Inclusive heavy meson photoproduction in $pPb$ and $PbPb$ collisions

This paper investigates inclusive heavy meson ($B^0$ and $D^0$) photoproduction in ultraperipheral $pPb$ and $PbPb$ collisions at LHC energies using the color dipole formalism with various unintegrated gluon distribution models, presenting first-time predictions for $B^0$ mesons and demonstrating that future experimental data will significantly constrain high-energy hadronic structure descriptions.

The Gist

Imagine you are trying to understand the internal structure of a giant, complex machine (like a car engine or a human cell), but you can't take it apart. Instead, you shine a very bright, high-powered flashlight at it from a distance and watch what flies off. By studying the debris, you can figure out how the machine is built inside.

This paper is about doing exactly that, but with the "machines" being atomic nuclei (the cores of atoms) and the "flashlight" being a beam of light (photons) created by smashing heavy atoms together at nearly the speed of light.

Here is a breakdown of the paper's story, using simple analogies:

1. The Setup: The "Giant Billiard" Game

The scientists are looking at collisions at the Large Hadron Collider (LHC). They aren't smashing the atoms head-on (which would be like crashing two cars together). Instead, they are doing Ultraperipheral Collisions.

• The Analogy: Imagine two massive trucks driving past each other on a highway at incredible speed, but they don't touch. However, because they are so big and moving so fast, they create a massive electromagnetic "wind" (a flash of light).
• The Result: This flash of light hits the other truck. It's like a photon (a particle of light) hitting a nucleus. This interaction is gentle enough that the trucks don't shatter, but the light is so powerful it knocks out tiny, heavy pieces from inside the nucleus.

2. The Target: Finding the "Heavy Mesons"

When the light hits the nucleus, it creates heavy particles called Heavy Mesons (specifically $D^0$ and $B^0$).

• The Analogy: Think of the nucleus as a dense fruitcake. The light is a laser beam that slices through the cake. Usually, you get crumbs (light particles). But sometimes, the laser is so strong it knocks out a heavy, dense fruit (the heavy meson).
• Why it matters: These "fruits" are made of heavy quarks (charm and bottom). How they are created tells us about the "glue" (gluons) holding the cake together.

3. The Mystery: How do we predict the debris?

The scientists want to predict exactly how many of these heavy fruits will fly out and where they will land. To do this, they need a map of the "glue" inside the nucleus. This map is called the Unintegrated Gluon Distribution (UGD).

• The Analogy: Imagine trying to guess how many marbles will bounce out of a jar if you shake it. You need to know how the marbles are packed inside.
• The Problem: There are different theories (maps) about how these marbles are packed.
  • Theory A (Linear): The marbles are packed neatly in rows.
  • Theory B (Non-linear): The marbles are squished together so tightly they start interacting in complex, messy ways (like a crowd of people pushing against each other).

The paper tests these different theories to see which one matches reality.

4. The New Ingredients: "The Recipe"

The authors made two major updates to their recipe for predicting these collisions:

• Update 1: The "Fragmentation" (How the fruit breaks apart):
  Previously, scientists used a simple, static rule to guess how a heavy quark turns into a meson (like assuming a cookie always breaks into the same shape). This paper uses a dynamic rule (like a recipe that changes based on how hot the oven is). They found that this new rule changes the prediction significantly, especially for particles moving very fast.
• Update 2: The "New Targets" (pPb and B-mesons):
  • pPb Collisions: They looked at collisions between a Proton (a small particle) and a Lead nucleus (a huge particle). This is like shining a flashlight at a small pebble next to a boulder.
  • B-mesons: They predicted the creation of a specific type of heavy particle ($B^0$) for the first time in this context. This is like predicting a new type of fruit that no one has seen fly out of the cake before.

5. The Findings: What the Data Says

The authors compared their predictions with real data from the CMS and ALICE experiments at the LHC.

• The "Squish" Effect: They found that when they accounted for the nucleus being "squished" (non-linear effects) and the heavy particles breaking apart in a specific way, their predictions matched the real data much better.
• The "B-meson" Potential: They concluded that while $B^0$ mesons are harder to catch (they are rarer), future experiments should be able to see them. Finding them would be a huge win, helping us understand the "glue" inside the nucleus even better.
• The "Bottom" Contribution: They also checked if some of the $D^0$ particles came from a different source (bottom quarks decaying). They found this happens, but it's a tiny fraction (like finding a single raisin in a sea of chocolate chips).

The Big Picture

This paper is essentially a theoretical roadmap. It tells experimentalists:

1. "If you look at these specific angles and speeds, you will see these heavy particles."
2. "If you use our new, more complex recipe (the dynamic fragmentation), our predictions will match your data better."
3. "Go ahead and try to find the $B^0$ mesons; it's possible, and it will teach us a lot about how the universe is held together at the smallest scales."

In short, by studying how light knocks heavy particles out of atomic nuclei, these scientists are refining the map of the invisible "glue" that holds matter together, proving that our current theories need to be a bit more complex (and a bit more "squishy") to be accurate.

Technical Summary

1. Problem Statement and Motivation

The paper addresses the theoretical description of inclusive heavy meson photoproduction (specifically $D^0$ and $B^0$ mesons) in ultraperipheral collisions (UPCs) of protons and lead ions (pPb) and lead-lead (PbPb) at Large Hadron Collider (LHC) energies.

• Context: While exclusive photoproduction (where both incident particles remain intact) has been extensively studied, experimental data for inclusive processes (where one incident hadron breaks up) has only recently become available (CMS and preliminary ALICE data).
• Gap: Existing theoretical descriptions often rely on simplified fragmentation models (e.g., scale-independent Peterson functions) and may not fully account for non-linear QCD dynamics or nuclear effects in the unintegrated gluon distribution (UGD).
• Goal: To update theoretical predictions for inclusive $D^0$ photoproduction using improved fragmentation functions, present first-time predictions for inclusive $B^0$ photoproduction, and investigate the impact of different QCD dynamics models (linear vs. non-linear, nuclear effects) on these observables.

2. Methodology

The authors employ the color dipole S-matrix formalism to calculate the differential cross-sections. The process is factorized into three main components:

1. Equivalent Photon Approximation (EPA): One hadron acts as a photon source, emitting a quasi-real photon. The effective photon flux is calculated considering the impact parameter ($b$) and "survival probabilities" against strong interactions ($P_{strong}$) and electromagnetic dissociation ($P$).
2. Photon-Hadron Interaction: The interaction $\gamma B \to Q\bar{Q} X$ is described using the color dipole model. The cross-section depends on the Unintegrated Gluon Distribution (UGD), $f(x, k)$, of the target hadron.
3. Fragmentation: The heavy quark ($Q$) fragments into a heavy meson ($H$). The authors compare two fragmentation function (FF) models:
   • Peterson FF: Scale-independent, non-perturbative parameterization.
   • KKSS FF: Scale-dependent, derived from global fits to $e^+e^-$ and $pp$ data and evolved via DGLAP equations.

Models for Gluon Distributions:
The study tests various models for the target UGD to probe QCD dynamics:

• Proton Target: CCFM (linear), KS Linear (linear rcBK), KS Nonlinear, and rcBK (non-linear Balitsky-Kovchegov equation).
• Nuclear Target (Pb): CCFM rescaled (no nuclear effects), PB-EPPS16 (linear with nuclear effects), and rcBK (non-linear with nuclear saturation).

Kinematics:

• PbPb: $\sqrt{s_{NN}} = 5.36$ TeV.
• pPb: $\sqrt{s_{NN}} = 8.1$ TeV.
• Masses used: $m_c = 1.4$ GeV, $m_b = 4.5$ GeV.

3. Key Contributions

• First Predictions for $B^0$: The paper provides the first theoretical predictions for the inclusive photoproduction of $B^0$ mesons in both pPb and PbPb collisions.
• Improved $D^0$ Modeling: Revisits $D^0$ predictions by replacing the static Peterson fragmentation function with the scale-evolving KKSS function, demonstrating the necessity of DGLAP evolution for high transverse momentum ($p_T$).
• Bottom-to-Charm Transition: Estimates the contribution of $b \to D^0$ transitions (where a bottom quark fragments into a $D^0$ meson), quantifying it as a sub-dominant but non-negligible background.
• Comprehensive Model Comparison: Systematically compares linear vs. non-linear QCD evolution and the presence vs. absence of nuclear effects across different rapidity and $p_T$ ranges.

4. Key Results

A. Impact of Fragmentation Functions

• Transverse Momentum ($p_T$): The choice of fragmentation function significantly affects the $p_T$ spectrum. The scale-evolving KKSS model predicts a suppression of heavy meson yields at large $p_T$ compared to the Peterson model. This is due to the DGLAP evolution reducing the fragmentation probability at high scales.
• Rapidity ($Y$): The rapidity distributions are largely insensitive to the fragmentation model because they are dominated by low-$p_T$ regions where both models agree.
• Data Comparison: When compared to recent CMS data for $D^0$ in PbPb, the KKSS model improves the description at high $p_T$ but slightly deteriorates the fit for negative rapidities in specific UGD combinations.

B. PbPb Collisions

• Nuclear Effects: Models incorporating nuclear effects (EPPS, rcBK) predict lower cross-sections than the CCFM model (which ignores nuclear effects).
• Electromagnetic Dissociation: Including electromagnetic dissociation (parameterized by $S$) reduces the normalization of the distributions. The effect is more pronounced at higher rapidities.
• Comparison with ALICE: Preliminary ALICE data for $D^0$ ($|Y|<0.9$) shows good agreement with predictions for $p_T \gtrsim 2$ GeV across different UGDs. However, data at lower $p_T$ is sensitive to the UGD model, favoring the EPPS parametrization.
• $B^0$ Predictions: The $B^0$ cross-sections are approximately $10^{-2}$ times smaller than $D^0$ due to the heavier mass. The relative trends regarding nuclear effects and dissociation mirror those of $D^0$.

C. pPb Collisions

• Probing Proton Structure: In pPb collisions, the photon typically originates from the Pb nucleus, probing the proton target.
• Non-linear vs. Linear: Predictions using non-linear evolution (rcBK, KS Nonlinear) yield significantly lower cross-sections (smaller normalization) compared to linear models (CCFM, KS Linear). This highlights the potential of inclusive photoproduction to constrain non-linear QCD effects (saturation) in the proton.
• Feasibility: Despite lower cross-sections compared to PbPb, the predicted rates are within the reach of current LHC luminosities.

D. Total Cross-Sections

• PbPb: Total cross-sections are roughly two orders of magnitude larger than in pPb (due to the $Z^2$ enhancement in photon flux).
  • $D^0$ (Central): ~31 mb (rcBK) to ~225 mb (CCFM).
  • $B^0$ (Central): ~0.28 mb (rcBK) to ~2.1 mb (CCFM).
• pPb:
  • $D^0$ (Central): ~1.3 mb (rcBK) to ~2.5 mb (CCFM).
  • $B^0$ (Central): ~0.015 mb (rcBK) to ~0.026 mb (CCFM).
• Forward Detectors: Cross-sections decrease by 1–2 orders of magnitude when restricted to forward rapidity ranges ($2.0 \le Y \le 4.5$).

E. Bottom-to-Charm Contribution

• The contribution from $b \to D^0$ fragmentation is found to be a small fraction of the total inclusive $D^0$ yield (dominated by direct $c \to D^0$), consistent with previous findings.

5. Significance and Conclusions

• Constraining Hadronic Structure: The paper demonstrates that inclusive heavy meson photoproduction is a powerful probe for the hadronic structure at high energies. Specifically, it can constrain:
  • The Unintegrated Gluon Distribution (UGD) of protons and nuclei.
  • The importance of non-linear QCD effects (saturation) vs. linear evolution.
  • The magnitude of nuclear effects (shadowing/saturation) in heavy ions.
• Experimental Feasibility: The authors conclude that future experimental analyses of inclusive $B^0$ photoproduction in PbPb and $D^0$/$B^0$ in pPb collisions are feasible at the LHC.
• Complementarity: These inclusive measurements provide complementary constraints to exclusive processes, offering a broader picture of QCD dynamics in the small-$x$ regime.

In summary, this work provides a rigorous theoretical framework for upcoming LHC data, emphasizing the critical role of scale-dependent fragmentation functions and non-linear gluon dynamics in accurately describing heavy meson production in ultraperipheral collisions.