Inclusive ${\pi }^0$, $\eta$, and direct photon production at high transverse momentum in $p+p$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

We report a measurement of high-$p_T$ inclusive ${\pi }^0$, $\eta$, and direct photon production in $p+p$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$ at midrapidity ($0<\eta <1$). Photons from the decay ${\pi }^0\to \gamma \gamma$ were detected in the barrel electromagnetic calorimeter of the STAR experiment at the Relativistic Heavy Ion Collider. The $\eta \to \gamma \gamma$ decay was also observed and constituted the first $\eta$ measurement by STAR. The first direct photon cross-section measurement by STAR is also presented; the signal was extracted statistically by subtracting the ${\pi }^0$, $\eta$, and $\omega$$(782)$ decay background from the inclusive photon distribution observed in the calorimeter. The analysis is described in detail, and the results are found to be in good agreement with earlier measurements and with next-to-leading-order perturbative QCD calculations.

Figure 1

(a) Distribution of $r=E_{\text{BEMC}}/(E_{\text{BEMC}}+p_{\text{TPC}})$ in $d+\mathrm{Au}$ events, which shows beam background at $r>0.8$. The curve corresponds to a second-order polynomial fit, constrained to pass through zero at $r=1$, used to estimate the false rejection rate. (b) Distribution of $r$ in $p+p$ events.

Figure 2

Centrality selection in the $d+\mathrm{Au}$ data based on the FTPC multiplicity $N_{\text{FTPC}}$. Three centrality classes were defined, containing $0$%–$$$20\%$ most central, $20$%–$40\%$ midcentral, and $40$%–$$$100\%$ most peripheral events, respectively.

Figure 3

Electron energy measured in the BEMC after calibration, divided by the momentum measured in the TPC, in the $p+p$ data. The solid line is a Gaussian fit, which shows that the peak is centered at unity.

Figure 4

Distribution of the distances $D$ between BEMC points and their closest tracks, obtained from $p+p$ HighTower-$$1 data in the bin $4<p_T<5\hspace{0.5em}\mathrm{GeV}/c$. The curve shows a fit to Eq. (3); the vertical line indicates the CPV cut.

Figure 5

The energy asymmetry $Z_{\gamma \gamma }$ of photon pairs reconstructed in $p+p$ data (symbols) and in Monte Carlo simulation (histograms) for various triggers, normalized to unity for each trigger.

Figure 6

Distribution of ${\pi }^0$ candidates obtained from the $p+p$ data, as a function of (a) $\eta$ and (b) $\phi$, and (c) $p_T$ and (d) $m_{\gamma \gamma }$.

Figure 7

The same-event invariant mass distribution (crosses) and combinatorial background (histogram) observed in one $p_T$ bin of the $p+p$ data. Background estimated (a) from random event mixing and (b) from a linear combination of random and jet-aligned mixing; (c) background-subtracted distribution. The shaded areas indicate the regions where the mixed-event background was normalized to the same-event distributions.

Figure 8

A schematic view of two superimposed events, where the jet axes are aligned to preserve the jet-induced correlations in the mixed event.

Figure 9

The simulated low-mass background distributions from erroneous splitting of single photons in three bins of the reconstructed pair $p_T$. The distributions extend to larger invariant masses with increasing $p_T$ and move into the ${\pi }^0$ region (shown for $p_T=15\hspace{0.5em}\mathrm{GeV}/c)$.

Figure 10

The invariant mass distribution observed in one $p_T$ bin of the $p+p$ data (a) before and (b) after the low-mass background subtraction.

Figure 11

(a) Invariant mass spectrum of ${\pi }^0$’s reconstructed in the simulation (histogram) in comparison to the $p+p$ HighTower-$$1 data (symbols) in the $4<p_T<5\hspace{0.5em}\mathrm{GeV}/c$ bin. (b) Peak position and (c) width in the real data (solid symbols) and in the simulation (open symbols). The horizontal line in panel (b) shows the true ${\pi }^0$ mass.

Figure 12

(a) Invariant mass spectrum of $\eta$ mesons reconstructed in the simulation (histogram) in comparison to the $p+p$ HighTower-$$1 data (symbols) in the $4<p_T<5\hspace{0.5em}\mathrm{GeV}/c$ bin. (b) Peak position and (c) width in the real data (solid symbols) and in the simulation (open symbols). The horizontal line in panel (b) shows the true $\eta$ mass.

Figure 13

Acceptance and efficiency correction factor ${\varepsilon }_{\mathrm{acc}}$ for (a) ${\pi }^0$ and (b) $\eta$ calculated from the Monte Carlo simulation for the $p+p$ data.

Figure 14

Acceptance and efficiency correction factor ${\varepsilon }_{\mathrm{acc}}$ for the $p+p$ HighTower-$$1 data, with the standard set of cuts (solid symbols) and with the SMD quality cut removed (open symbols).

Figure 15

(a) Invariant yield of ${\pi }^0$ per MinBias $p+p$ and $d+\mathrm{Au}$ collision. Curves are the power law fits given in the text. Invariant yield divided by the fit to the (b) $p+p$ and (c) $d+\mathrm{Au}$ data. The error bars are statistical and brackets in the lower panels are the systematic uncertainties.

Figure 16

(a) Invariant yield of $\eta$ per MinBias $p+p$ and $d+\mathrm{Au}$ collision. Curves are the power law fits given in the text. Invariant yield divided by the fit to the (b) $p+p$ and (c) $d+\mathrm{Au}$ data. The error bars are statistical and brackets in the lower panels are the systematic uncertainties.

Figure 17

Relative neutral hadron contribution to the photon candidate yields, $C_0$. The filled area is the upper limit for the $p+p$ HighTower-$$2 data sample; the dashed curve is the upper limit in the extreme scenario where all photon candidates were a result of showering $\mathrm{n̄}$’s.

Figure 18

(a) Acceptance and efficiency factor ${\varepsilon }_{\mathrm{acc}}^{\gamma }$ for photons exclusively from the decay ${\pi }^0\to \gamma \gamma$. The observed rise of the efficiency at high $p_T$ is caused by the merging of the ${\pi }^0$ decay daughters. (b) The ${\varepsilon }_{\mathrm{acc}}^{\gamma }$ factor for single photons, used to correct the fraction of the photon sample that exceeded the simulated ${\pi }^0$ decay contribution.

Figure 19

(a) Inclusive photon invariant yield per MinBias $p+p$ and $d+\mathrm{Au}$ collision. Curves are the power law fits given in the text. Invariant yield divided by the fit to the (b) $p+p$ and (c) $d+\mathrm{Au}$ data. The neutral hadron contamination was not subtracted (see text) and is expected to be significant at $2\lesssim p_T\lesssim 4\hspace{0.5em}\mathrm{GeV}/c$. The error bars are statistical and brackets in the lower panels are the systematic uncertainties. Data points for the overlapping $p_T$ bins in the lower panels are horizontally displaced for clarity.

Figure 20

The estimated yield of $\eta$ and $\omega$(782) mesons in $d+\mathrm{Au}$ collisions, relative to the measured ${\pi }^0$ yield, determined from the $m_T$ scaling as described in the text.

Figure 21

The simulated number of photons per input pion ${\gamma }_{\mathrm{decay}}/{\pi }^0$ from hadronic decays in $d+\mathrm{Au}$ collisions as a function of $p_T$. The included decay processes are listed in Table 4. The vertical line indicates the lower limit of the $p_T$ range that was used to fit the ${\pi }^0$ spectrum. The value of ${\gamma }_{\mathrm{decay}}/{\pi }^0$ below $p_T=4\hspace{0.5em}\mathrm{GeV}/c$ is, therefore, less accurate; however, it was not used for further analysis (see text).

Figure 22

(a) Cross section for inclusive ${\pi }^0$ production in $p+p$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$, divided by the corresponding NLO pQCD calculations [52] for (b) $p+p$ and (c) $d+\mathrm{Au}$ collisions. The error bars are statistical and shaded bands are $p_T$-correlated systematic uncertainties. Normalization uncertainties are indicated by shaded bands around unity in the lower panels.

Figure 23

Cross section for inclusive ${\pi }^0$ production in (a) $p+p$ and (b) $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$, divided by NLO pQCD calculations [52] and compared to the STAR ${\pi }^{\pm }$[23, 24] and PHENIX ${\pi }^0$[6, 26] measurements. The error bars are statistical and the shaded bands are $p_T$-correlated systematic uncertainties. Normalization uncertainties are indicated by shaded bands around unity in each panel.

Figure 24

The $\eta /{\pi }^0$ ratio measured in (a) $p+p$ and (b) $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$, compared to the PHENIX measurements [27] and the $m_T$ scaling predictions. The error bars are statistical and the shaded bands are $p_T$-correlated systematic uncertainties.

Figure 25

Nuclear modification factor $R_{dA}$ for (a) ${\pi }^0$ and (b) $\eta$, compared to the $\text{STAR}\hspace{0.5em}{\pi }^{\pm }$ [23, 24] and $\text{PHENIX}\hspace{0.5em}{\pi }^0$ measurements [27, 28]. The error bars are statistical and the shaded bands are $p_T$-correlated systematic uncertainties. Normalization uncertainties are indicated by shaded bands around unity in each panel.

Figure 26

Nuclear modification factor $R_{\mathit{CP}}$ measured in $d+\mathrm{Au}$ collisions, compared to STAR ${\pi }^{\pm }$ measurement [24]. The error bars are statistical and the shaded bands are $p_T$-correlated systematic uncertainties. Common normalization uncertainty is indicated by a shaded band around unity.

Figure 27

The direct photon yield in (a) $p+p$ and (b) $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$, expressed in terms of the double ratio $R_{\gamma }$. The error bars are statistical and the shaded bands are $p_T$-correlated systematic uncertainties. The curves correspond to NLO pQCD calculations of the differential cross sections for direct photon [68] and ${\pi }^0$[52] production in $p+p$ collisions for different factorization scales $\mu$ (the upper pQCD curve corresponds to $\mu =p_T/2)$. The upper limit of the fractional neutral hadron contamination $C_0$ is shown as the shaded band at $R_{\gamma }=0$.

Figure 28

The differential cross section for direct photon production at midrapidity in $p+p$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\hspace{0.5em}\mathrm{GeV}$, compared to the PHENIX measurement [29] and the NLO pQCD calculation [68], which was scaled with $\langle$$T_{\mathit{dA}}$$$$\rangle$ [Eq. (23)] in the case of $d+\mathrm{Au}$ collisions. The error bars are statistical and the the shaded bands are $p_T$-correlated systematic uncertainties. The arrows correspond to the $95\%$ confidence limits, as defined in the text.

Figure 29

(a) The cross sections per nucleon for direct photon production in $d+\mathrm{Au}$ collisions, compared to the measurements in $p+p$ and $p+A$ collisions by the E706 experiment [70] at the comparable nucleon-nucleon center-of-mass energies. The theoretical curves were calculated with the incnlo program [72] with $\mu =p_T/2$. All data have statistical and systematic uncertainties summed in quadrature. The vertical arrows indicate our estimate of the $95\%$ confidence level. (b) The ratio of the data and the corresponding calculations.

Figure 30

The relative contribution of the fragmentation ($$$D_{\gamma /q}$$$) and the pQCD hard scattering processes to the total direct photon cross section [68]. Both contributions are shown as a function of the $p_T$ of the produced photon.