CPLEAR Experiment Research Articles

On the Way to Experimental Test of the Time Reversal Invariance in the Nuclear Reactions.

Time (T) violation can be related with charge-parity (CP) violation through the CPT theorem. The CP violation was discovered experimentally in the K0-meson decays about 35 years ago. The T violating interaction related with the CP violation violates parity as well. However, an extension of the theory beyond the locality of the interactions might violate the CPT theorem. The result of the CPLEAR experiment [1], which has given direct evidence of T violation in the elementary-particle phenomena, could be considered under assumption of the CPT invariance.

On the Way to Experimental Test of the Time Reversal Invariance in the Nuclear Reactions

T violation can be related with the CP-violation through Luders–Pauli's CPT theorem, which is related with a local Lorentz invariant field theory. The CP violation was discovered experimentally in the K 0-meson decays about 35 years ago. The T violating interaction related with the CP violation violates parity as well. However, an extension of the theory beyond the locality of the interactions might violate the CPT theorem. The result of CPLEAR experiment [Angelopolos A. et al., (1998), “First direct observation of time-reversal non-invariance in the neutral-kaon system”, Phys. Lett. B 444 43], which has given direct evidence of T violation in the elementary-particle phenomena, could be considered under assumption of the CPT invariance.

The CPLEAR experiment

LEAR offered unique opportunities to study the symmetries which exist between matter and antimatter. At variance with other approaches, CPLEAR was an experiment devoted to the study of CP, T and CPT symmetries in the neutral-kaon system. A number of measurements allowed us to specify with high precision and in a rather complete way, the parameters which describe the time evolution of the neutral kaons and their antiparticles, including decay amplitudes, and the related symmetry properties. A brief account of the main features of the experiment and its performances is given here, together with the results achieved on T and CPT symmetries, including tests of Quantum Mechanics.

TESTS OF DISCRETE SYMMETRIES WITH CPLEAR

▪ Abstract We discuss the neutral-kaon system and demonstrate the advantage of strangeness tagging as performed by the CPLEAR experiment. The main results of CPLEAR on tests of discrete symmetries are reviewed.

Decoherence of entangled kaons and its connection to entanglement measures

We study the time evolution of the entangled kaon system by considering the Liouville - von Neumann equation with an additional term which allows for decoherence. We choose as generators of decoherence the projectors to the 2-particle eigenstates of the Hamiltonian. Then we compare this model with the data of the CPLEAR experiment and find in this way an upper bound on the strength $\lambda$ of the decoherence. We also relate $\lambda$ to an effective decoherence parameter $\zeta$ considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e. the von Neumann entropy $S$, the entanglement of formation $E$ and the concurrence $C$, and we relate the decoherence parameter $\zeta$ to the loss of entanglement: $1 - E$.

$\mathrm{\cal T}$ -violation and $\mathrm{\cal CPT}$ -invariance measurements in the CPLEAR experiment: a detailed description of the analysis of neutral-kaon decays to $\mathrme \pi \nu$

A detailed description of the analysis of neutral kaons decaying to $\mathrme \pi \nu$ is given, based on the complete set of data collected with the CPLEAR experiment. Using a novel approach involving initially strangeness-tagged $\mathrm{K^0}$ and $\mathrm{\overline{K}}{}^0$ , time-dependent decay-rate asymmetries were measured. These asymmetries enabled $\mathrm{\cal T}$ - and $\mathrm{\cal CPT}$ -violation parameters to be measured in the context of a systematic study. The highlights of this study are the first direct observation of $\mathrm{\cal T}$ violation and the direct determination of the $\mathrm{\cal CPT}$ parameter $\mathrm{Re}(\delta)$ with an accuracy improved by two orders of magnitude with respect to the current value.

A review of the latest CPLEAR results on T violation and CPT invariance in the neutral-kaon system

The CPLEAR experiment has studied the symmetries which may exist between matter and antimatter by comparing the time evolution of K 0 and K 0 . A number of measurements allowed the determination, with high precision and in a rather complete way, of the parameters of the time evolution and the related symmetry properties. T and CPT could be disentangled from CP and the first direct measurement of T violation was performed. The CPT invariance was directly tested through the parameter Re(δ), while Im(δ) was best determined from the Bell-Steinberger relation. The K 0 and K 0 mass and decay width differences were then bound to less than a few times 10 −18 GeV.

A Generalized Bell Inequality and Decoherence for the K 0 K O

First, a generalized Bell inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter [1] if the quantum theory is used to recalculate the probabilities. Next, the quantum mechanical probabilities are modified by the decoherence approach, which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter ζ, which measures the degree of decoherence. This result is compared with the experimental value [2, 3] of the decoherence parameter ζ deduced from the data of the CPLEAR experiment [4].

A detailed description of the analysis of the decay of neutral kaons to ${\mathrm{\pi^+\pi^-}}$ in the CPLEAR experiment

A detailed description is given of the analysis of neutral kaons decaying to \({\mathrm{\pi^+\pi^-}}\), based on the complete set of data collected with the CPLEAR experiment. Using a novel approach involving initially strangeness-tagged \({\mathrm{K^0}}\) and \({\mathrm{\overline{K}^0}}\), the time-dependent decay-rate asymmetry has been measured. This asymmetry, resulting from the interference between the \({\mathrm{K_S}}\) and \({\mathrm{K_L}}\) decay amplitudes, has enabled both the magnitude and phase of the CP-violation parameter, \(\eta_{+-}\), to be measured, with a precision comparable to that of the current world-average values.

CPLEAR results on T and CPT violation

We report the results of the CPLEAR experiment on T and CPT symmetries in the neutral-kaon system. Time-reversal non-invariance is observed for the first time by comparing the probabilities of a K ̄ 0 transforming into K 0 and of K 0 transforming into K ̄ 0 as a function of the neutral-kaon eigentime. CPT invariance is tested by measuring the parameter Re( δ CPT) with a precision of a few 10 −4, while Im( δ CPT) is determined from the Bell–Steinberger relation, with a precision of 10 −5. Moreover, the Bell–Steinberger constraint allows the CPT violation parameter Re( y) for the neutral-kaon semileptonic decays to be determined for the first time.

Quantum mechanics, Furry’s hypothesis, and a measure of decoherence in theK0K0system

We consider strangeness correlations of the EPR type in K^0 \bar{K}^0 pairs created in a J^{PC} = 1^{--} state as a function of time under the hypothesis that spontaneous decoherence takes place. We parameterize the degree of decoherence by a factor (1-\zeta) which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in the K^0--\bar{K}^0 space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' \zeta inferred from experimental data are basis-dependent as well. We illustrate this point by estimating the value of \zeta for the two bases {K_L, K_S} and {K^0, \bar{K}^0} with the help of recent data of the CPLEAR experiment.

Comments on CP, T and CPT violation in neutral kaon decays

We comment on CP, T and CPT violation in the light of interesting new data from the CPLEAR and KTeV Collaborations on neutral kaon decay asymmetries. Other recent data from the CPLEAR experiment, constraining possible violations of CPT and the Δ S=Δ Q rule, exclude the possibility that the semileptonic-decay asymmetry A T measured by CPLEAR could be solely due to CPT violation, confirming that their data constitute direct evidence for T violation. The CP-violating asymmetry in K L→ e − e + π − π + recently measured by the KTeV Collaboration does not by itself provide direct evidence for T violation, but we use it to place new bounds on CPT violation.

Contribution of CPLEAR to the physics of the neutral-kaon system

We report the results of the CPLEAR experiment on CP-, T-, and CPT-symmetries in the neutral kaon system. CP-violation parameters are given for the K 0, K 0 → 2π, 3π decay channels. For the first time, T-violation is measured by a direct method using semileptonic decays. The CPT symmetry is tested through the parameters Im(δ) with a precision of 10 −5 and Re(δ) with a precision of a few 10 −4. With these two measurements, the difference in mass and width of K 0 and K 0 are bound to within 10 −18 GeV. In the limit of CPT invariance in the neutral kaon decays, the K 0 and K 0 masses are equal within 10 −19 GeV.

Observed asymmetry in [formula omitted] and relation to reciprocity

The charge-asymmetry observed in a recent CPLEAR experiment was interpreted by the authors as a direct observation of T-noninvariance. While this is the simplest and most natural interpretation, and the observed effect agrees in sign and magnitude with theoretical expectation, adherents of T-invariance could argue that the effect observed by CPLEAR is entirely ascribable to TCP-noninvariance. This radical alternative could be excluded by sufficiently precise measurements on neutral kaon beta-decay. In any case, the CPLEAR experiment significantly restricts possible TCP-noninvariance in neutral kaon mixing.

Violation of time-reversal invariance and CPLEAR measurements

Motivated by the recent CPLEAR measurement on the time-reversal non-invariance, we review the situation concerning the experimental measurements of charge conjugation, parity violation and time reversibility, in systems with non-Hermitean Hamiltonians. This includes in particular neutral meson systems, like K 0− K ̄ 0 , D 0− D ̄ 0 and B 0− B ̄ 0 . We discuss the formalism that describes particle-antiparticle mixing and time evolution of states, paying particular emphasis to the orthogonality conditions of incoming and outgoing states. As a result, we confirm that the CPLEAR experiment makes a direct measurement of violation of time-reversal without any assumption of unitarity and CPT-violation. The asymmetry which signifies T-violation, is found to be independent of time and decay processes.

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

Data from the CPLEAR experiment, together with the most recent world averages for some of the neutral-kaon parameters, were constrained with the Bell–Steinberger (or unitarity) relation, allowing the T-violation parameter Re( ϵ) and the CPT-violation parameter Im( δ) of the neutral-kaon mixing matrix to be determined with an increased accuracy: Re( ϵ)=(164.9±2.5)×10 −5, Im( δ)=(2.4±5.0)×10 −5. Moreover, the constraint allows the CPT-violation parameter for the neutral-kaon semileptonic decays, Re( y), to be determined for the first time. The ΔS≠ ΔQ parameters Re( x −) and Im( x +) are given with an increased accuracy. The quantity Re( y+ x −), which enters the T-violation CPLEAR asymmetry previously published, is determined to be (−0.2±0.3)×10 −3. The value obtained for Re( δ) is in agreement with the one resulting from a previous unconstrained fit and has a slightly smaller error.

Contribution of CPLEAR to the physics of the neutral-kaon system

We report the results of the CPLEAR experiment on CP-, T- and CPT-symmetries in the neutral kaon system. CP-violation parameters are given for different decay channels. For the first time T-violation is measured by a direct method using semileptonic decays. The CPT symmetry in the kaons decays is tested through the parameters Im( δ ), from the Bell-Steinberger relation, with a precision of 10 −5 and Re( δ ) with a precision of a few 10 −4 (two order of magnitude better than the previous measurement). These two measurements allow us to bound the difference in mass and width of K 0 and ¯K 0 to be equal within 10 −18 GeV. In the limit of CPT invariance in the neutral kaon decays, the K 0 and ¯K 0 masses are equal within 10 −19 GeV.

First direct observation of time-reversal non-invariance in the neutral-kaon system

We report on the first observation of time-reversal symmetry violation through a comparison of the probabilities of K 0 transforming into K 0 and K 0 into K 0 as a function of the neutral-kaon eigentime t. The comparison is based on the analysis of the neutral-kaon semileptonic decays recorded in the CPLEAR experiment. There, the strangeness of the neutral kaon at time t=0 was tagged by the kaon charge in the reaction p p → K ±π ∓ K 0 ( K 0 ) at rest, whereas the strangeness of the kaon at the decay time t= τ was tagged by the lepton charge in the final state. An average decay-rate asymmetry 〈 R( K 0 t=0→ e + π − ν t=τ)−R( K 0 t=0→ e − π + ν t=τ) R( K 0 t=0→ e + π − ν t=τ)+R( K 0 t=0→ e − π + ν t=τ) 〉=(6.6±1.3 stat ±1.0 syst )×10 −3 was measured over the interval 1 τ S <τ<20 τ S , thus leading to evidence for time-reversal non-invariance.

A determination of the CPT violation parameter Re( δ)from the semileptonic decay of strangeness-tagged neutral kaons

We have improved by two orders of magnitude the limit currently available for the CPT violation parameter Re( δ). To this purpose we have analyzed the full sample of neutral-kaon decays to e πν recorded in the CPLEAR experiment, where the strangeness of the neutral kaons was tagged at production and decay time. An appropriate function of the measured decay rates, including information from the analysis of π +π − decay channel, gives directly Re( δ). The result Re( δ)=(3.0±3.3 stat±0.6 syst)×10 −4 is compatible with zero. Values for the parameters Im( δ), Re( x −) and Im( x +) were also obtained.

Direct determination of two-pion correlations for pp→ 2π+2π− annihilation at rest

We study ππ correlations in the exclusive reaction pp → 2π+2π− at rest measured by the CPLEAR experiment. Avoiding the introduction of an arbitrary reference sample, we analyse differential distributions for equal charge pion pairs removing the phase-space factor event by event. A peak at small relative momenta is most pronounced for large total momentum of the pair. The physical implications of bosonic symmetrization for the properties of the pion source, in particular its radius, are briefly discussed. The two extremes considered are the chaotic Hanbury-Brown-Twiss mechanism and the coherent Skyrmion model.