Measurements of the transverse-momentum-dependent cross sections of $J/\psi$ production at mid-rapidity in $\mathrm{proton}+\mathrm{proton}$ collisions at $\sqrt{s}=510$ and 500 GeV with the STAR detector

We present measurements of the differential cross sections of inclusive $J/\psi$ meson production as a function of transverse momentum ($p_T^{J/\psi }$) using the ${\mu }^{+}{\mu }^{-}$ and $e^{+}{e}^{-}$ decay channels in $\mathrm{proton}+\mathrm{proton}$ collisions at center-of-mass energies of 510 and 500 GeV, respectively, recorded by the STAR detector at the Relativistic Heavy Ion Collider. The measurement from the ${\mu }^{+}{\mu }^{-}$ channel is for $0<p_T^{J/\psi }<9\mathrm{GeV}/c$ and rapidity range $|y^{J/\psi }|<0.4$, and that from the $e^{+}{e}^{-}$ channel is for $4<p_T^{J/\psi }<20\mathrm{GeV}/c$ and $|y^{J/\psi }|<1.0$. The $\psi (2S)$ to $J/\psi$ ratio is also measured for $4<p_T^{\text{meson}}<12\mathrm{GeV}/c$ through the $e^{+}{e}^{-}$ decay channel. Model calculations, which incorporate different approaches toward the $J/\psi$ production mechanism, are compared with experimental results and show reasonable agreement within uncertainties.

Figure 1

The ${\mu }^{+}{\mu }^{-}$ invariant mass spectrum in $\mathrm{proton}+\mathrm{proton}$ collisions at $\sqrt{s}=510\mathrm{GeV}$. The red solid line depicts a fit using a Gaussian function (blue line) for $J/\psi$ signal and a second-order polynomial function (red dashed line) for background.

Figure 2

(a) The $J/\psi$ decay kinematic acceptance and (b) the MTD geometric acceptance as a function of $J/\psi$ $p_T$ with different polarization assumptions in the $J/\psi \to {\mu }^{+}{\mu }^{-}$ analysis. The black solid line is the unpolarized, the red dashed line is longitudinally polarized, the pink dotted line is zero transversely polarized, the blue dashed-dotted line is positively transversely polarized, and the green dashed-dotted-dotted line is negatively transversely polarized.

Figure 3

The total $J/\psi$ efficiency as a function of $J/\psi$ $p_T$ in the $J/\psi \to {\mu }^{+}{\mu }^{-}$ analysis. Individual contributions are also shown. The green solid circles are the TPC tracking efficiency; the magenta open triangles are the trigger efficiency; the blue open circles are the MTD efficiency including response and matching; the red open squares are the muon identification efficiency; and the blue solid triangles are the total reconstruction efficiency.

Figure 4

Fits to the efficiency-corrected $M_{\mu \mu }$ spectra of the $J/\psi$ candidates in different $p_T$ regions. The solid red line is a combined fit to the signal and background with a single Gaussian plus a background template from the pairs of same-sign charged tracks in the TPC.

Figure 5

The statistical and individual systematic uncertainties as a function of $J/\psi$ $p_T$. The black dashed-dotted line is the statistical uncertainty; the orange dashed-dotted-dotted line is the signal extraction uncertainty; the red dashed line is the TPC tracking efficiency uncertainty; the blue shaded line is the MTD response and matching efficiency uncertainty; the blue dotted line is MTD trigger efficiency uncertainty; the green shaded line is the muon identification uncertainty; the magenta dashed line is the vertex finding efficiency uncertainty; the black dashed line is the total systematic uncertainty; a common luminosity uncertainty of 11.2% is not included.

Figure 6

The fiducial (open black stars) and full (solid blue stars) cross sections multiplied by the branching ratio as a function of $J/\psi$ $p_T$. The bars and boxes are the statistical and systematic uncertainties, respectively. The gray shaded band is the polarization envelope. A common luminosity uncertainty of 11.2% is not included.

Figure 7

The invariant mass distributions of $e^{+}{e}^{-}$ pairs before and after the like-sign background (the green histogram) subtraction, as shown in black histogram and red solid circles, respectively. The blue curve is a fit to the mass spectrum. The green-dashed line indicates the residual background and a Crystal-Ball function is used to describe the $J/\psi$ and $\psi (2S)$ signals, where $\psi (2S)$ is shown in the insert. The error bars depict the statistical uncertainties.

Figure 8

Dielectron mass distributions after the like-sign background subtraction (red solid circles) in different $p_T$ ranges. The solid blue line is a combined fit to the signal and residual background with a Crystal-Ball function plus an exponential function. The error bars depict the statistical error.

Figure 9

The individual electron efficiencies for the triggered electrons as a function of $p_T^e$ including $pc/E$ cut (magenta solid circles), the number of hits for the $dE/dx$ measurement (blue up-triangles), identification (gray down-triangles), tracking (black open circles), and trigger (green solid boxes).

Figure 10

(a) The $J/\psi$ and $\psi (2S)$ detection efficiencies as a function of $p_T$ as shown in the black solid circles and the blue open circles, respectively. (b) The detection efficiency ratio of $\psi (2S)$ to $J/\psi$ as a function of $p_T$ and the red dashed-line is a line at unity.

Figure 11

The statistical and individual systematic uncertainties as a function of $J/\psi$ $p_T$. The black dashed-dotted line is the statistical uncertainty. The violet dashed-dotted-dotted line is the signal extraction uncertainty; the red dashed line is the TPC tracking uncertainty; the yellow dashed line is the electron identification ($n{\sigma }_e$) uncertainty; the green shaded line is the trigger uncertainty; the blue dashed line is the $J/\psi$ internal conversion uncertainty; the black dashed line is the total systematic uncertainty; a common luminosity uncertainty of 8.1% is not included.

Figure 12

The fiducial (open black stars) and full (solid red stars) cross sections multiplied by the branching ratio as a function of $J/\psi$ $p_T$. The boxes are the total systematic uncertainty. The bars are the statistical uncertainty and are too small to be visible in the figure. The gray shaded band is the polarization envelope. A common luminosity uncertainty of 8.1% is not included.

Figure 13

The cross section ratio of $\psi (2S)$ over $J/\psi$ as a function of their $p_T$ measured by STAR (red solid star) is compared to results from CDF (open circles), PHENIX (open boxes), HERA-B (solid-down-triangles and open-up-triangles), ATLAS (gray crosses), CMS (gray solid and open triangle-crosses) experiments, and the prediction from ICEM (purple band). The bar and box indicates the statistical and total systematic uncertainty, respectively.

Figure 14

(a) The $J/\psi$ differential full production cross sections as a function of $p_T^{J/\psi }$ in $\mathrm{proton}+\mathrm{proton}$ collisions at $\sqrt{s}=510$ and 500 GeV measured through the ${\mu }^{+}{\mu }^{-}$ (blue stars) and $e^{+}{e}^{-}$ decay channels (red circles). The shaded region around the data points denotes the polarization envelope and the green curve is the estimation of the $B$-hadrons feed-down from FONLL [40]. (b, c, d) Ratios of data and different model calculations to the Levy fit function. The bars and boxes indicate the statistical and total systematic uncertainty, respectively. A common luminosity uncertainties of 11.2% and 8.1% for the ${\mu }^{+}{\mu }^{-}$ and $e^{+}{e}^{-}$ decay channels are not included.

Figure 15

The $x_T$ dependence of pion, proton, and $J/\psi$ from different experiments.