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October 12, 2004 SPIN-2004, Trieste Spin Transfers in Polarized Hadronic Collisions (RHIC-Spin in mind) V. L. Rykov and K. Sudoh RIKEN
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 2 Outlook: Introduction. Spin transfer observables in spin ½ - 0 and spin ½ - ½ collisions. How can cross-section A LL be measured... without measuring cross-section A LL ? Spin transfer for heavy flavor production in gluon fusion processes. Summary.
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 3 Introduction The spin correlations in collisions of polarized particles are not limited to a few “standard” cross-section asymmetries (e.g. A N, A LL ) plus polarizations P N of final spin non-zero particles in unpolarized collisions. Beyond that, there is the whole World of correlations between the spins of the initial and final particles, which are usually called “spin transfers”. For about a decade, the spin transfer phenomena did not enjoy much attention in the high-energy spin physics community. For example, in the RHIC Spin Proposal as of 1993, there is no virtually a single word about spin transfers ¥). The spin transfer experimental data at high energies (√S ≥ ~10 GeV) are still scarce. We are aware of only 3 experiments, all with 0 : 2 deep inelastic #), and 1, using the 200 GeV polarized proton beam collided with the hydrogen target §). In 2 of the 3 experiments, the significantly non-zero, but rather large spin transfers have been observed. ---- ¥) Beyond the implicit, rather trivial involvement of the W and Z polarizations in their parity violating production and decays. One page on spin transfer to 0 appeared 7 years later in the “Prospects for Spin Physics at RHIC”, G. Bunce et al., Ann. Rev. Nucl. Part. Sci. 50 (2000) 525. #) M. R. Adams, et al (E665), EPJ C17 (2000) 263; A. Airapetian, et al (HERMES), PR D64 (2001) 112005. E665 also measured spin transfer to anti- 0. §) A. Bravar, et al (E704) PRL 78 (1997) 4003.
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 4 Introduction (cont.) Meanwhile, since approximately 1998, there is the evident “burst of activity” on spin transfers on the theoretical side. Here is just a partial list of theoretical papers on spin transfers, which surfaced for the last 6 years: D. de Florian, et al. PRL 81 (1998) 530; D. de Florian, et al. PL B439 (1998) 176; K. Ohkuma, K Sudoh, T. Morii, PL B491 (2000) 117; K. Ohkuma, T. Morii, hep-ph/0306285; Bo-Qiang Ma, et al. NP A703 (2002) 346; Xu Qing-hua, Liang Zuo-tang, PR D70 (2004) 034015; Many by J. Soffer, W. Vogelsang, Bo-Q. Ma, M. Stratmann, et al. The theoretical justification and benefit of spin transfer measurements at high energies has been laid down basically in three domains: 1) Understanding the spin-dependent fragmentation functions; 2) Sensitivity to gluon spin-dependent structure functions of proton in “virtual- + g → heavy-flavor + X” processes; 3) sensitivity to gluon spin-dependent structure functions in gluon dominant productions of hyperons and vector mesons. In most cases, significantly non-zero spin transfers from a polarized projectile to the final spin nonzero particle have been predicted. Here, we discuss some issues, illustrating why we think the spin transfer measurements worth the efforts, using spin transfer to the charmed Λ c + as an example.
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 5 P-invariant cross-section for production of a spin ½ fermion by a polarized spin ½ fermion at unpolarized target
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 6 Notations: L N L N S X Z Y
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 7 Spin kinematics relations between spin-transfer observables (Examples)
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 8 Case of polarized spin ½ - spin ½ collisions In collisions of two polarized fermions (protons), there are two non-overlapping “worlds”: same and opposite helicities (or spin directions) of initial fermions: LNLN ++/-- +-/-+ σ ++ =σ -- σ +- =σ -+
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 9 Measuring A LL … without measuring A LL ++/-- +-/-+ +0/-0 σ ++ = σ -- σ +- = σ -+ σ + = σ - No external relative luminosity monitoring of ++/-- and +-/-+ collisions is necessary for measuring D L Π. In other words, these A LL measurements are free from the systematic errors due to relative luminosity monitoring. As soon as A LL is known, the process itself could potentially be used for the relative luminosity monitoring.
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 10 gluon fusion Spin transfer in gluon dominant processes Recently, there have been a few suggestions on using the G/G sensitive spin transfer processes as an alternative approach (to the cross-section A LL ) for uncovering the gluon polarization in protons. In Xu Qing-hua, Liang Zuo-tang, PR D70 (2004) 034015, it is shown that the spin transfer to high P T + -hyperon in the process p p + X is sensitive to G/G in the forward kinematic region. Using helicity-to-helicity transfers for measuring G/G in presumably gluon fusion dominant processes p p c X and p p D *+ X have been suggested and discussed in K. Ohkuma, K Sudoh, T. Morii, PL B491 (2000) 117, and K. Ohkuma, T. Morii, hep-ph/0306285. The attractiveness of these processes is that the heavy c- and b-quark spin fragmentation functions are expected (may be naively) to be rather simple. Here, we extended the analysis by Okhuma et al. to the proton helicity transfer to the transverse c + polarization in production plane (parameter D LS ), and for collisions of two polarized protons. D LS expected to be nonzero at P T of a few GeV due to the large c-quark mass.
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 11 Leading order (LO) spin transfers in gluon fusion (gg → q ↑ q bar center-of-mass frame)
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 12 LO spin transfer in p ↑ +p ↑ → Λ c +↑ +X, √S=200 GeV (pp center-of-mass frame)
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October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 13 Summary Spin transfer measurements in inclusive reactions with two colliding polarized protons, along with the “traditional” cross-section asymmetries, offer many – up to 10 more - of virtually independent views at the same, undoubtedly complex object: spin structure of hadronic interactions. The significantly non-zero spin transfer effect have been observed experimentally in the high-energy domain, and much more have been predicted in the recent theoretical studies. It is shown that both spin transfer component D LL and D LS in inclusive Λ c + production are equally sensitive to ΔG/G. In the central region at √S=200 GeV, the effect is expected at ~5-15%, well above the achievable at RHIC statistical errors ~1%, which are also small enough to clearly distinguish, e.g. AAC and GRSV parameterizations for ΔG/G. The larger spin transfers, up to ~20-30%, are expected at η~2 and beyond.
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