Sensitive Test for Models of Bose-Einstein Correlations

Abstract

Accurate and sensitive measurements of higher order cumulants open up new approaches to pion interferometry. It is now possible to test whether a given theoretical prediction can match cumulants of both second and third order. Our consistency test utilizes a new sampling technique combining theoretically predicted functions with experimentally determined weights in a quasi -Monte Carlo approach. Testing a simplified version of a quantum statistics-based framework of Bose-Einstein correlations with this technique, we find that predictions for third order cumulants differ significantly from UA1 data. This discrepancy may point the way to more detailed dynamical information.[S0031-9007(97)03528-X] PACS numbers: 13.85. Hd, 05.30.Jp, 12.40.Ee, 25.75.Gz Pion interferometry has been a vital part of multiparticle physics for several decades [1]. While traditionally experimental effort in this field has centered around second order correlations, much progress has been made recently in accurately quantifying higher order correlations by means of so-called correlation integrals [2], to the point where these now yield statistically significant conclusions not only for moments but also for higher order cumulants. Because cumulants are so sensitive to details of the dynamics, they represent a stringent testing ground for proposed theoretical models.A number of theoretical predictions for higher orders exist [3][4][5]. In particular, Andreev, Plümer, and Weiner (APW) [6] have suggested a very general quantumstatistical framework, based on the classical source current formalism applied successfully in quantum optics. Its basic assumptions are (1) a Gaussian density functional for the classical random currents and (2) isotropy in isospin space. These two assumptions determine all higher order correlation functions in terms of the basic correlator, independent of the structure of the sources. All further assumptions concern only a more detailed specification of the space-time evolution of the sources. Thus, the APW framework includes as special cases more specific models of Bose-Einstein correlations such as the GKW model [7] and the approach of Biyajima et al. [4]. Because the APW model is so important, we test a simple version of its predictions below. It will also serve as an example to show how our approach works.While higher order cumulant measurements are valuable in their own right, they can be used to even greater effect in consistency checks: once an assumed parametrization is found to fit the second order data, the same set of parameter values ought to fit all predicted higher order correlations as well. Departing from tried and tested ways, we therefore concentrate not so much on numerical values of source parameters, but rather on utilizing their required constancy over cumulants of different orders to test for consistency and ultimately falsifiability of a given theoretical prediction.Pion interferometry measures correlations in terms of pair variables such as three-or four-momentum differences of two particles. In...

Multidimensional HBT correlations in pp̄ collisions at s = 630 GeV

“…Second, we believe that the same peak may well be responsible for the power-law form and higher-order effects seen in our earlier work with one-dimensional distributions [4]. First, the peak persists even without the Coulomb or split-track corrections.…”

“…[1] and a 15-fold increase compared to earlier UA1 HBT analyses [2, 3,4]. This represents a twofold increase in statistics over Ref.…”

“…This is hardly surprising, as the four abovementioned parameters collectively depend strongly on the exact shape of the peak in the very small (q L , q T ) region -the very region that experimental measurement struggles to resolve. Either way, it is clear that the superiority of the power-law fit to the one-dimensional invariant four-momentum moment R 2 (Q) over Gauss and exponential fits [4] is not repeated in the R 2 (q L , q T ) case due to the hyperbolic shape of our "product powerlaw" parametrisation 3 compared to the elliptic form of the R 2 (q L , q T ) data shown in Fig. 2, the gauss and Edgeworth fits reproduce the shape of R 2 at intermediate (q L , q T ) rather well but lacks the strong peak exhibited in the data, 2 while the exponential and product power-law parametrisations are more peaked but fail to describe the shape at intermediate (q L , q T ).…”

Higher order Bose-Einstein Correlations test the Gaussian density matrix and the space-time approach

“…From these results one is able to calculate the correlation function (and its integral for each defined bin), as determined by equations (4)- (6) and (18)- (20).…”

“…In [20] the same momentum-space model ( [12,13,15]) as that used in [11] was applied and compared with UA1-collaboration data. This time a new technique for estimating the correlation data was used but only second and third order correlations were considered.…”