What can we learn from Spin?

June 28th 2007 SQM2007 Levoca 1

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 - Hyperon

• Conclusions


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

_ _


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.


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


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


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


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^


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


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


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



• 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


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


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


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


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.


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.


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


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


11

00

11

00

00

00

Tr =111 + 00 + -1-1 =1211 + 00 =1

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What can we learn from Spin?