Transverse Single-Spin Asymmetries for Di-Jet Production in pp Collisions
By Steve Vigdor
The
STAR Collaboration has just submitted for publication the
first paper
reporting results from the long polarized proton collision run
enabled at RHIC in 2006 by a sponsored research grant from
Renaissance Technologies Corporation. The paper reports the
first measurement in pp collisions that directly probes possible
transverse motion preferences of quarks or gluons that are
correlated with the proton’s transverse spin orientation. This
so-called Sivers effect measures the degree to which the partons
participating in a given hard-scattering process prefer to move
leftward or rightward with respect to the plane formed by the
parent proton’s momentum and transverse spin vectors. It can
arise from spin-orbit correlations in the proton wave function,
thus providing a window into the elusive orbital angular
momentum contributions to the proton’s overall spin.
Di-jet production arises from the hard scattering of partons provided by the two colliding proton beams, and an initial-state transverse motion preference of these partons would produce a characteristic kinematic boost of the two jets. In the absence of such a preference, momentum conservation demands that the two jet axes be back-to-back in azimuthal direction. The measurement is thus a very simple one: do the two jets appear to tilt leftward or rightward, vis-à-vis back-to-back, when one proton’s spin points upward, with the reversed preference when that proton’s spin is flipped? STAR’s large acceptance includes coverage when both jets go forward with respect to one proton beam; in that kinematic regime, the asymmetries measured with respect to the two proton beam spins provide complementary information about Sivers preferences in the valence and sea regions of the parton distributions.
A rapid analysis of the data for this paper was made possible by focusing at first on jet azimuthal angles measured with STAR’s electromagnetic calorimeters (EMC’s) alone. This information was saved online by a dedicated software (level 2) trigger designed specifically to filter candidate jet events for this measurement and to facilitate a fast offline analysis. The robustness of the EMC-only angle information was demonstrated subsequently by comparison to analysis of a small subsample with full jet reconstruction including charged tracks from STAR’s Time Projection Chamber. According to simulations, the overall resolution in azimuthal opening angle of the two jets, with respect to the simulated opening angle between the two parent partons, leads only to a 15% dilution of any parton-level Sivers asymmetry.
The measured asymmetries for 2.6 million di-jet events filtered by the level 2 trigger are all statistically consistent with zero (see figure), and are much smaller than measured spin asymmetries sensitive to the quark Sivers effect in semi-inclusive deep inelastic scattering (SIDIS) of electrons from a transversely polarized proton target. Initial theoretical estimates available at the time of the run predicted di-jet asymmetries of comparable magnitude to those measured in SIDIS. However, the theory has evolved very rapidly in parallel with, and partially stimulated by, the data analysis, and can now accommodate di-jet asymmetries as small as we measure by cancellations among contributions. The Sivers effect involves a triple vector correlation that is naively odd under time reversal, but it can evade time-reversal violation by virtue of initial- and/or final-state interactions among partons from the participating protons. In pp collisions, both initial- and final-state interactions are important, and their contributions tend to cancel. In addition, contributions from up and down quarks tend to cancel to different extents than in SIDIS or in the sizable transverse spin asymmetries measured at RHIC for inclusive forward hadron production in pp collisions. If we can adequately constrain a unified theoretical account for all these and subsequent transverse spin asymmetry measurements in high-energy scattering, we should approach an understanding of spin-orbit correlations among the partons in the proton.
Measured and calculated (with three different models) asymmetries vs. di-jet pseudo-rapidity sum for the beams headed in the +z (left) and –z (right) directions at STAR. (a,b) Fraction of the di-jet cross section in QCD calculations that involves a participating quark from the +z beam or gluon from the –z beam. (c,d) The integrated (over azimuthal opening angle z ) asymmetry for di-jets to tilt left vs. right for a spin-up proton beam. Quark Sivers functions in the calculations are constrained by measured spin asymmetries in semi-inclusive deep inelastic scattering at HERA. (e,f) Asymmetries calculated from yields weighted by sin z to suppress truly back-to-back di-jets, for a more robust theory comparison. Sivers functions are constrained in the calculations by transverse spin asymmetries for inclusive forward hadron production at Fermilab and RHIC.
The Relativistic Heavy Ion Collider at Brookhaven National
Laboratory is a world-class scientific research facility primarily
funded by the U.S. Department of Energy Office of Science. Hundreds
of physicists from around the world use RHIC to study what the
universe may have looked like in the first few moments after its
creation. What physicists learn from these collisions may help us
understand more about why the physical world works the way it does,
from the smallest subatomic particles, to the largest stars.