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What can we learn from Spin?

What can we learn from Spin?. O. Villalobos Baillie School of Physics and Astronomy The University of Birmingham. Plan of Talk. Models of polarization Symmetry constraints The spin ½ case Advantages for spin >½ Vector Mesons The W - Hyperon Conclusions.

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What can we learn from Spin?

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  1. What can we learn from Spin? O. Villalobos Baillie School of Physics and Astronomy The University of Birmingham SQM2007 Levoca

  2. Plan of Talk • Models of polarization • Symmetry constraints • The spin ½ case • Advantages for spin >½ • Vector Mesons • The W- Hyperon • Conclusions SQM2007 Levoca

  3. Hyperon Inclusive Transverse Polarization Data • Benchmark: L0 polarization in pp • Negative w.r.t. production plane, increases linearly with pT below 1 GeV/c, constant thereafter • Increases linearly with xF from zero at xF = 0 • Independent of beam energy • The L0 and X0are unpolarized • The S+ and S- have polarizations of similar magnitude but opposite sign • Polarization of the S+decreases with xF • The X- and X0 polarizations have the same sign • Both have xF-independent polarization _ _ SQM2007 Levoca

  4. Models of Polarization • Perturbative QCD-based models are naturally valid only at high pT, and have not been very successful • Numerous phenomenological models have been proposed for polarization in hadronic reactions (Λ0 unless otherwise stated) • pp reactions • B. Andersson et al., Phys. Lett. B85 (1979) 417. • T.A. DeGrand and H.J. Miettinen Phys. Rev. D24 (1981) 2419. – Polarizationof Λ0 owing to Thomas precession and quark momentum ordering. • AA reactions • A.D. Panagiotou, Phys. Rev. C33 (1986) 1999; L.M. Montaño and G. Herrera, Phys. Lett. B381 (1996) 337; A. Ayala et al., Phys. Rev. C65 (2002) 024902.- No polarizationof Λ0 in QGP as these come from coalescence of random sea quarks. • Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005) 102301 – Erratum Phys. Rev. Lett. 96 (2006) 039901, Phys. Lett. B629 (2005) 20. - Polarizationfor all particles in non-central AA interactions owing to momentum gradient along impact parameter vector. SQM2007 Levoca

  5. De Grand and Miettinen Model • For L, a ud diquark from a beam proton combines with a much slower sea s quark, assumed to have some pT. The s quark is then accelerated longitudinally, i.e. in a direction different from its momentum vector, and feels the effect of the Thomas precession wT. This enters the effective Hamiltonian as a term U = S. wT = - 1/r (dV/dr) L.S. • Predicts • Sign of L transverse polarization • Qualitative behaviour with pT and xF. • Fails to predict • Magnitudes at large xF. • Systematics of relative polarizations for different hyperon species. For example L and X-polarization predicted to be the same, when X-polarization actually factor of two smaller. • Systematics of beam species. For example L polarization in pp interactions predicted to be the same as in K-p interactions, while latter polarization is actually factor of two larger. SQM2007 Levoca

  6. No polarization in QGP? • In certain models hadronization in a QGP comes from association of quarks collected together at random. In such models the expectation is that there will be no correlation between the spins of the quarks, and therefore no net polarization. • “L0s coming from the zone where the critical density for QGP formation has been achieved, are produced through the coalescence of independent slow sea u, d, and s quarks and are emitted via an evaporationlike process. Consequently, these plasma created L0s should show zero polarization.” • A.D. Panagiotou, Phys. Rev. C33 (1986) 1999 • L.M. Montaño and G. Herrera, Phys. Lett. B381 (1996) 337 • A. Ayala et al., Phys. Rev. C65 (2002) 024902 SQM2007 Levoca

  7. beam x reaction plane y Polarization in non-central AA collisions Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005) 102301 Erratum Phys. Rev. Lett. 96 (2006) 039901, Phys. Lett. B629 (2005) 20 S. Voloshin nucl:th/0410089 • In non-central collisions, there is a longitudinal momentum gradient along the direction of the impact parameter vector, which gives rise to angular momentum between partons. This is expected to lead to quark polarization through spin-orbit coupling. SQM2007 Levoca

  8. Restrictions (1) Production Plane • In an inclusive reaction ab → C + X, the production plane is specific to particle C: • There is no longitudinal polarization when parity is conserved. • When the initial state particles are identical, there is no transverse polarization at xF=0. SQM2007 Levoca

  9. Restrictions (2) Reaction Plane STAR Coll. PRL 92 (2004) 062301 • Reaction plane applies to all particles in an event. Its axis, but not direction, can be obtained from a v2 analysis. • Direction can be obtained from a v1 analysis, but difficult at mid-rapidity as v1 tends to zero as xF→0. If ambiguity is not solved, in practice the event sample will behave as in the production plane case. • In ALICE, and later STAR publications, this problem may be solved through use of ZDC to define sign of reaction plane. SQM2007 Levoca

  10. Spin ½ case • For spin-½ particles there are only two spin sub-states, ↑ and ↓. If analysis is done near xF=0, transverse polarization with respect to production plane will go to zero. • Polarization transverse to reaction plane could also disappear at xF=0, if there is an ambiguity in the sign of the plane normal. Lack of knowledge of Direction of reaction plane Populates both r++ and r--; Looks like unpolarized case SQM2007 Levoca

  11. Au+Au @ 200GeV (20-70%) Au+Au @ 62GeV (0-80%) STAR Preliminary (GeV/c) STAR J. Chen, QM06 arXiv:nucl-ex/0705.1691 Christoph Blume Monday Global  PolarizationResults Pb+Pb at 158A GeV minimum bias (12.5–43.5%) No significant polarization P observed Similar to RHIC measurements NA49 preliminary stat. errors only NA49 preliminary stat. errors only SQM2007 Levoca

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  13. Spin > ½; Alignment • For particles with spin greater than ½, it is possible to distinguish an unpolarized state from one where the direction of the quantization axis used is uncertain. • Use diagonal terms only – not clear what interference means for inclusive production • This can be characterised in terms of the alignment, A=(1-3p0), where p0 is the probability to get projection L=0. Tr r =1 r11 + r00 + r-1-1 =1 2r11 + r00 =1 ←Parity conservation SQM2007 Levoca

  14. STAR pT dependence Reaction Plane Jin Hui Chen STAR Collab. Sunday STAR Preliminary K*0(0.8<pT<5.0 GeV/c): ρ00 = 0.33 +- 0.04 +- 0.12 φ (0.4<pT<5.0 GeV/c): ρ00 = 0.34 +- 0.02 +- 0.03 There is no significant spin alignment observed for vector mesons – model prediction for spin alignment is also small – difficult to observe ! SQM2007 Levoca

  15. STAR STAR Preliminary pT dependence Production Plane Jin Hui Chen STAR Collab. Sunday pT<2.0 GeV/c ρ00(K*) = 0.43 +- 0.04 +- 0.08 ; ρ00(φ) = 0.42 +- 0.02 +- 0.04 pT>2.0 Gev/c ρ00(K*) = 0.38 +- 0.04 +- 0.06 ; ρ00(φ) = 0.38 +- 0.03 +- 0.05 In p+p, ρ00(φ) = 0.40 +- 0.04 +- 0.06 SQM2007 Levoca

  16. Ω- Decays ALICE PPR Vol II: J. Phys. G 32 (2006) 1295 W- LK- L pp- • Vertex requirements in general lead to favourable S/B for hyperon decay products. • The W- hyperon could display polarization or alignment with respect to the reaction plane normal. • Given W- is spin 3/2, as for vector mesons, the density matrix allows one to distinguish up/down alignment from non-polarization. • Cascade (i.e. two-step) decay allows cross checks on L longitudinal polarization, owing to the weak decay. SQM2007 Levoca

  17. Remarks on Ω- Decays • In fact, W- quantum numbers have never been measured! • Best evidence comes from K-p measurement - see e.g. M. Baubillier et al., Phys. Lett. 78B (1978) 342 which established that J>½. • Hyperon beam experiments did not resolve issue because W turns out to be unpolarized in pp. • If Liang-Wang model works, this issue may finally be resolved in heavy ion interactions. SQM2007 Levoca

  18. Conclusions • Pattern of transverse polarization in pp remains a mystery – no model accounts for all the observations. • Non-central nucleus-nucleus collisions might still give an interesting mechanism for generating polarization. • First results not very promising • Measurements harder at mid-rapidity owing to unavoidable symmetry restrictions. • Study of angular distribution for particles with spin >½ helps overcome possible ambiguities • Study of W- decays, which have low background owing to well-separated decay vertex, should be an interesting possibility. • If we are lucky, could end 40-year wait for the W- quantum numbers. SQM2007 Levoca

  19. Phi analysis preview at SQM06 Ma Yugang SINAP China STAR analysis: • Vector-meson (phi) spin alignment in Au+Au (global polarized QGP?). Ideals: Recombination of q-qbar in polarized QGP; recombination of q(qbar) in polarized QGP with unpolarized qbar(q); fragmentation from polarized q(qbar) see: Liang, Wang, PRL 94(05)102301; PLB629(05)20; EXCHARM Coll, PLB 485 (00) 334 SQM2007 Levoca

  20. STAR or Hadronization does not wash out quark polarization • Global spin alignment is sensitive to different hadronization scenarios in different kinematic region[1] • Coalescence (ρ00<1/3) • Fragmentation (ρ00>1/3) [1] Z.T. Liang and X.N. Wang, Phys. Lett. B 629 (2005) 20. • Global hyperon polarization andglobal vector meson spin alignment • Measured through decay products angular distribution w.r.t. reaction plane SQM2007 Levoca

  21. Tr r =1 r11 + r00 + r-1-1 =1 2r11 + r00 =1 SQM2007 Levoca

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