1. October 12, 2004 SPIN-2004, Trieste Spin Transfers in Polarized Hadronic Collisions (RHIC-Spin in mind) V. L. Rykov and K. Sudoh RIKEN

2. 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.

3. 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.

4. 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.

5. 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

6. October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 6 Notations: L N L N S   X Z Y

7. October 12, 2004, SPIN-2004, Trieste V. L. Rykov and K. Sudoh, RIKEN 7 Spin kinematics relations between spin-transfer observables (Examples)

8. 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 -+

9. 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.

10. 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.

11. 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)

12. 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)

13. 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.