Measurement of inclusive $J/\psi$ polarization in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ by the STAR experiment

We report on new measurements of inclusive $J/\psi$ polarization at midrapidity in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ by the STAR experiment at the Relativistic Heavy Ion Collider. The polarization parameters, ${\lambda }_{\theta }$, ${\lambda }_{\varphi }$, and ${\lambda }_{\theta \varphi }$, are measured as a function of transverse momentum ($p_{\mathrm{T}}$) in both the helicity and Collins-Soper (CS) reference frames within $p_{\mathrm{T}}<10\mathrm{GeV}/c$. Except for ${\lambda }_{\theta }$ in the CS frame at the highest measured $p_{\mathrm{T}}$, all three polarization parameters are consistent with 0 in both reference frames without any strong $p_{\mathrm{T}}$ dependence. Several model calculations are compared with data, and the one using the Color Glass Condensate effective field theory coupled with nonrelativistic QCD gives the best overall description of the experimental results, even though other models cannot be ruled out due to experimental uncertainties.

Figure 1

Invariant mass spectra of electron-positron pairs in different $p_{\mathrm{T}}$ bins (from left to right: $p_{\mathrm{T}}=0–2$, 2–4, 4–6, 6–8, $8–14\mathrm{GeV}/c$). The black markers (blue filled histograms) are the spectra from opposite-sign (same-sign) charge pairs, while the red markers represent those obtained by subtracting the same-sign spectra from the opposite-sign ones. The number of $J/\psi$ candidates ($N_{J/\psi }$) is given by the number of opposite-sign charge pairs minus that of same-sign charge pairs within $3.0<m_{e^{+}{e}^{-}}<3.15\mathrm{GeV}/c^2$. The S/B ratio is the ratio between $N_{J/\psi }$ and that of the same-sign charge pairs within $3.0<m_{e^{+}{e}^{-}}<3.15\mathrm{GeV}/c^2$.

Figure 2

Normalized two-dimensional $N_{J/\psi }(\cos \theta ,\varphi )/N_{J/\psi }^{\text{total}}$ distributions in different $p_{\mathrm{T}}$ bins (from left to right: $p_{\mathrm{T}}=0–2$, 2–4, 4–6, 6–8, $8–14\mathrm{GeV}/c$). The top (bottom) row shows the distributions in the HX (CS) frame. The size of the boxes represents the absolute value of the $J/\psi$ yield. The boxes with crosses are entries with negative values.

Figure 3

Two-dimensional $A\times ϵ(\cos \theta ,\varphi )$ distributions in different $p_{\mathrm{T}}$ bins (from left to right: $p_{\mathrm{T}}=0–2$, 2–4, 4–6, 6–8, $8–14\mathrm{GeV}/c$). The top (bottom) row shows the distributions in the HX (CS) frame. The size of the boxes represents the value of the $J/\psi$ reconstruction efficiency times acceptance.

Figure 4

The number of $J/\psi$ candidates as a function of $\cos \theta$ in different $p_{\mathrm{T}}$ bins (from left to right: $p_{\mathrm{T}}=0–2$, 2–4, 4–6, 6–8, $8–14\mathrm{GeV}/c$). The top (bottom) row shows the distributions in the HX (CS) frame. The solid lines correspond to the expected distributions based on the $J/\psi$ polarization parameter values extracted from data. The dashed lines are the expected distributions with assumed values of $({\lambda }_{\theta },{\lambda }_{\varphi },{\lambda }_{\theta \varphi })=(\pm 1,0,0)$. The counts are after arbitrary normalization.

Figure 5

The number of $J/\psi$ candidates as a function of $\varphi$ in different $p_{\mathrm{T}}$ bins (from left to right: $p_{\mathrm{T}}=0–2$, 2–4, 4–6, 6–8, $8–14\mathrm{GeV}/c$). The top (bottom) row shows the distributions in the HX (CS) frame. The solid lines correspond to the expected distributions based on the $J/\psi$ polarization parameter values extracted from data. The dashed lines are the expected distributions with assumed values of $({\lambda }_{\theta },{\lambda }_{\varphi },{\lambda }_{\theta \varphi })=(0,\pm 1,0)$. The counts are after arbitrary normalization.

Figure 6

Differences of the extracted $J/\psi$ polarization parameters, ${\lambda }_{\theta }$, ${\lambda }_{\varphi }$ and ${\lambda }_{\mathrm{inv}}$, in the ToyMC and the input values in both the HX and CS frames. Data points of different markers correspond to the three different tests. See the text for details.

Figure 7

The invariant mass spectrum of opposite-sign muon pairs for $p_{\mathrm{T}}<10\mathrm{GeV}/c$. The solid line depicts the fitting result, consisting of a Gaussian function representing the signal (shaded area) and a polynomial function describing the background (dashed line). Data points in the $\psi (2\mathrm{S})$ mass region ($3.6<{\mathrm{M}}_{\mu \mu }<3.8\mathrm{GeV}/c^2$) are excluded from the fit.

Figure 8

Upper: the raw $J/\psi$ yield and $A\times ϵ$ from the last iteration as a function of ${\mu }^{+}\cos \theta$ (left) and $\varphi$ (right) in the HX frame for $0<p_{\mathrm{T}}^{J/\psi }<1\mathrm{GeV}/c$. Lower: the acceptance and efficiency corrected $J/\psi$ yields along with the simultaneous fit. The counts are after arbitrary normalization.

Figure 9

Upper: the raw $J/\psi$ yield and $A\times ϵ$ from the last iteration as a function of ${\mu }^{+}\cos \theta$ (left) and $\varphi$ (right) in the CS frame for $0<p_{\mathrm{T}}^{J/\psi }<1\mathrm{GeV}/c$. Lower: the acceptance and efficiency corrected $J/\psi$ yields along with the simultaneous fit. The counts are after arbitrary normalization.

Figure 10

The $J/\psi$ polarization parameters (from top to bottom: ${\lambda }_{\theta }$, ${\lambda }_{\varphi }$, ${\lambda }_{\theta \varphi }$) as a function of $p_{\mathrm{T}}$ in the HX (left) and CS (right) frames. Open and filled symbols are for measurements through the dielectron and dimuon decay channels covering different rapidity ranges. The vertical bars represent the statistical errors, while the boxes around data points depict the systematic uncertainties. The data points are placed at the mean $p_{\mathrm{T}}$ value determined from the inclusive $p_{\mathrm{T}}^{J/\psi }$ spectrum measured in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ [23]. Model calculations [8, 14, 20, 42] are also shown for comparison. The ICEM and two NLO NRQCD calculations are for prompt $J/\psi$, while the $\mathrm{CGC}+\mathrm{NRQCD}$ is for direct $J/\psi$.

Figure 11

${\lambda }_{\mathrm{inv}}$ of $J/\psi$ vs $p_{\mathrm{T}}$ in both HX (circles) and CS (diamonds) reference frames. The open and filled symbols are for measurements through the dielectron and dimuon decay channels, respectively. The vertical bars represent the statistical errors, while the boxes around data points depict the systematic uncertainties. $\mathrm{CGC}+\mathrm{NRQCD}$ [20] calculations are also shown for comparison.