Hadronic resonance production in $d+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV measured at the BNL Relativistic Heavy Ion Collider

We present the first measurements of the $\rho (770){}^0,K^{*}(892),\Delta (1232){}^{++},\Sigma (1385)$, and $\Lambda (1520)$ resonances in $d+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, reconstructed via their hadronic decay channels using the STAR detector (the solenoidal tracker at the BNL Relativistic Heavy Ion Collider). The masses and widths of these resonances are studied as a function of transverse momentum $p_T$. We observe that the resonance spectra follow a generalized scaling law with the transverse mass $m_T$. The $\langle p_T\rangle$ of resonances in minimum bias collisions are compared with the $\langle p_T\rangle$ of $\pi ,K$, and $\overline{p}$. The ${\rho }^0/{\pi }^{-},K^{*}/K^{-},{\Delta }^{++}/p,\Sigma (1385)/\Lambda$, and $\Lambda (1520)/\Lambda$ ratios in $d+\mathrm{Au}$ collisions are compared with the measurements in minimum bias $p+p$ interactions, where we observe that both measurements are comparable. The nuclear modification factors ($R_{d\mathrm{Au}}$) of the ${\rho }^0,K^{*}$, and ${\Sigma }^{*}$ scale with the number of binary collisions ($N_{\mathrm{bin}}$) for $p_T>$ 1.2 GeV/$c$.

Figure 1

$\mathit{dE}/\mathit{dx}$ for charged particles vs momentum measured by the TPC in $d+\mathrm{Au}$ collisions. The curves are the Bichsel function [25] for different particle species.

Figure 2

${\rho }^0$ reconstruction efficiency×detector acceptance as a function of the invariant mass for minimum bias $d+\mathrm{Au}$. The error shown is due to the available statistics in the simulation.

Figure 3

$K^{*0}$ and $K^{\pm }$ reconstruction efficiency×detector acceptance as a function of $p_T$ for minimum bias $d+\mathrm{Au}$ and three different centralities.

Figure 4

${\Delta }^{++}$ reconstruction efficiency×detector acceptance as a function of the invariant mass for minimum bias $d+\mathrm{Au}$ and $p+p$. The error shown is due to the available statistics in the simulation.

Figure 5

${\Lambda }^{*}$ reconstruction efficiency×detector acceptance as a function of $p_T$ for minimum bias $d+\mathrm{Au}$. The error shown is due to the available statistics in the simulation.

Figure 6

${\Sigma }^{*\pm }$ reconstruction efficiency×detector acceptance as a function of $p_T$ for minimum bias $d+\mathrm{Au}$ and three different centralities. The error shown is due to the available statistics in the simulation.

Figure 7

Raw ${\pi }^{+}{\pi }^{-}$ invariant mass distribution at midrapidity after subtraction of the like-sign reference distribution for minimum bias $d+\mathrm{Au}$ collisions with the hadronic cocktail fit.

Figure 8

${\rho }^0$ mass as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ interactions and 0–20%, 20–40%, and 40–100% of the total $d+\mathrm{Au}$ cross section (upper panel). The errors shown are statistical only. The comparison of the ${\rho }^0$ mass as a function of $p_T$ at $\left|y\right|<0.5$ measured in minimum bias $d+\mathrm{Au}$, $p+p$, and high multiplicity $p+p$ [3] interactions (lower panel). The brackets indicate the systematic uncertainty ,and it is shown only for the minimum bias $d+\mathrm{Au}$ measurement for clarity. The diamonds have been shifted to lower values on the abscissa by 100 MeV/$c$ in $p_T$ for clarity.

Figure 9

Invariant ${\pi }^{+}{\pi }^{-}$ mass distribution after background subtraction for minimum bias $p+p$ collisions measured by NA27. For details, see Ref. [34]. The vertical dash-dotted line represents the average of the ${\rho }^0$ mass 775.8 ± 0.5 MeV/$c^2$ measured in $e^{+}{e}^{-}$ [26]. The vertical dashed line is the ${\rho }^0$ mass 762.6 ± 2.6 MeV/$c^2$ reported by NA27 [34].

Figure 10

Mixed-event background subtracted $K\pi$ raw invariant mass distribution for a particular $K^{*0}$ $p_T$ bin (upper panel) and the mixed-event background subtracted $K_S^0{\pi }^{\pm }$ raw invariant mass distribution integrated over the $K^{*\pm }$ $p_T$ (lower panel) at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ interactions. The dashed lines are the linear function that describes the residual background.

Figure 11

$K^{*}$ mass (upper panel) and width (lower panel) as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions. In the upper panel, the solid line is the PDG $K^{*0}$ mass (0.8961 GeV/$c^2$) [26]. The dashed line is the PDG $K^{*\pm }$ mass (0.8917 GeV/$c^2$) [26]. In the lower panel, the solid line is the $K^{*0}$ and $K^{*\pm }$ widths (0.0507 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties.

Figure 12

Mixed-event background subtracted $p\pi$ raw invariant mass distribution for a particular $p_T$ bin at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions (upper panel) and for minimum bias $p+p$ collisions (lower panel). The dashed lines are the linear function that describes the residual background.

Figure 13

${\Delta }^{++}$ mass (upper panel) and width (lower panel) as functions of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions. The solid lines are the PDG ${\Delta }^{++}$ mass (1.232 GeV/$c^2$) and width (0.120 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties.

Figure 14

${\Delta }^{++}$ mass (upper panel) and width (lower panel) as functions of $p_T$ at midrapidity for minimum bias $p+p$ interactions. The solid lines are the PDG ${\Delta }^{++}$ mass (1.232 GeV/$c^2$) and width (0.120 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties.

Figure 15

Mixed-event background subtracted $\Lambda \pi$ raw invariant mass distribution integrated over the ${\Sigma }^{*}$ $p_T$ at $\left|y\right|<0.75$ for minimum bias $d+\mathrm{Au}$ collisions.

Figure 16

Mixed-event background subtracted $\mathit{pK}$ raw invariant mass distribution integrated over the ${\Lambda }^{*}$ $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions. The dashed line is the linear function that describes the residual background.

Figure 17

${\Sigma }^{*}$ mass as a function of $p_T$ at $\left|y\right|<0.75$ for minimum bias $d+\mathrm{Au}$ collisions. The solid line is the PDG ${\Sigma }^{*}$ mass average between the masses of ${\Sigma }^{*+}$ and ${\Sigma }^{*-}$ (1.3850 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties.

Figure 18

${\Lambda }^{*}$ mass as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions. The solid line is the PDG ${\Lambda }^{*}$ mass (1.5195 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties.

Figure 19

${\Lambda }^{*}$ width as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions. The solid line is the PDG ${\Lambda }^{*}$ width (0.0156 GeV/$c^2$) [26]. The brackets indicate the systematic uncertainties. Our simulations, including both the detector resolution and kinetic cuts, show a width of 0.022 GeV/$c^2$.

Figure 20

${\rho }^0$ invariant yields as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ interactions and 0–20%, 20–40%, and 40–100% of the total $d+\mathrm{Au}$ cross section. The lines are fits to a Levy function [Eq. (8)]. The errors are statistical only and smaller than the symbols.

Figure 21

($K^{*}+{\overline{K}}^{*}$)/2 together with the ($K^{*+}+K^{*-})/2$ invariant yields as a function of $p_T$ at $\left|y\right|<0.5$ for minimum bias $d+\mathrm{Au}$ collisions and three different centralities. The lines are fits to a Levy function [Eq. (8)]. The errors are statistical only and smaller than the symbols.

Figure 22

$({\Delta }^{++}+{\overline{\Delta }}^{--})/2$ invariant yields as a function of $p_T$ at $\left|y\right|<$ 0.5 for minimum bias $p+p,d+$ Au interactions, and 0–20%, 20–40%, and 40–100% of the total $d+\mathrm{Au}$ cross section. The lines are fits to an exponential function [Eq. (9)]. The errors are statistical only and smaller than the symbols for the spectra measured in $d+\mathrm{Au}$. In the $p+p$ measurement, the errors shown also include the systematic uncertainties.

Figure 23

${\Sigma }^{*}$ invariant yields as a function of $p_T$ at $\left|y\right|<$ 0.75 for minimum bias $d+\mathrm{Au}$ collisions and three different centralities. The lines are fits to an exponential function [Eq. (9)].

Figure 24

${\Lambda }^{*}$ invariant yields as a function of $p_T$ at $\left|y\right|<$ 0.5 for minimum bias $d+\mathrm{Au}$ collisions. The line is a fit to an exponential function [Eq. (9)].

Figure 25

Proton and pion spectra [56] plotted together with the rescaled minimum bias $d+\mathrm{Au}$ spectra of ${\rho }^0,K^{*},{\Delta }^{++}$, and ${\Sigma }^{*}$, where the transverse mass scaling is observed. The inset plot is a zoom-in of the region $1⩽m_T⩽2$ GeV/$c^2$ on a linear scale.

Figure 26

${\rho }^0$ and $K^{*}$ $\langle p_T\rangle$ as a function of $\langle {\mathit{dN}}_{\mathrm{ch}}/d\eta \rangle$ compared with that of ${\pi }^{-},K^{-}$, and $\overline{p}$ for minimum bias $p+p$, minimum bias $d+\mathrm{Au}$, and 0–20%, 20–40%, and 40–100% of the total $d+\mathrm{Au}$ cross section [55]. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 27

${\Delta }^{++},{\Sigma }^{*}$, and ${\Lambda }^{*}$ $\langle p_T\rangle$ as a function of $\langle {\mathit{dN}}_{\mathrm{ch}}/d\eta \rangle$ compared with those of ${\pi }^{-},K^{-}$, and $\overline{p}$ for minimum bias $p+p$, minimum bias $d+\mathrm{Au}$, and 0–20%, 20–40%, and 40–100% of the total $d+\mathrm{Au}$ cross section [55]. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 28

$\langle p_T\rangle$ of various particles for different systems, minimum bias $p+p$ and $d+\mathrm{Au}$, and central $\mathrm{Au}+\mathrm{Au}$ collisions. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 29

${\rho }^0/{\pi }^{-}$ ratios in $p+p$, various centralities in $d+\mathrm{Au}$, and in peripheral $\mathrm{Au}+\mathrm{Au}$ collisions as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 30

$K^{*}/K^{-}$ ratios in $p+p$ and various centralities in $d+\mathrm{Au}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 31

${\Delta }^{++}/p$ ratios in $p+p$ and various centralities in $d+\mathrm{Au}$ collisions as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 32

${\Sigma }^{*}/\Lambda$ ratios in $p+p$, various centralities in $d+\mathrm{Au}$, and in central $\mathrm{Au}+\mathrm{Au}$ collisions as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 33

${\Lambda }^{*}/\Lambda$ ratios in $p+p$, minimum bias $d+\mathrm{Au}$, and two different centralities in $\mathrm{Au}+\mathrm{Au}$ collisions as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 34

Resonance ratios normalized by their ratio measured in $p+p$ collisions at the same beam energy as a function of ${\mathit{dN}}_{\mathrm{ch}}/d\eta$. The errors shown are the quadratic sum of the statistical and systematic uncertainties.

Figure 35

${\rho }^0$ $R_{d\mathrm{Au}}$ compared with the charged hadrons $R_{d\mathrm{Au}}$. The shaded box is the error on the overall normalization and the black box is the error on $N_{\mathrm{bin}}$.

Figure 36

Same as Fig. 35, but for the $K^{*}$ $R_{d\mathrm{Au}}.$

Figure 37

Same as Fig. 35, but for ${\Sigma }^{*}$ $R_{d\mathrm{Au}}$.