C. Ciocca, M. Cuffiani, G. Giacomelli

• Definition of the variables

• Motivations

• Results

• Summary

Position-momentum correlations in e+e- annihilations at 91.2 GeV

2

qtq0 = E1 – E2 > 0

ql

1

2

B-E correlation functions in bins of qt, ql and q0 ...

thrust axis

3

• Y: pair rapidity

• kT : pair transverse momentum

)pp(2

1k 21T

)]p-)/(Epln[(E2

1Y suml,sumsuml,sum

... as a function of Y and kt ;

4

2l0

220

20l

22l

2t

2t

0lt)vq(qγR)vq(qγRqRλe1)q,q,C(q

v is the source velocity as measured in the observation frame

space-momentum correlations fit parameters depend on Y and kt

Ri are source parameters as measured in the source rest frame (R0 measures the duration of particle emission)

fit the correlation functions to the Yano-Koonin-Podgoretsky (YK) parameterization (see e.g. S. Chapman, J.R. Nix and U. Heinz, Phys. Rev. C52 (1995) 2694)

5

If the production volume (source element) moves relative to the observation frame with velocity v along the event axis, then after the

Lorentz transformation ql (ql-vq0) q0 (q0-vql)

the correlation function can be written in the form YK where the qi are measured in the observation frame, while Ri measure the source in the rest frame of the production volume.

YYK YYK

Y Y

static source: weak position-momentum correlations

if strong position-momentum correlations are present, then

Study YYK = ½ ln[(1+v)/(1-v)] as a function of Y

GIBS Phys. Lett. B 397 (1997) 30.

NA49 Eur. Phys. J. C2 (1998) 661

WA97 J. Phys. G 27 (2001) 2325.

PHOBOS subm. to Phys. Rev. C

7

In H.I. data Rl and Rt are observed to depend on kt and Y

EHS/NA22 Z. Phys. C71 (1996) 405

Y

Rl

8

G. Alexander, Phys. Lett. B506 (2001) 45

DELPHI and L3 (unpublished)

mt = sqrt( kt2 + m

2 )

9

Results of the YK 6-parameter fits

C(qt,ql,q0)=N(1e )-Rt2qt

2 -Rl22 (ql – vq0)2 –R0

2 (q0 –vql)

same event and track selections as in Eur. Phys. J. C16 (2000) 423

inclusive sample (no two-jet selections)

bin size = 40 MeV

CEXP. =(NLIKE / NUNLIKE )DATA

(NLIKE / NUNLIKE )JETSET

10

ql = q0/v (q0 – vql) = 0 and (ql – vq0) = ql/

small range in q0boost available for fitting, large uncertainty in R0

2

slope = 1/v

legenda

projections: |qother| < 0.12 GeV

qt < 0.12 GeV

11

Include long-range linear terms

C(qt,ql,q0)=N(1+e )-Rt2qt

2 -Rl22 (ql – vq0)2 –R0

2 (q0 –vql)

(1+ctqt+clql+c0q0)

12

v

13

R02 Rl

2

14

Rt2

15

Factorize the YK function into longitudinal and transverse terms

C(qt,ql,q0)=N(1+e )-Rl22 (ql – vq0)2 –R0

2 (q0 –vql)

fit the experimental C (qt < 0.12 GeV) to 5 parameter “longitudinal” YK function:

and the experimental C (ql < 0.12 GeV, q0 < 0.12 GeV) to 3 parameter “transverse” YK function:

C(qt,ql,q0)=N(1+e )-Rt2qt

2

16

5 param fit 6 param fit

17

5 param fit 6 param fit

18

5 param fit 6 param fit

19

v

20

Source rapidity YYK = ½ ln[(1+v)/(1-v)] as a function of

pair rapidity Y (sum over all kt)

21

R02 Rl

2

22

6 param fit 3 param fit

23

Rt2

24

Further checks

Edgeworth expansion

C=N(1+e )(1 + H3 ( 2 Rq)/6)-R2q2

H3 (x) = x3 – 3x is the third-order Hermite polinomial

Maximize likelihood function

E-802 Collaboration, Phys. Rev. C66 (2002) 054906.

25

Dependence on Y at fixed Kt Dependence on Kt at fixed Y

Gauss vs. Edgeworth

26

Dependence on Y at fixed Kt Dependence on Kt at fixed Y

inclusive sample vs. two-jet events

27

data/Jetset vs. data

Dependence on Kt at fixed YDependence on Y at fixed Kt

28

data 2 vs. data (likelihood)

Dependence on Kt at fixed YDependence on Y at fixed Kt

29

weak dependence on kt

sum over kt and study Rl dependence on Y

5 param. fit

6 param. fit

30

Summary

• The puzzle of negative R02 looks to have been solved;

however, it seems difficult to get a value of the emission duration from YK fits.

• Clean dependence of v on Y; Yano-Koonin rapidity scales approximately with pair rapidity.

• There is some indication of a decrease of Rt and of Rl with increasing kt and at larger Y, even if systematics due to the fit choice are large.

• Is this of some interest to the h.i. community ?