Finite-size effect on two-particle production in continuous and discrete spectrum
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inite-Size Effect on Two-Particle Production in Continuous and Discrete Spectrum¶ R. Lednicky' Joint Institute for Nuclear Research, Dubna, Moscow Region, 141980 Russia Institute of Physics ASCR, Na Slovance 2, 18221 Prague 8, Czech Republic e-mail: [email protected] Abstract—The formalism allowing one to account for the effect of a finite space-time extent of particle production region is given. Its applications to the lifetime measurement of hadronic atoms produced by a highenergy beam in a thin target, as well as to the femtoscopy techniques widely used to measure space-time characteristics of the production processes, are discussed. Particularly, it is found that the neglect of the finite-size effect on the pionium lifetime measurement in the experiment DIRAC at CERN could lead to the lifetime overestimation comparable with the 10% statistical error. The theoretical systematic errors arising in the calculation of the finite-size effect due to the neglect of non-equal emission times in the pair center-of-mass system, the space-time coherence and the residual charge are shown to be negligible. PACS numbers: 03.65, 25.75, 36.10 DOI: 10.1134/S1063779609030034
1. INTRODUCTION The determination, on a percent level accuracy, of the breakup probability of the π+π– atoms produced by a high-energy beam in a thin target is of principle importance for a precise lifetime measurement of these atoms in the experiment DIRAC at CERN [1–4]. This experiment aims to measure the lifetime τ10 of the π+π– atoms in the ground state with 10% precision. As this lifetime of order 10–15 s is determined by the probability 0
2
of the annihilation π+π– π0π0: 1/τ10 ~ | a 0 – a 0 |2, the DIRAC measurement enables to determine the absolute 0
2
value of the difference a 0 – a 0 of the s-wave isoscalar and isotensor ππ scattering lengths to 5%. This represents a factor of 4 improvement of the accuracy achieved in previous studies [5], and is comparable with the precision of the most recent experiments E865 at BNL [6] and NA48/2 at CERN [7]. The former is based on a study of Ke4 decays and yields the statistical 0
error of 6% in a 0 ; this measurement essentially exploits other experimental data together with dispersion relations (Roy equations), the systematic and theoretical errors being estimated on the level of several percent. The latter studied the cusp effect at the π+π– threshold in the distribution of the 2π0 effective mass in 0
2
K± π±π0π0 decays and yields | a 0 – a 0 | with a few percent statistical precision and ~5% theoretical error. Both these measurements are in agreement with the ¶ The
preliminary DIRAC result based on ~40% of the collected statistics [4] as well as with the prediction of the standard chiral perturbation theory [8]. It should be stressed that the theoretical prediction 0 2 for the difference a 0 – a 0 depends on the structure of the QCD vacuum. Thus, on the standard assumption of 0 2 a strong quark condensate one has a 0 – a 0 = 0.374 ± 0.006 fm [8]. With the decreasing condensate this difference increases an
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