Longitudinal double-spin asymmetries for ${\pi }^0\mathrm{s}$ in the forward direction for 510 GeV polarized $pp$ collisions

The STAR Collaboration reports measurements of the longitudinal double-spin asymmetry, $A_{LL}$, for neutral pions produced at forward directions in polarized proton-proton collisions, at a center-of-mass energy of 510 GeV. Results are given for transverse momenta in the range $2<p_T<10\mathrm{GeV}/c$ within two regions of pseudorapidity that span $2.65<\eta <3.9$. These results are sensitive to the polarized gluon parton distribution function, $\mathrm{\Delta }g(x)$, down to the region of Bjorken $x\sim {10}^{-3}$. The asymmetries observed are less than $\pm 5\times {10}^{-3}$ in magnitude and will help constrain the contribution to the spin of the proton from polarized gluons at low $x$, when combined with other measurements as part of a global analysis.

Figure 1

Top Panel: Monte Carlo simulations of $x_1$ vs $x_2$ for $pp\to {\pi }^{0}X$ collisions at $\sqrt{s}=510\mathrm{GeV}$. The outgoing pion has kinematic cuts in pseudorapidity, transverse momentum and energy of: $2.65<\eta <3.90$, $3<p_T<10\mathrm{GeV}/c$ and $30<E<70\mathrm{GeV}$, where positive $\eta$ is defined with respect to the direction of proton 1 (containing partonic $x_1$), heading into the detector. These simulations use PYTHIA Version 6.4.28 [15], as described in the text. The scales in both plots are arbitrarily normalized. Lower panel: One-dimensional projections of $x_1$ and $x_2$ of the two dimensional histogram.

Figure 2

Schematic diagram of the forward meson spectrometer. The detector is an octagonal arrangement of 788 large and 476 small lead glass cells that surround the beam pipe approximately 7 m from the interaction point. The shaded cells on the periphery do not participate in the definition of the event trigger. Circles are labeled with values of pseudorapidity cuts used in the analysis, which divide the detector into inner and outer regions.

Figure 3

Typical invariant mass spectra for di-photon events which pass the cuts described in the text. The top plot is for the pseudorapidity range $2.65<\eta <3.15$ and the bottom plot is for $3.15<\eta <3.90$. All energy corrections have been applied. The interval between lines A and B indicate the limits for defining a neutral pion, with a side-band region defined by the interval BC at larger invariant mass for asymmetry calculations in these bins.

Figure 4

Longitudinal double-spin asymmetry, $A_{LL}$ vs ${\pi }^0$ transverse momentum in polarized $pp$ collisions at $\sqrt{s}=510\mathrm{GeV}$ in the pseudorapidity (energy) ranges $2.65<\eta <3.15$ ($30<E_{\pi }<70\mathrm{GeV}$) (top) and $3.15<\eta <3.90$ ($30<E_{\pi }<100\mathrm{GeV}$) (bottom). Data collected in 2012 and 2013 have been combined. Vertical error bars on the data represent the statistical uncertainties from pion yields and polarization measurements only. The vertical extent of the shaded boxes gives the combined systematic uncertainties from the relative luminosity and polarization measurements. Measurements of the beam polarization give a multiplicative uncertainty on these data due to the factor $1/P_Y{P}_B$ equal to $\pm 6.7\%$ [30], which is not shown. The horizontal extent of the shaded boxes represents the $p_T$ systematic uncertainty, described in the text. On the same graphs we plot theoretical calculations of $A_{LL}$ for neutral pions [31], using the NNPDFpol1.1 [32] (black solid line and error band for the 100 replicas in the set) and DSSV14 [33] (blue dashed line) sets of polarized PDFs. In both cases, we use the DSS fragmentation functions [34].