June 28th 2007SQM2007 Levoca1 What can we learn from Spin? O. Villalobos Baillie School of Physics and Astronomy The University of Birmingham

June 28th 2007SQM2007 Levoca2 Plan of Talk Models of polarization Symmetry constraints The spin ½ case Advantages for spin >½ Vector Mesons The  - Hyperon Conclusions

June 28th 2007SQM2007 Levoca3 Hyperon Inclusive Transverse Polarization Data Benchmark:  0 polarization in pp Negative w.r.t. production plane, increases linearly with p T below 1 GeV/c, constant thereafter Increases linearly with x F from zero at x F = 0 Independent of beam energy The  0 and   are unpolarized The  + and  - have polarizations of similar magnitude but opposite sign Polarization of the  + decreases with x F The  - and  0 polarizations have the same sign Both have x F -independent polarization __

June 28th 2007SQM2007 Levoca4 Models of Polarization Perturbative QCD-based models are naturally valid only at high p T, and have not been very successful Numerous phenomenological models have been proposed for polarization in hadronic reactions (Λ 0 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) – Polarization of Λ 0 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) No polarization of Λ 0 in QGP as these come from coalescence of random sea quarks. Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005) – Erratum Phys. Rev. Lett. 96 (2006) , Phys. Lett. B629 (2005) Polarization for all particles in non-central AA interactions owing to momentum gradient along impact parameter vector.

June 28th 2007SQM2007 Levoca5 De Grand and Miettinen Model For  a ud diquark from a beam proton combines with a much slower sea s quark, assumed to have some p T. 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  T. This enters the effective Hamiltonian as a term U = S.  T = - 1/r (dV/dr) L.S. Predicts Sign of  transverse polarization Qualitative behaviour with p T and x F. Fails to predict Magnitudes at large x F. Systematics of relative polarizations for different hyperon species. For example  and    polarization predicted to be the same, when   polarization actually factor of two smaller. Systematics of beam species. For example  polarization in pp interactions predicted to be the same as in K - p interactions, while latter polarization is actually factor of two larger.

June 28th 2007SQM2007 Levoca6 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. –“  0 s 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  0 s 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)

June 28th 2007SQM2007 Levoca7 Polarization in non-central AA collisions 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. x y beam reaction plane Z.T. Liang and X.N. Wang, Phys. Rev. Lett. 94 (2005) Erratum Phys. Rev. Lett. 96 (2006) , Phys. Lett. B629 (2005) 20 S. Voloshin nucl:th/

June 28th 2007SQM2007 Levoca8 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 x F =0.

June 28th 2007SQM2007 Levoca9 Restrictions (2) Reaction Plane Reaction plane applies to all particles in an event. Its axis, but not direction, can be obtained from a v 2 analysis. Direction can be obtained from a v 1 analysis, but difficult at mid- rapidity as v 1 tends to zero as x F →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. STAR Coll. PRL 92 (2004)

June 28th 2007SQM2007 Levoca10 Spin ½ case For spin-½ particles there are only two spin sub-states, ↑ and ↓. If analysis is done near x F =0, transverse polarization with respect to production plane will go to zero. Polarization transverse to reaction plane could also disappear at x F =0, if there is an ambiguity in the sign of the plane normal. Lack of knowledge of Direction of reaction plane Populates both  ++ and  -- ; Looks like unpolarized case

June 28th 2007SQM2007 Levoca11 Global  Polarization Results Pb+Pb at 158A GeV minimum bias (12.5–43.5%) No significant polarization P  observed 200GeV (20-70%) 62GeV (0-80%) (GeV/c) STAR Preliminary STAR J. Chen, QM06 arXiv:nucl-ex/ Similar to RHIC measurements NA49 preliminary stat. errors only Christoph Blume Monday

June 28th 2007SQM2007 Levoca12

June 28th 2007SQM2007 Levoca13 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=(1-3p 0 ), where p 0 is the probability to get projection  =0. Spin > ½; Alignment Tr  =1  11 +  00 +  -1-1 =1 2  11 +  00 =1 ← Parity conservation

June 28th 2007SQM2007 Levoca14 p T dependence STAR There is no significant spin alignment observed for vector mesons – model prediction for spin alignment is also small – difficult to observe ! STAR Preliminary K *0 (0.8<p T <5.0 GeV/c): ρ 00 = φ (0.4<p T <5.0 GeV/c): ρ 00 = Jin Hui Chen STAR Collab. Sunday Reaction Plane

June 28th 2007SQM2007 Levoca15 p T dependence p T <2.0 GeV/c ρ 00 (K*) = ; ρ 00 (φ) = p T >2.0 Gev/c ρ 00 (K * ) = ; ρ 00 (φ) = In p+p, ρ 00 (φ) = STAR STAR Preliminary Production Plane Jin Hui Chen STAR Collab. Sunday

June 28th 2007SQM2007 Levoca16 Ω - Decays Vertex requirements in general lead to favourable S/B for hyperon decay products. The  - hyperon could display polarization or alignment with respect to the reaction plane normal. Given  - 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  longitudinal polarization, owing to the weak decay. ALICE PPR Vol II: J. Phys. G 32 (2006) 1295    K -  p  

June 28th 2007SQM2007 Levoca17 Remarks on Ω - Decays In fact,  - 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  turns out to be unpolarized in pp. If Liang-Wang model works, this issue may finally be resolved in heavy ion interactions.

June 28th 2007SQM2007 Levoca18 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  - 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  quantum numbers.

June 28th 2007SQM2007 Levoca19 Phi analysis preview at SQM06 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 Ma Yugang SINAP China

June 28th 2007SQM2007 Levoca20 Hadronization does not wash out quark polarization Global spin alignment is sensitive to different hadronization scenarios in different kinematic region [1] –Coalescence (ρ 00 <1/3) –Fragmentation (ρ 00 >1/3) [1] Z.T. Liang and X.N. Wang, Phys. Lett. B 629 (2005) 20. or STAR  Global hyperon polarization and global vector meson spin alignment – Measured through decay products angular distribution w.r.t. reaction plane

June 28th 2007SQM2007 Levoca21 Tr  =1  11 +  00 +  -1-1 =1 2  11 +  00 =1