Non-mesonic weak decay of hypernuclei in effective field theory

[cat] En aquesta tesi hem descrit la interacció feble LambdaN->NN, la qual és la principal responsable de la desintegració d’hipernuclis pesats, en el marc de teories efectives de camps. La teoria efectiva de camps (EFT) s’ha desenvolupat fins a segon ordre en “q”, on “q” és el moment transferit entre els barions interactuants. En particular s’han calculat tots els diagrames d’intercanvi de dos pions que apareixen al segon ordre en l’expansió de moments. Els valors numèrics de les constants de baixa energia s’han obtingut de dues maneres. Primer,s’ha fet un ajust als observables de desintegració hipernuclear per a tres hipernuclis lleugers, 5-lambda/He,11-lambda/B i 12-lambda/C. Per una banda, aquest càlcul ha involucrat la EFT a primer ordre per a la transició feble LambdaN->NN, i per l’altra, una descripció adequada dels estats nuclears inicials i finals en un formalisme de molts cossos. Segon, la EFT s’ha comparat al model d’intercanvi d’un mesó que descriu la mateixa interacció. Expandint els potencials d’intercanvi d’un mesó en potències de moment, les constants de baixa energia que apareixen en la EFT s’han escrit en termes dels paràmetres dels mesons pesats. Per tal d’obtenir una descripció de la desintegració feble d’hipernuclis menys depenent de model s’ha estudiat la desintegració de l’hipernucli més lleuger, l’hipertritó, el qual pot ser descrit en el marc de teoria efectiva de camps tan en el sector feble com en el sector fort. En aquest cas, les constants de baixa energia no s’han pogut ajustar a observables hipernuclears degut a la manca de dades experimentals per a la desintegració feble de l’hipertritó. Alternativament, s’ha estudiat com el ritme de la desintegració feble de l’hipertritó depèn de les constants de baixa energia de primer ordre.[eng] In this thesis we have described the weak Lambda N to NN interaction, which is the main responsible for the decay of heavy hypernuclei, within the effective field theory (EFT) framework. The EFT is developed up to second order in “q”, where “q” is the transferred momentum between the interacting baryons. In particular, all the two-pion exchange diagrams entering at second order in the momentum expansion have been calculated. Numerical values for the leading order low-energy constants are obtained by two means. First, a fit to the hypernuclear decay observables for three light hypernuclei, 5-Lambda/He, 11-lLambda/B i 12/Lambda/C, has been performed. This calculation has involved a proper description of the initial and final nuclear states within a many-body formalism. Second, the EFT has been compared to the one-meson-exchange model describing the same interaction. By expanding the one-meson-exchange potentials in powers of momentum, the low energy constants appearing in the EFT description have been written in terms of the heavy meson parameters. In order to obtain a less model dependent description of the weak decay of hypernuclei we have studied the decay of the lightest hypernucleus, the hypertriton, which can be described within an effective field theory framework in both the strong and the weak sectors

Next-to-leading order effective field theory ΛN → NN potential in coordinate space

The potential in coordinate space for the ΛN→NNΛN→NN weak transition, which drives the weak decay of most hypernuclei, is derived within the effective field theory formalism up to next-to-leading order. This coordinate space potential allows us to discuss how the different contributions to the potential add up at the different scales. Explicit expressions are given for each two-pion-exchange diagram contributing to the interaction. The potential is also reorganized into spin and isospin operators, and the coefficient for each operator is given in analytical form and represented in coordinate space. The relevance of explicitly including the mass differences among the baryons appearing in the two-pion-exchange diagrams is also discussed in detail

Constraints on the effective field theory for the Lambda N --> NN transition

We consider the ΛN → 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