Limits on intrinsic charm production from the SeaQuest experiment

Background: A nonperturbative charm production contribution, known as intrinsic charm, has long been speculated but has never been satisfactorily proven. The SeaQuest experiment at the Fermi National Accelerator Laboratory (FNAL) is in an ideal kinematic region to provide evidence of $J/\psi$ production by intrinsic charm.

Purpose: $J/\psi$ production in the SeaQuest kinematics is calculated with a combination of perturbative quantum chromodynamics (QCD) and intrinsic charm to see whether the SeaQuest data can put limits on an intrinsic charm contribution.

Methods: $J/\psi$ production in perturbative QCD is calculated to next-to-leading order in the cross section. Cold nuclear matter effects include nuclear modification of the parton densities, absorption by nucleons, and $p_T$ broadening by multiple scattering. The $J/\psi$ contribution from intrinsic charm is calculated assuming production from a $|uudc\overline{c}\rangle$ Fock state.

Results: The nuclear modification factor $R_{pA}$ is calculated as a function of $x_F$ and $p_T$ for $p+\mathrm{C}, p+\mathrm{Fe}$, and $p+\mathrm{W}$ interactions relative to $p+\mathrm{d}$. Previous data from the E866 experiment at FNAL is also shown and compared with the calculations.

Conclusions: The SeaQuest kinematic acceptance is ideal for testing the limits on intrinsic charm in the proton.

Figure 1

The $J/\psi$ production cross sections in the CEM in $p+p$ collisions at $\sqrt{s}=15.4$ GeV as a function of (a) $x_F$ and (b) $p_T$, integrated over all phase space, are shown. The solid curves show the central values while the dashed curves outline the upper and lower limits of the uncertainty band.

Figure 2

The contributions to the $J/\psi$ production cross sections in the CEM in $p+p$ collisions at $\sqrt{s}=15.4$ GeV as a function of (a) $x_F$ and (b) $p_T$ are shown for the $gg$ (solid), $q\overline{q}$ (dashed) and $qg$ (dot-dashed) initial states.

Figure 3

The EPPS16 ratios, with uncertainties, are shown at the scale of (a) the $J/\psi$ mass for gluons, (b) the up sea quark distribution, and (c) the valence up quark distribution as a function of momentum fraction $x$. The central set is denoted by the solid curves while the dashed curves give the upper and lower limits of the uncertainty bands. The results are given for $A=12$ (black), 56 (red), and 184 (blue). The vertical lines indicate the $x$ range of the SeaQuest measurement, $0.068<x<0.136$.

Figure 4

The probability distributions for $J/\psi$ production from a five-particle proton Fock state as a function of (a) $x_F$ and (b) $p_T$. The results are shown for different values of the $k_T$ range for the light and charm quarks. The red curve employs the default values, $k_q^{\max }=0.2$ GeV and $k_c^{\max }=1.0$ GeV while the blue dashed curve increases $k_q^{\max }$ and $k_c^{\max }$ by a factor of two and the dot-dashed magenta curve employs half the values of $k_q^{\max }$ and $k_c^{\max }$. The solid black curve shows the $x$ and $p_T$ distributions for a single charm quark from the state.

Figure 5

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $x_F$ for pQCD production alone for (a) carbon, (b) iron, and (c) tungsten targets relative to deuterium. Results are shown for nPDF effects alone (red), nPDFs with an additional $k_T$ kick (magenta), nPDFs and absorption (blue), and nPDFs, absorption and $k_T$ broadening (cyan). The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 6

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $p_T$ for pQCD production alone for (a) carbon, (b) iron, and (c) tungsten targets relative to deuterium. Results are shown for EPPS16 nPDFs alone (red), EPPS16 with an additional $k_T$ kick (magenta), nPDFs with absorption (blue), and nPDFs, absorption and $k_T$ broadening (cyan). The solid lines show the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 7

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $x_F$ for the combined pQCD and intrinsic charm cross section ratios for (a) carbon, (b) iron and (c) tungsten targets relative to deuterium. All calculations are shown with ${\sigma }_{\mathrm{abs}}=0$. Results with nPDF effects and the same $k_T$ in $p+\mathrm{d}$ and $p+A$ are shown in the red, blue, and black curves while nPDF effects with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.1% in the red and magenta curves; 0.31% in the blue and cyan curves; and 1% in the black and green curves. The solid lines show the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 8

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $p_T$ for the combined pQCD and intrinsic charm cross section ratios for (a) carbon, (b) iron, and (c) tungsten targets relative to deuterium. All calculations are shown with ${\sigma }_{\mathrm{abs}}=0$. Results with nPDF effects and the same $k_T$ in $p+\mathrm{d}$ and $p+A$ are shown in the red, blue, and black curves while nPDFs with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.1% in the red and magenta curves; 0.31% in the blue and cyan curves; and 1% in the black and green curves. The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 9

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $x_F$ for the combined pQCD and intrinsic charm cross section ratios for (a) carbon, (b) iron, and (c) tungsten targets relative to deuterium. All calculations are shown with nuclear absorption included. Results with EPPS16 and the same $k_T$ in $p+\mathrm{d}$ and $p+A$ are shown in the red, blue, and black curves while EPPS16 with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.1% in the red and magenta curves; 0.31% in the blue and cyan curves; and 1% in the black and green curves. The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 10

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $pT$ for the combined pQCD and intrinsic charm cross section ratios for (a) carbon, (b) iron, and tungsten targets relative to deuterium. All calculations are shown with nuclear absorption included. Results with EPPS16 and the same $k_T$ in $p+\mathrm{d}$ and $p+A$ are shown in the red, blue, and black curves while EPPS16 with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.1% in the red and magenta curves; 0.31% in the blue and cyan curves; and 1% in the black and green curves. The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 11

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of (a) $x_F$ and (b) $p_T$ for the combined pQCD and intrinsic charm cross section ratios for carbon (red and magenta curves), iron (blue and cyan curves), and tungsten (black and green curves) targets relative to a proton target. All calculations are shown with nuclear absorption included. Results with EPPS16 and the same $k_T$ in $p+p$ and $p+A$ are shown in the red, blue, and black curves while EPPS16 with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.31% in all cases. The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 12

The nuclear modification factors for $J/\psi$ production in SeaQuest as a function of $p_T$ for the combined pQCD and intrinsic charm cross section ratios for carbon (red and magenta curves), iron (blue and cyan curves), and tungsten (black and green curves) targets relative to a proton target. All calculations are shown with nuclear absorption included. Results with EPPS16 and the same $k_T$ in $p+\mathrm{d}$ and $p+A$ are shown in the red, blue, and black curves while EPPS16 with an enhanced $k_T$ kick in the nucleus are shown in the magenta, cyan, and green curves. The probability for IC production is 0.31% in all cases. A broader IC distribution is assumed here, corresponding to the blue dashed curve in Fig. 4. The solid lines shown the results with the central EPPS16 set while the dashed curves denote the limits of adding the EPPS16 uncertainties in quadrature.

Figure 13

The exponent $\alpha$ as a function of (a) $x_F$ and as a function of $p_T$ for the (b) low-$x_F$, (c) intermediate-$x_F$, and (d) high-$x_F$ regions. The dotted magenta curves are without intrinsic charm while the solid red, dashed blue, and dot-dashed green curves employ $P_{\mathrm{ic}5}^0=0.1\%$, 0.31%, and 1% respectively. The E866 data [6] are shown by the black points.

Figure 14

The $J/\psi$ cross sections in $p+p$ collisions at $\sqrt{s}=38.8$ GeV with and without an intrinsic charm contribution as a function of (a) $x_F$ and $p_T$ at (b) low-$x_F$, (c) intermediate-$x_F$, and (d) high-$x_F$. The solid curves do not include intrinsic charm while the dashed, dot-dashed, and dotted curves are calculated with $P_{\mathrm{ic}5}^0=0.1\%$, 0.31%, and 1%, respectively. The vertical bars on the $x_F$ distributions show the upper and lower limits of the $x_F$ ranges for the corresponding $p_T$ distributions shown in panels (b)–(d). The color of the bars matches the color of the curves in panels (b)–(d).