Nonmesonic Weak Decay Research Articles

Effective two-body ΛN → NN weak potentials deduced from three-body ΛNN → NNN interactions and hypernuclear non-mesonic weak decay rates

Abstract We intend to study the role of the three-body weak ΛNN → NNN interaction in two-nucleon induced hypernuclear non-mesonic weak decay. The three-body weak interactions are constructed on the basis of the meson-pair exchange (MPE) model and then we derive the effective two-body ΛN → NN weak potentials from the three-body interactions based on the Loiseau–Nogami–Ross approximation. The strong coupling constants of MPE are taken from the Nijmegen ESC and GESC models and the weak ones of MPE are evaluated in the weak Λ–n mixing model by Dalitz and Von Hippel [Phys. Lett. 10, 153 (1964)]. The effective two-body ΛN → NN weak potentials are applied to evaluate hypernuclear non-mesonic decay rates, which should give a certain additional contribution to the two-nucleon induced decay rate Γ2N. Calculations of $\Gamma ^{({\text{eff.2B}})}_{nm}$ are done for $^5_\Lambda {\rm He}$, $^{11}_\Lambda {\rm B}$, and $^{12}_\Lambda {\rm C}$ and the results are compared with experimental data $\Gamma ^\mathrm{exp}_{2N}$. We have demonstrated the possibility of accounting for the two-nucleon induced non-mesonic decays of light and p-shell hypernuclei by introducing the effective two-body potentials deduced from the three-body weak interactions, though the calculated $\Gamma ^{(\text{eff.2B})}_{nm}$ still includes uncertainties. Discussions and limitations of our “effective two-body ΛN → NN model” are given.

Final state interaction in the pn and nn decay channels of $$^4_\varLambda $$He

We study the effects of final state interactions in the non-mesonic weak decay $\Lambda N \rightarrow nN$ (n is a neutron and N is either a neutron or a proton) of the hypernucleus $_\Lambda^4$He. Using a three-body model the effects of distortion of the interaction of the emitted nucleon pair with the residual nucleus is considered. We also study the influence of the final state interaction between the emitted nucleons using the Migdal-Watson model. The effect of spin symmetries in the final state of the pair is also considered. Based on our calculations, we conclude that final state interactions play a minor role in the kinetic energy spectrum of the emitted nucleon pair.

Hypernuclear non-mesonic weak decays in the extended meson exchange model

Hypernuclear non-mesonic weak decays in the extended meson exchange model

Effects of ΛΛ−ΞN mixing in the decay of S=−2 hypernuclei

We study the non-mesonic weak decay of the doubly-strange hypernucleus $^{\Lambda\Lambda}_6$He within a model which considers the exchange of pseudoscalar and vector mesons. Special attention is paid into quantifying the strong interaction effects, focussing on the interaction among the two {\Lambda} hyperons which induces novel weak transitions, whereby {\Lambda}{\Lambda}, {\Xi}N and {\Sigma}{\Sigma} states decay into a hyperon-nucleon pair. The initial strangeness -2 wave function is obtained from the solution of a G-matrix equation with the input of realistic strong baryon-baryon potentials, while the final hyperon-nucleon wave functions are derived analogously from a microscopic T-matrix calculation. The new {\Lambda}{\Lambda} $\to$ Y N decay rate studied in this work, $\Gamma_{\Lambda n} + \Gamma_{\Sigma^0 n} + \Gamma_{\Sigma^- p}$ , represents 3-4% of the total one-baryon induced non-mesonic decay and is remarkably affected by strong interaction effects. In particular, the relative importance of the partial decay rates, encoded in the ratio $\Gamma_{\Lambda n} / (\Gamma_{\Sigma^0 n} + \Gamma_{\Sigma^- p})$, gets inverted when the mixing to {\Xi}N states is incorporated in the initial correlated {\Lambda}{\Lambda} wave function. This sensitivity can be used experimentally to learn about the strong interaction in the strangeness -2 sector.

Λ N → NN EFT potentials and hypertriton non-mesonic weak decay

The potential for the Λ N → NN weak transition, the main responsible for the non-mesonic weak decay of hypernuclei, has been developed within the framework of effective field theory (EFT) up to next-to-leading order (NLO). The leading order (LO) and NLO contributions have been calculated in both momentum and coordinate space, and have been organised into the different operators which mediate the N → NN transition. We compare the ranges of the one-meson and two-pion exchanges for each operator. The non-mesonic weak decay of the hypertriton has been computed within the plane-wave approximation using the LO weak potential and modern strong EFT NN potentials. Formally, two methods to calculate the final state interactions among the decay products are presented. We briefly comment on the calculation of the mesonic weak decay.

Nonmesonic weak decay of charmed hypernuclei

We present a study of the nonmesonic weak decay (NMWD) of charmed hypernuclei using a relativistic formalism. We work within the framework of the independent particle shell model and employ a (π, K) one-meson-exchange model for the decay dynamics. We implement a fully relativistic treatment of nuclear recoil. Numerical results are obtained for the one-neutron-induced transition NMWD rates of the N. The effect of nuclear recoil is sizable and goes in the direction to decrease the nuclear decay rate. We found that the NMWD decay rate of is of the same order of magnitude as the partial decay rate for the corresponding mesonic decay , suggesting the feasibility of experimental detection of such heavy-flavor nuclear processes.

Nonmesonic weak decay of Λ hypernuclei: The ΛN−ΣN coupling

The nonmesonic weak decay of $\mathrm{\ensuremath{\Lambda}}$ hypernuclei is studied within a microscopic diagrammatic approach which is extended to include the $\mathrm{\ensuremath{\Lambda}}N\ensuremath{-}\mathrm{\ensuremath{\Sigma}}N$ strong interaction coupling. We adopt a nuclear matter formalism which, through the local density approximation, allows us to model finite hypernuclei. One-meson-exchange potentials are used for the weak and strong four-baryon interactions. The rates for the neutron- and proton-induced weak decays, $\mathrm{\ensuremath{\Lambda}}N\ensuremath{\rightarrow}nN$ and $\mathrm{\ensuremath{\Lambda}}N\ensuremath{\rightarrow}\mathrm{\ensuremath{\Sigma}}N\ensuremath{\rightarrow}nN$ ($N=n$ or $p$; $\mathrm{\ensuremath{\Sigma}}={\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}, {\mathrm{\ensuremath{\Sigma}}}^{0}$, and ${\mathrm{\ensuremath{\Sigma}}}^{+}$), are predicted for $_{\mathrm{\ensuremath{\Lambda}}}^{12}\mathrm{C}, _{\mathrm{\ensuremath{\Lambda}}}^{28}\mathrm{Si}, _{\mathrm{\ensuremath{\Lambda}}}^{56}\mathrm{Fe}$, and $_{\mathrm{\ensuremath{\Lambda}}}^{208}\mathrm{Pb}$. The $\mathrm{\ensuremath{\Lambda}}N\ensuremath{-}\mathrm{\ensuremath{\Sigma}}N$ coupling turns out to provide a contribution of about 23% (5%) to the total neutron-induced rate (proton-induced rate). Again as an effect of the hyperon coupling, the total one-nucleon-induced rate increases by about 9%, while the ${\mathrm{\ensuremath{\Gamma}}}_{n}/{\mathrm{\ensuremath{\Gamma}}}_{p}$ ratio increases by about 17%. The saturation property of the nonmesonic rates with increasing hypernuclear mass number is clearly obtained and explained. The above percentage modifications remain almost unaltered through the hypernuclear mass number. All the non-negligible changes introduced by the $\mathrm{\ensuremath{\Lambda}}N\ensuremath{-}\mathrm{\ensuremath{\Sigma}}N$ coupling lead to a definite improvement of our predictions once compared with the available KEK and FINUDA data.

Nonmesonic weak decay of Λ hypernuclei: The three-nucleon induced mode

Abstract The nonmesonic weak decay of Λ hypernuclei is studied within a microscopic diagrammatic approach which is extended to include the three-nucleon induced mechanism. We adopt a nuclear matter formalism which, through the local density approximation, allows us to model finite hypernuclei, a one-meson-exchange weak transition potential and a Bonn nucleon–nucleon strong potential. One-, two- and three-nucleon induced weak decay rates are predicted for C Λ 12 by including ground state correlations up to second order in the nucleon–nucleon potential and the recoil of the residual nucleus. Three-nucleon stimulated decays, Λ N N N → n N N N ( N = n or p ), are considered here for the first time. The obtained decay rates compare well with the latest KEK and FINUDA data. The three-nucleon induced rate turns out to be dominated by nnp - and npp -induced decays, it amounts to ∼ 7 % of the total nonmesonic rate and it is ∼ 1 / 2 of the neutron-induced decay rate. The reduction effect of the nuclear recoil is particularly relevant for the three-nucleon induced rates ( ∼ 15 % ), less important for the two-nucleon induced rates ( ∼ 4 % ) and negligible for the one-nucleon induced rates. Given the non-negligible size of the three-nucleon induced contribution and consequently its importance in the precise determination of the complete set of decay rates, new measurements and/or experimental analysis are encouraged.

Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay (NMWD) of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the only noteworthy difference is that the ratio is appreciably higher and closer to the experimental value in the relativistic calculation. The ability of describing existing data, including the most recent ones, on NMWD of Λ-hypernuclei, warrants application of the formalism to evaluate similar decay processes in charmed nuclei.

Determination of non-mesonic weak decay widths of 5ΛHe and 11ΛB Hypernuclei

The recent determination of the partial decay widths for the one-proton and the two-nucleon induced Non-Mesonic Weak Decay of Λ-Hypernuclei in the A=5–16 range permitted to reconstruct the full pattern of decay widths for 5ΛHe and 11ΛB. A consistency check on 12ΛC decay widths confirms the validity of the adopted method.

Nonmesonic weak decay of double-Λhypernuclei: A microscopic approach

The nonmesonic weak decay of double-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei is studied within a microscopic diagrammatic approach. In addition to the nucleon-induced mechanism, $\mathrm{\ensuremath{\Lambda}}N\ensuremath{\rightarrow}nN$ and $\mathrm{\ensuremath{\Lambda}}NN\ensuremath{\rightarrow}nNN$, widely studied in single-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei, additional hyperon-induced mechanisms, $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}n$, $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}n$, and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p$, are accessible in double-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei and are investigated here. As in previous works on single-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one-meson exchange weak transition potential (including the ground-state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two-pion-exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei ${}_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{10}\mathrm{Be}$ and ${}_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{B}$. Our predictions are compared with a few previous evaluations. The rate for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}n$ decay is dominated by $K$-, ${K}^{*}$-, and $\ensuremath{\eta}$-exchange and turns out to be about 2.5% of the free $\mathrm{\ensuremath{\Lambda}}$ decay rate, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{free}}$, while the total rate for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}n$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p$ decays, dominated by $\ensuremath{\pi}$-exchange, amounts to about 0.25% of ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{free}}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the nonmesonic decay of strangeness $\ensuremath{-}2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$ dibaryon.

Nonmesonic weak decay dynamics from proton spectra of Λ-hypernuclei

A novel comparison between the data and the theory is proposed for the nonmesonic (NM) weak decay of hypernuclei. Instead of confronting the primary decay rates, as is usually done, we focus our attention on the effective decay rates that are straightforwardly related with the number of emitted particles. Proton kinetic energy spectra of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], measured by FINUDA, are evaluated theoretically. The independent particle shell model (IPSM) is used as the nuclear structure framework, while the dynamics is described by the one-meson-exchange (OME) potential. Only for the [Formula: see text], [Formula: see text] and [Formula: see text] hypernuclei it is possible to make a comparison with the data, since for the rest there is no published experimental information on number of produced hypernuclei. Considering solely the one-nucleon-induced (1N-NM) decay channel, the theory reproduces correctly the shapes of all three spectra at medium and high energies (Ep ≳ 40 MeV). Yet, it greatly overestimates their magnitudes, as well as the corresponding transition rates when the full OME (π + K + η + ρ + ω + K*) model is used. The agreement is much improved when only the π + K mesons with soft dipole cutoff parameters participate in the decay process. We find that the IPSM is a fair first-order approximation to disentangle the dynamics of the 1N-NM decay, the knowledge of which is indispensable to inquire about the baryon–baryon strangeness–flipping interaction. It is shown that the IPSM provides very useful insights regarding the determination the 2N-NM decay rate. In a new analysis of the FINUDA data, we derive two results for this quantity with one of them close to that obtained previously.

First determination of the one-proton induced Non-Mesonic Weak Decay width of p-shell Λ-Hypernuclei

Previous studies of proton and neutron spectra from Non-Mesonic Weak Decay of eight Λ-Hypernuclei (A=5–16) have been revisited. New values of the ratio of the two-nucleon and the one-proton induced decay widths, Γ2N/Γp, are obtained from single proton spectra, Γ2N/Γp=0.50±0.24, and from neutron and proton coincidence spectra, Γ2N/Γp=0.36±0.14stat−0.04sys+0.05sys, in full agreement with previously published ones. With these values, a method is developed to extract the one-proton induced decay width in units of the free Λ decay width, Γp/ΓΛ, without resorting to Intra Nuclear Cascade models but by exploiting only experimental data, under the assumption of a linear dependence on A of the Final State Interaction contribution. This is the first systematic determination ever done and it agrees within the errors with recent theoretical calculations.

Non-mesonic weak decay of hypernuclei with effective field theory

The ΛN → NN interaction, the main responsible for the decay of heavy hypernuclei, is described within the effective field theory (EFT) framework. The EFT is developed up to (q⃗2), where q⃗ is the transferred momentum between the interacting baryons. Numerical values for the leading order low-energy constants are obtained by two means. First, from a fit to the hypernuclear decay observables, and second, by comparing the EFT to the one-meson-exchange model describing the same interaction. All the two-pion exchange diagrams entering at the next-to-leading in the EFT have been calculated.

Nonmesonic Weak Decay Spectra of Light Hypernuclei

The nonmesonic weak decay spectra of light hypernuclei have been evaluated in a systematic way. As theoretical framework we adopt the independent particle shell model with three different one-meson-exchange transition potentials. Good agreement with data is obtained for proton and neutron kinetic energy spectra of $^4_\Lambda$He, and $^5_\Lambda$He, when the recoil effect is considered. The coincidence spectra of proton-neutron pairs are also accounted for quite reasonably, but it was not possible to reproduce the data for the neutron-neutron pair spectra. It is suggested that the $\pi+K$ meson-exchange model with soft monopole form factors could be a good starting point for describing the dynamics responsible for the decays of these two hypernuclei. The $^4_\Lambda$H~ spectra are also presented.

THE LAST RESULTS FROM THE FINUDA EXPERIMENT

FINUDA was a complex magnetic spectrometer installed on the DAΦNE e+e- collider, the Italian ϕ-factory put in operation at the INFN National Laboratories of Frascati, near Rome. It was carefully designed and specially dedicated to an extensive program of hypernuclear physics, mainly focussed on spectroscopy of light Λ-hypernuclei and on systematic study of their decay modes. Among the latest FINUDA results, of particular importance are the first observation of the neutron-rich Λ-hypernucleus [Formula: see text] and the first experimental evidence of the so-called hypernucleus two-nucleon induced non-mesonic weak decay.

One-loop contributions in the effective field theory for theΛN→NNtransition

We consider the $\ensuremath{\Lambda}N\ensuremath{\rightarrow}NN$ weak transition, responsible for a large fraction of the nonmesonic weak decay of hypernuclei. We follow the previously derived effective field theory and compute the next-to-leading one-loop corrections. Explicit expressions for all diagrams are provided, which result in contributions to all relevant partial waves.

Weak decay of Λ hypernuclei: Experimental status

Abstract The FINUDA experiment has recently completed an extensive study of the weak decay of p -shell Λ hypernuclei including both Mesonic and Non-Mesonic modes. The present paper is focused on the study of proton spectra from Non-Mesonic Weak Decay, both single and in coincidence with a neutron, which has triggered the investigation of the two nucleon-induced Λ N N → n N N decay channel. Furthermore thanks to the excellent performance of FINUDA in terms of long-term instrumental stability and fully reliable reconstruction and analysis programs it has been possible to isolate and kinematically reconstruct single events related to the occurrence of rare physical processes. Three events corresponding quite safely to the observation of the 2 N -induced Non-Mesonic Weak Decay were analyzed and fully reconstructed. They are the experimental evidence for such a process, up to now conjectured only by indirect measurements. Discussion of the results is outlined.

The Strong Three-body Weak Interaction Contribution in the Nonmesonic Weak Decay of p-shell Λ Hypernuclei

The fundamental motivation to study the non-mesonic weak decay (NMWD) of hypernuclei is that it provides the unique means for study of baryon–baryon weak interaction in SU3f symmetry group. The new channel of NMWD, namely the recently confirmed three-body channel, seems to have a surprisingly big branching ratio so that it makes its accurate measurement prerequisite of the baryon–baryon weak interaction study. We report a new result of \({\Gamma_{2N}(^{11}_{\Lambda} {\rm B})}\) from E508 experiment of KEK-PS, though preliminary yet, which agrees with the previous result of \({^{12}_{\Lambda}}\) C from the same experiment, those from FINUDA experiment and those of the recent theoretical predictions.

Theoretical developments in weak hypernuclear decay

We present a theoretical overview of the developments in hypernuclear weak decay occurred in the last ten years or so, with special emphasis on the one- and two-nucleon-induced non-mesonic modes. Recent progress is discussed which lead to the solution of long-standing puzzles on the Γ n / Γ p ratio and the asymmetry parameter for Λ -hypernuclei. The theory–experiment agreement reached for the two-nucleon-induced rates is also analyzed. The various theoretical approaches adopted in the literature are summarized, highlighting those key ingredients of the baryon–baryon weak interaction that turned out to be relevant for the explanation of data. Perspectives for future studies on the Δ I = 1 / 2 isospin rule in non-mesonic weak decay and on rare non-mesonic weak decays allowed to strangeness −2 hypernuclei are also indicated.