The invariant mass distribution for the coherently produced $\rho^{0}$ candidates obtained from the topology sample with the cut on the $\rho^{0}$ transverse momentum $p_{T}$ < 150 MeV/c. The hatched area is the contribution from the combinatorial background. The solid line corresponds to Eq. 3 which encompasses the Breit-Wigner (dashed), the mass independent contribution from the direct $\pi^{+}\pi^{-}$ production (dash-dotted), and the interference term(dotted).

The ratio |B/A| as a function of $y_{\rho^{0}}$ for the minimum bias data, obtained by fitting Eq.3 to the invariant mass distributions in bins of $y_{\rho^{0}}$.

Coherent $\rho^{0}$ production cross-section for the minimum bias data set as a function of $y_{\rho^{0}}$ (black dots) overlaid by the $d\sigma/dy$ distribution predicted by the KN model [22] (solid line).

$\rho^{0}$ production cross-section as a function of the momentum transfer squared $t$, together with the fit of Eq. 5. The fit parameters are shown in Table I.

Comparison of theoretical predictions to the measured differential cross-section for coherent $\rho^{0}$ production. The statistical errors are shown by the solid vertical line at each data point. The sum of the statistical and systematic error bars is shown by the grey band.

Projections of the two dimensional efficiency corrected $\Phi_{h}$ vs $cos(\Theta_{h})$ distributions obtained with the minimum bias data set. The solid line shows the result of the two-dimensional fit to the data with Eq. 6 and the coefficients given in Tab. III.

Projections of the two dimensional efficiency corrected $\Phi_{h}$ vs $cos(\Theta_{h})$ distributions obtained with the minimum bias data set. The solid line shows the result of the two-dimensional fit to the data with Eq. 6 and the coefficients given in Tab. III.

Experimental correlation moments $R^2_{x2}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^2_{x2}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^2_{y2}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^2_{y2}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x6}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x6}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{y6}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{y6}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{x2y2}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{x2y2}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{x4}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{x}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{y4}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^4_{y4}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x2y4}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x2y4}(q)$ Fit. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x4y2}(q)$ Data. Systematic errors are less than the statistical errors.

Experimental correlation moments $R^6_{x4y2}(q)$ Fit. Systematic errors are less than the statistical errors.

Source function profile $S(r_x)$ Image in the PCMS.

Source function profile $S(r_x)$ Fit in the PCMS. The blue line represents the Hump fit.

Source function profile $S(r_y)$ Image in the PCMS.

Source function profile $S(r_y)$ Fit in the PCMS. The blue line represents the Hump fit.

Source function profile $S(r_z)$ Image in the PCMS.

Source function profile $S(r_z)$ Fit in the PCMS. The blue line represents the Hump fit.

Associated correlation profile $C(q_x)$ Image in the PCMS.

Associated correlation profile $C(q_x)$ Fit in the PCMS.

Associated correlation profile $C(q_y)$ Image in the PCMS.

Associated correlation profile $C(q_y)$ Fit in the PCMS.

Associated correlation profile $C(q_z)$ Image in the PCMS.

Associated correlation profile $C(q_z)$ Fit in the PCMS.

Source function comparison between Therminator calculation and image for $S(r_x)$ in PCMS.

Source function comparison between Therminator calculation and image for $S(r_x)$ in PCMS.

Source function comparison between Therminator calculation and image for $S(r_y)$ in PCMS.

Source function comparison between Therminator calculation and image for $S(r_y)$ in PCMS.

Source function comparison between Therminator calculation and image for $S(r_z)$ in PCMS.

Source function comparison between Therminator calculation and image for $S(r_z)$ in PCMS.

$\Delta$$t_{LCM}$ from Therminator events compared with various assumptions for $\Delta\tau$ and resonance emissions.

$\Delta$$t_{LCM}$ from Therminator events compared with various assumptions for $\Delta\tau$ and resonance emissions.

<p>Jet-pair distributions for associated baryons for $1 < p_{T,assoc} < 1.3\ \mathrm{GeV}/c$ and $1.6 < p_{T,assoc} < 2.0\ \mathrm{GeV}/c$. Results are for a hadron trigger $2.5 < p_T < 4.0\ \mathrm{GeV}/c$ and centrality selections of 0-20% and 20-40%.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Conditional jet yeilds for associated mesons for near-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Conditional jet yeilds for associated mesons for away-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Conditional jet yeilds for associated baryons for near-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Conditional jet yeilds for associated baryons for away-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Ratio of jet-associated baryons to jet-associated mesons for near-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

<p>Ratio of jet-associated baryons to jet-associated mesons for away-side jets.</p> <p><i>Note that only statistical uncertainties are available.</i></p>

J/PSI invariant (1/(2PI*PT))*D2(N)/DPT/DYRAP versus PT at mid rapidity (-0.35<y<0.35) in D+AU collisions.

J/PSI invariant (1/(2PI*PT))*D2(N)/DPT/DYRAP versus PT at forward rapidity (1.2<y<2.2) in D+AU collisions.

J/PSI invariant (1/(2PI*PT))*D2(N)/DPT/DYRAP versus centrality at backward rapidity (-2.2<y<-1.2) in D+AU collisions.

J/PSI invariant (1/(2PI*PT))*D2(N)/DPT/DYRAP versus centrality at mid rapidity (-0.35<y<0.35) in D+AU collisions.

J/PSI invariant (1/(2PI*PT))*D2(N)/DPT/DYRAP versus centrality at forward rapidity (1.2<y<2.2) in D+AU collisions.

Nuclear modification factor versus rapidity in D+AU collisions, over 3 bins of rapidity.

Nuclear modification factor versus rapidity in D+AU collisions, over 5 bins of rapidity.

Nuclear modification factor versus PT at backward rapidity (-2.2<y<-1.2) in D+AU collisions.

Nuclear modification factor versus PT at mid rapidity (-0.35<y<0.35) in D+AU collisions.

Nuclear modification factor versus PT at forward rapidity (1.2<y<2.2) in D+AU collisions.

Nuclear modification factor versus centrality at backward rapidity (-2.2<y<-1.2) in D+AU collisions.

Nuclear modification factor versus centrality at mid rapidity (-0.35<y<0.35) in D+AU collisions.

Nuclear modification factor versus centrality at forward rapidity (1.2<y<2.2) in D+AU collisions.

Mean PT^2 versus rapidity, extracted from a fit to the data, for DEUT + Au reactions. The mean value of PT^2 is calculated from the data for PT < 5 Gev/c.

Mean PT^2 versus rapidity, extracted from a fit to the data, for P + P reactions. The mean value of PT^2 is calculated from the data for PT < 5 Gev/c.

Breakup cross section of c-c_bar pairs inside cold nuclear matter,integrated over the whole domain of rapidity.The breakup cross section is calculated with two models of shadowing for nuclear PDFs ; the EKS model and the NDSG model. The uncertainties given, containing statistical and systematical error, are corresponding to one standard deviation.

Breakup cross section of c-c_bar pairs inside cold nuclear matter for different ranges of rapidity.The breakup cross section is calculated with two models of shadowing for nuclear PDFs ; the EKS model and the NDSG model. The uncertainties given, containing statistical and systematical error, are corresponding to one standard deviation.

Breakup cross section of c-c_bar pairs inside cold nuclear matter, integrated over the whole domain of rapidity.The breakup cross section is calculated with two models of shadowing for nuclear PDFs ; the EKS model and the NDSG model. The uncertainties given, containing statistical and systematical error, are corresponding to one standard deviation.

Breakup cross section of c-c_bar pairs inside cold nuclear matter for different ranges of rapidity.The breakup cross section is calculated with two models of shadowing for nuclear PDFs ; the EKS model and the NDSG model. The uncertainties given, containing statistical and systematical error, are corresponding to one standard deviation.

(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].

(Color online) $\Lambda$ and $\overline{\Lambda}$ spectra on the deuteron and on the gold side in $d$ + Au minimum bias collisions. The data points on the gold side are multiplied by 2 for better visibility. The statistical errors are smaller than the points marking the measurements. The curves show a fit with a Boltzmann function in transverse mass to the data points.

(Color online) (a) Comparison of the measured $\overline{\Lambda}$ yield with model calculations. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic er- rors including the overall normalization uncertainty. In both panels the target and projectile beam rapidities are indicated by arrows.

(Color online) (b) Comparison of the net $\Lambda$ yield with model calculations. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic er- rors including the overall normalization uncertainty. In both panels the target and projectile beam rapidities are indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Minimum bias $\overline{\Lambda}/\Lambda$ ratio compared to model calculations. On the deuteron side HIJING/BB shows the best agreement with the results, while on the Au side only AMPT and EPOS give a satisfactory description of the data.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

(Color online) Net $\Lambda dN/dy$ for central, mid-central and peripheral events on both the deuteron and the Au side of the collision. The data are compared to calculations of the distribution of net baryons obtained with the Multichain model [16] with $\alpha$ = 2.9, scaled by 0.1 to account for the conversion from net baryons to net $\Lambda$. An overall scale uncertainty of 10% on the model curves from this conversion is not shown. See text for details.

Differential cross section for indicent photon energy 825 MeV.

Differential cross section for indicent photon energy 875 MeV.

Differential cross section for indicent photon energy 925 MeV.

Differential cross section for indicent photon energy 975 MeV.

Differential cross section for indicent photon energy 1025 MeV.

Differential cross section for indicent photon energy 1075 MeV.

Differential cross section for indicent photon energy 1125 MeV.

Differential cross section for indicent photon energy 1175 MeV.

Differential cross section for indicent photon energy 1225 MeV.

Differential cross section for indicent photon energy 1275 MeV.

Differential cross section for indicent photon energy 1325 MeV.

Differential cross section for indicent photon energy 1375 MeV.

Differential cross section for indicent photon energy 1425 MeV.

Differential cross section for indicent photon energy 1475 MeV.

Differential cross section for indicent photon energy 1525 MeV.

Differential cross section for indicent photon energy 1575 MeV.

Differential cross section for indicent photon energy 1625 MeV.

Differential cross section for indicent photon energy 1675 MeV.

Differential cross section for indicent photon energy 1725 MeV.

Differential cross section for indicent photon energy 1775 MeV.

Differential cross section for indicent photon energy 1825 MeV.

Differential cross section for indicent photon energy 1875 MeV.

Differential cross section for indicent photon energy 1925 MeV.

Differential cross section for indicent photon energy 1975 MeV.

Differential cross section for indicent photon energy 2025 MeV.

Differential cross section for indicent photon energy 2075 MeV.

Differential cross section for indicent photon energy 2125 MeV.

Differential cross section for indicent photon energy 2175 MeV.

Differential cross section for indicent photon energy 2225 MeV.

Differential cross section for indicent photon energy 2275 MeV.

Differential cross section for indicent photon energy 2325 MeV.

Differential cross section for indicent photon energy 2375 MeV.

Differential cross section for indicent photon energy 2425 MeV.

Differential cross section for indicent photon energy 2475 MeV.

Differential cross section for indicent photon energy 2525 MeV.

Differential cross section for indicent photon energy 2575 MeV.

Differential cross section for indicent photon energy 2625 MeV.

Differential cross section for indicent photon energy 2675 MeV.

Differential cross section for indicent photon energy 2725 MeV.

Differential cross section for indicent photon energy 2775 MeV.

Differential cross section for indicent photon energy 2825 MeV.

Differential cross section for indicent photon energy 2875 MeV.

$R_{AA}$ as a function of $p_{T}$ from $0-5\%$ and $60-80\%$ central Au+Au events for $\Lambda$. Stat. and syst. errors added in quadrature.The band at unity shows the systematic uncertainty on $⟨N_{bin}⟩$. The dashed line below unity shows the expected value of RAA should the yields scale with $⟨N_{part}⟩$, and the band around it shows the systematic uncertainty on ⟨Npart ⟩. $N_{bin}$ Scaling 1 $\pm$ 0.16 and $N_{part}$ Scaling 0.168 $\pm$ 0.02 .

$R_{AA}$ as a function of $p_{T}$ from $0-5\%$ and $60-80\%$ central Au+Au events for $\Xi^{-} + \bar{\Xi}^{+}$. Stat. and syst. errors added in quadrature. The band at unity shows the systematic uncertainty on $⟨N_{bin}⟩$. The dashed line below unity shows the expected value of RAA should the yields scale with $⟨N_{part}⟩$, and the band around it shows the systematic uncertainty on ⟨Npart ⟩. $N_{bin}$ Scaling 1 $\pm$ 0.16 and $N_{part}$ Scaling 0.168 $\pm$ 0.02 .

$R_{AA}$ as a function of $p_{T}$ from $0-5\%$ and $60-80\%$ central Au+Au events for inclusive $p+\bar{p}$. Stat. and syst. errors added in quadrature. The band at unity shows the systematic uncertainty on $⟨N_{bin}⟩$. The dashed line below unity shows the expected value of RAA should the yields scale with $⟨N_{part}⟩$, and the band around it shows the systematic uncertainty on ⟨Npart ⟩. $N_{bin}$ Scaling 1 $\pm$ 0.16 and $N_{part}$ Scaling 0.168 $\pm$ 0.02 .

$R_{AA}$ from HIJING as a function of $p_{T}$ from $0-5\%$ central Au+Au events for inclusive $p+\bar{p}$.

$R_{AA}$ from HIJING as a function of $p_{T}$ from $0-5\%$ central Au+Au events for $\Lambda$.

$R_{AA}$ from HIJING as a function of $p_{T}$ from $0-5\%$ central Au+Au events for $\Xi^{-}+\bar{\Xi}^{+}$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $0-5\%$ central Au+Au events for inclusive $p+\bar{p}$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $0-5\%$ central Au+Au events for $\Lambda$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $0-5\%$ central Au+Au events for $\Xi^{-}+\bar{\Xi}^{+}$.

$R_{AA}$ from HIJING as a function of $p_{T}$ from $60-80\%$ central Au+Au events for inclusive $p+\bar{p}$.

$R_{AA}$ from HIJING as a function of $p_{T}$ from $60-80\%$ central Au+Au events for $\Lambda$.

$R_{AA}$ from HIJING as a function of $p_{T}$ from $60-80\%$ central Au+Au events for $\Xi^{-}+\bar{\Xi}^{+}$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $60-80\%$ central Au+Au events for inclusive $p+\bar{p}$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $60-80\%$ central Au+Au events for $\Lambda$.

$R_{AA}$ from EPOS as a function of $p_{T}$ from $60-80\%$ central Au+Au events for $\Xi^{-}+\bar{\Xi}^{+}$.

(Color online) Global polarization of $\Lambda$–hyperons as a function of centrality given as fraction of the total inelastic hadronic cross section. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the results for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of $\overline{\Lambda}$ transverse momentum $p^{\overline{\Lambda}}_{t}$. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the results for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of $\overline{\Lambda}$ pseudorapidity $\eta^{\overline{\Lambda}}$. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%). A constant line fit to these data points yields $P_{\Lambda}=(1.8\pm 10.8)\times 10^{-3}$ with $\chi^{2}/ndf=5.5/10$. Open squares show the results for Au+Au collisions as $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). A constant line fit gives $P_{\Lambda}=(-17.6\pm 11.1)\times 10^{-3}$ with $\chi^{2}/ndf=8.0/10$. Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of as a function of centrality. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the result for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Acceptance correction function $A_{0}(p^{H}_{t}, \eta^{H})$ defined in (10) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from unity affects the overall scale of the measured global polarization according to Eq. 9. See the text for details and discussions on $A_{0}$ $p^{H}_{t}$ and $\eta^{H}$ dependence.

(Color online) Acceptance correction function $A_{0}(p^{H}_{t}, \eta^{H})$ defined in (10) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from unity affects the overall scale of the measured global polarization according to Eq. 9. See the text for details and discussions on $A_{0}$ $p^{H}_{t}$ and $\eta^{H}$ dependence.

(Color online) Function $A_{2}(p^{H}_{t}, \eta^{H})$ defined in (11) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from zero defines the contribution to the observable (3) from $P^{(2)}_{H} (p^{H}_{t}, \eta^{H})$ in the expansion (6).

(Color online) Function $A_{2}(p^{H}_{t}, \eta^{H})$ defined in (11) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from zero defines the contribution to the observable (3) from $P^{(2)}_{H} (p^{H}_{t}, \eta^{H})$ in the expansion (6).

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.