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Position-momentum correlations in e + e - annihilations at 91.2 GeV. C. Ciocca, M. Cuffiani, G. Giacomelli. Definition of the variables Motivations Results Summary. B-E correlation functions in bins of q t , q l and q 0. 2. q 0 = E 1 – E 2 > 0. q t. 1.
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Position-momentum correlations in e+e- annihilations at 91.2 GeV C. Ciocca, M. Cuffiani, G. Giacomelli • Definition of the variables • Motivations • Results • Summary
B-E correlation functions in bins of qt, ql and q0 ... 2 q0 = E1 – E2 > 0 qt 1 thrust axis ql
... as a function of Y and kt ; • Y: pair rapidity • kT : pair transverse momentum
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) v is the source velocity as measured in the observation frame Riare source parameters as measured in the source rest frame (R0 measures the duration of particle emission) space-momentum correlations fit parameters depend on Y and kt
If the production volume (source element) moves relative to the observation frame with velocity v along the event axis, then after the Lorentz transformation qlg(ql-vq0) q0g(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. Study YYK = ½ ln[(1+v)/(1-v)] as a function of Y static source: weak position-momentum correlations if strong position-momentum correlations are present, then YYK YYK Y 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
EHS/NA22 Z. Phys. C71 (1996) 405 Rl Y In H.I. data Rl and Rt are observed to depend on kt and Y
DELPHI and L3 (unpublished) G. Alexander,Phys. Lett. B506 (2001) 45 mt = sqrt( kt2 + mp2 )
Results of the YK 6-parameter fits C(qt,ql,q0)=N(1+le ) -Rt2qt2 -Rl2g2 (ql – vq0)2 –R02g2 (q0 –vql)2 same event and track selections as in Eur. Phys. J. C16 (2000) 423 inclusive sample (no two-jet selections) bin size = 40 MeV (NLIKE / NUNLIKE )DATA CEXP.= (NLIKE / NUNLIKE )JETSET
qt < 0.12 GeV slope = 1/v legenda projections: |qother| < 0.12 GeV ql = q0/v g(q0 – vql) = 0 and g(ql – vq0) = ql/g small range in q0boost available for fitting, large uncertainty in R02
Include long-range linear terms . C(qt,ql,q0)=N(1+le ) -Rt2qt2 -Rl2g2 (ql – vq0)2 –R02g2 (q0 –vql)2 . (1+ctqt+clql+c0q0)
l v
R02 Rl2
Factorize the YK function into longitudinal and transverse terms fit the experimental C (qt < 0.12 GeV) to 5 parameter “longitudinal” YK function: C(qt,ql,q0)=N(1+le ) -Rl2g2 (ql – vq0)2 –R02g2 (q0 –vql)2 and the experimental C (ql < 0.12 GeV, q0 < 0.12 GeV) to 3 parameter “transverse” YK function: C(qt,ql,q0)=N(1+le ) -Rt2qt2
5 param fit 6 param fit
5 param fit 6 param fit
5 param fit 6 param fit
v l
Source rapidity YYK = ½ ln[(1+v)/(1-v)] as a function of pair rapidity Y (sum over all kt)
R02 Rl2
6 param fit 3 param fit
Further checks Edgeworthexpansion C=N(1+le )(1 + k 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.
Gauss vs.Edgeworth Dependence on Y at fixed Kt Dependence on Kt at fixed Y
inclusive samplevs.two-jet events Dependence on Y at fixed Kt Dependence on Kt at fixed Y
data/Jetset vs.data Dependence on Y at fixed Kt Dependence on Kt at fixed Y
data (c2)vs.data (likelihood) Dependence on Y at fixed Kt Dependence on Kt at fixed Y
weak dependence on kt sum over kt and study Rl dependence on Y 5 param. fit 6 param. fit
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 ?
