In a groundbreaking study that marks a pivotal advancement in particle physics, researchers from the CMS Collaboration have unveiled compelling evidence concerning the quantum characteristics of all-charm tetraquarks, exotic hadrons composed exclusively of charm quarks. Utilizing state-of-the-art statistical techniques rooted in likelihood ratio tests, this investigation meticulously distinguishes among competing spin-parity hypotheses, offering unprecedented insight into the fundamental nature of these complex particles.
Central to the analysis is the test statistic ( q = -2 \ln \left( \frac{\mathcal{L}{Jj^P}}{\mathcal{L}{J_i^P}} \right) ), where (\mathcal{L}) represents the likelihood function for given signal hypotheses (J_i^P) and (Jj^P). This ratio is constructed from two critical observables: the four-lepton invariant mass (m{4\mu}) and the discriminant (\mathcal{D}{ij}), designed to heighten sensitivity to differences in spin-parity states. Systematic uncertainties inherent in detector sensitivity and modeling nuances—including variations in mass shape and signal-background discrimination—are rigorously incorporated as constrained nuisance parameters in the maximum likelihood fits.
Illustrated through extensive pseudo-experiments simulated using observed data inputs, the distributions of (q) unequivocally favor the (2_{\mathrm{m}}^{+}) spin-parity assignment over the competing (0^{-}) hypothesis. These pseudo-experiments, crucial for establishing robust expectations, comprehensively integrate systematic uncertainties to faithfully represent the complex experimental landscape. This rigorous approach echoes methodologies foundational to the landmark 2012 Higgs boson discovery and characterization, ensuring statistical robustness and reproducibility.
A comprehensive battery of pairwise comparisons spanning eight distinct (Ji^P) models reveals a consistent preference for the (2{\mathrm{m}}^{+}) scenario. The statistical power of this conclusion is encapsulated in detailed distributions of the test statistic (q), which highlight observed values as black markers against a backdrop of 68.3%, 95.4%, and 99.7% confidence intervals. The analyses extend beyond pure states to consider mixtures of interaction structures, acknowledging and quantifying potential admixtures between scalar and tensor configurations. Notably, the study explores 10 incremental mixing steps between (0{\mathrm{m}}^{+}) and (0{\mathrm{h}}^{+}), as well as (2{\mathrm{m}}^{-}) and (2{\mathrm{h}}^{-}), with the former exhibiting interference effects that are carefully treated in the statistical modeling.
Through these nuanced investigations, the analyses decisively reject spin-parity-charge conjugation assignments of (0^{-+}) and (1^{-+}) with significance exceeding five standard deviations relative to the preferred tensor model. The (2^{-+}) hypothesis and higher-spin states bearing identical parity and charge conjugation quantum numbers are excluded at a robust three standard deviation level. This rigorous exclusion validates the assignment of parity (P=+1) and charge conjugation (C=+1) to the observed tetraquark states across multiple energy levels.
Further constraints apply to lower-spin alternatives; the (1^{++}) hypothesis is ruled out with greater than 99% confidence, while the (0^{++}) scenario, when considered as potential amplitude mixtures, is excluded at over 95% confidence. It is critical to acknowledge that the (2_{\mathrm{m}}^{+}) model is one among several possible realizations of the spin-two tensor assignment. The presence of other amplitude combinations could potentially mimic angular distributions of nominally scalar or axial-vector states, thus motivating continued examination of angular correlations and decay dynamics.
From a physical standpoint, the likelihood of (J=2) over higher spins arises from underlying energetic and dynamical considerations. Higher angular excitations necessitate additional energy input to the hadronic system, which is disfavored given the mass spectra and decay patterns observed for the fully charmed tetraquark states, notably X(6600), X(6900), and X(7100). These states thus collectively underscore the (2^{++}) quantum number configuration, shedding light on the complex interplay of quark interactions within multiquark systems.
The implications of this research extend beyond mere classification, offering a window into the interplay of quantum chromodynamics (QCD) in exotic hadrons, and casting light on how charm quarks bind and manifest collective quantum states in matter. Such insights are crucial benchmarks for theoretical models predicting the properties of multiquark systems and their role in the broader hadronic landscape.
The methodological rigor of this work, from likelihood ratio construction to the treatment of systematic uncertainties and interference effects, sets a new standard for characterizing elusive exotic particles. The researchers have demonstrated that the statistical framework originally developed for Higgs boson studies maintains extraordinary utility when applied to the complex domain of tetraquark states, thereby bridging discoveries across different sectors of high-energy physics.
This analysis epitomizes the synergy between theoretical predictions and experimental verification, leveraging complex decay final-state particle distributions and cutting-edge analysis frameworks. The clear establishment of quantum numbers not only corroborates existing theoretical frameworks but also guides future searches for exotic hadrons in LHC experiments and beyond, promising deeper understanding of the strong force in novel regimes.
As particle physicists continue to explore the vast landscape of hadronic matter, this determination of spin and parity for all-charm tetraquarks represents a landmark achievement, offering a refined lens to view the subatomic world and the exotic particles that populate it with unprecedented clarity and confidence.
Subject of Research: Determination of the spin and parity quantum numbers of fully charmed tetraquarks, specifically the exotic X states such as X(6600), X(6900), and X(7100).
Article Title: Determination of the spin and parity of all-charm tetraquarks.
Article References:
The CMS Collaboration. Determination of the spin and parity of all-charm tetraquarks. Nature 648, 58–63 (2025). https://doi.org/10.1038/s41586-025-09711-7
Image Credits: AI Generated
DOI: 10.1038/s41586-025-09711-7 (Published 04 December 2025)
Keywords: Spin-parity, tetraquarks, all-charm states, CMS Collaboration, likelihood ratio test, quantum chromodynamics, exotic hadrons, statistical analysis, LHC, high-energy physics, particle physics, systematic uncertainties
