Diffractive open charm photoproduction in ultraperipheral lead-lead and proton-lead collisions at the LHC

This paper calculates diffractive $D^0$ photoproduction in ultraperipheral lead-lead and proton-lead collisions at the LHC using the G$\gamma$A--FONLL framework to quantify coherent contributions rejected by current neutron-tagged selections and to provide predictions for both inclusive and diffractive cross sections.

The Gist

Imagine the Large Hadron Collider (LHC) not just as a machine smashing particles together, but as a giant, high-speed light show. When massive lead ions (think of them as heavy, charged bowling balls) zoom past each other without actually hitting, they don't just pass by; they generate a blinding flash of light. In the world of physics, this light is made of "photons," and because the ions are moving so fast, these photons are incredibly powerful.

This paper is about what happens when these powerful flashes of light hit a lead nucleus, specifically looking for a type of heavy particle called "charm" (which eventually turns into a particle called a $D^0$). The authors are trying to solve a puzzle about how often this happens and, more importantly, how to spot the "special" cases where the lead nucleus stays perfectly intact after the hit.

Here is the breakdown of their work using everyday analogies:

1. The Setup: The "Ghost" Collision

Usually, when two heavy objects collide, they shatter into a million pieces. But in these "ultraperipheral collisions," the lead ions miss each other by a hair's breadth. They don't touch physically. Instead, the electromagnetic field of one ion shoots a photon at the other.

• The Analogy: Imagine two speeding trains passing each other on parallel tracks. They don't crash, but one train throws a glowing ball of energy (the photon) at the other train. The paper studies what happens when that ball hits the second train.

2. The Mystery: The "Intact" vs. "Broken" Target

The researchers are interested in two types of outcomes when the photon hits the lead nucleus:

• The "Smash" (Inclusive): The photon hits, creates a charm particle, and the lead nucleus gets shaken up or breaks apart. This is the standard, messy outcome.
• The "Ghost" (Diffractive): The photon hits, creates a charm particle, but the lead nucleus remains perfectly intact, like a ghost passing through a wall. In physics, this is called "diffraction." It leaves a huge empty space (a "rapidity gap") where no other debris is created.

The Problem: The experimentalists at the LHC (specifically the CMS experiment) have a rule for picking which events to study. They look for collisions where one side of the detector sees no neutrons (meaning the photon-emitting train didn't break) and the other side sees at least one neutron (meaning the target train broke).

• The Conflict: The "Ghost" events (where the target stays intact) are the most interesting for studying the structure of the nucleus, but the experimental rule rejects them because they don't see a neutron break on that side. The paper calculates exactly how many of these "Ghost" events are being thrown away by this rule.

3. The Tool: The "Shadow" Map

To predict how often these "Ghost" events happen, the authors use a theoretical framework called G$\gamma$A–FONLL.

• The Analogy: Think of the lead nucleus as a dense forest. To know how likely a photon is to hit a tree (a parton) and create a charm particle, you need a map of the forest.
• The Twist: In a normal forest, trees are scattered. But in a heavy nucleus, the trees (protons and neutrons) are so close together that they cast "shadows" on each other. This is called nuclear shadowing.
• The authors use a method called LTA (Leading Twist Shadowing) to draw a new map. This map accounts for the fact that the photon might interact with a tree, but that tree is "shadowed" by its neighbors, making the interaction different than if the tree were alone. They found that this shadowing effect is very strong—it suppresses the "Ghost" events significantly compared to what you'd expect if the nucleus were just a pile of loose particles.

4. The Results: Counting the Ghosts

The paper does two main things:

1. Lead-Lead Collisions (Pb-Pb): They calculated how many "Ghost" events (diffractive $D^0$ production) occur in lead-on-lead collisions. They found that while these events do happen, they are rare (only about 5% to 15% of the total events, depending on how strong the "shadowing" is). Crucially, they showed that the experimental rule requiring a neutron break on one side removes almost all of these "Ghost" events from the data. This means the current measurements are missing a specific, clean slice of physics.
2. Proton-Lead Collisions (p-Pb): They extended their study to collisions between a single proton and a lead ion. Here, the lead ion acts as the flashlight (emitting the photon) and the proton is the target. They predicted how often the proton stays intact (diffractive) versus how often it breaks (inclusive). This provides a new set of predictions for future experiments to test.

5. Why It Matters

The authors aren't just counting particles for fun. They are providing a "correction factor" for the scientists at the LHC.

• The Takeaway: If you look at the data the CMS experiment has collected, you are looking at a filtered view. The filter (the neutron rule) accidentally threw away the cleanest, most interesting "Ghost" events. This paper tells the experimentalists: "Here is exactly how many Ghost events you missed, and here is what they would have looked like."

In short, this paper is a detailed guidebook for understanding the "invisible" side of heavy-ion collisions, using the concept of shadows and light to explain how heavy nuclei behave when hit by a flash of energy, and helping scientists correct their data to see the full picture.

Technical Summary

Technical Summary: Diffractive Open Charm Photoproduction in Ultraperipheral Lead-Lead and Proton-Lead Collisions at the LHC

Problem Statement
Ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) serve as effective photon-hadron colliders, offering a unique probe of nuclear gluon densities at small momentum fractions ($x$). While inclusive open-charm photoproduction in Pb–Pb UPCs has been measured by the CMS collaboration, the experimental analysis employs a specific neutron-tagged event selection ($X_n0_n$). This selection requires zero neutrons in the zero-degree calorimeter (ZDC) on the photon-emitting side and at least one neutron on the target side.

This selection introduces a significant bias against coherent diffractive events. In coherent diffraction, the target nucleus remains intact after the hard scattering, failing the $X_n$ requirement unless it undergoes an additional, independent electromagnetic dissociation (breakup). Previous theoretical frameworks, such as the G$\gamma$A–FONLL model, accounted for electromagnetic dissociation but lacked a dedicated calculation of the diffractive fraction removed by the $X_n0_n$ condition. Consequently, there was no precise theoretical quantification of how much coherent diffraction was rejected from the measured inclusive sample. Furthermore, while diffractive open-charm production was studied at HERA in electron-proton collisions, a dedicated measurement and theoretical prediction for this channel in photon-nucleus collisions at the LHC were missing.

Methodology
The authors extend the G$\gamma$A–FONLL framework to calculate diffractive $D^0$ photoproduction in both Pb–Pb and proton-lead (p–Pb) UPCs. The methodology integrates several key components:

1. Framework Extension (G$\gamma$A–FONLL): The calculation combines the Fixed-Order Next-to-Leading Log (FONLL) formalism for heavy-quark production with nuclear parton distribution functions (PDFs) and UPC photon fluxes. The framework includes corrections for electromagnetic dissociation (EMD) to match experimental neutron-tagging criteria.
2. Diffractive PDFs:
   • For Protons: Diffractive PDFs are constrained by HERA data (H1 and ZEUS) using a two-component model (Pomeron and Reggeon exchanges) with Regge factorization.
   • For Nuclei: Nuclear diffractive PDFs are calculated using the Leading-Twist Shadowing Approach (LTA). This approach expresses nuclear diffractive PDFs as a Gribov–Glauber series of multiple coherent interactions with nucleons. The model accounts for nuclear attenuation, where the diffractively produced state $X$ undergoes elastic rescattering on the remaining nucleons. Two scenarios are considered: "low shadowing" and "high shadowing," corresponding to variations in the effective interaction cross-section $\sigma_{soft}$.
3. Photon Flux and Event Selection: The photon fluxes are parametrized using the Equivalent Photon Approximation (EPA) with realistic nuclear charge distributions. Crucially, the flux is corrected for specific neutron classes:
   • $AnAn$: No conditions on forward neutrons.
   • $An0n$: Zero neutrons on the photon-emitting side.
   • $X_n0_n$: Zero neutrons on the emitting side and at least one on the target side.
     The probability of electromagnetic breakup is modeled to determine the effective flux for the $X_n0_n$ class, explicitly quantifying the suppression of coherent diffractive events that do not undergo secondary breakup.
4. Kinematics: The calculation covers the kinematic range relevant to LHC measurements ($\sqrt{s_{NN}} = 5.36$ TeV for Pb–Pb), integrating over the diffractive momentum fraction $x_{\mathbb{P}}$ up to 0.1.

Key Contributions

• Quantification of Experimental Bias: The paper provides the first dedicated theoretical prediction for the coherent diffractive contribution to $D^0$ photoproduction in Pb–Pb UPCs. It explicitly calculates the fraction of diffractive events rejected by the $X_n0_n$ selection used in the CMS measurement, correcting a gap in previous inclusive predictions.
• Extension to p–Pb UPCs: The G$\gamma$A–FONLL framework is extended to proton-lead collisions, where the dominant configuration involves photon emission from the lead ion scattering off the proton. Predictions are provided for both inclusive and diffractive $D^0$ production in this system.
• Refined Flux Modeling: The authors improve the treatment of UPC photon fluxes by incorporating realistic nuclear charge distributions and explicitly modeling the suppression factors associated with different neutron-tagging classes ($An0n$ vs. $X_n0n$).
• Nuclear Shadowing Analysis: The study utilizes the LTA model to demonstrate the strong suppression of nuclear diffractive PDFs relative to the impulse approximation due to nuclear shadowing, contrasting this with saturation-based predictions.

Results

• Pb–Pb Collisions:
  • The diffractive cross section for $D^0$ production decreases with increasing rapidity ($y$) and transverse momentum ($p_T$).
  • The ratio of diffractive to inclusive production is largest at low $p_T$ and large positive rapidity (probing the smallest gluon $x$).
  • At $p_T = 2$ GeV, the diffractive fraction is approximately 5% in the "low shadowing" scenario and 10–15% in the "high shadowing" scenario. At $p_T = 8$ GeV, this fraction drops to a few percent.
  • The $X_n0_n$ selection significantly suppresses the inclusive cross section compared to the fully inclusive case, primarily because coherent diffractive events (where the nucleus stays intact) are excluded unless they undergo independent EMD.
• p–Pb Collisions:
  • Predictions for inclusive and diffractive $D^0$ production are presented, with the diffractive fraction evaluated using proton diffractive PDFs constrained by HERA.
  • The dominant configuration is identified as photon emission from the lead nucleus followed by $\gamma p$ scattering.
• Flux Suppression: The analysis of photon fluxes reveals that the $X_n0n$ selection leads to a strong suppression of the effective flux at small photon energy fractions ($z$), while the $An0n$ selection suppresses the flux more significantly at large $z$.

Significance
The paper establishes a necessary theoretical baseline for interpreting current and future LHC measurements of open-charm photoproduction. By quantifying the bias introduced by the $X_n0_n$ neutron-tagging requirement, the authors enable a more accurate extraction of inclusive cross sections from experimental data. Furthermore, the predictions for diffractive $D^0$ production in both Pb–Pb and p–Pb UPCs provide a unique opportunity to test nuclear diffractive parton distributions and the interplay between hard diffraction, coherent multiple scattering, and nuclear shadowing in a regime complementary to electron-ion facilities. The work highlights that while inclusive measurements are now available, dedicated measurements of the diffractive channel remain a critical open goal for understanding the gluonic structure of nuclei.