Ke4 Decay Research Articles

Improved Ke3 radiative corrections sharpen the K\u03bc2\u2013Kl3 discrepancy

The measurements of Vus in leptonic (Kμ2) and semileptonic (Kl3) kaon decays exhibit a 3σ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the Ke3 decay rates that achieves an unprecedented level of precision of 10−4, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the “list of culprits” responsible for the Kμ2–Kl3 discrepancy.

High statistics measurement of the K+ → π0e+ν(Ke3) decay formfactors

The decay K+→π0e+ν(Ke3) is studied using in-flight decays detected with ‘OKA’ spectrometer. About 6M events are collected for the analysis. The λ+ slope parameter of the decay formfactor f+(t) in the linear approximation (average slope) is measured: λ+=(29.86±0.2)×10−3. If the quadratic term is added to the parametrization, the result for the linear slope becomes: λ+′=(24.6±0.7)×10−3, the quadratic coefficient in this fit is λ+″=(2.05±0.3)×10−3. Several alternative parametrizations are tried: the Pole fit parameter is found to be: MV=891±3MeV; the parameter of the Dispersive parametrization is measured to be Λ+=(24.6±0.17)×10−3. All the results are very preliminary, the systematics effects are under study.

Detailed study of Ke4 decay properties by the NA48/2 experiment at CERN

A sample of 1.13 million Ke4+−(K±→π+π−e±ν) decays and 65210Ke400(K±→π0π0e±ν) decays has been collected in 2003–2004 by the NA48/2 collaboration at the CERN SPS. Branching ratio and form factors in the S- and P-wave have been measured at a percent level precision. The comparison of Branching ratio and form factor values in both modes sheds new light on isospin symmetry breaking effects. Form factor measurements are major inputs to the study of low energy QCD and bring stringent tests of Chiral Perturbation Theory predictions.

Detailed study of the Ke4 decay mode properties

The NA48/2 collaboration at CERN has accumulated an unprecedented statistics of the semileptonic Ke4 charged kaon decay in the “charged pions” (Ke4(+-)) mode K±→π+π−eν and in the “neutral pions” (Ke4(00)) mode K±→π0π0eν with respectively <1% and ∼1% background contamination, allowing a detailed study of the decay properties.More than one million Ke4(+-) decays have been analyzed leading to the improved determination of the branching ratio and detailed studies of the form factors. The resulting BR(K±e4(+−))=(4.257±0.004stat±0.016syst±0.031ext)×10−5 is 3 times more precise than the corresponding PDG value and the error is dominated by the external uncertainty from the branching ratio of the normalization decay mode. It has been possible to obtain the absolute value of the form factor fs=5.705±0.017exp±±0.017syst±0.031ext and we can now translate into absolute form all the relative form factors previously published by NA48/2. This result complements the study of the S and P wave hadronic form factors obtained by NA48/2 in a simultaneous analysis of the ππ scattering length obtained from the same data sample.Concurrently, 65,210 K± decays into π0π0e±ν have been collected, increasing the world available statistics by several orders of magnitude. A study of the differential rate provides the first measurement of the form factors. The achieved precision makes possible also the observation of small effects such as the evidence for a cusp-like structure in the distribution of the π0π0 invariant mass squared around the threshold 4mπ+2. Using a model independent description of the form factors we have obtained the final result, inclusive of radiative decays, BR(K±e4(00))=(2.552±0.010stat±0.010syst±0.032ext)×10−5, also dominated by the external uncertainty from the branching ratio of the normalization decay mode, and improving the world average precision by an order of magnitude.The detailed study of form factors is sensitive to small isospin symmetry breaking effects and brings new inputs to low energy QCD description and crucial tests of predictions from Chiral Perturbation Theory and lattice QCD calculations.

K e4 decay as a source of information about the σ-particle mass and about the nature of spin-1 mesons

Data on the form factors for Ke4 decay make it possible to fix the value of a parameter that is not determined by the theory itself and which is contained in the Lagrangian for the system formed by 0+ and 0− mesons. This makes it possible to find the mass of the lightest σ meson: mσ = 663 MeV. As for the nature of spin-1 mesons, which also contribute to the form factors for Ke4 decay, data on them give no way to interpret spin-1 mesons as gauge bosons of chiral theory

Masses and widths of scalar–isoscalar multi-channel resonances from data analysis

The peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed, analyzing the experimental data on processes in the IGJPC = 0+0++ channel in a model-independent approach based on analyticity and unitarity, and using an uniformization procedure. We show that it is possible to obtain a good description of the ππ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the Particle Data Group tables as preferred. However, in this case, first, the representation of the ππ background is unsatisfactory; second, the data on the coupled process are not well described even qualitatively above 1.15 GeV when using the resonance parameters from only the ππ scattering analysis. The combined analysis of these coupled processes is needed, and is carried out satisfactorily. Then, both of the above-indicated issues related to the analysis of ππ scattering only are overcome. The most remarkable change of parameters with respect to the values of the ππ scattering only analysis appears for the mass of the f0(600), which is now in some accordance with the Weinberg prediction on the basis of mended symmetry and with an analysis using the large-Nc consistency conditions between the unitarization and resonance saturation. The obtained ππ scattering length , in the case where we are restricted to the analysis of the ππ scattering or where we consider the so-called A-solution (with a lower mass and width of f0(600) meson), agrees well with the prediction of the chiral perturbation theory and with data extracted at CERN by the NA48/2 collaboration from the analysis of the Ke4 decay and by the DIRAC collaboration from the measurement of the π+π− lifetime.

New measurement of the [formula omitted][formula omitted] decay branching ratio and hadronic form factors

A sample of more than one million K±→π+π−e±ν (Ke4) decay candidates with less than one percent background contamination has been collected by the NA48/2 experiment at the CERN SPS in 2003–2004, allowing a detailed study of the decay properties. The branching ratio, inclusive of Ke4γ decays, is measured to be BR(Ke4)=(4.257±0.016exp±0.031ext)×10−5 with a total relative error of 0.8%. This measurement complements the study of S- and P-wave hadronic form factors by assigning absolute values to the relative hadronic form factors obtained earlier in a simultaneous analysis of the ππ scattering lengths conducted on the same data sample. The overall form factor normalization fs=5.705±0.017exp±0.031ext is obtained with a total relative precision of 0.6%.

RECENT NA48/2 RESULTS ON Ke4 AND K3π DECAYS AND DETERMINATION OF THE ππ SCATTERING LENGTHS

Large samples of K± → 3π and K± → π+π-e±ν (Ke4) decays have been collected by the NA48/2 experiment at CERN SPS. At the π+π- threshold, the π0π0 invariant mass spectrum of the decay K± → π±π0π0 xhibits a Wigner cusp, from which the S-wave ππ scattering lengths are extracted with high precision. The same scattering lengths are also independently determined from the accurate measurement of the form factors in the Ke4 decay K± → π+π-e±ν.

New high statistics measurement of Ke4 decay form factors and ππ scattering phase shifts

We report results from a new measurement of the Ke4 decay K±→π+π-e±ν by the NA48/2 collaboration at the CERN SPS, based on a partial sample of more than 670 000 Ke4 decays in both charged modes collected in 2003. The form factors of the hadronic current (F,G,H) and ππ phase difference (δ=δs-δp) have been measured in ten independent bins of the ππ mass spectrum to investigate their variation. A sizeable acceptance at large ππ mass, a low background and a very good resolution contribute to an improved experimental accuracy, a factor two better than in the previous measurement, when extracting the ππ scattering lengths a0 0 and a0 2. Under the assumption of isospin symmetry and using numerical solutions of the Roy equations, the following values are obtained in the plane (a0 0,a0 2): a0 0=0.233±0.016stat±0.007syst,a0 2=-0.0471±0.011stat±0.004syst. The presence of potentially large isospin effects is also considered and will allow comparison with precise predictions from Chiral Perturbation Theory.

Recent results from the KLOE experiment at DAΦNE

The physics program of the KLOE experiment at DAΦNE is described, and recent results are presented. Preliminary measurements obtained using ~17 pb−1 of data from the year 2000 include those of the ratio of branching ratios BR(KS → π+π−)BR(KS → π0π0), the BR for the Ke3 decay of the KS, the ratio BR(φ → η′γ)BR(φ → ηγ) and the pseudoscalar mixing angle ϕP, and the BR's for the decays φ → f0γ and φ → a0γ. Future directions for the KLOE physics program are summarized.

Symmetries of QCD

The distinction between charges defined at a fixed time and those specified on a null plane is briefly discussed. The talk then addresses the approximate flavour symmetries of QCD that arise because some of the quarks happen to be light. In particular, the role of the quark condensate for the low energy structure of QCD, the dependence of Mπ on mu, and md and the low energy theorems for the ππ scattering amplitude are reviewed. The new data on Ke4 decay beautifully confirm the standard picture, according to which the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.

Radiative corrections for Ke4 decay

Radiative corrections for Ke4 decay

Status of the Cabibbo theory

Abstract The Cabibbo theory of semi-leptonic processes is examined on the basis of recent experimental and theoretical results. Although the gross features of the experimental situation conform with the theory, the detailed analysis is not completely satisfactory at the present time. Thus, the Ke3 decay rates, the neutron lifetime, the Ξ− beta-decay rate, the asymmetry αΣ−e(Σ− → n + e + ν), and the 26Al ft value require explanation or further precise experimentation. The problem of universality of weak interactions is discussed on the basis of two models which assume the validity of current algebra at small distances and for which the secondorder radiative corrections to GV/Gμ are finite: the first assumes a special form for the space-space part of the current algebra, the second assumes the existence of the intermediate boson. Although the present experimental situation as described by the 14O data is consistent with both models, it is possible that a clarification of the Ke3 decay rates and the “26Al problem”, as well as precise calculations of symmetry-breaking corrections to Ke3 amplitudes, may discriminate against one of them. The need for accurate calculations of second-order symmetry-breaking effects to vector matrix elements and of electromagnetic corrections of order Zα2 is emphasized.

A note on the Ke4 and Kμ4 decay rates

Abstract Numerical values are given for the coefficients of the form factors in the decay rate for K l 4 . In this evaluation explicit account has been taken of the pole term in the f 3 form factor. Predictions for the decay rates K + → π + π − l + v , K + → π o π o l + v and K 2 o → π − π o l + v are given using the form factors obtained from current algebra and those obtained in a recent analysis of the decay K + → π + π − e + v .

The pion-pion interaction in the Ke4 decay

The Ke4 decay mode has a certain importance in the study of the pion-pion interaction. For this reason it is useful to study that K-meson decay when this interaction is taken into account. Here the problem is attacked using the method ofJacob, Mahoux andOmnes. The momentum distribution of the pions in their center-of-mass system is calculated for three values of the ππ coupling constant, as well as the decay rate enhancement factor. The shape of the momentum distribution is found to be sensitive to the ππ final state interaction, but the decay rate turns out to be very little increased. The results are compared to those obtained using the Fermi method.

Kμ3 and Ke3 decay and the nature of strangeness violating weak interactions

There is at present only partial and incomplete information available on the nature of strangeness violating weak interactions. From the theoretical point of view the confirmation of universal vector-axial vector interaction is of the foremost importance. The best source of the required information is to be found in the analysis of the spectra of the decay products of K μ3 and K e3. A theoretical discussion of these spectra is carried out in this paper. It is shown that there exists an angular correlation dT d cos α between the direction of the neutrino momentum in the center-of-mass system of the lepton pair and the direction of the pion. This angular correlation is quadratic in cos α independently of the structure of the form factors and provides the best means of identification of the type of coupling. Additional information concerning the form factor structure, in particular, can be learned from the pion spectrum. A quantitative test independent of the form factors, of the universality of the muon, and electron interaction is suggested. Some quantitative properties of the electron spectrum in K e3-decay, independent of the form factor structure, have been established. They are characteristic of the type of coupling. It is shown how one can obtain the form factor from the knowledge of the electron spectrum if there is only one type of interaction.

Kμ3 and Ke3 decay and the nature of strangeness violating weak interactions : S. W. Mac Dowell

Kμ3 and Ke3 decay and the nature of strangeness violating weak interactions : S. W. Mac Dowell

Ke3Decay as a Test of UniversalV−ALepton Coupling

It is shown that the experimental spectrum of electrons from Ke3 decay provides a direct test of universal vectoraxial vector lepton coupling. The test is independent of the K -- pi form factor. Methods of treating the data so as to obtain information about the form factor itself are discussed.

Some features of the electron energy spectrum in the Ke3 decay process

It is shown that there exist some characteristic features in the theoretical energy spectrum of the electrons in K/sub e3/ decay, and the experimental analysis of these simple features seems to be easier than the investigation for the correlation with the pion energy. The electron-pion energy correlation function is given. The ratio of high-energy secondary electrons to lowenergy electrons is investigated. (W.D.M.)

On the abundances of the K μ3 and Ke3 decay modes of positive K mesons

The abundances of the Kμ3 and Ke3 decay modes were checked in a large stack ofBirgeet al. (1), using the additional criteria ofAlexanderet al. (2). Our results agree completely with those ofBirgeet al. The weighted average of these and comparable corrected results of others yields a relative abundance of (3.9 ± .5)% for Kμ3 and of (5.1 ± .8)% for Ke3 decay. Available experimental data on the electron spectrum of the Ke3 decay mode are compiled and compared to theoretical calculations byFuruichiet al. (3). No evidence is found for an abnormally short mean free path of the positive secondary pions from Kπ2 decay as previously reported byAlexanderet al. (2).