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

Abstract

Determination of the T-and CPT-violation parameters in the neutral-kaon system using theBell-Steinberger relation and data from CPLEAR. CPLEAR CollaborationA. Apostolakis 1) , E. Aslanides 11) , G. Backenstoss 2) , P. AbstractData 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( ) and the CPT-violation parameter Im(δ) of the neutral-kaon mixing matrix to be determined with an increased accuracy:−5 . Moreover, the constraint allows the CPT-violation parameter for the neutralkaon semileptonic decays, Re(y), to be determined for the first time. The ∆S = ∆Q 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. (Submitted to Physics Letters B) IntroductionThe CPLEAR experiment has directly measured for the first time the violation of T invariance in the neutral-kaon system [1] and has provided a new, more accurate limit for the CPT-violation parameter Re(δ) [2]. These results were obtained by analysing the rate asymmetries between K 0 and K 0 for decays to e ± π ∓ ν, as a function of the decay time t = τ .In continuation of this work we have studied the constraints on our results deriving from the Bell-Steinberger (or unitarity) relation [3][4][5]. The Bell-Steinberger relation relates all decay channels of neutral kaons to the parameters describing T and CPT non-invariance. With the present precision of the two-pion decay parameters the dominant uncertainties arise from the three-pion and semileptonic decays. Moreover, the semileptonic decays enter the relation with the parameter Re(y), describing CPT violation in semileptonic decays and as yet not measured. Having improved the precision of three-pion decays [7,8] and measured precisely the semileptonic decay rates, CPLEAR allows the determination of all parameters with an unprecedented accuracy. We stress here that they are obtained free of theoretical assumptions, apart from unitarity, unlike others obtained previously also using the unitarity relation [6].

Plate with a hole obeys the averaged null energy condition

“…(The new, more precise values of δ ℓ [99,100] do not change this conclusion). We note in passing [45] Re(y) = (0.5 ± 3.0) × 10 −3 .…”

Determination ofCPandCPTviolation parameters in the neutral kaon system using the Bell-Steinberger relation and data from the KLOE experiment

“…A determination of Re( ) and Im(δ) using the BSR was performed by CPLEAR [7] in 1999. In the analysis of ref.…”

“…In the analysis of ref. [7], some of the parameters of the semileptonic channels were evaluated together with Re( ) and Im(δ) from a combined fit to the time-dependent semileptonic asymmetries imposing the constraint of the BSR. A recent update of the determination of Re( ) and Im(δ) is given in ref.…”

“…[8]. In this latter analysis, however, some of the results of the CPLEAR fit [7], which used the unitarity constraint, have been used as input again to the BSR. It is not clear whether this fact was accounted for in [8].…”

“…However, we stress that the BSR analysis of ref. [8] is questionable: some of the results of the CPLEAR fit [7], which used the unitarity constraint, have been used as input to a different unitarity test (with partially updated input values). The limits on Im(δ) and Re(δ) can be used to constrain the mass and width difference between K 0 and K 0 via…”