Nuclear modification factor $R_{dA}$ for $\pi^0$, d + Au, compared to the STAR $\pi^{+-}$ [23,24] and PHENIX $\pi^0$ measurements [27,28]. Nucleon-nucleon inelastic cross section $\sigma^{NN}$ = 42 mb and expected number of collisions $<N_{coll}>$ = 7.5 +- 0.4 from Glauber model. Shaded bands in plot are $p_T$-correlated systematic uncertainties and the error bars are statistical uncertainties. Normalization uncertainty of 14.0% indicated by a shaded band around unity.

Nuclear modification factor $R_{dA}$ for eta, d + Au, compared to PHENIX $\eta$ measurements [27,28]. Nucleon-nucleon inelastic cross section $\sigma^{NN}$ = 42 mb and expected number of collisions $<N_{coll}>$ = 7.5 +- 0.4 from Glauber model. Shaded bands in plot are $p_T$-correlated systematic uncertainties and the error bars are statistical uncertainties. Normalization uncertainty of 14.0% indicated by a shaded band around unity.

Nuclear modification factor $R_{CP}$ for $\pi^0$ measured in d + Au collisions, compared to STAR $\pi^{+-}$ measurements [24]. Peripheral d + Au collisions were used where $R_{CP}$ = ratio of particle production in 40-100% centrality (P) events and 0-20% centrality (C) events. Shaded bands in plot are $p_T$-correlated systematic uncertainties and the error bars are statistical uncertainties. Normalization uncertainty of 11.0% indicated by a shaded band around unity.

Direct photon yield in p + p collisions at $\sqrt{s_{NN}}$ = 200 GeV in terms of the double ration $R_{\gamma}$. Shaded bands in plot are $p_T$-correlated systematic uncertainties and the error bars are statistical 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.

Direct photon yield in d + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in terms of the double ration $R_{\gamma}$. Shaded bands in plot are $p_T$-correlated systematic uncertainties and the error bars are statistical 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.

Cross sections for direct photon production at midrapidity in p + p and d + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, compared to the PHENIX measurement [29] and to the NLO pQCD calculation [68], which was scaled with $<T_{dA}>$ [Eq. (23)] in case of d + Au collisions. The error bars are statistical the shaded bands are $p_T$-correlated systematic uncertainties. The arrows correspond to the 95% confidence limits, as defined in the text. Normalization uncertainties of 11.7% for p+p and 5.3% for d+Au are not shown. Separate columns in the table show upper 95% confidence limits. The 95% confidence limits for the cross section are used when $R_{\gamma}$ did not correspond to a significant direct photon signal, assuming that the statistical and systematic errors both followed a Gaussian distribution, and using the fact that $R_{\gamma}\geq 1$ by definition.

Background-subtracted charge-independent (AAT ) correlated hadron pair density in 40-80% Au+Au collisions for 3<p(t)⊥<10 GeV/cand 1<p(a)⊥<3 GeV/c. The results are for near-side correlated hadrons within |∆φ1,2|<0.7, and corrected for the 3-particle ∆η-∆η acceptance. Statistical errors at (∆η1,∆η2)∼(0,0)are approximately 0.058 for Au+Au respectively..

Background-subtracted charge-independent (AAT ) correlated hadron pair density in 0-12% Au+Au collisions for 3<p(t)⊥<10 GeV/cand 1<p(a)⊥<3 GeV/c. The results are for near-side correlated hadrons within |∆φ1,2|<0.7, and corrected for the 3-particle ∆η-∆η acceptance. Statistical errors at (∆η1,∆η2)∼(0,0)are approximately 0.084 for Au+Au respectively..

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum 0-12% Au+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. In 0-12% Au+Au collisions, the average denstiy drops more slowly andbecomes approximately constant aboveR>1, indicatingthe presence of the ridge.

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum 40-80% Au+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. For 40-80% Au+Au collisions the average density at R>1 is consistent with zero, indicating no ridge contribution

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum d+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. For d+Au collisions the average density at R>1 is consistent with zero, indicating no ridge contribution

Radial dependence of average 3-particle correlation pair density for 0-12% Au+Au (like-sign triplets) data. The results are shown in Fig. 3(b) Indeed, no jet-like component is apparent in A^±A^±T^±.The A^±A^±T^∓ result contains both jet-like and ridge components.

Radial dependence of average 3-particle correlation pair density for 40-80% Au+Au (like-sign triplets) data. The contribution from other charge combinations, namely A^±A^∓ T^±, are simply the difference between AAT in Fig.3(a) and (A^±A^±T^± + A^±A^± T^∓) in Fig. 3(b). We found this to be equal to twice the A^±A^± T^∓contribution within errors.

Radial dependence of average 3-particle correlation pair density for d+Au (AAT) data. We expect the ridge contributions in the correlated pair density to be the same in all charge combinations. We verified this for large ∆η correlatedpair densities within our current statistics, as can be seen from Fig. 3(b). Therefore the total ridge particle pair density (ˆPrr) can be obtained as four times A^±A^±T^±. The remaining jet-like signal, the sum of jet-like correlated particle pairs (ˆPjj) and cross pairs of a jet-like and a ridge particle (ˆPjr), can then be obtained by subtracting the total ridge from AAT.

for same-sign associated particles (A^\pm A^\pm T^\pm and A^\pm A^\pm T^\mp) in 0-12% Au+Au collisions Systematic uncertainties are shown in the shaded boxes due to background normalization and in the solid curves due to flow.

The R dependence of the average〈ˆPrr〉and〈ˆPjj〉+〈ˆPjr〉in 0-12% Au+Au collisions.The ridge pair density is consistent with a constant 60.14±0.02 (χ2/ndf=5.8/7). Gaussian fits indicate a best fit value σ = 2.1 (χ2/ndf=4.8/6, solid curve) and σ >1.4 (dashed curve) with 84% confidence level. On the otherhand, the jet-like component is narrow with a Gaussianσ=0.34+0.13−0.09(χ2/ndf=0.8/6, dominated by statistical errors), comparing well to those from the correlated single hadron density.

The average correlated hadron pair density per trigger particle in 0-12% Au+Au collisions for the jet-like andridge components as a function of R. The solid curves are Gaussian fits. The dashed curve is a Gaussian fit with a fixed σ=1.4 to the ridge data. The systematic uncertainities on the ridge data are shown in shaded boxes due to background normalization and in open boxes due to flow.

The R dependence of the average in 0-12% Au+Au collisions.for the ridge as a function of ξ within R<1.4. The solid curves are Gaussian fits. To investigate possible structures in the ridge, we show in Fig. 4(b) the average ridge particle pair density as a function of ξ = arctan(∆η2/∆η1) within R<1.4. The data are consistent with a uniform distribution in ξ(χ2/ndf=1.7/7). This suggests that the ridge particles are uncorrelated in ∆η not only with the trigger particle but also between themselves. In other words,the ridge appears to be uniform in ∆η event-by-event.

The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$ in polarized proton-proton collisions at $\sqrt{s} = 200 GeV$ for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$ in polarized proton-proton collisions at $\sqrt{s} = 200$ GeV for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, in polarized proton-proton collisions at $\sqrt{s} = 200$ GeV for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

Efficiency corrected $t_{\perp}$ spectrum for $\rho^{0}$ from (top) minium bias and (bottom) topology data, for mid-rapidity (left) and larger rapidity (right) samples. The points are the data, while the solid lines are the results of fits to Eq. (3).

Efficiency corrected $t_{\perp}$ spectrum for $\rho^{0}$ from (top) minium bias and (bottom) topology data, for mid-rapidity (left) and larger rapidity (right) samples. The points are the data, while the solid lines are the results of fits to Eq. (3).

Efficiency corrected $t_{\perp}$ spectrum for $\rho^{0}$ from (top) minium bias and (bottom) topology data, for mid-rapidity (left) and larger rapidity (right) samples. The points are the data, while the solid lines are the results of fits to Eq. (3).

Efficiency corrected $t_{\perp}$ spectrum for $\rho^{0}$ from (top) minium bias and (bottom) topology data, for mid-rapidity (left) and larger rapidity (right) samples. The points are the data, while the solid lines are the results of fits to Eq. (3).

Analyzing powers A_N(-x_F) in x_F bins at < eta > =3.3 and x_F < 0.

Analyzing powers versus pi^0 transverse momentum (p_T) for events with scaled pi^0 longitudinal momentum x_F > 0.4.

Analyzing powers versus pi^0 transverse momentum (p_T) for events with scaled pi^0 longitudinal momentum x_F < -0.4.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.25 < x_F < 0.30 bin.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.30 < x_F < 0.35 bin.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.35 < x_F < 0.40 bin.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.40 < x_F < 0.47 bin.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.47 < x_F < 0.56 bin.

Analyzing powers versus pi^0 transverse momentum (p_T) in 0.56 < x_F < 0.80 bin.

(a) The solid curve represents the fraction of $\Delta G$ for GRSV-std that has $x > x_{min}$ for scale $Q^{2}$ = 100 $GeV^{2}/c^{2}$. The histograms show the $x_{gluon}$ sampled in the lowest and highest jet $p_{T}$ bins. (b) Confidence levels for several gluon polarization distributions, characterized by their $\Delta G$ at an input scale of 0.4 $GeV^{2}/c^{2}$ [4, 14, 23].

(a) The solid curve represents the fraction of $\Delta G$ for GRSV-std that has $x > x_{min}$ for scale $Q^{2}$ = 100 $GeV^{2}/c^{2}$. The histograms show the $x_{gluon}$ sampled in the lowest and highest jet $p_{T}$ bins. (b) Confidence levels for several gluon polarization distributions, characterized by their $\Delta G$ at an input scale of 0.4 $GeV^{2}/c^{2}$ [4, 14, 23].

Measured and calculated asymmetries vs. di-jet pseudorapidity sum for $+\hat{z}$ (left) and $−\hat{z}$ (right) beams. (a,b): Fraction of the calculated di-jet cross section with a quark (gluon) from the $+\hat{z}$ $(−\hat{z})$ beam. (c,d): Unweighted asymmetries compared with pQCD calculations [20] (histograms) for two models of quark Sivers functions fitted to SIDIS results [8]. (e,f): Asymmetries for $|\sin\zeta|$-weighted yields, compared with calculations [20, 21] based on twist-3 quark-gluon correlations. Vertical (horizontal) bars on the data indicate statistical uncertainties (bin widths). The systematic error bands exclude a $\pm12\%$ beam polarization normalization uncertainty.