Measurements of $B\to J/\psi$ at forward rapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$

We report the first measurement of the fraction of $J/\psi$ mesons coming from $B$-meson decay ($F_{B\to J/\psi }$) in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$. The measurement is performed using the forward silicon vertex detector and central vertex detector at PHENIX, which provide precise tracking and distance-of-closest-approach determinations, enabling the statistical separation of $J/\psi$ due to $B$-meson decays from prompt $J/\psi$. The measured value of $F_{B\to J/\psi }$ is $8.1\%\pm 2.3\%(\text{stat})\pm 1.9\%(\text{syst})$ for $J/\psi$ with transverse momenta $0<p_T<5\mathrm{GeV}/c$ and rapidity $1.2<|y|<2.2$. The measured fraction $F_{B\to J/\psi }$ at PHENIX is compared to values measured by other experiments at higher center of mass energies and to fixed-order-next-to-leading-logarithm and color-evaporation-model predictions. The $b\overline{b}$ cross section per unit rapidity [$d\sigma /dy(pp\to b\overline{b})$] extracted from the obtained $F_{B\to J/\psi }$ and the PHENIX inclusive $J/\psi$ cross section measured at 200 GeV scaled with color-evaporation-model calculations, at the mean $B$ hadron rapidity $y=\pm 1.7$ in 510 GeV $p+p$ collisions, is $3.63_{-1.70}^{+1.92}\mu \mathrm{b}$. It is consistent with the fixed-order-next-to-leading-logarithm calculations.

Figure 1

The PHENIX detector setup for the 510 GeV $p+p$ data taking in 2012.

Figure 2

(a) 3D and (b) 2D projection of a muon from a $B$ meson to $J/\psi$ to dimuon decay to the transverse vertex plane ($x\text{−}y$) and definition of ${\mathrm{DCA}}_{\mathrm{R}}$.

Figure 3

The invariant mass of dimuons in the (a),(c) $1.2<y<2.2$ and (b),(d) $-2.2<y<-1.2$ regions. Raw yields (black solid), the combinatorial background using mixed events (red open rectangular) and like-sign dimuon pairs (green open triangle) are shown in panels (a) and (b). The combinatorial background subtracted yields are shown in panels (c) and (d). The magenta dashed lines represent the mass cut used to select $J/\psi$ candidates.

Figure 4

Comparison of the normalized ${\mathrm{DCA}}_{\mathrm{R}}$ distributions of single muons from inclusive $J/\psi$ events in data (red open circle) and simulation (blue solid triangle). Panels (a) and (b) show the comparison for integrated momenta and panels (c) and (d) show the comparison for the momentum-dependent ${\mathrm{DCA}}_{\mathrm{R}}$ resolution. There is good agreement between data and simulation.

Figure 5

Normalized ${\mathrm{DCA}}_{\mathrm{R}}$ distributions of simulated prompt $J/\psi$ (blue open circle) and $B\text{−}\text{meson}\to J/\psi$ events (green circle). The muon ${\mathrm{DCA}}_{\mathrm{R}}$ distributions are normalized by the total number of entries in the ${\mathrm{DCA}}_{\mathrm{R}}$ range of ($-0.4\mathrm{cm}$, 0.4 cm). Solid lines stand for the fits defined in Eq. (3) and Eq. (4).

Figure 6

The raw yields of data ([black] closed circles) and estimated background ${\mathrm{DCA}}_{\mathrm{R}}$ distributions within the $J/\psi$ mass window ($2.7–3.5\mathrm{GeV}/c^2$) are shown for (a) rapidity $1.2<y<2.2$ and (b) $-2.2<y<-1.2$ The combinatorial background defined as $f_{\text{combinatorial}}$ in Eq. (8) ([magenta] open triangle), the heavy-flavor-continuum ($c\overline{c}+b\overline{b}$) background defined as $f_{c\overline{c}+b\overline{b}}$ in Eq. (8) ([green] solid triangle) and the detector mismatching background defined as $f_{\text{mismatch}}$ in Eq. (8) ([blue] open circle) are determined using techniques described in the text.

Figure 7

Fit of dimuon mass spectra to determine the heavy-flavor-continuum background for (a) rapidity $1.2<y<2.2$ and (b) $-2.2<y<-1.2$. The fit function ([black] solid curve) includes the $J/\psi$ and $\psi \prime$ yields which already include the FVTX-MuTr mismatching background, the combinatorial background ([red] dashed curve) and the heavy-flavor-continuum background ([blue] dash-dotted curve). The total background ([yellow] solid-dotted curve) shows the combinatorial and the heavy-flavor-continuum background.

Figure 8

$B\to J/\psi$ fraction fit to muon ${\mathrm{DCA}}_{\mathrm{R}}$ in the (a) $1.2<y<2.2$ and (b) $-2.2<y<-1.2$ regions. The ([red] solid curve) stands for the total fit, which includes the prompt $J/\psi$ (solid blue), the $B\text{−}\text{meson}\to J/\psi$ ([green] filled region), the combinatorial background ([magenta] dashed curve), the $c\overline{c}+b\overline{b}$ background ([brown] long-dashed curve) and the detector mismatching background ([purple] short-dashed curve).

Figure 9

Comparison of PHENIX $B\to J/\psi$ fraction with the global data from CDF [3], ALICE [4], CMS [5] and LHCb [6, 7] experiments for $J/\psi p_T$ and also with $0<p_T<5\mathrm{GeV}/c$, (a) as a function of center of mass energy integrated in the $J\psi$ interval $0<p_T<5\mathrm{GeV}/c$, and (b) as a function of inclusive $J/\psi p_T$. The uncertainty of the PHENIX measurement is statistical and systematic combined.

Figure 10

In $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ and $1.2<|y|<2.2$ rapidity region, comparison of PHENIX $B\to J/\psi$ fraction ($F_{B\to J/\psi }$) measured in integrated $J/\psi p_T$ range of $p_T<5\mathrm{GeV}/c$ with $J/\psi p_T$ dependent (shown in solid red) and $p_T$ integrated within $0–5\mathrm{GeV}/c$ region (shown in dashed blue) $B\to J/\psi$ fraction predicted by the $\mathrm{FONLL}+\mathrm{CEM}$ [12, 21, 22] model in 500 GeV $p+p$ collisions. The uncertainty of the PHENIX measurement is statistical and systematic combined.

Figure 11

The average $b\overline{b}$ cross section per unit rapidity [$d\sigma /dy(pp\to b\overline{b}+X)$] is determined by the $B\to J/\psi$ fraction ($F_{B\to J/\psi }$) discussed in the paper and the inclusive $J/\psi$ cross section in 510 GeV $p+p$ collisions extrapolated from PHENIX 200 GeV $p+p$ measurements and the energy scaling factor provided by the CEM [22]. The extrapolated $d\sigma /dy(pp\to b\overline{b})$ (shown as open red circles) at $B$ hadron mean rapidity $y=\pm 1.7$ in 510 GeV $p+p$ collisions is compared with the rapidity-dependent $B$ cross section (shown as blue solid line) calculated in FONLL. The PHENIX result is also comparable with the value of UA1 630 GeV $p+\overline{p}$ $d\sigma /dy(p\overline{p}\to b\overline{b})$ extracted from $p_T>8\mathrm{GeV}/c$ to $p_T>0$ range [28, 29] and unscaled with energy. The uncertainty of the extrapolated value at PHENIX (UA1) combines the statistical and systematic uncertainty from experiment with the CEM uncertainty. The uncertainty of the FONLL calculations contains both $b$ quark mass and scaling uncertainties.