Bose–Einstein correlations in charged current muon–neutrino interactions in the NOMAD experiment at CERN
Introduction
The quantum mechanical wave function of two identical bosons has to be symmetric under particle exchange. The symmetrization gives rise to an observable interference pattern which enhances the number of identical bosons emitted close to one another in phase space. Such Bose–Einstein correlations (BEC) were observed for the first time in astronomical measurements of photon pairs emitted by stars [1] and soon after for like-sign hadrons produced in annihilations [2]. Since then BEC, were also measured in several other types of particle interactions (for a review see [3]). The shape of the BEC depends on the spatial and temporal distributions of the boson source and on its degree of coherence. The theoretical aspects of the BEC were developed in the papers of Kopylov and Podgoretskii [4] and Cocconi [5]. From these studies it appears that the measurements of BEC may be important to gain an understanding on the dynamics of the particle interactions yielding like-sign bosons in the final state.
Previous measurements of the BEC effects in neutrino interactions have been performed by the Big European Bubble Chamber Collaboration (BEBC) [6] including data collected on a variety of targets by both BEBC at CERN and the 15-foot Bubble Chamber at Fermilab. Nevertheless, the number of events globally collected by these experiments is still about one order of magnitude smaller than the data set collected by NOMAD and used in this paper.
Section snippets
The phenomenology of BEC
The BEC effect can be parametrized in terms of the two particle correlation function R defined as where p1,2 are the particle four-momenta, D(p1,p2) is the measured two-particle density and D0(p1,p2), the particle density in the absence of BEC. D0(p1,p2) should include any other two-particle correlations such as those coming from phase space, long-range correlations, charge effects, etc. which in the ratio should be divided out leaving only the BEC effects.
The NOMAD experiment
The main goal of the NOMAD experiment [7] was the search for νμ→ντ oscillations in a wide-band neutrino beam from the CERN SPS. The full data sample, corresponding to about 1.3 million νμ charged-current (CC) interactions collected in four years of data taking (1995–1998) in the detector fiducial volume, is used in the present analysis. The data are compared to the results of a Monte Carlo simulation based on modified versions of the LEPTO 6.1 [8] and the JETSET 7.4 [9] generators for neutrino
The reference samples
We have studied several alternatives for the choice of the reference sample D0(p1,p2) used in Eq. (1). In principle the Monte Carlo events, which do not contain BEC, would be good candidates. However the capability of the Monte Carlo to accurately reproduce the data (except for BEC) especially in the tiny phase-space region where BEC are present is limited and other methods based on the data themselves must be found. Several methods have been used in previous experiments to build the reference
Results
This section presents the results on the chaoticity parameter λ and the source radius R obtained following the Goldhaber, KP and (Q‖, Q⊥) parametrizations.
Systematic errors
We focus the discussion of systematic errors to the inclusive BEC study using the Goldhaber parametrization.
Coulomb interactions between particles which affect like-sign and unlike-sign pairs in opposite ways, can alter the correlations. This effect changes the two pion cross section by the Gamow factor [16], a significant correction only at very small values of Q. We checked that the effect enhances both λ and RG by only a few percent therefore we decided not to apply it.
We identify three
Final results
Table 10 summarizes our final results on λ and RG including also the systematic errors from variations of the cuts discussed in the previous section (added in quadrature).
Comparison with the results of other experiments
Fig. 12 and Table 11 display a compilation of some measurements of λ and RG in the ππ channel in high statistics lepton-induced reactions: neutrino interactions [6], muon DIS [18], electron–proton DIS [21], [27], e+e− collisions [20], [23], [24], [25]. These experiments were performed at different energies; they have different selection criteria and biases and also different parametrizations for the long-range correlation (see Table 11).
Our results agree within errors with those of the combined
Conclusions
The NOMAD experiment has measured BEC in charged-current neutrino interactions using different parametrizations for this effect. The general picture emerging from the data is that the size and the chaoticity of the pion source are about 1 fm and about 0.4 respectively, quite independent of the final state rapidity sign of the emitted pions. A difference of about 40% is found between the longitudinal and transverse size of the source. We observe a decrease of the Goldhaber radius as a function
Acknowledgements
We thank the management and staff of CERN and of all participating institutes for their vigorous support of the experiment. Particular thanks are due to the CERN accelerator and beam-line staff for the magnificent performance of the neutrino beam. The following funding agencies have contributed to this experiment: Australian Research Council (ARC) and Department of Education, Science, and Training (DEST), Australia; Institut National de Physique Nucléaire et Physique des Particules (IN2P3),
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- 1
Deceased.
- 2
Now at Scuola Normale Superiore, Pisa, Italy.
- 3
Now at University of Perugia and INFN, Italy.