CMS heads towards solving a decades-long quarkonium puzzle

Quarkonia – charm or beauty quark/antiquark bound states – are prototypes of elementary systems governed by the strong force. Owing to the large masses and small velocities of the quarks, their mutual interaction becomes simpler to describe, therefore opening unique insights into the mechanism of strong interactions. For decades, research in the area of quarkonium production in hadron collisions has been hampered by anomalies and puzzles in theoretical calculations and experimental results, so that, until recently, the studies were stuck at a validation phase. Now, new CMS data are enabling a breakthrough by accomplishing cross-section measurements for quarkonium production that reach unprecedentedly high values of transverse momentum (p_T).

The latest and most persistent “quarkonium puzzle”, lasting for more than 10 years, was the seeming impossibility of theory to reproduce simultaneously quarkonium yields and polarizations, as observed in hadronic interactions. Polarization is particularly sensitive to the mechanism of quark–antiquark (qq) bound-state formation, because it reveals the quantum properties of the pre-resonance qq pair. For example, if a ³S₁ bound state (J/ψ or Υ) is measured to be unpolarized (isotropic decay distribution), the straightforward interpretation is that it evolved from an initial coloured ¹S₀ qq configuration. To extract this information from differential cross-section measurements requires an additional layer of interpretation, based on perturbative calculations of the pre-resonance qq kinematics in the laboratory reference frame. The fragility of this additional step will reveal itself, a posteriori, as the cause of the puzzle.

In recent years, CMS provided the first unambiguous evidence that the decays of ³S₁ bottomonia (Υ(1,2,3S)) and charmonia (J/ψ, ψ(2S)) are always approximately isotropic (CMS Collaboration 2013): the pre-resonance qq is a ¹S₀ state neutralizing its colour into the final ³S₁ bound state. This contradicted the idea that quarkonium states are produced mainly from a transversely polarized gluon (coloured ³S₁ pre-resonance), as deduced traditionally from cross-section measurements. After having exposed the polarization problem with high-precision measurements, CMS is now providing the key to its clarification.

The new cross-section measurements allow a theory/data comparison at large values of the ratio p_T/mass, where perturbative calculations are more reliable. First attempts to do so, not yet exploiting the exceptional high-p_T reach of the newest data, were revealing. With theory calculations restricted to their region of validity, the cross-section measurements are actually found to agree with the polarization data, indicating that the bound-state formation through coloured ¹S₀ pre-resonance is dominant (G Bodwin et al. 2014, K-T Chao et al. 2012, P Faccioli et al. 2014).

Heading towards the solution of a decades-long puzzle, what of the fundamental question: how do quarks and antiquarks interact to form bound states? Future analyses will disclose the complete hierarchy of transitions from pre-resonances with different quantum properties to the family of observed bound states, providing a set of “Kepler” laws for the long-distance interactions between quark and antiquark.