Physics at CPLEAR

doi:10.1016/S0370-1573(02)00367-8

Physics Reports

Volume 374, Issue 3, January 2003, Pages 165-270

https://doi.org/10.1016/S0370-1573(02)00367-8 Get rights and content

Abstract

LEAR offered unique opportunities to study the symmetries which exist between matter and antimatter. At variance with other approaches at this facility, CPLEAR was an experiment devoted to the study of $CP$ , $T$ and $CPT$ symmetries in the neutral-kaon system. A variety of measurements allowed us to determine with high precision the parameters which describe the time evolution of the neutral kaons and their antiparticles, including decay amplitudes, and the related symmetry properties. Limits concerning quantum-mechanical predictions (EPR, coherence of the wave function) or the equivalence principle of general relativity have been obtained. An account of the main features of the experiment and its performances is given here, together with the results achieved.

Introduction

The CPLEAR experiment at CERN [1] has performed measurements concerning a vast variety of subjects, such as symmetry properties of weak interactions $(T, CP, CPT)$ , 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, (|K_S〉 and |K_L〉), 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, $(| K ̄^{0} 〉)$ . The oscillation frequency can conveniently be observed, as it happens to be comparable to the decay rate of the short-lived state, |K_S〉. Its magnitude $(ω=5.3×10^{9} s^{−1})$ 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 |K_S〉 and |K_L〉, $ℏω=3.5×10^{−12} MeV$ , sets the scale for the sensitivity of the detection of a possible energy difference between |K⁰〉 and $| K ̄^{0} 〉$ . Such a difference could e.g. occur from a $CPT$ -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, $K^{0} K ̄^{0}$ , 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 vector $|ψ〉=ψ_{K^{0}} (t)| K^{0} 〉+ψ_{K̄^{0}} (t)| K ̄^{0} 〉+ ∑ m c_{m} (t)|m〉$ which satisfies the Schrödinger equation $i d |ψ〉 d t = H |ψ〉 .$ In the Hamiltonian, $H = H_{0} + H_{wk}$ , $H_{0}$ governs the strong and electromagnetic interactions. It is invariant with respect to the transformations $C$ , $P$ , $T$ , and it conserves the strangeness S. The states |K⁰〉 and $| K ̄^{0} 〉$ are common stationary eigenstates of $H_{0}$ and S, with the mass m₀ and with opposite strangeness: $H_{0} | K$

Experimental method

The method chosen by CPLEAR was to make use of the charge-conjugate particles K⁰ and $K ̄^{0}$ produced in $p ̄ p$ collisions, which have a flavour of strangeness different for particles (K⁰) and antiparticles $(K ̄^{0})$ . The strangeness, properly monitored, is an ideal tool to label (tag) K⁰ and $K ̄^{0}$ , whose subsequent evolution in time under weak interaction can thus be analysed and compared.

Initially-pure K⁰ and $K ̄^{0}$ states were produced concurrently by antiproton annihilation at rest in a hydrogen target via

The pionic decay channels $(CP)$

When a neutral kaon decays to pions exclusively, this final state is a $CP$ eigenstate. The final states π⁺π⁻ and π⁰π⁰ have a $CP$ eigenvalue equal to +1, π⁰π⁰π⁰ a $CP$ 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 $K ̄^{0}$ decaying to one of these eigenstates is a sign of $CP$ violation.

The semileptonic decay channels ( $T$ and $CPT$ )

The simultaneous comparison between K⁰ and $K ̄^{0}$ 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 $T$ 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(K_S→e⁺e⁻) [16]

The decay K_S→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 $200 MeV /c$ , 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 $K ̄^{0}$ [4], the change of strangeness content with time was predicted, as a consequence, for beams starting as pure K⁰ or $K ̄^{0}$ [5]. Proposals followed on how to monitor the strangeness oscillations and measure the K_L−K_S mass difference Δm, that is the oscillation frequency modulus ℏ. It was suggested that starting with a pure K⁰ (or $K ̄^{0}$ ) beam, one could observe the building up of a $K ̄^{0}$ (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 $L$ depending on the parameters $Δ m, φ_{+−}$ and τ_S, 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 $K^{0} − K ̄^{0}$ system is then described by a 2×2 density matrix ρ, which obeys $ρ ̇ =− i [Λρ−ρΛ^{†}]+ δ ̸ Λρ,$

Measurements related to the $p ̄ p$ 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 $K ̄^{0}$ 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 $K ̄^{0}$ time evolutions. The use of $p ̄ p$ -annihilation channels $p ̄ p → K^{∓} π^{±} K^{0}$ and $p ̄ p → K^{±} π^{∓} K ̄^{0}$ 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 $K ̄^{0}$ (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

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Physics at CPLEAR

Abstract

Introduction

Section snippets

Time evolution

Experimental method

The pionic decay channels (CP)

The semileptonic decay channels (T and CPT)

Upper limit of the BR(KS→e+e−) [16]

Measurement of Δm (method c) [26]

φ+− and Δm [27]

Probing a possible loss of QM coherence [31]

Measurements related to the p̄p annihilation process

Overview and conclusions

Acknowledgements

Nucl. Instr. Meth. A

Nucl. Instr. Meth. A

Phys. Lett. B

Phys. Lett. B

Z. Phys. C

Eur. Phys. J. C

Phys. Lett. B

Phys. Lett. B

Rev. Mod. Phys.

Rev. Mod. Phys.

Phys. Lett. B

Phys. Rev. D

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 CP violation parameter η00 using tagged K̄0 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 K̄0 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, T-violation and CPT-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 p̄p →π+π− and p̄p →K+K−

Phys. Lett. B

CPLEAR Collaboration, Inclusive measurement of p̄p 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 p̄p → 2π+ 2π− annihilation at rest

Eur. Phys. J. C

Regeneration of arbitrary coherent neutral kaon statesa new method for measuring the K0−K̄0 forward scattering amplitude

Z. Phys. C

CPLEAR Collaboration, Measurement of neutral kaon regeneration amplitudes in carbon at momenta below 1GeV/c

Phys. Lett. B

CPLEAR Collaboration, An EPR experiment testing the non-separability of the K̄0K0 wave function

Phys. Lett. B

CPLEAR Collaboration, K0 ⇌ K̄0 transitions monitored by strong interactionsa new determination of the KL−KS mass difference

Phys. Lett. B

CPLEAR Collaboration, Determination of the T- and CPT-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 CPT 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.

The pionic decay channels $(CP)$

The semileptonic decay channels ( $T$ and $CPT$ )

Upper limit of the BR(K_S→e⁺e⁻) [16]

φ₊₋ and Δm [27]

Measurements related to the $p ̄ p$ annihilation process

CPLEAR Collaboration, A determination of the CP violation parameter η₊₋ from the decay of strangeness-tagged neutral kaons

CPLEAR Collaboration, A detailed description of the analysis of the decay of neutral kaons to π⁺π⁻ in the CPLEAR experiment

CPLEAR Collaboration, Measurement of the $CP$ violation parameter η₀₀ using tagged $K ̄^{0}$ and K⁰

CPLEAR Collaboration, CPLEAR results on the CP parameters of neutral kaons decaying to π⁺π⁻π⁰

CPLEAR Collaboration, The neutral kaons decays to π⁺π⁻π⁰a detailed analysis of the CPLEAR data

CPLEAR Collaboration, Search for CP violation in the decay of tagged $K ̄^{0}$ and K⁰ to π⁰π⁰π⁰

CPLEAR Collaboration, $T$ -violation and $CPT$ -invariance measurements in the CPLEAR experimenta detailed description of the analysis of neutral-kaon decays to eπ ν

CPLEAR Collaboration, Measurement of the energy dependence of the form factor f₊ in K_e3⁰, decay

CPLEAR Collaboration, An upper limit for the branching ratio of the decay K_S → e⁺e⁻

CPLEAR Collaboration, Determination of the relative branching ratios for $p ̄ p →π^{+} π^{−}$ and $p ̄ p → K^{+} K^{−}$

CPLEAR Collaboration, Inclusive measurement of $p ̄ p$ annihilation at rest in gaseous hydrogen to final states containing ρ and f₂

CPLEAR Collaboration, M.P. Locher, V.E. Markushin, Direct determination of two-pion correlations for $p ̄ p → 2π^{+} 2π^{−}$ annihilation at rest

Regeneration of arbitrary coherent neutral kaon statesa new method for measuring the $K^{0} − K ̄^{0}$ forward scattering amplitude

CPLEAR Collaboration, Measurement of neutral kaon regeneration amplitudes in carbon at momenta below $1 GeV / c$

CPLEAR Collaboration, An EPR experiment testing the non-separability of the $K ̄^{0} K^{0}$ wave function

CPLEAR Collaboration, $K^{0} ⇌ K ̄^{0}$ transitions monitored by strong interactionsa new determination of the K_L−K_S mass difference

CPLEAR Collaboration, Determination of the $T$ - and $CPT$ -violation parameters in the neutral-kaon system using the Bell–Steinberger relation and data from CPLEAR

CPLEAR Collaboration, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Tests of $CPT$ symmetry and quantum mechanics with experimental data from CPLEAR