Investigation of the $K^{-}pp$ Bound State via the \( K^{-} + {}^{3}\mathrm{He} \) Reaction

TL;DR

This study uses four-body equations to explore the formation of a kaonic bound state in helium-3 reactions, suggesting it could be observed experimentally regardless of the interaction model details.

Contribution

It provides a theoretical analysis of the K^{-}pp bound state formation using four-body equations, demonstrating its potential observability in low-energy reactions.

Findings

Signal of K^{-}pp state appears in the πΣp spectrum

Results are consistent across different ar{K}N interaction models

Supports experimental search for K^{-}pp in helium-3 reactions

Abstract

Using the four-body Alt-Grassberger-Sandhas (AGS) equations for the \( K^{-}ppn \) system, we investigate the possible formation of a \( K^{-}pp \) quasi-bound state through the low-energy \( K^{-} + {}^{3}\mathrm{He} \) reaction. The neutron missing mass spectrum in the final state was calculated for different models of the \( \bar{K}N \) interaction. The results indicate that, irrespective of the specific nature of the \( \Lambda(1405) \) structure or the details of the \( \bar{K}N \) interaction model, a signal corresponding to the \( K^{-}pp \) quasi-bound state could appear in the \( \pi \Sigma p \) mass spectrum. This supports the feasibility of observing the \( K^{-}pp \) cluster in low-energy kaon-induced reactions on helium-3.