Longitudinal double-spin asymmetry for inclusive jet and dijet production in $pp$ collisions at $\sqrt{s}=510\mathrm{GeV}$

We report the first measurement of the inclusive jet and the dijet longitudinal double-spin asymmetries, $A_{LL}$, at midrapidity in polarized $pp$ collisions at a center-of-mass energy $\sqrt{s}=510\mathrm{GeV}$. The inclusive jet $A_{LL}$ measurement is sensitive to the gluon helicity distribution down to a gluon momentum fraction of $x\approx 0.015$, while the dijet measurements, separated into four jet-pair topologies, provide constraints on the $x$ dependence of the gluon polarization. Both results are consistent with previous measurements made at $\sqrt{s}=200\mathrm{GeV}$ in the overlapping kinematic region, $x>0.05$, and show good agreement with predictions from recent next-to-leading order global analyses.

Figure 1

Fractions of the next-to-leading-order cross section [19, 20] for inclusive jet production arising from quark-quark, quark-gluon, and gluon-gluon scattering in $pp$ collisions at $\sqrt{s}=200$ and 500 GeV, as a function of $x_T=2p_T/\sqrt{s}$.

Figure 2

The upper panel shows the jet yields vs detector jet $p_T$ in data and simulation for each of the three trigger categories. The points show the data, and the histograms show the simulation. The lower three panels show the relative differences between data and simulation.

Figure 3

Distributions of the charged hadrons within the jets as a function of the hadron longitudinal momentum fraction, $z$, for two typical detector jet $p_T$ bins. The blue points show the data, and the red histograms show the simulation.

Figure 4

Distributions of the charged hadrons within the jets as a function of the hadron momentum transverse to the thrust axis, $j_T$, for two typical detector jet $p_T$ bins. The blue points show the data, and the red histograms show the simulation.

Figure 5

The upper panel shows the electromagnetic fraction distribution, $R_{\mathrm{EM}}$, for jets in a low-$p_T$ bin. The bias in favor of large $R_{\mathrm{EM}}$, driven by the proximity to the JP0 threshold, is clear. The lower panel shows the $R_{\mathrm{EM}}$ distributions in a higher $p_T$ bin for each of the three jet categories. For this case, JP0 and JP1 jets have a bias in favor of small $R_{\mathrm{EM}}$, as discussed in the text. The points show the data, and the histograms show the simulation.

Figure 6

Dijet yield vs invariant mass as measured at the detector level. In the top panel the data and simulations for the JP0, JP1 and JP2 trigger samples are represented by the points and histograms, respectively. The differences between data and simulation, normalized to the data yields, are shown for each of the trigger samples in the three bottom panels.

Figure 7

Dijet opening angle $\mathrm{\Delta }\varphi$ (top) and $\mathrm{\Delta }\eta$ (bottom) distributions. The blue points represent the data, and the red histograms the simulation.

Figure 8

Distributions of the charged hadrons within the off-axis cones as a function of hadron $p_T$. The blue points show the data, and the red histogram shows the simulation. The inset shows the ratio of simulation to data for $p_T<2\mathrm{GeV}/c$.

Figure 9

The upper panel shows the mean underlying event correction to the jet transverse momentum, $d{p}_T$, as a function of detector jet $p_T$. The lower panel shows the mean underlying event correction to the dijet mass, $d{M}_{\mathrm{inv}}$, as a function of $M_{\mathrm{inv}}$. In both cases, the blue points show the data, and the red histogram shows the simulation.

Figure 10

Observed $A_{LL}^{d{p}_T}$ vs detector jet $p_T$. Note that no corrections have been made for detector acceptance, efficiency, or resolution.

Figure 11

The ${\widehat{a}}_{LL}$-weighted gluon $x$ distributions for two inclusive jet $p_T$ bins. The histograms represent all parton jets, independent of whether the jets satisfy the trigger and reconstruction requirements, while the points show the triggered detector jets. Comparisons without the ${\widehat{a}}_{LL}$ weight are qualitatively similar.

Figure 12

$A_{LL}$ as a function of parton jet $p_T$ for inclusive jets with $|\eta |<0.9$ in $\sqrt{s}=510\mathrm{GeV}$ $pp$ collisions. The bars show statistical errors, while the size of the boxes show the point-to-point systematic uncertainties on $A_{LL}$ (vertical) and $p_T$ (horizontal). The gray band on the horizontal axis represents the combined relative luminosity and underlying event uncertainties, which are common to all the points. The results are compared to predictions from DSSV14 [13] and NNPDFpol1.1 [14], including the solid blue uncertainty band for the latter. The green curves are predictions from the 100 equally probable NNPDFpol1.1 replicas.

Figure 13

$A_{LL}$ as a function of $x_T$ for inclusive jets in $\sqrt{s}=510\mathrm{GeV}$ $pp$ collisions (red solid lines), compared to previous measurements of $A_{LL}$ at $\sqrt{s}=200\mathrm{GeV}$ (blue dotted lines) [7]. The size of the boxes show the systematic uncertainties. Predictions from DSSV14 [13] and NNPDFpol1.1 [14], including the solid blue uncertainty band for the latter, are shown for $\sqrt{s}=510\mathrm{GeV}$. Predictions for $\sqrt{s}=200\mathrm{GeV}$ are similar.

Figure 14

Left: Leading order extractions from the embedding sample of the $x_1$ (red) and $x_2$ (blue) distributions in dijet events with $M_{\mathrm{inv}}=17–20\mathrm{GeV}/c^2$ for topological bins A-D, which are defined in detail in Table 1. The small figures illustrate the approximate orientations of the two jets relative to the beam line. Right: Dijet $A_{LL}$ for the same topological bins in $\sqrt{s}=510\mathrm{GeV}$ $pp$ collisions. The results are compared to theoretical predictions from DSSV14 and NNPDFpol1.1.