$J/\psi$ and $\psi \mathbf{(}2S\mathbf{)}$ production at forward rapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section, mean transverse momentum, mean transverse momentum squared of inclusive $J/\psi$, and cross section ratio of $\psi (2S)$ to $J/\psi$ at forward rapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ via the dimuon decay channel. Comparison is made to inclusive $J/\psi$ cross sections measured at $\sqrt{s}=200\mathrm{GeV}$ and 2.76–13 TeV. The result is also compared to leading-order nonrelativistic QCD calculations coupled to a color-glass-condensate description of the low-$x$ gluons in the proton at low transverse momentum ($p_T$) and to next-to-leading order nonrelativistic QCD calculations for the rest of the $p_T$ range. These calculations overestimate the data at low $p_T$. While consistent with the data within uncertainties above $\approx 3\mathrm{GeV}/c$, the calculations are systematically below the data. The total cross section times the branching ratio is BR $d{\sigma }_{pp}^{J/\psi }/dy(1.2<|y|<2.2,0<p_T<10\mathrm{GeV}/c)=54.3\pm 0.5(\mathrm{stat})\pm 5.5(\mathrm{syst})\mathrm{nb}$.

Figure 1

A side view of the PHENIX detector, concentrating on the muon arm instrumentation.

Figure 2

Raw unlike-sign dimuon spectra (closed [black] circles) along with normalized like-sign background (upward [red] triangles) and normalized mixed-event background (inverted [blue] triangles) for (a) one $p_T$ bin and (b) one rapidity bin. Panels (c) and (d) show the background-subtracted spectra fitted as described in the text for (c) one $p_T$ bin and (d) one rapidity bin.

Figure 3

Raw unlike-sign dimuon spectrum summed over $p_T$ and the whole backward rapidity range, $-2.2<y<-1.2$.

Figure 4

$A{ϵ}_{\mathrm{rec}}$ as a function of $p_T$ for $1.2<y<2.2$ (closed [red] circles) and $-2.2<y<-1.2$ (open [blue] circles).

Figure 5

The inclusive $J/\psi$ differential cross section as a function of $p_T$ at $1.2<|y|<2.2$ at 510 GeV (closed [red] circles) and at 200 GeV (open [blue] squares). The error bars represent the statistical uncertainties, and gray shaded bands (although too small to appear on the data points) are added representing the quadratic sum of type-B systematic uncertainties. NRQCD calculations at 510 GeV [8] are also shown.

Figure 6

The inclusive $J/\psi$ differential cross section integrated over $0<p_T<10$ $\mathrm{GeV}/c$ as a function of rapidity at 510 GeV (closed [red] circles) and at 200 GeV (open [blue] squares). The error bars represent the statistical uncertainties, and the gray shaded band represents the quadratic sum of type-B systematic uncertainties. NLO-NRQCD calculations [8] are also shown.

Figure 7

Comparison of world data on the ratio of $\psi (2s)$ to $J/\psi$ mesons in dilepton decays [7, 17, 30, 31, 32, 33, 34, 35, 36, 37, 38]. The associated uncertainties are the quadrature sum of the statistical and systematic uncertainties.

Figure 8

$⟨p_T⟩$ as a function of $\sqrt{s}$ for $J/\psi$ from this work at 510 GeV (closed [red] circle), from PHENIX at 200 GeV [2] at midrapidity (closed [blue] square) and forward rapidity (open [blue] square), and from ALICE at different energies [6] (closed [green] diamonds).

Figure 9

$⟨p_T^2⟩$ as a function of $\sqrt{s}$ for $J/\psi$. The figure includes results from this work at 510 GeV (closed [red] circle) and PHENIX results at 200 GeV [2] at midrapidity (closed [blue] square) and forward rapidity (open [blue] square). Also, shown are higher-energy data from CDF [41] (closed [cyan] downward triangle) and ALICE [6] (closed [green] diamonds). Also, shown at lower energies are data from NA38/NA50/NA51 [2, 42] (open [black] circles) and E789 [44] (closed [magenta] upward triangle).

Figure 10

Inclusive $J/\psi$ differential cross section as a function of rapidity at $\sqrt{s}=7\mathrm{TeV}$ [3] fitted with different pythia tunes at the same energy.

Figure 11

Inclusive $J/\psi$ differential cross section, $d\sigma /dy$, as a function of $\sqrt{s}$. The vertical errors correspond to the quadratic sum of the statistical and type-B systematic uncertainties.