$J/\psi$ and $\psi \left(2S\right)$ polarization in proton-proton collisions at energies available at the CERN Large Hadron Collider using PYTHIA8

The production mechanisms of charmonium states in both hadronic and heavy-ion collisions hold great significance for investigating the hot and dense QCD matter. Studying charmonium polarization in ultrarelativistic collisions can also provide insights into the underlying production mechanisms. With this motivation, we explore the $J/\psi$ and $\psi \left(2S\right)$ polarization in proton$+$proton collisions at $\sqrt{s}=7$, 8, and 13 TeV using a pQCD-inspired Monte Carlo event generator called pythia8. This work considers reconstructed quarkonia through their dimuons decay channel in the ALICE forward rapidity acceptance range of $2.5<y_{\mu \mu }<4$. Further, we calculate the polarization parameters ${\lambda }_{\theta }, {\lambda }_{\varphi }, {\lambda }_{\theta \varphi }$ from the polar and azimuthal angular distributions of the dimuons in helicity and Collins-Soper frames. This study presents a comprehensive measurement of the polarization parameters as a function of transverse momentum, charged-particle multiplicity, and rapidity at the LHC energies. Our findings of charmonium polarization are in qualitative agreement with the corresponding experimental data.

Figure 1

Illustration of the three different definitions of the polarization axis, $z$, in the helicity (HF), Collins-Soper (CS), Gottfried-Jackson (GJ) reference frames, with respect to the direction of motion of the colliding beams (Beam 1 and Beam 2) and of the quarkonia.

Figure 2

The cosine of the polar angle (top panel) and the azimuthal angle (bottom panel) distribution in $pp$ collisions for $J/\psi$ and $\psi \left(2S\right)$ at $\sqrt{s}$ = 13 TeV in helicity (left panel) and Collins-Soper (right panel) reference frame.

Figure 3

The $J/\psi$ and $\psi \left(2S\right)$ polarization parameters as a function of transverse momentum for $pp$ collisions at $\sqrt{s}$ = 7, 8, and 13 TeV using pythia8. The obtained results are compared with the $J/\psi$ polarization measurement in pp collisions from ALICE at $\sqrt{s}$ = 7, 8 TeV, LHCb at $\sqrt{s}$ = 7 TeV and the NLO-NRQCD model predictions in color singlet (CS) and color-singlet $+$ color-octet ($\mathrm{CS}+\mathrm{CO}$) states at $\sqrt{s}$ = 7 TeV in both helicity and Collins-Soper reference frames.

Figure 4

Polarization of $J/\psi$ (left) and $\psi \left(2S\right)$ (right) as a function of transverse momentum obtained from pythia8 compared with the LHCb experimental data in $pp$ collisions at $\sqrt{s}$ = 7 TeV in the rapidity interval $2.5<y<4.0$ in helicity frame. The MC simulation results are compared with NLO CSM from [53] and NLO NRQCD calculation from (1) [53], (2) [54], and (3) [55, 56].

Figure 5

The $J/\psi$ and $\psi \left(2S\right)$ polarization parameters as a function of charged-particle multiplicity for $pp$ collisions at $\sqrt{s}$ = 7, 8, and 13 TeV using pythia8 in both helicity and Collins-Soper reference frames.

Figure 6

The $J/\psi$ and $\psi \left(2S\right)$ polarization parameters as a function of rapidity for $pp$ collisions at $\sqrt{s}$ = 7, 8, and 13 TeV using pythia8 in both helicity and Collins-Soper reference frames.

Figure 7

The $J/\psi$ polarization parameters as a function of transverse momentum with “MPI: ON, CR: ON” (Red Marker) and “MPI: OFF, CR: ON” (Green Marker) for $pp$ collisions at $\sqrt{s}$ = 7 using pythia8 in helicity and Collins-Soper reference frames.