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Data-driven measurements of the beauty hadron production in p-Pb collisions at \sqrt{s_{\mathrm{NN}}} = 5.02 and 8.16 TeV

This paper presents the first data-driven Bayesian unfolding analysis of open beauty hadron production in p-Pb collisions at 5.02 and 8.16 TeV, providing precise, full-rapidity nuclear modification factors that reveal weaker cold nuclear matter suppression than charm and offer critical constraints for nuclear parton distribution functions.

Original authors: Liang Dong, Tianle Liu, Guangsheng Li, Xiaozhi Bai, Fabrizio Grosa, Yifei Zhang, Jianhui Zhu

Published 2026-10-06

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CC BY 4.0

Original authors: Liang Dong, Tianle Liu, Guangsheng Li, Xiaozhi Bai, Fabrizio Grosa, Yifei Zhang, Jianhui Zhu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To understand the universe at its smallest scales, physicists study how particles smash together at nearly the speed of light. When protons collide, they create a shower of new particles, some of which are heavy and short-lived, carrying the imprint of the fundamental forces that govern matter. Among these are particles containing "beauty" quarks, a heavy type of building block that behaves differently than its lighter cousins. Scientists are particularly interested in what happens when a single proton smashes into a heavy nucleus, like lead, rather than another proton. In these collisions, the proton must pass through a dense cloud of other particles before the main crash occurs. This environment, known as cold nuclear matter, can alter the behavior of the particles created, acting like a fog that distorts the path of light. By measuring exactly how these heavy beauty particles are produced in such collisions, researchers can map out the internal structure of the atomic nucleus and learn how the heavy quarks interact with the surrounding matter. This knowledge is essential for distinguishing between the effects of ordinary nuclear matter and the extreme, super-hot state of matter called the quark-gluon plasma, which is created in even more violent collisions between heavy nuclei.

A team of researchers has now taken a significant step forward in this field by measuring the production of beauty particles in collisions between protons and lead nuclei at the Large Hadron Collider. The study focused on two specific energy levels, where the collision energy was equivalent to 5.02 and 8.16 trillion electron volts. Because beauty particles decay almost instantly into other, lighter particles, the scientists could not observe the beauty particles directly. Instead, they looked for the specific debris left behind: particles called non-prompt D0 mesons and J/psi mesons, which are the direct offspring of decaying beauty particles. The challenge was to work backward from these visible fragments to reconstruct the original speed and direction of the invisible beauty parent. To do this, the team used a sophisticated statistical method called Bayesian unfolding. This technique acts like a high-powered lens, taking the messy, measured data of the decay products and mathematically reversing the process to reveal the true distribution of the original beauty particles.

The researchers combined data from two major experiments, ALICE and LHCb, which observed these collisions from different angles and at different speeds. By merging these diverse measurements, they were able to create a complete picture of beauty particle production across the entire range of angles, from the center of the collision to the far edges. The results showed that the data from the different decay channels and different experiments were consistent with one another, confirming that the mathematical reconstruction was reliable. The team then calculated a value called the nuclear modification factor, which compares how many beauty particles are produced in a proton-lead collision versus a proton-proton collision. If the lead nucleus had no effect, this value would be one. Instead, the measurements showed a slight suppression, meaning fewer beauty particles were produced than expected, but this suppression was noticeably weaker than what is seen with lighter charm particles. This finding aligns with the theoretical expectation that heavier particles are less affected by the nuclear environment, a pattern known as the mass hierarchy of nuclear effects.

The study also provided the first comprehensive measurement of how this suppression changes as the angle of the collision varies, covering a wide range of speeds and directions. The results matched well with existing theoretical models that describe how the particles inside the nucleus are distributed. Furthermore, the team calculated the total number of beauty particle pairs produced in these collisions, finding that at the higher energy level, the total production was significantly greater than at the lower energy. The mean speed of the particles, however, remained largely unchanged between the proton-lead and proton-proton collisions, suggesting that the shape of the speed distribution is not significantly altered by the presence of the lead nucleus. These precise measurements offer a new, data-driven constraint for physicists trying to refine their models of the atomic nucleus, helping to separate the effects of cold nuclear matter from other phenomena in high-energy physics.

Technical Summary: Data-driven measurements of the beauty hadron production in p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ and $8.16$ TeV

Problem and Motivation
The production of hadrons containing heavy quarks serves as a critical testing ground for Quantum Chromodynamics (QCD). While perturbative QCD (pQCD) calculations are reliable for charm and beauty production due to the large quark masses, isolating the effects of the Quark-Gluon Plasma (QGP) in heavy-ion collisions requires a precise quantification of Cold Nuclear Matter (CNM) effects. These effects, arising from the nuclear environment in the absence of deconfinement, modify parton distribution functions (nPDFs) and kinematic distributions.

Beauty hadrons are particularly valuable probes of CNM effects due to their large mass, which ensures perturbative calculability and creates a distinct mass hierarchy in nuclear modifications compared to charm. However, previous measurements of beauty production in proton–nucleus (p–Pb) collisions have relied on reconstructing decay products (non-prompt $D^0$ and $J/\psi$ mesons) or decay electrons. These methods do not provide direct access to the kinematics of the parent beauty hadron, limiting the ability to constrain nPDFs across the full kinematic phase space. This work addresses the need for a direct, data-driven determination of inclusive beauty-hadron production cross sections and nuclear modification factors ( $R_{p\text{Pb}}$ ) over a wide rapidity range.

Methodology
The study employs a data-driven Bayesian unfolding technique to infer the parent beauty-hadron kinematic distributions from measured non-prompt daughter spectra. The analysis utilizes inputs from the ALICE and LHCb collaborations:

Inputs: Non-prompt $D^0$ meson spectra at midrapidity ( $-0.96 < y < 0.04$ ) and non-prompt $J/\psi$ meson spectra covering midrapidity, forward ( $1.5 < y < 4.0$ ), and backward ( $-5.0 < y < -2.5$ ) rapidities in p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ and $8.16$ TeV.
Unfolding Framework: An iterative Bayesian procedure (following the D'Agostini prescription) is applied. The response matrix, encoding the probability of a true parent beauty hadron yielding a reconstructed daughter, is derived from EvtGen 2.0 simulations.
Branching Fractions: The conversion of daughter yields to parent cross sections relies on inclusive branching fractions. For $J/\psi$ , the value is taken from the PDG. For $D^0$ , the inclusive probability is calculated by combining PDG values for specific decay modes with $b$ -hadron production fractions ( $f_u, f_d$ ) measured by LHCb in pp collisions.
Reference Calculation: Since no pp data exists at $\sqrt{s} = 8.16$ TeV, the pp reference cross section is obtained by extrapolating unfolded pp results from $\sqrt{s} = 5.02$ and $13$ TeV using the ratio of FONLL (Fixed-Order Next-to-Leading Log) predictions as a scaling factor.
Uncertainty Propagation: Systematic uncertainties are treated as fully correlated across $p_T$ bins. Sources include experimental input uncertainties, branching ratio uncertainties, response matrix statistics, iteration dependence, and low- $p_T$ extrapolation.

Key Contributions and Results
The paper presents the first unfolding-based measurement of beauty-hadron production that spans the full rapidity range ( $-4.0 < y < 4.0$ ) in p–Pb collisions.

Cross Sections: The study reports $p_T$ - and $y$ -differential cross sections for open beauty production. The unfolded results from different decay channels ( $D^0$ and $J/\psi$ ) and different collaborations (ALICE and LHCb) are mutually consistent when mapped to common kinematic intervals.
Nuclear Modification Factor ( $R_{p\text{Pb}}$ ): The $R_{p\text{Pb}}$ $R_{p Pb}$ is reported as a function of transverse momentum and rapidity. The results cover the full rapidity range with a precision comparable to or better than existing direct measurements.
- The unfolded $R_{p\text{Pb}}$ values are compatible with existing experimental measurements (non-prompt $D^0$ , $J/\psi$ , and $B$ mesons) and theoretical calculations based on nPDF sets (EPPS16, nCTEQ15, EPPS16*).
- The analysis provides a data-constrained determination of $R_{p\text{Pb}}$ that offers complementary information for future global nPDF fits.
Mass Hierarchy: A comparison between beauty and charm hadrons at midrapidity reveals a systematically larger $R_{p\text{Pb}}$ for beauty hadrons. This indicates a weaker CNM suppression for beauty compared to charm, consistent with the expected mass hierarchy of cold-nuclear-matter effects.
Total Cross Sections: The total inclusive $b\bar{b}$ $b \overset{ˉ}{b}$ production cross sections in p–Pb collisions are reported:
- $\sigma_{b\bar{b}}^{\sqrt{s_{NN}}=5.02\text{ TeV}} = 38.33 \pm 1.33 \text{ (stat.)} \pm 2.40 \text{ (sys.) mb}$
- $\sigma_{b\bar{b}}^{\sqrt{s_{NN}}=8.16\text{ TeV}} = 64.60 \pm 1.81 \text{ (stat.)} \pm 5.87 \text{ (sys.) mb}$
  These results are consistent with previous phase-space extrapolations.
Spectral Shape: The mean squared transverse momentum $\langle p_T^2 \rangle$ is found to be consistent between p–Pb and pp collisions at both energies, indicating no significant modification of the $p_T$ -spectrum shape in p–Pb collisions within current uncertainties.

Significance
The paper establishes a robust methodology for extracting inclusive beauty-hadron kinematics from semi-inclusive decay channels using Bayesian unfolding. By providing the first $R_{p\text{Pb}}$ results covering the full rapidity range with high precision, the work directly constrains nuclear parton distribution functions, particularly the nuclear gluon distribution at low $x$ . The observation of a weaker suppression for beauty than for charm reinforces the theoretical understanding of mass-dependent CNM effects. These results serve as essential benchmarks for isolating QGP signatures in heavy-ion collisions and provide critical inputs for future global nPDF fits.

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