Physics at CPLEAR
Introduction
The CPLEAR experiment at CERN [1] has performed measurements concerning a vast variety of subjects, such as symmetry properties of weak interactions , quantum coherence of the wave function, Bose–Einstein correlations in multipion states, regeneration of the short-lived kaon component in matter, the Einstein–Rosen–Podolski paradox using entangled neutral-kaon pair states, and the equivalence principle of general relativity.
To this end, 12 Tbytes of measured information were recorded (on 50 000 magnetic tapes), and 200 million productions and decays of neutral kaons have been reconstructed. In a most general analysis, the values of more than two dozens of parameters, mainly describing neutral kaons and their weak and electromagnetic decays, have been deduced, some with unprecedented precision, some for the first time.
The main reason that many experiments in nuclear and particle physics have focused on the study of symmetry properties of physical laws, is, that these properties lead, in a very direct way, to symmetries in experimentally observable quantities. This is exemplified in Table 1, below, where the relation of a particular symmetry of the Hamiltonian of the weak interaction to the corresponding asymmetry parameter, as measured by CPLEAR, is shown.
The main reason that the CPLEAR experiment has been able to contribute to so many fields of physics lies in the properties of the neutral kaons, paired with the high-intensity antiproton beam at CERN [2] and with the high-speed detector [3], which is able to visualize the complete event and to measure the locations, the momenta, and the charges of all the accompanying (charged) tracks, as well at the production of the neutral kaon, as at its decay. This allows one to know the quantum numbers of the kaon at its production and, in principle, at its decay.
A neutral kaon has the remarkable property [4], [5] that the one physical quantity, strangeness, which could possibly distinguish it from its antiparticle, is not conserved, owing to the weak interaction. As a consequence, it becomes a very sensitive two-state system, (|KS〉 and |KL〉), which has a behaviour analogous to a (slowly decaying) particle of spin 1/2 in a magnetic field, with which an NMR precession experiment is being performed. It is described by a wave function with an oscillation between the two states of strangeness +1, (|K0〉), and of strangeness −1, . The oscillation frequency can conveniently be observed, as it happens to be comparable to the decay rate of the short-lived state, |KS〉. Its magnitude and the wave length of the resulting visible interference pattern in space (some cm, for CPLEAR energies), corresponding to the interfering wave functions, fit perfectly well to the technical performances of high-energy physics measuring equipment.
The tiny energy difference between the two states |KS〉 and |KL〉, , sets the scale for the sensitivity of the detection of a possible energy difference between |K0〉 and . Such a difference could e.g. occur from a -violating interaction or from a gravitational field which would act differently on a particle than on an antiparticle. It has also been conceived that quantum mechanics might be apparently violated by gravitation in such a way that pure states may develop into mixed states, which is highly forbidden otherwise. This would reduce the phase coherence of the wave functions and thus diminish the observable interference effects. CPLEAR has given limits to parameters describing these situations.
The neutral kaons used by the CPLEAR experiment are produced by antiproton annihilations in a high-pressure hydrogen gas. Sometimes, a pair of a neutral kaon and a neutral antikaon, , is also produced. These happen to be (mostly) in an odd angular momentum state (L=1), and, due to Bose statistics, are governed by a two-particle wave function, which is antisymmetric with respect to particle–antiparticle interchange. In this way, quantum mechanics predicts a high correlation in the behaviour of the two particles, even after they have gone far apart from each other, reminiscent of the EPR paradox. CPLEAR presents a measurement of this effect.
CPLEAR results and analyses were published timely [3], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. As a completion of 15-years’ work, we wish to present here a global and coherent view of the CPLEAR experiment.
The history of symmetry violations, in particular the one of neutral kaons, is full of beautiful surprises. Appendix A gives a summary of facts and literature [4], [5], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60]. These matters were dealt with in textbooks, see [61], [62], [63], [64], [65] and the most recent [66], [67], [68], and review papers, see e.g. [69], [70], [71]. The present study is limited to the neutral-kaon states, as encountered in the experiments, without any attempt to interpret the results at the quark level, see, however, Appendix B.
Section snippets
Time evolution
The time evolution of a neutral kaon and of its decay products may be represented by the state vectorwhich satisfies the Schrödinger equationIn the Hamiltonian, , governs the strong and electromagnetic interactions. It is invariant with respect to the transformations , , , and it conserves the strangeness S. The states |K0〉 and are common stationary eigenstates of and S, with the mass m0 and with opposite strangeness:
Experimental method
The method chosen by CPLEAR was to make use of the charge-conjugate particles K0 and produced in collisions, which have a flavour of strangeness different for particles (K0) and antiparticles . The strangeness, properly monitored, is an ideal tool to label (tag) K0 and , whose subsequent evolution in time under weak interaction can thus be analysed and compared.
Initially-pure K0 and states were produced concurrently by antiproton annihilation at rest in a hydrogen target via
The pionic decay channels
When a neutral kaon decays to pions exclusively, this final state is a eigenstate. The final states π+π− and π0π0 have a eigenvalue equal to +1, π0π0π0 a eigenvalue equal to −1, and that of π+π−π0 is +1 or −1 depending on the kinematical configuration. Any difference in the rates of K0 and decaying to one of these eigenstates is a sign of violation.
The semileptonic decay channels ( and )
The simultaneous comparison between K0 and behaviour with respect to decay rates is particularly powerful when decays to semileptonic decays are considered. The principle of some of the measurements then becomes straightforward, for instance for the establishment of violation, as discussed in Section 2.1.
CPLEAR measured eπν decays. The two strangeness states of the neutral kaons were tagged at production, as in the case of the pionic channels, taking advantage of the associate kaon-pair
Upper limit of the BR(KS→e+e−) [16]
The decay KS→e+e− is a flavour-changing neutral-current process, suppressed in the Standard Model and dominated by the two-photon intermediate state. Full event reconstruction together with e/π separation in the calorimeter, and in the PID for momenta below , allowed powerful background rejection and high signal acceptance. A constrained fit was performed with the hypothesis of this decay, and both secondary tracks had to be recognized as electrons in the calorimeter by exploiting
Measurement of Δm (method c) [26]
Very early, after the hypothesis of particle mixture had been advanced for K0 and [4], the change of strangeness content with time was predicted, as a consequence, for beams starting as pure K0 or [5]. Proposals followed on how to monitor the strangeness oscillations and measure the KL−KS mass difference Δm, that is the oscillation frequency modulus ℏ. It was suggested that starting with a pure K0 (or ) beam, one could observe the building up of a (or K0) flux by measuring either
φ+− and Δm [27]
Given the different strong correlation of the measurement of φ+− and Δm for most of the experiments, averaging the measurements of φ+− and Δm independently is not the appropriate method. Better results are obtained if all the available experimental information, including correlation terms, is used to construct a global likelihood distribution depending on the parameters and τS, as the product of individual likelihood distributions corresponding to the various experiments. The best
Probing a possible loss of QM coherence [31]
The phenomenological framework of Section 2 is constructed, according to the QM of a closed system, on solutions of Eq. (5) which are pure states and evolve as such in time. Some approaches to quantum gravity [142] suggest that topologically non-trivial space–time fluctuations (space–time foam) entail an intrinsic, fundamental information loss, and therefore transitions from pure to mixed states [143]. The system is then described by a 2×2 density matrix ρ, which obeys
Measurements related to the annihilation process
In general the cuts imposed by the trigger selection prevented, despite very high statistics, the precise study of the annihilation processes such as to bring a significant contribution to this field, nor was this necessary to achieve the main aim of the experiment. The annihilation study was limited to correct modelling of the simulation for the K0 and source and the annihilation sources of background. Nevertheless, new results were achieved by the measurement of the fraction of P-wave
Overview and conclusions
The CPLEAR experiment has performed studies of particle–antiparticle properties through a direct comparison of K0 and time evolutions. The use of -annihilation channels and and the detection of the charged particles, K∓ and π∓, has allowed the identification of the produced neutral kaon as a K0 or as a (strangeness tagging). This method has become practical due to the availabilty of intense beams of slow antiprotons. It implies furthermost detecting the low
Acknowledgements
This report is based on the work of the CPLEAR Collaboration: it recalls the measurements performed but also the ideas which took shape in many discussions. We are indebted to the many colleagues who successively contributed to the experiment.
We would like to thank the CERN LEAR staff for their support and co-operation, as well as the technical and engineering staff of our institutes. This work was supported by the following agencies: the French CNRS/Institut National de Physique Nucléaire et
References (152)
CPLEAR Collaboration
Nucl. Instr. Meth. A
(1996)CPLEAR Collaboration
Nucl. Instr. Meth. A
(1997)CPLEAR Collaboration, Measurement of the KL−KS mass difference using semileptonic decays of tagged neutral kaons
Phys. Lett. B
(1998)CPLEAR Collaboration, Experimental measurement of the KSKS / KSKL ratio in antiproton annihilations at rest in gaseous hydrogen at 15 and 27 bar
Phys. Lett. B
(1997)CPLEAR Collaboration, Bose–Einstein correlations in antiproton–proton annihilations at rest
Z. Phys. C
(1994)CPLEAR Collaboration, M.P. Locher, V.E. Markushin, Pion correlations and resonance effects in annihilation at rest to 2π+ 2π− π0
Eur. Phys. J. C
(1999)CPLEAR Collaboration, Evaluation of the phase of the -violation parameter η+− and the KL−KS mass difference from a correlation analysis of different experiments
Phys. Lett. B
(1996)CPLEAR Collaboration, mass and decay-width differencesCPLEAR evaluation
Phys. Lett. B
(1999)- G.D. Rochester, C.C. Butler, Nature (London) (1947)...
Rev. Mod. Phys.
(1981)Rev. Mod. Phys.
(1981)
Phys. Lett. B
Phys. Rev. D
CP and CPT violation in neutral kaon decays
E731
Phys. Rev. Lett.
Phys. Rev.
Phys. Rev. D
Phys. Rev.
Phys. Rev.
CPLEAR Collaboration, A determination of the CP violation parameter η+− from the decay of strangeness-tagged neutral kaons
Phys. Lett. B
CPLEAR Collaboration, A detailed description of the analysis of the decay of neutral kaons to π+π− in the CPLEAR experiment
Eur. Phys. J. C
CPLEAR Collaboration
Z. Phys. C
CPLEAR Collaboration, Measurement of the violation parameter η00 using tagged and K0
Phys. Lett. B
CPLEAR Collaboration, CPLEAR results on the CP parameters of neutral kaons decaying to π+π−π0
Phys. Lett. B
CPLEAR Collaboration, The neutral kaons decays to π+π−π0a detailed analysis of the CPLEAR data
Eur. Phys. J. C
CPLEAR Collaboration, Search for CP violation in the decay of tagged and K0 to π0π0π0
Phys. Lett. B
CPLEAR Collaboration, First direct observation of time-reversal non-invariance in the neutral-kaon system
Phys. Lett. B
CPLEAR Collaboration, A determination of the CPT violation parameter Re(δ) from the semileptonic decay of strangeness-tagged neutral kaons
Phys. Lett. B
CPLEAR Collaboration, -violation and -invariance measurements in the CPLEAR experimenta detailed description of the analysis of neutral-kaon decays to eπ ν
Eur. Phys. J. C
CPLEAR Collaboration, Measurement of the energy dependence of the form factor f+ in Ke30, decay
Phys. Lett. B
CPLEAR Collaboration, An upper limit for the branching ratio of the decay KS → e+e−
Phys. Lett. B
CPLEAR Collaboration, Determination of the relative branching ratios for and
Phys. Lett. B
CPLEAR Collaboration, Inclusive measurement of annihilation at rest in gaseous hydrogen to final states containing ρ and f2
Z. Phys. C
CPLEAR Collaboration, M.P. Locher, V.E. Markushin, Direct determination of two-pion correlations for annihilation at rest
Eur. Phys. J. C
Regeneration of arbitrary coherent neutral kaon statesa new method for measuring the forward scattering amplitude
Z. Phys. C
CPLEAR Collaboration, Measurement of neutral kaon regeneration amplitudes in carbon at momenta below
Phys. Lett. B
CPLEAR Collaboration, An EPR experiment testing the non-separability of the wave function
Phys. Lett. B
CPLEAR Collaboration, transitions monitored by strong interactionsa new determination of the KL−KS mass difference
Phys. Lett. B
CPLEAR Collaboration, Determination of the - and -violation parameters in the neutral-kaon system using the Bell–Steinberger relation and data from CPLEAR
Phys. Lett. B
CPLEAR Collaboration, M.P. Locher, V.E. Markushin, Dispersion relation analysis of the neutral kaon regeneration amplitude in carbon
Eur. Phys. J. C
CPLEAR Collaboration, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Tests of symmetry and quantum mechanics with experimental data from CPLEAR
Phys. Lett. B
CPLEAR Collaboration, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Tests of the equivalence principle with neutral kaons
Phys. Lett. B
Inward Bound
Phys. Rev.
Phys. Rev.
Phys. Rev.
Proceedings of the International Conference, Pisa, 1955
Nuovo Cimento Supp.
Prog. Theor. Phys.
Prog. Theor. Phys.
Phys. Rev.
Phys. Rev. Lett.
Phys. Rev.
Z. Phys.
Z. Phys.
Phys. Rev.
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