DOE review, 09/15/2003 1

spin correlations and spin selected HBT

Fei Du, Sandweiss’ group, Yale

Outline:• Lambda and its decay• Spin correlations• Spin selected HBT

DOE review, 09/15/2003 2

and its decay

(uds)– m = 1115.683 ± 0.006 MeV– c = 7.9 cm

Asymmetry in decay

cos64.01cos

d

dw

p

DOE review, 09/15/2003 3

detection at STAR

Topological method: pair up decay products (p and ) with geometry and invariant mass cuts

Preliminary

DOE review, 09/15/2003 4

How to find out the spin

Two transformations:

• 1st: transform to the CMS of the di- pair

• 2nd: transform each proton to the rest frame of its parent .

• Take the proton momentum direction as an indicator of the spin direction.

DOE review, 09/15/2003 5

spin correlations

• Spin correlation at low : due to Fermi-Dirac statistics.

• For system, at low Q, s-wave state (l=0) dominates (symmetrical space wavefunction), thus total spin S = 0. (↑↓-↓↑)

• Spins are anti-aligned.

221 )( qqQ

DOE review, 09/15/2003 6

Complication I – Q is never 0

• Finite Q → source radius

3/

3/2

3/

2

onscontributi 1 offraction :

onscontributi 0 offraction :

10

11

10

00

1

0

FF

FC

FF

FC

SF

SF

DOE review, 09/15/2003 7

Complication II – spin direction is not perfectly measured

Calculation done by G. Alexander et. al.:Use of Spin-Correlations to Study Low Energy and Space Symmetries and Resonances, Phys. Lett. B352:162, 1995

)1( 1374.01

)0( 4122.01

cos

trans.2after protons obetween tw angle :

Sydy

dN

Sydy

dN

y

DOE review, 09/15/2003 8

Spin correlation golden formula

Q

Qy

dy

dN

Q

Qe

y

yydy

dN

Qr

,1

0 ,4122.01

,4/3

0 ,0 ),1(

4

3

)3

41(4122.01

)1374.01()4122.01)(1(

22

DOE review, 09/15/2003 9

ALEPH data

DOE review, 09/15/2003 10

Preliminary

PreliminaryPreliminary

Preliminary

PreliminaryPreliminary

DOE review, 09/15/2003 11

Fit dN/dy to 1 + ky

Q (MeV) k

0 – 200 -0.15 ± 0.14

200 – 400 -0.25 ± 0.06

400 – 600 -0.03 ± 0.04

600 – 800 0.003 ± 0.03

800 – 1000 -0.009 ± 0.03Preliminary

DOE review, 09/15/2003 12

HBT (Bose-Einstein correlation)

)1()()(

)()(

][2

1

22

12212211

21

2,12,12

)()(12

Qr

rkrkirkrki

eNkPkP

kkPkkC

ee

DOE review, 09/15/2003 13

HBT (Fermi-Dirac correlation)

• Aligned spins: • Anti-aligned spins:

DOE review, 09/15/2003 14

Better treatment

22

12212211

1)(

][2

1 )()(012

Qr

rkrkirkrkiS

eQC

ee

22

12212211

1)(

][2

1 )()(112

Qr

rkrkirkrkiS

eQC

ee

22

2222

5.01

)1(75.0)1(25.0)(Qr

QrQr

e

eeQC

DOE review, 09/15/2003 15

HBT with spin selection

< /2

(y > 0)

/2

(y < 0)

triplet 0.534 0.466

singlet 0.397 0.603

222222

6.01)1(8.0)1(2.0)(

2.0)0|0( ,8.0)0|1(QrQrQr eeeQC

ySPySP

DOE review, 09/15/2003 16

aligned)-(anti 06.005.0

(aligned) 12.028.0

pairs) (all 08.016.0

1)(22

QreQC

Preliminary

PreliminaryPreliminary

DOE review, 09/15/2003 17

Outlook

• With next year’s data (~ 20x more statistics than shown in the plots here), things will become much clearer.

• Also we can use tighter cut on spin alignment with more statistics.