Status and prospects of Di-jet production in high-energy polarized proton-proton collisions at RHIC at s**(1/2) = 200-GeV
SStatus and prospects of di-jet production inhigh-energy polarized proton-proton collisions atRHIC at √ s = GeV
Bernd Surrow (For the STAR Collaboration)
Massachusetts Institute of Technology77 Massachusetts Avenue, Cambridge, MA 02139, USA
Abstract.
The STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory (BNL) is carrying out a spin physics program colliding transversely or longitu-dinally polarized proton beams at √ s = −
500 GeV to gain deeper insight into the spin structureand dynamics of the proton. These studies provide fundamental insight into Quantum Chromody-namics (QCD). One of the main objectives is the determination of the polarized gluon distributionfunction, ∆ g , through the measurement of the longitudinal double-spin asymmetry, A LL , for variousprocesses. Inclusive hadron and jet production from polarized pp collision data collected so far at √ s =
200 GeV using the STAR detector at RHIC have placed important constraints on ∆ g . Di-jetproduction provides direct access to the initial parton kinematics at leading order (LO) QCD andthus provides sensitivity to the Bjorken- x dependence of ∆ g . The status of the mid-rapidity di-jetcross section analysis from the 2005 RHIC run and the longitudinal double-spin asymmetry at mid-rapidity for the 2006 data sample are discussed in these proceedings. Projections on future di-jetmeasurements at STAR are provided. Keywords:
BNL, RHIC, STAR, pp collisions, QCD, proton spin, A LL , gluon polarization, globalanalysis PACS:
INTRODUCTION
The longitudinal STAR spin physics program profits enormously from the unique capa-bilities of the STAR experiment for measuring large acceptance jet production, identifiedhadron production and photon production. Constraining the polarized gluon distributionfunction, ∆ g , through inclusive measurements has been, so far, the prime focus of thephysics analysis program of the Run 3/4 [1], Run 5 [2] and Run 6 [3] data samples.The recent STAR inclusive jet [2, 3] results along with the PHENIX neutral pion results[4] have been used for the first time to constrain ∆ g in a NLO global analysis alongwith semi-inclusive and inclusive DIS data [5]. The RHIC data sets have been shownto provide strong constraints on ∆ g for 0 . < x < . x region for agiven jet transverse momentum region. While those measurements provide a strong con-straint on the value of ∆ g integrated over a range in x , those measurements do not permita direct sensitivity to the actual x dependence. This motivates the need for correlationmeasurements in polarized proton-proton collisions. a r X i v : . [ h e p - e x ] N ov TAR preliminary - Run 5 D a t a / P y t h i a N o r m a li ze d y i e l d FIGURE 1.
Comparison of data (2005 RHIC run) and a PYTHIA-MC sample for three di-jet variables,the invariant mass (M), the mean of the di-jet pseudo-rapidities ( / ( η + η ) ) and the cosine of thecenter-of-mass scattering angle ( cos θ ∗ ). STATUS AND PROSPECTS OF DI-JET PRODUCTION
Correlation measurements such as those for di-jet production allow for a better constraintof the partonic kinematics and thus the shape of ∆ g . At LO, the di-jet invariant mass, M , is proportional to the product of the x values of the partons, M = √ s √ x x , whereasthe pseudorapidity sum of the final-state jets, η + η , is proportional to the logarithm ofthe ratio of the x values, η + η = ln ( x / x ) . Photon-jet coincidence measurements areexpected to provide a theoretically clean way to extract ∆ g [6]. A LO extraction of ∆ g alone would allow a model-independent way to constrain the x dependence, which wouldbe an important contribution, without making an a priori assumption on the functionalform of ∆ g as is currently required in a global analysis. This has been shown for photon-jet events in simulations [6]. The feasibility for a LO extraction of ∆ g as a function of x for the case of di-jet production still has to be demonstrated. Measurements at both √ s =
200 GeV and √ s =
500 GeV are preferred to maximize the kinematic reach in x and possibly provide a means to observe effects of scaling violations at fixed x bymeasuring different p T values. The wide acceptance of the STAR experiment permitsreconstruction of di-jet events with different topological configurations, i.e. different η / η combinations, ranging from symmetric ( x = x ) partonic collisions to asymmetric( x < x or x > x ) partonic collisions. This, together with the variation of the center-of-mass energy, constrains ∆ g over a wide range in x of approximately ∼ · − < x < . R ≡ (cid:112) ∆ η + ∆ φ [3]. The jet axis was required to be within a fiducial rangeof − . < η JET < . ( − . < η Detector < . ) for the 2005 (2006) data sample with acone radius of R = . ( . ) . The dominant fraction of di-jet events in both the 2005 and TAR preliminary - Run 6 (a) (b)
FIGURE 2. (a) Statistical uncertainty of the longitudinal double-spin asymmetry, A LL , as a function ofthe di-jet invariant mass, M, for the 2006 RHIC data sample. (b) Statistical precision of the longitudinaldouble-spin asymmetry, A LL , for di-jet production as function of the ratio M / √ s for different topologicalcombinations of the STAR BEMC and the STAR EEMC acceptance region. ∆ η × ∆ φ = . × .
0. This triggerwas taken in coincidence with a minimum-bias condition using the STAR Beam-BeamCounter (BBC). The di-jet analysis status presented below is based on an integratedluminosity of approximately 2 pb − and 5pb − for the 2005 and 2006 data samples.Figure 1 shows a comparison of data based on the 2005 RHIC run and a PYTHIA-MC sample for three di-jet variables, the invariant mass ( M ), the mean of the di-jet pseudorapidities (1 / ( η + η ) ) and the cosine of the center-of-mass scatteringangle (cos θ ∗ ). The top panels show the actual yield for each variable. The bottompanels display ratios of the data and MC histograms to quantify the comparison of dataand MC distributions. The relative normalization has been fixed by the invariant massdistribution and then applied to both the 1 / ( η + η ) and cos θ ∗ distributions, i.e. thedata/MC comparison reflects only one normalization factor. The comparison is carriedout for asymmetric transverse momentum cuts on both jets using min ( p T ) ≥ ( p T ) ≥ ( p T ) (max ( p T ) ) refers to the p T of the jet in the di-jetpair with the smaller (larger) jet p T . Such an asymmetric requirement on the final-statejet transverse momenta has been suggested as a means to keep NLO calculations undercontrol since soft gluon emissions in a back-to-back jet configuration are not taken intoaccount and would require resummations. The shape for each di-jet variable in data andMC is in good agreement. This agreement between data and MC is not dependent on theasymmetric jet transverse momentum requirement and even holds for symmetric cuts. Adirect comparison of the actual di-jet cross section to NLO calculations requires furtherstudies such as the completion of a full evaluation of hadronization and underlying eventeffects.Figure 2 a) shows the statistical precision of the longitudinal double-spin asymmetry, A LL , as a function of the di-jet invariant mass, M . These uncertainties, extracted fromthe 2006 data sample, are compared to a LO MC evaluation of A LL computed with aPYTHIA MC sample using different event weights to account for different polarizedgluon distribution functions of GRSV [8] and DSSV [5] similar to the ones discussedn [3]. The size of the statistical uncertainty at the highest invariant mass bin is at thelevel of the difference between GRSV-STD and DSSV.Figure 2 b) shows the statistical precision of the longitudinal double-spin asymmetry, A LL , for di-jet production as a function of M / √ s for different topological combinationsof the STAR BEMC and the STAR Endcap Electromagnetic Calorimeter (EEMC) ac-ceptance regions. At LO, the ratio M / √ s is equal to √ x x . Taking into account thedifferent η ranges covered, and equivalently, the different cos θ ∗ regions being probed,each panel represents a different range in x / x . At LO, cos θ ∗ amounts to tanh (cid:0) η − η (cid:1) .The upper left panel effectively probes asymmetric partonic collisions where predomi-nantly a low-x gluon collides with a high-x quark at large invariant masses. The effectivevariation of x and x amounts to 0 . < x < . . < x < .
2. In contrast, a kine-matic region of larger x values in ∆ g is probed at predominantly symmetric partoniccollisions such as the one shown in the lower right panel. The effective variation of x and x is roughly equal and given by the horizontal axis of the lower right panel. Theprojected uncertainties are shown for a luminosity of 50 pb − and a beam polarizationof 60%. Those projected uncertainties are compared to a LO evaluation of A LL and afull NLO A LL calculation. Scale uncertainties are shown as a shaded band for DSSVand GRSV-STD reflecting a variation of the invariant mass M as a hard scale of 2 M and 0 . M . Asymmetric cuts are imposed for the LO MC and the NLO determination ofmin ( p T ) ≥ ( p T ) ≥ ∆ g is also shown. This particular choice of ∆ g is reflected in a large positivegluon polarization at low x , a node around x ∼ . x at the initial scale of 4 GeV . GS-C is still consistent with the current inclusivejet results [3]. A cone radius of R = . A LL and a full NLO calculation. Scale uncertainties arefound to be small in comparison to the variation of the chosen polarized gluon distribu-tion functions, in particular, at large values of M . The projected uncertainties are thoserequested in the STAR Beam Use Proposal for the upcoming RHIC data taking period at √ s =
200 GeV in 2009. Di-jet production will play a critical role in the future, deepeningour understanding of ∆ g , in particular, by constraining its shape. ACKNOWLEDGEMENT
The contribution by Tai Sakuma is acknowledged by the author of this proceedingscontribution.
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