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June 28th 2007 SQM2007 Levoca 1
What can we learn from Spin?
O. Villalobos Baillie
School of Physics and Astronomy
The University of Birmingham
June 28th 2007 SQM2007 Levoca 2
Plan of Talk
• Models of polarization
• Symmetry constraints
• The spin ½ case
• Advantages for spin >½
• Vector Mesons
• The - Hyperon
• Conclusions
June 28th 2007 SQM2007 Levoca 3
Hyperon Inclusive Transverse Polarization Data
• Benchmark: 0 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 0 and are unpolarized• The + and - have polarizations of similar
magnitude but opposite sign• Polarization of the + decreases with xF
• The - and 0 polarizations have the same sign• Both have xF-independent polarization
_ _
June 28th 2007 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. – Polarization
of 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 polarization of 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. - Polarization for all particles in non-central AA interactions owing to momentum gradient along impact parameter vector.
June 28th 2007 SQM2007 Levoca 5
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 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 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 pT and xF.
• Fails to predict• Magnitudes at large xF.• 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.
xf P
xi P
pT
pL
s
sp
.T
June 28th 2007 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.– “0s 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 0s 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
June 28th 2007 SQM2007 Levoca 7
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) 102301 Erratum Phys. Rev. Lett. 96 (2006) 039901, Phys. Lett. B629 (2005) 20S. Voloshin nucl:th/0410089
June 28th 2007 SQM2007 Levoca 8
Restrictions (1) Production Plane
||ˆ
Ca
CaC pp
ppn
• 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.
pa
pC
nC^
June 28th 2007 SQM2007 Levoca 9
Restrictions (2) Reaction Plane
||ˆ
bp
bpn
a
aR
• 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.
A
B
b
pb
pa
nR^
STAR Coll.PRL 92 (2004)062301
June 28th 2007 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 ofDirection of reaction plane Populates both ++ and --;Looks like unpolarized case
June 28th 2007 SQM2007 Levoca 11
Global PolarizationResults
Pb+Pb at 158A GeVminimum bias (12.5–43.5%)
No significant polarization P observed
Au+Au @ 200GeV (20-70%)Au+Au @ 62GeV (0-80%)
Tp (GeV/c)
P
STAR PreliminarySTARJ. Chen, QM06arXiv:nucl-ex/0705.1691
Similar to RHIC measurements NA49 preliminary
NA49 preliminary
stat. errors only
stat. errors only
Christoph BlumeMonday
June 28th 2007 SQM2007 Levoca 13
• 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 =0.
Spin > ½; Alignment
11
00
11
00
00
00
Tr =111 + 00 + -1-1 =1211 + 00 =1 ← Parity conservation
June 28th 2007 SQM2007 Levoca 14
pT dependence
2
2)(
00 3
1
q
qfrag
P
P
2
2)(
00 3
1
q
qrec
P
P
2
2)(
00 3
1
q
qfrag
P
P
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<pT<5.0 GeV/c): ρ00 = 0.33 +- 0.04 +- 0.12φ (0.4<pT<5.0 GeV/c): ρ00 = 0.34 +- 0.02 +- 0.03
Jin Hui ChenSTAR Collab.Sunday
Reaction Plane
June 28th 2007 SQM2007 Levoca 15
pT dependence
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
STAR
STAR Preliminary
Production Plane
Jin Hui ChenSTAR Collab.Sunday
June 28th 2007 SQM2007 Levoca 16
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.
)(GeV/cM1.66 1.68 1.7 1.72 1.74
0
10
20
30
40
)(GeV/cM1.66 1.68 1.7 1.72 1.74
0
10
20
30
40
Signal
Background
ALICE PPR Vol II: J. Phys. G 32 (2006) 1295
K-
p
June 28th 2007 SQM2007 Levoca 17
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 2007 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- 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 2007 SQM2007 Levoca 19
Phi analysis preview at SQM06STAR 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 2007 SQM2007 Levoca 20
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.
sq
sqrecK
PP
PP
3
1)*(00,
3
12
2)(
00s
srec
P
P
Vqq
2
2
2
2)(*
00 3
1
3
1
s
s
ss
s
q
q
ss
sfragK
P
P
fn
n
P
P
fn
f
2
2)(
00 3
1
s
sfrag
P
P
XVq XVq or
STAR
Global hyperon polarization and global vector meson spin alignment
– Measured through decay products angular distribution w.r.t. reaction plane