Azimuthal transverse single-spin asymmetries of inclusive jets and charged pions within jets from polarized-proton collisions at $\sqrt{s}=500\mathrm{GeV}$

We report the first measurements of transverse single-spin asymmetries for inclusive jet and $\text{jet}+{\pi }^{\pm }$ production at midrapidity from transversely polarized proton-proton collisions at $\sqrt{s}=500\mathrm{GeV}$. The data were collected in 2011 with the STAR detector sampled from $23{\mathrm{pb}}^{-1}$ integrated luminosity with an average beam polarization of 53%. Asymmetries are reported for jets with transverse momenta $6<p_T<55\mathrm{GeV}/c$ and pseudorapidity $|\eta |<1$. Presented are measurements of the inclusive-jet azimuthal transverse single-spin asymmetry, sensitive to twist-3 initial-state quark-gluon correlators; the Collins asymmetry, sensitive to quark transversity coupled to the polarized Collins fragmentation function; and the first measurement of the “Collins-like” asymmetry, sensitive to linearly polarized gluons. Within the present statistical precision, inclusive-jet and Collins-like asymmetries are small, with the latter allowing the first experimental constraints on gluon linear polarization in a polarized proton. At higher values of jet transverse momenta, we observe the first nonzero Collins asymmetries in polarized-proton collisions, with a statistical significance of greater than $5\sigma$. The results span a range of $x$ similar to results from semi-inclusive deep-inelastic scattering but at much higher $Q^2$. The Collins results enable tests of universality and factorization breaking in the transverse momentum-dependent formulation of perturbative quantum chromodynamics.

Figure 1

Azimuthal angle definitions, following the conventions described in Ref. [43]. The direction of the beam polarization is denoted by ${\overrightarrow{S}}_{\mathrm{beam}}$, while the momenta of the polarized beam, jet, and pion are, respectively, ${\overrightarrow{p}}_{\mathrm{beam}}$, ${\overrightarrow{p}}_{\text{jet}}$, and ${\overrightarrow{p}}_{\pi }$.

Figure 2

Range of $x$ and $Q^2$ covered by Collins asymmetry measurements from SIDIS experiments at HERMES [32, 33], COMPASS [34], and Jefferson Lab Hall-A [35] in comparison to the $(x,Q^2)$ covered by the present data as the jet $p_T$ and $\eta$ vary.

Figure 3

Fraction of next-to-leading order (NLO) cross section [49, 50] arising from quark-quark (dot-dashed line), gluon-gluon (dotted line), or quark-gluon (solid line) interactions. The fractions are shown as a function of jet $p_T$ for jets produced within the pseudorapidity range $-1<{\eta }_{\text{jet}}<1$ from collisions of an energy $\sqrt{s}=500\mathrm{GeV}$. See Sec. 2c for discussions of the jet definitions and reconstruction.

Figure 4

Comparison of data to embedded Monte Carlo simulations for data and simulated events that satisfy the JP0 trigger. The embedding Monte Carlo distribution is normalized to match the number of data counts across the range $16.3<p_T<45.0\mathrm{GeV}/c$.

Figure 5

Mean corrected pion $z$, jet $p_T$, and pion $j_T$ as a function of each kinematic variable for pions within jets. Reconstructed kinematic variables are corrected to their underlying values at the pythia particle-jet level. Uncertainties are the quadrature combinations of statistical and systematic contributions.

Figure 6

Underlying parton $x$ distribution for all Monte Carlo simulated jets (points) within the specified range of $p_T$ compared to those passing the indicated event trigger condition (histogram). Uncertainties are from Monte Carlo statistics. The upper panel shows quark $x$ values for high-$p_T$ jets, comparing JP2 to unbiased events, while the bottom panel presents gluon $x$ values for low-$p_T$ jets, comparing VPDMB to unbiased events. For JP2, deviations can arise both from reconstruction effects and from bias in the event trigger. For VPDMB events, deviations from the unbiased sample arise from reconstruction and pileup effects.

Figure 7

$n_{\sigma }(\pi )$ vs $m^2$ (left) and a multi-Voigt-profile fit to $m^2$ (right) for VPDMB-triggered events with positively charged particles carrying momentum fractions of $0.10<z<0.15$ from jets with $8.4<p_T<9.9\mathrm{GeV}/c$. For the example fit shown, the charged particles are required to satisfy $-1.5<n_{\sigma }(\pi )<2.5$. The individual contributions to the overall fit from pions, kaons, and protons are shown.

Figure 8

Multi-Gaussian fit to the distribution of $n_{\sigma }(\pi )$ for positively charged particles from jets with $22.7<p_T<26.8\mathrm{GeV}/c$ carrying momentum fractions of $0.15<z<0.20$. The overall fit is shown along with the individual portions for pions, kaons, protons, and electrons.

Figure 9

Inclusive jet asymmetries $A_{UT}^{\sin ({\varphi }_S)}$, also often referred to as $A_N$, as a function of particle-jet $p_T$. Statistical uncertainties are shown as error bars, while systematic uncertainties are shown as shaded error boxes. An additional 3.5% vertical scale uncertainty from polarization is correlated across all bins. Events are separated into different regions of jet $\eta$, calculated relative to the polarized beam. Across the full range of jet $p_T$, the measured asymmetries are consistently small.

Figure 10

Collins-like asymmetries as a function of particle-jet $p_T$ (left) and as a function of pion $z$ (right). ${\pi }^{-}$ points are shifted horizontally for clarity. Statistical uncertainties are shown as error bars, while systematic uncertainties are shown as shaded error boxes. An additional 3.5% vertical scale uncertainty from polarization is correlated across all bins. Events are separated into different regions of jet $\eta$, calculated relative to the polarized beam. The jet $p_T$ dependence is shown for three bins of pion $z$: $0.1<z<0.2$, $0.2<z<0.3$, and $0.3<z<0.8$. The pion $z$ dependence is shown for three bins of jet $p_T$: $6.0<p_T<13.8\mathrm{GeV}/c$, $13.8<p_T<22.7\mathrm{GeV}/c$, and $22.7<p_T<55.0\mathrm{GeV}/c$. Asymmetries are consistently small.

Figure 11

Collins-like asymmetries as a function of particle-jet $p_T$ for pions reconstructed with $0.1<z<0.3$ (left) and as a function of pion $z$ for jets reconstructed with $6.0<p_T<13.8\mathrm{GeV}/c$ (right). Asymmetries are shown combining ${\pi }^{+}$ and ${\pi }^{-}$ and integrating over the full range of jet pseudorapidity, $-1<\eta <1$. Statistical uncertainties are shown as error bars, while systematic uncertainties are shown as shaded error boxes. An additional 3.5% vertical scale uncertainty from polarization is correlated across all bins. Shaded bands represent maximal predictions from Ref. [74] utilizing two sets of fragmentation functions [75, 76]. The asymmetries are consistently small across the full range of jet $p_T$ and pion $z$ and provide the first experimental constraints on model calculations.

Figure 12

Collins asymmetries as a function of particle-jet $p_T$ (left) and as a function of pion $z$ (right). ${\pi }^{-}$ points are shifted horizontally for clarity. Asymmetries are shown separately for ${\pi }^{+}$ and ${\pi }^{-}$ for two bins of jet $\eta$ (relative to the polarized beam). The jet $p_T$ dependence is presented in three bins of pion $z$: $0.1<z<0.2$, $0.2<z<0.3$, and $0.3<z<0.8$. The pion $z$ dependence is presented in three bins of jet $p_T$: $6.0<p_T<13.8\mathrm{GeV}/c$, $13.8<p_T<22.7\mathrm{GeV}/c$, and $22.7<p_T<55.0\mathrm{GeV}/c$. Statistical uncertainties are shown as error bars, while systematic uncertainties are shown as shaded error boxes. An additional 3.5% vertical scale uncertainty from polarization is correlated across all bins. The asymmetry is observed to be nonzero for higher values of jet $p_T$ and is the first such observation in polarized proton collisions.

Figure 13

Collins asymmetries as a function of pion $j_T$ for jets reconstructed with $22.7<p_T<55.0\mathrm{GeV}/c$. Asymmetries are shown separately for ${\pi }^{+}$ and ${\pi }^{-}$ for two bins of jet $\eta$ (relative to the polarized beam) and three bins of pion $z$: $0.1<z<0.2$, $0.2<z<0.3$, and $0.3<z<0.8$. Statistical uncertainties are shown as error bars, while systematic uncertainties are shown as shaded error boxes. An additional 3.5% vertical scale uncertainty from polarization is correlated across all bins. Asymmetries appear to show a dependence upon $j_T$ with the largest effects at the lower $j_T$ values.

Figure 14

Collins asymmetries as a function of pion $z$ for jets reconstructed with $22.7<p_T<55.0\mathrm{GeV}/c$ and $0<\eta <1$. The asymmetries are shown in comparison with model calculations from Refs. [74, 78]. The calculations are based upon SIDIS and $e^{+}{e}^{-}$ results and assume robust factorization and universality of the Collins function. The $\mathrm{DMP}+2013$ [74] and KPRY [78] predictions assume no TMD evolution, while the KPRY-NLL [78] curves assume TMD evolution up to next-to-leading log. All predictions are shown with shaded bands corresponding to the size of their associated theoretical uncertainties. The general agreement between the data and the model calculations is consistent with assumptions of robust TMD factorization and universality of the Collins function.