Measurement of the inclusive J/\(\psi \) polarization at forward rapidity in pp collisions at \(\mathbf {\sqrt{s} = 8}\) TeV

Abstract

We report on the measurement of the inclusive J/\(\psi \) polarization parameters in pp collisions at a center of mass energy \(\sqrt{s} = 8\) TeV with the ALICE detector at the LHC. The analysis is based on a data sample corresponding to an integrated luminosity of 1.23 pb\(^{-1}\). J/\(\psi \) resonances are reconstructed in their di-muon decay channel in the rapidity interval \(2.5< y < 4.0\) and over the transverse-momentum interval \(2< p_\mathrm{T} < 15\) \(\mathrm {GeV}/c\). The three polarization parameters (\(\lambda _\theta \), \(\lambda _\varphi \), \(\lambda _{\theta \varphi }\)) are measured as a function of \(p_\mathrm{T}\) both in the helicity and Collins-Soper reference frames. The measured J/\(\psi \) polarization parameters are found to be compatible with zero within uncertainties, contrary to expectations from all available predictions. The results are compared with the measurement in pp collisions at \(\sqrt{s} = 7\) TeV.

A preprint version of the article is available at ArXiv.

Introduction

More than 40 years after the J/\(\psi \) discovery, its production mechanism in hadronic collisions remains an open issue [1]. Quarkonia states constitute an important test bench for the study of Quantum ChromoDynamics (QCD) both in the vacuum and in high-energy density environments, as those produced in heavy-ion collisions, where the creation of the Quark–Gluon Plasma (QGP) is observed [2]. Consequently, the understanding of the J/\(\psi \) production mechanism is an important scientific question in the sense that it addresses basic concepts of QCD, the theory of the strong interaction, and its application to heavy-ion collisions allows the characterisation of the QGP properties created in the laboratory.

Different theoretical models have been developed in an attempt to describe the whole production mechanism from partonic interaction to heavy-quark pair (Q\(\overline{\mathrm{Q}}\)) hadronisation in quarkonia. All approaches are based on the factorisation hypothesis between hard and soft scales. First phenomenological attempts (e.g. the Color Evaporation Model [3]) have been replaced by a rigorous effective field theory, the Non-Relativistic QCD (NRQCD) [4]. In this framework, two models can be derived according to the sub-processes taken into account: the Color-Singlet Model (CSM) [5, 6] and the Color-Octet Mechanism (COM) [4]. The CSM assumes no evolution of the quantum color-singlet state between the Q\(\overline{\mathrm{Q}}\) production and the quarkonium formation, with a wave function computed at zero Q\(\overline{\mathrm{Q}}\) separation, i.e. without any free parameter. The COM introduces Long-Distance Matrix Elements (LDMEs) for the hadronisation probability in a quarkonium state. The LDMEs are free parameters of the theory which must be fixed from experimental data.

Recent measurements at the LHC confirm that color-octet terms are crucial for a good description of the J/\(\psi \) and \(\psi \)(2S) differential production cross sections [7]. However, the failure in predicting the \(\eta _\mathrm{c}\) production cross section [8, 9] poses serious challenges to the NRQCD approach.

In this context, alternative measurements at different energies and in different rapidity regions can help to disentangle tensions between quarkonium measurements and the theoretical predictions. One of the most relevant observables apart from the production cross section is the polarization of quarkonia. The polarization of \(\mathrm J^\mathrm{PC} = 1^{-}\) states like the J/\(\psi \) is specified by three polarization parameters (\(\lambda _\theta \), \(\lambda _\varphi \), \(\lambda _{\theta \varphi }\)), which are a function of the three decay amplitudes with respect to the three angular momentum states. The two cases (\(\lambda _\theta = 1\), \(\lambda _\varphi = 0\), \(\lambda _{\theta \varphi } = 0\)) and (\(\lambda _\theta = -1\), \(\lambda _\varphi = 0\), \(\lambda _{\theta \varphi } = 0\)) correspond to the so-called transverse and longitudinal polarizations, respectively. Theoretical models at Next-to-Leading Order (NLO) predict strongly transverse-momentum dependent polarizatio