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.

(color online) $A_{N}$ as a function of the corrected mean $p_{T}$ for 2006 transverse data. The panels present $A_{N}$ for four different $\eta$ bins. $A_{N}$ is the left-right single-spin asymmetry for a transversely polarized beam. The errors shown combine the statistical uncertainties, which dominate, with all systematic uncertainties except trigger and reconstruction bias. See Sect. V A for a discussion of the latter.

(color online) $A_{\Sigma}$ versus corrected mean $p_{T}$ for 2006 transverse data, averaged over the range $|\eta|$ < 0.8$. A_{\Sigma}$, the transverse double-spin asymmetry for transversely polarized beams, is defined in more detail in the text.

(color online) Measured transverse double-spin asymmetry versus azimuthal angle $\phi$ for 2006 transverse data. The points are fit with the function $A_{\sigma}+A_{TT}cos(2\phi)$. These data are averaged over $7.5<p_{T}<40$ GeV/c and $|\eta|<0.8$.

(color online) $A_{LL}$ for inclusive jet production versus corrected jet $p_{T}$ for 2005 data. For 2005 data we used a cone radius equal to 0.4 and a pseudorapidity range for the jet thrust axis of $0.2<\eta<0.8$. The error bars are statistical. The gray boxes show the systematic uncertainties.

(color online) $A_{LL}$ for inclusive jet production versus corrected jet $p_{T}$ for 2006 data. For 2006 data we used a jet cone radius equal to 0.7 and a pseudorapidity range of $−0.7<\eta<0.9$ to reflect the increased detector coverage. The error bars are statistical. The gray boxes show the systematic uncertainties.

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda+\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'Two-year-combined $\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{LL}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\Lambda$ $D_{LL}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'particle jet pt as a function of $\Lambda$ z'

'particle jet pt as a function of $\overline{\Lambda}$ z'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'Two-year-combined $\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{TT}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\Lambda$ $D_{TT}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'particle jet pt as a function of $\Lambda$ z'

'particle jet pt as a function of $\overline{\Lambda}$ z'

The upper panel shows the jet yield vs detector jet pT in data and simulation for each of the three trigger categories. The lower three panels show the relative differences between data and simulation (JP1)

The upper panel shows the jet yield vs detector jet pT in data and simulation for each of the three trigger categories. The lower three panels show the relative differences between data and simulation (JP2)

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum fraction,z, for two typical detector jet pT bins

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum fraction,z, for two typical detector jet pT bins

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum transverse to the thrust axis,jT, for two typical detector jet pT bins (data, 8GeV/c)

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum transverse to the thrust axis,jT, for two typical detector jet pT bins (simulation, 8GeV/c)

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum transverse to the thrust axis,jT, for two typical detector jet pT bins (data, 34.4GeV/c)

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum transverse to the thrust axis,jT, for two typical detector jet pT bins (simulation, 34.4GeV/c)

The upper panel shows the electromagnetic fraction distribution for jets in a low-pT bin. The lower panel shows the electromagnetic fraction distributions in a higher pT bin for each of the three jet categories (JP0, 34.4GeV/c)

The upper panel shows the electromagnetic fraction distribution for jets in a low-pT bin. The lower panel shows the electromagnetic fraction distributions in a higher pT bin for each of the three jet categories

Dijet yield vs invariant mass as measured at the detector level. (JP0)

Dijet yield vs invariant mass as measured at the detector level. (JP1)

Dijet yield vs invariant mass as measured at the detector level. (JP2)

Dijet opening angle Delta phi distribution

Dijet opening angle Delta eta distribution

Distributions of the charged hadrons within the offaxis cones as a function of hadron pT

The ratio of simulation to data for pT < 2 GeV/c

the mean underlying event correction to the jet transverse momentum, as a function of detector jet pT

the mean underlying event correction to the dijet mass, as a function of detector dijet invariant mass, from data

the mean underlying event correction to the dijet mass, as a function of detector dijet invariant mass, from simulation

the observed longitudinal double-spin asymmetry of the underlying event contributions, as a function of detector jet pT

the sampled gluon x distributions, weighted by the partonic asymmetry (triggered detector jets, 8.0 GeV/c)

the sampled gluon x distributions, weighted by the partonic asymmetry (triggered detector jets, 34.4 GeV/c)

the sampled gluon x distributions, weighted by the partonic asymmetry (all parton jets, 8.0 GeV/c)

the sampled gluon x distributions, weighted by the partonic asymmetry (all parton jets, 34.4 GeV/c)

the inclusive jet asymmetries and systematic uncertainties,as function of pT compared to the theoretical predictions (Run12)

the inclusive jet asymmetries and systematic uncertainties,as function of pT compared to the theoretical predictions (DSSV14)

the inclusive jet asymmetries and systematic uncertainties,as function of pT compared to the theoretical predictions (NNPDFpol.1)

the inclusive jet asymmetries and systematic uncertainties,as function of pT compared to the theoretical predictions (NNPDFpol.1 -rep)

the inclusive jet asymmetries and systematic uncertainties, as function of xT compared to the theoretical predictions (Run12)

the inclusive jet asymmetries and systematic uncertainties, as function of xT compared to the theoretical predictions (Run9)

the inclusive jet asymmetries and systematic uncertainties, as function of xT compared to the theoretical predictions (DSSV14)

the inclusive jet asymmetries and systematic uncertainties, as function of xT compared to the theoretical predictions (NNPDFpol1.1)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,A,x1)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,A,x2)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,B,x1)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,B,x2)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,C,x1)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,C,x2)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,D,x1)

Leading order extractions from the embedding sample of the x1 and x2 distributions in dijet events for topological bins A-D (a,D,x2)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,A,DSSV14)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,B,DSSV14)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,C,DSSV14)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,D,DSSV14)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,A,NNPDF11)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,B,NNPDF11)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,C,NNPDF11)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,D,NNPDF11)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,A,data)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,B,data)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,C,data)

Dijet asymmetries for the same topological bins in 510 GeV pp collisions (b,D,data)

Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $0.5<|\eta|<1$.

Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $|\eta|<0.5$.

Parton dijet invariant mass $M_{inv}$ and $A_{LL}$ values with associated uncertainties for the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology.

Parton dijet invariant mass $M_{inv}$ and $A_{LL}$ values with associated uncertainties for the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology.

Parton inclusive-jet $p_T$, $x_T$, and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $|\eta|<1$.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $0.5<|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $|\eta|<0.5$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region and jets in the $0.5<|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $0.5<|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $0.5<|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for dijet measurements with the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for dijet measurements with the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling dijet measurements with the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology and the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

Parton dijet $M_{inv}$ vs $A_{LL}$ values with associated uncertainties, for topology C.

Parton dijet $M_{inv}$ vs $A_{LL}$ values with associated uncertainties, for topology D.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements.The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology A). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology A). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology B) with forward-central dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology B) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology C) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

(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].

Balance functions in pseudorapidity windows -1 < eta < 1 for 0.15 < pT < 2 GEV/c.

Balance functions in pseudorapidity windows -1.3 < eta < 1.3 for 0.15 < pT < 2 GEV/c.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -1 < eta < -0.2.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -0.8 < eta < 0.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -0.4 < eta < 0.4.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and 0 < eta < 0.8.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and 0.2 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -0.3 < eta < 0.3.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and 0 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1 < eta < 0.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -0.5 < eta < 0.5.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1.3 < eta < 1.3.

The pT dependence of the width of the BF in 60-80% centrality.

The pT dependence of the width of the BF in 30-60% centrality.

The pT dependence of the width of the BF in 10-30% centrality.

The pT dependence of the width of the BF in 0-10% centrality.

The centrality dependence of the width of the BF in 0.15 < pT < 0.4 GEV/c.

The centrality dependence of the width of the BF in 0.4 < pT < 0.7 GEV/c.

The centrality dependence of the width of the BF in 0.7 < pT < 1 GEV/c.

The centrality dependence of the width of the BF in 1 < pT < 2 GEV/c.