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Measurement of prompt and non-prompt ${\rm D}^{\rm *+}$ -meson spin alignment in pp collisions at $\sqrt{s}$ = 13.6 TeV$

Using ALICE data from proton-proton collisions at 13.6 TeV, this study presents a precise measurement of ${\rm D}^{\rm *+}$ -meson spin alignment, revealing that prompt mesons are unpolarized while non-prompt mesons exhibit a deviation consistent with weak beauty-hadron decays, thereby establishing a crucial baseline for future heavy-ion collision studies.

Original authors: ALICE Collaboration

Published 2026-10-01

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CC BY 4.0

Original authors: ALICE Collaboration

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

In the subatomic world, particles are not just tiny, hard spheres; they possess an intrinsic property called spin, which can be thought of as a form of internal rotation. For certain particles known as vector mesons, this spin can point in different directions relative to the way the particle is moving. When these particles are created in high-energy collisions, physicists can measure whether their spins are randomly oriented or if they prefer to line up in a specific direction, a phenomenon known as spin alignment. Understanding this alignment is crucial because it acts as a sensitive probe into the complex process of hadronization, the moment when free-floating quarks and gluons bind together to form the stable particles that make up our universe. If the spins of these newly formed particles are not random, it suggests that the forces governing their creation are more intricate than previously thought, potentially revealing hidden details about the fundamental laws of nature or the conditions of the early universe.

A researcher using the ALICE detector at the Large Hadron Collider in Geneva has now taken a closer look at this phenomenon by studying a specific type of particle called the D*+ meson. These particles are created in collisions between protons at an energy level of 13.6 tera-electronvolts, a record-breaking energy that allows scientists to observe rare events with unprecedented clarity. The researcher focused on two distinct sources of these particles: those created directly in the collision, known as prompt D*+ mesons, and those that are born from the decay of heavier beauty particles, known as non-prompt D*+ mesons. By analyzing millions of these events, the researcher measured the orientation of the spin for both groups across a wide range of speeds, specifically looking at how the spin aligned with two different reference directions: the direction the particle was flying and the geometry of the collision itself.

The results revealed a striking difference between the two types of particles. For the prompt D*+ mesons, which are born directly from the collision of quarks, the spin orientation was found to be completely random. The data showed that these particles had no preference for any particular spin direction, matching the expectation that they are produced without any inherent alignment. This finding holds true even at very high speeds, extending the range of previous observations significantly. It suggests that the process of a charm quark turning into a D*+ meson does not impose a specific spin direction, effectively washing out any initial polarization that might have existed. This provides a clean baseline for future studies, confirming that in simple proton collisions, these particles behave in a statistically neutral way.

In contrast, the non-prompt D*+ mesons told a different story. Because these particles are the result of a heavy beauty particle decaying into a charm particle, they carry the imprint of that weak decay process. The measurements showed a clear and consistent deviation from randomness; the spins of these particles were not distributed equally. Instead, they exhibited a specific alignment that matched the predictions of theoretical models which account for the rules of weak nuclear force and the conservation of angular momentum during the decay. The data aligned perfectly with computer simulations that explicitly model these decay mechanics, confirming that the observed alignment is a natural consequence of how beauty particles transform into charm particles. This distinction is vital because it proves that the two sources of D*+ mesons are governed by different physical mechanisms, and that the alignment seen in the non-prompt group is a direct signature of the decay process rather than the initial collision.

These findings are particularly important because they establish a precise reference point for future experiments involving heavier collisions, such as those between lead nuclei. In those more complex environments, scientists hope to detect signals from the extreme conditions of the early universe, but they must first be certain that any observed spin alignment is not simply a result of the standard decay processes seen here. By confirming that prompt particles remain unaligned while non-prompt particles show a predictable pattern, the researcher has provided the necessary tools to separate the signal of the medium from the background of standard particle physics. The study successfully extends our understanding of how heavy quarks behave in high-energy environments, offering a clearer picture of the forces that shape the building blocks of matter.

Technical Summary: Measurement of Prompt and Non-Prompt $D^{*+}$ -Meson Spin Alignment in pp Collisions at $\sqrt{s} = 13.6$ TeV

Problem and Motivation
The production of heavy-flavour hadrons serves as a critical probe for Quantum Chromodynamics (QCD), particularly regarding the non-perturbative dynamics of hadronisation. While perturbative QCD calculations successfully describe production cross-sections, the mechanism by which heavy-quark spin is transferred to final-state hadrons remains poorly constrained. Spin-alignment measurements offer a sensitive probe of these fragmentation and decay dynamics. In relativistic heavy-ion collisions, spin-related observables are of particular interest due to the large orbital angular momentum and strong electromagnetic fields generated, which may influence hadron formation. However, to isolate medium-induced effects in heavy-ion collisions, a precise baseline from proton-proton (pp) collisions is required to disentangle intrinsic production and decay mechanisms from environmental effects.

Previous measurements at $\sqrt{s} = 13$ TeV by the ALICE Collaboration indicated that prompt $D^{*+}$ mesons (directly produced) are consistent with an unpolarised state, while non-prompt $D^{*+}$ mesons (originating from beauty-hadron decays) exhibit spin alignment consistent with weak decay kinematics. This paper extends those findings using LHC Run 3 data at a higher collision energy ( $\sqrt{s} = 13.6$ TeV) to test these mechanisms with improved precision, extended kinematic reach, and a new reference frame.

Methodology
The analysis utilizes pp collision data collected by the ALICE experiment at $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of $6.49 \pm 0.15$ pb $^{-1}$ . The study focuses on $D^{*+}$ mesons (and charge conjugates) reconstructed at midrapidity ( $|y| < 0.8$ ) via the decay chain $D^{*+} \to D^0 \pi^+ \to K^- \pi^+ \pi^+$ .

Detector Upgrades: The analysis leverages the upgraded ALICE detector, specifically the new Inner Tracking System (ITS) based on Monolithic Active Pixel Sensors (MAPS) and the Gas Electron Multiplier (GEM) Time Projection Chamber (TPC). These upgrades enable continuous readout, improved vertex resolution, and enhanced particle identification (PID) via $dE/dx$ and Time-of-Flight (TOF) measurements, allowing for operation at interaction rates up to 2 MHz.
Signal Extraction and Separation: $D^{*+}$ candidates are selected using a multiclass Boosted Decision Tree (BDT) algorithm. This classifier simultaneously suppresses combinatorial background and separates prompt from non-prompt contributions based on topological variables (e.g., decay vertex distance, impact parameters) and PID information.
Spin Alignment Measurement: The spin alignment is quantified by the diagonal element $\rho_{00}$ of the spin-density matrix. This is extracted from the angular distribution of the decay products in the $D^{*+}$ rest frame, specifically the polar angle $\vartheta^*$ . The distribution follows the form $dN/d\cos\vartheta^* \propto (1-\rho_{00}) + (3\rho_{00}-1)\cos^2\vartheta^*$ .
Reference Frames: The measurement is performed with respect to two distinct quantisation axes:
1. Helicity Axis: Defined by the vector-meson momentum in the laboratory frame.
2. Production Axis: Defined by the normal to the plane spanned by the beam direction and the vector-meson momentum.
Prompt/Non-Prompt Separation: The observed $\rho_{00}$ is treated as a linear combination of prompt and non-prompt contributions. For $p_T < 30$ GeV/c, the fractions are determined via a data-driven method using BDT scores to extract the pure components. For $p_T > 30$ GeV/c, where statistics are limited, the non-prompt contribution is constrained using PYTHIA 8 + EvtGen simulations.

Key Contributions

Extended Kinematic Reach: The analysis extends the transverse momentum ( $p_T$ ) range for prompt $D^{*+}$ measurements up to 100 GeV/c (previously limited to lower $p_T$ ) and up to 30 GeV/c for non-prompt $D^{*+}$ .
First Production-Axis Measurement: This work presents the first measurement of $D^{*+}$ spin alignment in pp collisions with respect to the production axis, providing a complementary perspective to the helicity frame to assess frame-dependent effects and the geometry of the scattering process.
High-Precision Baseline: Utilizing the upgraded detector and larger Run 3 dataset, the study provides significantly improved statistical precision compared to the $\sqrt{s} = 13$ TeV measurement.

Results

Prompt $D^{*+}$ Mesons: The measured $\rho_{00}$ values for prompt $D^{*+}$ mesons are consistent with the unpolarised expectation of $1/3$ across the entire $p_T$ range (3–100 GeV/c) for both the helicity and production axes. This indicates no evidence of spin alignment for directly produced charm mesons in pp collisions.
Non-Prompt $D^{*+}$ Mesons: In contrast, non-prompt $D^{*+}$ mesons exhibit a clear deviation from $1/3$ . The $\rho_{00}$ values are systematically larger than $1/3$ in the helicity frame and smaller than $1/3$ in the production frame. This behaviour is consistent with expectations from helicity conservation in weak beauty-hadron decays ( $b \to c$ transitions) and is well-described by PYTHIA 8 simulations coupled with the EvtGen decay package.
Theoretical Comparison: The prompt results are compared with theoretical calculations based on spin-dependent fragmentation functions ( $D_{1LL}$ ) tuned to $e^+e^-$ data. The data are compatible with these predictions within approximately one standard deviation. The non-prompt results align with the polarisation patterns observed for non-prompt $J/\psi$ and $\psi(2S)$ mesons by the CMS Collaboration, supporting the hypothesis that spin alignment in these cases arises from the decay of scalar B mesons.

Significance
The paper establishes a precise and robust baseline for the spin alignment of $D^{*+}$ mesons in pp collisions. By confirming the absence of spin alignment for prompt mesons and characterising the specific alignment pattern of non-prompt mesons, these results allow for the disentanglement of intrinsic QCD fragmentation and weak decay effects from potential medium-induced modifications in future heavy-ion collision studies. The extension to the production axis and higher $p_T$ ranges provides a more stringent test of spin-dependent heavy-quark fragmentation models and validates the use of event generators like PYTHIA 8 + EvtGen for describing these complex dynamics.

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