First Spin Results From the Polarized p+p Run at √s = 62.4 GeV
Single Spin Asymmetries of Pions, Kaons, and Protons
By J. H. Lee
The BRAHMS collaboration [1]
has submitted a paper [2]
to Physical Review Letters on the first spin results from the
RHIC/Run-6 polarized proton run at √s = 62.4 GeV. The paper
reports the measurements of transverse Single Spin Asymmetries (SSAs)
of identified charged hadrons, π±, K±, and
protons, from transversely polarized proton-proton collisions.
The measurements extend to high Feynman-x, xF = 2pL/√s
∼ 0.6 by utilizing the unique capability of the BRAHMS Forward
Spectrometer (FS) for measuring charged hadrons at the forward
kinematic region with particle identification.
The SSA is a "left-right" asymmetry of produced particles from the hadronic scattering of transversely polarized protons by unpolarized protons. SSA is customary defined as analyzing power AN, which is the difference of spin dependent cross-sections normalized by the sum when the hadron's spin vector (S⊥) is flipped: AN = (dσ(S⊥) − dσ(−S⊥))/(dσ(S⊥) + dσ(−S⊥)).
Despite conceptual simplicity, theoretical understanding of SSAs has been challenging since SSAs are expected to be negligibly small in the lowest-order QCD approximation. Measurements of large asymmetries of inclusive pion production and polarization in the production of hyperons in a wide energy range since the early seventies have motivated various theoretical efforts to understand the phenomena. The main theoretical focus to account for the observed SSAs in the framework of QCD has been on the role of transverse momentum dependent partonic effects in the structure of the initial transversely polarized nucleon ("Sivers" mechanism) and on the fragmentation process of a polarized quark into hadrons ("Collins" mechanism). Higher twist effects ("twist-3") arising from quark-gluon correlation effects have also been considered as a possible origin of SSA.
The newly available SSA measurements from RHIC in the intermediate energy regime at √s = 62.4 GeV in p↑+p can uniquely provide an opportunity to help clarify the nature of pQCD contribution to SSAs and their energy dependences. In particular, flavor dependent SSA measurements allow more complete and stringent tests of theoretical models due to flavor dependence in parton distribution functions and fragmentation processes.
The analyzing power AN for charged pions, AN(π+) and AN(π−) at √s = 62.4 GeV as a function of xF is shown in Fig. 1 for the two FS angle settings, 2.3° and 3° together with twist-3 and Sivers calculations. At a fixed xF value, the 3° setting samples higher pT pions. The mean pT values <pT> at xF=0.55 are 1.08 and 1.28 GeV/c at 2.3° and at 3°, respectively. The measured AN values show strong dependence in xF reaching large asymmetries up to ~40% at xF ~0.6 and no significant asymmetries at −xF. The SSAs for charged kaons as a function of xF are shown in Fig. 2 also with theoretical estimates. The asymmetry for K+(us) is positive as is the AN of π+(ud), which is expected if the asymmetry is mainly carried by valence quarks, but the measured positive SSAs of K−(us) seem to contradict the näive expectations of valence quark dominance.
A twist-3 pQCD model describes the xF dependence of AN for pions and the energy dependence at high pT (pT > ~1 GeV/c) where the calculations are applicable. However it remains a challenge for pQCD models to also describe the underlying spin-averaged cross-sections at this energy. Measurements of AN for kaons and protons suggest the possible manifestation of non-pQCD phenomena and call for more theoretical modeling with improved understanding of the fragmentation processes.
The BRAHMS collaboration is currently preparing publications on the spin averaged cross-section measurements at √s = 62.4 GeV and the SSA measurements at √s = 200 GeV of identified charged hadrons. A simultaneous description of SSAs and the unpolarized cross-sections in a wide kinematic range will be a crucial test for the partonic pQCD description. The energy and flavor dependent asymmetry measurements impose an important constraint on theoretical models describing fundamental mechanisms of transverse spin asymmetries and the Quantum Chromodynamical description of hadronic structure.
Figure 1: AN vs. xF for π+ and π− at √s = 62.4 GeV for positive and negative xF. Circle symbols are for π+ and box symbols are for π− measured in the FS at 2.3° (solid symbols) and 3° (open symbols). The curves are from theoretical calculations. Solid lines are to be compared with the data at 2.3° and dotted lines are for 3°. Thick (solid and dotted) lines are from the initial-state Twist-3 calculations, medium lines are from the final-state Twist-3 calculations. Predictions from the Sivers function calculations are shown as thin lines. Only statistical errors are shown where larger than symbols.
Figure 2: AN(K+) and AN(K−) vs. xF at √s = 62.4 GeV for positive and negative xF. Circle symbols are for K+ and box symbols are for K−. The solid (K+) and dotted (K−) lines are from the initial-state twist-3 calculations with (thick lines) and without (medium lines) sea- and anti-quark contribution. Calculations for the Sivers function are shown as thin lines. Errors are statistical only.
References
[1] Broad RAnge Hadron Magnetic Spectrometer at RHIC: http://www4.rcf.bnl.gov/brahms/WWW/
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