reach of the future Electron-Ion Collider (EIC).

Methodology
The study operates within the Color Glass Condensate (CGC) framework, where target color fields are treated as classical and described by Wilson lines. The methodology involves the following steps:

• Initial Conditions: The Wilson lines for the target nucleus are initialized on a transverse lattice using the IP-Glasma model. The initial geometry is constrained by fitting to exclusive $J/\psi$ production data from HERA, ensuring the setup contains no free parameters aside from quark masses.
• Evolution: The Wilson line configurations are evolved in rapidity ($y = \ln(1/x_{\mathbb{P}})$) using the JIMWLK equation, implemented via its Langevin formulation in the IP-Glasma code. The evolution accounts for the emission of gluons and the resulting non-linear dynamics.
• Cross Section Calculation: Diffractive deep inelastic scattering (DDIS) is modeled in the dipole picture. At leading order, a virtual photon fluctuates into a quark-antiquark ($q\bar{q}$) pair which interacts with the target's color field. The diffractive cross-section is calculated by squaring the scattering amplitude, which involves the trace of Wilson lines ($S_{01}$). The calculation includes both longitudinal and transverse photon polarizations and sums over quark flavors and helicities.
• Discretization: The general cross-section formula is discretized on a two-dimensional transverse lattice, incorporating ensemble averages over Wilson line configurations.

Key Contributions and Results

1. Proton Baseline Validation:

   • The authors computed the proton reduced cross-section ($x_{\mathbb{P}}\sigma_r^{D(3)}$) and compared it to HERA data. The $x_{\mathbb{P}}$ dependence derived from JIMWLK evolution is compatible with experimental data.
   • The slope parameter $B$, extracted from the $t$-spectrum of the cross-section (parametrized as $e^{-B|t|}$), shows an increase toward smaller $x_{\mathbb{P}}$. This is interpreted as an increase in the transverse size of the target color fields due to gluon radiation. The results align with H1 data, though the authors note the $Q^2$ evolution in their results is faster than observed in data, a systematic previously seen in inclusive $F_2$ calculations.

2. Nuclear Modification Predictions:

   • The paper presents the nuclear modification factor for the gold nucleus, defined as $F_{\lambda, \text{Au}}^{D(4)} / (A^2 \times F_{\lambda, \text{p}}^{D(4)})$.
   • The results indicate a strong nuclear suppression of the diffractive cross-section. This suppression is most pronounced for the transverse structure function, which dominates the cross-section in the studied kinematics.
   • The suppression is attributed to the transverse photon splitting into larger $q\bar{q}$ dipoles, which undergo non-linear multiple scattering. Consequently, the suppression is stronger at lower $Q^2$ values where the photon fluctuates into larger dipoles.

Significance and Claims
The authors claim that their setup, constrained by exclusive vector meson production data and utilizing JIMWLK evolution, successfully describes HERA reduced diffractive structure function data for the proton. The primary significance of the work lies in its predictive power for the EIC. Specifically, the paper provides predictions for:

• The nuclear modification factor for gold nuclei.
• The diffractive-to-total cross-section ratios (specifically the $eA$-to-$ep$ double ratio) in EIC kinematics.

The authors state that these predictions serve as a benchmark for future measurements at the EIC, allowing for the investigation of saturation effects and the geometry of the target-probe system in nuclear environments. The work does not propose new experimental setups but rather provides theoretical predictions to be tested against upcoming data.