Nuclear-modification factor for open-heavy-flavor production at forward rapidity in Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV

Background: Heavy-flavor production in $p$ + $p$ collisions is a good test of perturbative-quantum-chromodynamics (pQCD) calculations. Modification of heavy-flavor production in heavy-ion collisions relative to binary-collision scaling from $p$ + $p$ results, quantified with the nuclear-modification factor ($R_{AA}$), provides information on both cold- and hot-nuclear-matter effects. Midrapidity heavy-flavor $R_{AA}$ measurements at the Relativistic Heavy Ion Collider have challenged parton-energy-loss models and resulted in upper limits on the viscosity-entropy ratio that are near the quantum lower bound. Such measurements have not been made in the forward-rapidity region.

Purpose: Determine transverse-momentum ($p_T$) spectra and the corresponding $R_{AA}$ for muons from heavy-flavor meson decay in $p$ + $p$ and Cu $+$ Cu collisions at $\sqrt{s_{NN}}=200$ GeV and $y=1.65$.

Method: Results are obtained using the semileptonic decay of heavy-flavor mesons into negative muons. The PHENIX muon-arm spectrometers measure the $p_T$ spectra of inclusive muon candidates. Backgrounds, primarily due to light hadrons, are determined with a Monte Carlo calculation using a set of input hadron distributions tuned to match measured-hadron distributions in the same detector and statistically subtracted.

Results: The charm-production cross section in $p$ + $p$ collisions at $\sqrt{s}=200$ GeV, integrated over $p_T$ and in the rapidity range $1.4<y<1.9$, is found to be $d{\sigma }_{c\overline{c}}/dy=0.139\pm 0.029{\left(\mathrm{stat}\right)}_{-0.058}^{+0.051}\left(\mathrm{syst}\right)$ mb. This result is consistent with a perturbative fixed-order-plus-next-to-leading-log calculation within scale uncertainties and is also consistent with expectations based on the corresponding midrapidity charm-production cross section measured by PHENIX. The $R_{AA}$ for heavy-flavor muons in Cu $+$ Cu collisions is measured in three centrality bins for $1<p_T<4$ GeV/$c$. Suppression relative to binary-collision scaling ($R_{AA}<1$) increases with centrality.

Conclusions: Within experimental and theoretical uncertainties, the measured charm yield in $p$ + $p$ collisions is consistent with state-of-the-art pQCD calculations. Suppression in central Cu $+$ Cu collisions suggests the presence of significant cold-nuclear-matter effects and final-state energy loss.

Figure 1

Side view of the PHENIX muon detectors (2005).

Figure 2

Schematic representation of $r_{\mathrm{ref}}$ variable.

Figure 3

Schematic representation of track selection variables DG0 and DDG0.

Figure 4

$p\delta \theta$ distributions for negatively charged inclusive muon candidates, $3<p_T<4$ GeV/$c$, measured in the north muon arm for the $20\%$ most central $\mathrm{Cu}+\mathrm{Cu}$ collisions. (a) Comparison of the distribution inside (black squares) and outside (red triangles) the $\delta z$ cut. (b) Comparison of the same distributions, but the distribution outside the $\delta z$ cut (red triangles) is normalized to the distribution inside the $\delta z$ cut (black squares) in the region $p\delta \theta >{p\delta \theta }_{\max }$. In both panels, the vertical dashed line corresponds to ${p\delta \theta }_{\max }$.

Figure 5

Vertex $z$ distribution of muon candidates reconstructed in the north ($z>0$) MuID Gap4, relative to the event vertex $z$ distribution (black circles). The vertex $z$ dependencies of the various contributions to the inclusive muon spectra are represented schematically as colored boxes.

Figure 6

Pion cross sections as a function of $pt$ used as initial hadron cocktail input, for several rapidity intervals in $[1.0,2.2]$ (blue lines) compared to a fit to the PHENIX ${\pi }^0$ data at $y=0$ [29] (black line, open black circles) and BRAHMS ${\pi }^{-}$ data at $y=2.95$ [34] (open black circles).

Figure 7

Simulated $p_z$ distributions for particles that stop in MuID Gap3: (black squares) all particles; (red triangles) stopped hadrons; (blue circles) decay muons.

Figure 8

Vertex $z$ distribution of tracks reconstructed in the north ($z>0$) MuID Gap4 for two transverse-momentum bins. The real data (black solid circles) are compared to a given hadron-cocktail package (blue open diamonds). The offset between data and the hadron cocktail is the contribution from heavy-flavor decays. The ${\chi }_{\mathrm{Gap}4}^2$ is defined in the text.

Figure 9

Relative dispersion between the $N_C$ yields obtained with the five hadron cocktails for the $p+p$ analysis. Each hadron cocktail package is compared to the mean of the five packages for the south (a) and north (b) muon arm.

Figure 10

Production cross section of negative muons from heavy-flavor meson decay as a function of $p_T$ in $p+p$ collisions at $\sqrt{s}=200$ GeV. Vertical errors bars and boxes correspond to statistical and systematic uncertainties, respectively, as described in the text.

Figure 11

Invariant production yields of negative muons from heavy-flavor meson decay as a function $p_T$ in $p+p$ collisions at $\sqrt{s}=200$ GeV (open squares) and in $\mathrm{Cu}+\mathrm{Cu}$ collisions for three different centrality bins (40–94%, 20–40%, and 0–20%), scaled by powers of 10 for clarity (filled circles). The solid line associated with each set of points corresponds to a fit to the $p+p$ invariant yield distribution described in the text, scaled by the appropriate number of binary collisions $N_{\mathrm{coll}}$ when comparing to the $\mathrm{Cu}+\mathrm{Cu}$ measurements.

Figure 12

$c\overline{c}$ production cross section as a function of rapidity in $p+p$ collisions, measured using semileptonic decay to electrons from Adare et al. [38] (solid square) and to muons (solid circle).

Figure 13

Transverse-momentum distribution of $R_{AA}$ for negative muons from heavy-flavor meson decay in $\mathrm{Cu}+\mathrm{Cu}$ collisions in the following centrality bins: 40–94% (a), 20–40% (b), and 0–20% (c). Also shown in (c) is a theoretical calculation from Refs. [40, 41], discussed in Sec. 5.

Figure 14

Comparison of $R_{AA}$ as a function of $N_{\mathrm{part}}$ between negative muons from heavy-flavor decay reconstructed at forward rapidity ($1.4<y<1.9$) and $p_T>2$ GeV in $\mathrm{Cu}+\mathrm{Cu}$ collisions (red squares) and nonphotonic electrons reconstructed at midrapidity and $p_T>3$ GeV in $\mathrm{Au}+\mathrm{Au}$ collisions from Adare et al. [4]) (blue circles).