ΛN→NNweak interaction in effective-field theory

Abstract

The nonleptonic weak ͉⌬S͉ =1 ⌳N interaction, responsible for the dominant nonmesonic decay of all but the lightest hypernuclei, is studied in the framework of an effective-field theory. The long-range physics is described through tree-level exchange of the SU(3) Goldstone bosons, while the short-range potential is parametrized in terms of the lowest-order contact terms. We obtain reasonable fits to available weak hypernuclear decay rates and quote the values for the parity-violating asymmetry as predicted by the present effective-field theory. For the past 50 years, ⌳ hypernuclei, systems of one or more ⌳ hyperons bound to a core nucleus, have been used to extend our knowledge of both the strong and the weak baryon-baryon interaction from the NN case into the SU(3) sector. The nonmesonic hypernuclear weak decay, facilitated via the ͉⌬S͉ = 1 four-fermion interaction, thus complements the weak ⌬S =0 NN case, which allows the study of only the parity-violating amplitudes.In analogy to NN phenomenology, the nonmesonic hypernuclear decay has traditionally been modeled using a mesonexchange approach [1]. The long-range part of the interaction is naturally explained by one-pion exchange, which could approximately reproduce the total (one-nucleoninduced) nonmesonic decay rate, ⌳N → NN, but not the partial rates, the proton-induced ⌳p → np rate ⌫ p , and the neutron-induced ⌳n → nn rate ⌫ n [2]. Due to the ⌳N mass difference, the process ⌳N → NN produces nucleons with momenta around Ϸ420 MeV, suggesting that the short-range part of the interaction cannot be neglected. These contributions have been described either through the exchange of vector mesons [3,4], whose production thresholds are too high for the free ⌳ decay, or through direct quark exchange [5].In contrast to previous theoretical studies, we present an exploratory study in order to determine the possible efficacy of the use of effective-field theory (EFT) methods in hypernuclear decay. Studies in this direction have already begun in Ref. [6], where a Fermi ͑V-A͒ interaction was added to the one-pion-exchange (OPE) mechanism to describe the weak ⌳N → NN transition. The present approach is motivated by the remarkable success of EFT techniques based on chiral expansions in the (nonstrange) SU(2) sector [7-10], which suggests its extension to the SU(3) realm, even though stability of the chiral expansion is less clear for the SU(3) sector, due to the significant degree of SU(3) symmetry breaking. A well-known example of the problems facing the SU(3) chiral perturbation theory has been the prediction [11][12][13][14] The EFT approach is based on the existence of wellseparated scales in the physical process under study. Formally, the high-momentum (short-distance) modes in the four-baryon interaction Lagrangian are replaced by contact operators, compatible with the underlying physical symmetries, of increasing dimension. Built in such a way, the Lagrangian will contain an infinite number of terms, and a consistent power-counting scheme is needed in order to trunca...

Towards a solution of theΓn∕Γppuzzle in the nonmesonic weak decay ofΛhypernuclei

“…The results obtained in Ref. [16] are very encouraging and open a new door for systematic studies of hypernuclear weak decay based on effective field theory descriptions.…”

“…Moreover, the parity violating ΛN ( 3 S 1 ) → nN ( 3 P 1 ) transition, which contributes to both the n-and p-induced processes, is considerably enhanced by K-exchange and direct quark mechanisms and tends to increase Γ n /Γ p [6,14]. Very recently, the ΛN → nN interaction has been studied within an effective field theory framework [16]. The decay of sand p-shell hypernuclei was approached following the same formalism as in Refs.…”

A framework for exploring the interactions and decays of hyperons with lattice QCD

“…However, having made all of these negative statements based on our current theoretical understanding, there has been an important phenomenological analysis [10,11] recently completed by Parreño, Bennhold and Holstein (PBH) that gives one hope that an EFT can in fact be constructed to describe these processes. In PBH, contributions to the weak decay from weak-one-pion exchange (WOPE) and weak-one-kaon exchange (WOKE) were included along with contributions from local ∆s = 1 weak ΛNNN interactions.…”

“…Construction of a model-independent EFT description of these decays was initiated in Refs. [10,11]. The study of the ∆S = 1 ΛN interaction has the additional charm of allowing access to both the parity-conserving (PC) and the parity-violating (PV) part of the weak interaction, in contrast to its ∆S = 0 NN partner, where the PC weak signal is masked by the strong PC amplitude which is 10 orders of magnitude larger.…”

Intrinsic asymmetry parameter in nonmesonic hypernuclear decay: analytical proof of the independence on hypernucleus within an independent particle shell model

“…On the other hand, majority of the existing calculations based on strict one-meson exchange models (OMEM) [16]- [26] find values between −0.73 and −0.19 for 5 Λ He [27,28] and, when results are available in the same model, very similar values for 12 Λ C. Thus, there is now a renewed interest to solve this NMHD puzzle. A first application of effective field theory (EFT) to nonmesonic decay [29] and the inclusion of σ meson exchange plus direct-quark interaction, which strongly violates the ∆T = 1/2 rule [30], have stressed that the scalar-isoscalar type of interactions are specially important in explaining the asymmetry. Quite recently, two relevant works have pointed to possible solutions via the inclusion of: i) a one-meson-exchange potential supplemented by a correlated plus uncorrelated chirally motivated two-pion (2π)-exchange mechanism [31], within a model including final state interactions (FSI) for different cuts on the kinetic energy of the emitted nucleons; or ii) the a 1 meson exchange [32].…”