TABLE I. A summary of the fiducial and total cross sections of the $J/\psi$ production via the $\mu^{+}\mu^{-}$ decay channel in proton-proton collisions at $\sqrt{s}$ = 510 GeV. The fiducial volume is defined as $p_{T}^{\mu}$ < 1.3 GeV/c and $|\eta^{\mu}|$ < 0.5. A common luminosity uncertainty of 11.2% is not included.
| $p_T^{J/\psi} \rm range \\ (GeV/c)$ | $p_T^{J/\psi} \rm position \\ (GeV/c)$ | $\rm{BR} \times\frac{d\sigma^{2}_{fid}}{2\pi p_{T} dy dp_T}\pm\delta_{stat.}\pm\delta_{sys.} \rm \\ (pb/(GeV/c)^{2})$ | $\rm{BR} \times\frac{d\sigma^{2}_{full}}{2\pi p_{T} dy dp_T}\pm\delta_{stat.}\pm\delta_{sys.} \ ^{+\delta_{pol.}\ \rm upper}_{-\delta_{pol.}\ \rm lower} \rm \\ (pb/(GeV/c)^{2})$ |
| 0.0 - 1.5 | 0.67 | $(9.3 \pm1.6 \pm1.5) \times 10^{2}$ | $(5.4 \pm0.9 \pm0.9 ^{+11.5}_{-1.3}) \times 10^{3}$ |
| 1.5 - 3.0 | 2.07 | $(2.17 \pm0.21 \pm0.33) \times 10^{2}$ | $(1.81 \pm0.19 \pm0.27 ^{+7.26}_{-0.54}) \times 10^{3}$ |
| 3.0 - 5.0 | 3.65 | $(4.4 \pm0.4 \pm0.6) \times 10^{1}$ | $(2.57 \pm0.28 \pm0.35 ^{+7.19}_{-0.73}) \times 10^{2}$ |
| 5.0 - 7.0 | 5.68 | $(6.7 \pm0.9 \pm0.9) \times 10^{0}$ | $(2.62 \pm0.34 \pm0.33 ^{+4.26}_{-0.62}) \times 10^{1}$ |
| 7.0 - 9.0 | 7.73 | $(1.71 \pm0.33 \pm0.23) \times 10^{0}$ | $(4.6 \pm0.9 \pm0.6 ^{+3.7}_{-0.9}) \times 10^{0}$ |
TABLE II. A summary of the fiducial and total cross sections for the inclusive $J/\psi$ production via the $e^{+}e^{-}$ decay channel in proton-proton collisions at $\sqrt{s}$ = 500 GeV. A common luminosity uncertainty of 8.1% is not included.
| $p_T^{J/\psi} \rm range \\ (GeV/c)$ | $p_T^{J/\psi} \rm position \\ (GeV/c)$ | $\rm{BR} \times\frac{d\sigma^{2}_{fid}}{2\pi p_{T} dy dp_T}\pm\delta_{stat.}\pm\delta_{sys.} \rm \\ (pb/(GeV/c)^{2})$ | $\rm{BR} \times\frac{d\sigma^{2}_{full}}{2\pi p_{T} dy dp_T}\pm\delta_{stat.}\pm\delta_{sys.} \ ^{+\delta_{pol.}\ \rm upper}_{-\delta_{pol.}\ \rm lower} \rm \\ (pb/(GeV/c)^{2})$ |
| 4.0 - 4.5 | 4.23 | $(1.64 \pm0.20 \pm0.12) \times 10^{1}$ | $(1.32 \pm0.16 \pm0.10 ^{+0.72}_{-0.35}) \times 10^{2}$ |
| 4.5 - 5.0 | 4.73 | $(1.88 \pm0.16 \pm0.15) \times 10^{1}$ | $(9.0 \pm0.8 \pm0.7 ^{+5.2}_{-2.0}) \times 10^{1}$ |
| 5.0 - 5.5 | 5.23 | $(1.36 \pm0.07 \pm0.11) \times 10^{1}$ | $(4.6 \pm0.2 \pm0.4 ^{+2.6}_{-0.8}) \times 10^{1}$ |
| 5.5 - 6.0 | 5.73 | $(10.3 \pm0.7 \pm0.8) \times 10^{0}$ | $(2.69 \pm0.17 \pm0.20 ^{+1.59}_{-0.39}) \times 10^{1}$ |
| 6.0 - 6.5 | 6.23 | $(7.6 \pm0.4 \pm0.6) \times 10^{0}$ | $(1.64 \pm0.09 \pm0.13 ^{+0.97}_{-0.24}) \times 10^{1}$ |
| 6.5 - 7.0 | 6.73 | $(5.40 \pm0.29 \pm0.31) \times 10^{0}$ | $(10.6 \pm0.6 \pm0.6 ^{+5.4}_{-1.6}) \times 10^{0}$ |
| 7.0 - 7.5 | 7.23 | $(3.15 \pm0.20 \pm0.20) \times 10^{0}$ | $(5.8 \pm0.4 \pm0.4 ^{+2.9}_{-0.9}) \times 10^{0}$ |
| 7.5 - 8.0 | 7.73 | $(2.41 \pm0.16 \pm0.16) \times 10^{0}$ | $(4.26 \pm0.28 \pm0.28 ^{+1.76}_{-0.61}) \times 10^{0}$ |
| 8.0 - 8.5 | 8.23 | $(1.40 \pm0.11 \pm0.13) \times 10^{0}$ | $(2.40 \pm0.19 \pm0.23 ^{+0.97}_{-0.33}) \times 10^{0}$ |
| 8.5 - 9.0 | 8.73 | $(10.6 \pm0.8 \pm0.6) \times 10^{-1}$ | $(1.75 \pm0.14 \pm0.11 ^{+0.65}_{-0.23}) \times 10^{0}$ |
| 9.0 - 9.5 | 9.24 | $(7.5 \pm0.7 \pm0.4) \times 10^{-1}$ | $(12.0 \pm1.1 \pm0.7 ^{+4.0}_{-1.6}) \times 10^{-1}$ |
| 9.5 - 10.0 | 9.73 | $(5.26 \pm0.48 \pm0.33) \times 10^{-1}$ | $(8.3 \pm0.7 \pm0.5 ^{+2.4}_{-1.1}) \times 10^{-1}$ |
| 10.0 - 10.5 | 10.23 | $(3.26 \pm0.43 \pm0.21) \times 10^{-1}$ | $(5.06 \pm0.67 \pm0.32 ^{+1.57}_{-0.62}) \times 10^{-1}$ |
| 10.5 - 11.0 | 10.74 | $(2.31 \pm0.35 \pm0.14) \times 10^{-1}$ | $(3.51 \pm0.52 \pm0.22 ^{+1.02}_{-0.42}) \times 10^{-1}$ |
| 11.0 - 12.0 | 11.44 | $(1.58 \pm0.20 \pm0.13) \times 10^{-1}$ | $(2.33 \pm0.30 \pm0.19 ^{+0.62}_{-0.27}) \times 10^{-1}$ |
| 12.0 - 13.0 | 12.45 | $(7.5 \pm1.5 \pm0.6) \times 10^{-2}$ | $(10.7 \pm2.1 \pm0.9 ^{+2.3}_{-1.2}) \times 10^{-2}$ |
| 13.0 - 15.0 | 13.83 | $(3.5 \pm0.7 \pm0.6) \times 10^{-2}$ | $(4.9 \pm1.0 \pm0.8 ^{+1.0}_{-0.5}) \times 10^{-2}$ |
| 15.0 - 17.0 | 15.85 | $(2.02 \pm0.39 \pm0.31) \times 10^{-2}$ | $(2.7 \pm0.5 \pm0.4 ^{+0.4}_{-0.3}) \times 10^{-2}$ |
| 17.0 - 20.0 | 18.20 | $(0.84 \pm0.18 \pm0.17) \times 10^{-2}$ | $(1.07 \pm0.23 \pm0.22 ^{+0.13}_{-0.09}) \times 10^{-2}$ |