Measurement of Charmonium Polarization with the LHCb Detector

In particle physics, quantum chromodynamics (QCD) is the theory used to describe the interaction of colored particles. Heavy quarkonium is the bound state of heavy quark and its anti-quark, and its production cross section and polarization can be used to test the theory models in the framework of QCD. The computation of the heavy quarkonium production cross section by color singlet mechanism (CSM) underestimates the experimental measurements, while results from the calculation of non-relativistic QCD (NRQCD) can describe experimental data very well. However, the NRQCD predicts that the $S$ wave heavy quarkonium is heavily transversely polarized in the large transverse momentum region, which is contrary to experimental observations. LHCb, dedicated for precision measurement in bottom and charm physics, is one of the experiments located at the Large Hadron Collider (LHC). The LHCb detector, which is a forward region spectrometer covering the pseudo rapidity range 2-5, has fine particle reconstruction and identification systems. In the year 2011, the LHCb detector collected about 1.0 fb$^{-1}$ $pp$ collision data in a center-of-mass energy of 7 TeV. With integrated luminosity of about 370 pb$^{-1}$, the three polarization parameters $\lambda_\theta,\;\lambda_{\theta\phi}$ and $\lambda_\phi$ of prompt $J/\psi$ have been measured as a function of transverse momentum and rapidity in both the helicity and the Collins-Soper frame. In the helicity frame, in the kinematic range 2 < $p_\mathrm{T}$ < 15 GeV/$c$, 2.0 < $y$ <4.5, $\lambda_\theta\simeq-0.2$ decreases (in absolute value) with the increase of $J/\psi$ transverse momentum and rapidity, which means that $J/\psi$ is slightly longitudinally polarized, while $\lambda_{\theta\phi}$ and $\lambda_\phi$ are consistent with zero within errors. The $\psi(2S)$ polarization parameters have been measured with all 1.0 fb$^{-1}$ data. The results show that in both the helicity and the Collins-Soper frame, in most of the kinematic region, the three parameters are consistent with zero within errors, while in some bins the $\psi(2S)$ has slightly negative polarization with $\lambda_\theta$ between -0.2 and zero. The analysis provide detailed information of $J/\psi$ and $\psi(2S)$ polarization in the new energy scale and unique rapidity range, and the $\psi(2S)$ polarization result is the most precise one among all experiments. LHCb does not see strong transversely or longitudinally polarized $J/\psi$ or $\psi(2S)$ events, confirming previous measurements. The $J/\psi$ polarization measurements at LHCb are consistent with the results from ALICE in the overlapping kinematic region. The $J/\psi$ and $\psi(2S)$ polarization results disfavor the calculations of CSM or NRQCD at NLO.