Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Antikaon absorption in the nuclear medium: the role of hadron self-energies and implications for kaonic atoms

J. Óbertová, À. Ramos, J. Mareš

TL;DR

This work develops a fully microscopic description of the $K^-$-nuclear potential by embedding next-to-leading-order chiral, coupled-channel $K^-N$ amplitudes within a nuclear medium that includes Pauli blocking and self-energies for nucleons, hyperons, kaons, and pions, as well as multinucleon absorption channels. The authors solve the in-medium Bethe–Salpeter equation to obtain $K^-N$ and $K^-NN$ optical potentials and apply them to kaonic atoms via a Klein–Gordon framework with subthreshold kinematics, achieving a fit to 64 kaonic-atom data points with $\chi^2/\,\mathrm{d.p.}=1.5$, on par with the best phenomenological multi-nucleon potentials. They find that self-energies soften the amplitudes and reduce the potential depth at saturation density ($\mathrm{Re}V_{K^-}(\rho_0) \approx -30$ to $-25$ MeV, $\mathrm{Im}V_{K^-}(\rho_0) \approx -50$ to $-60$ MeV for the Pauli+YNKπ model), while multinucleon absorption remains substantial (≈60 MeV at $\rho_0$). The calculated mesonic and non-mesonic branching ratios in $^{12}$C and $^{20}$Ne are in fair agreement with data, though results are sensitive to final-state corrections, highlighting the importance of a fully microscopic, self-consistent treatment for interpreting kaonic-atom observables and high-density kaon-nucleus dynamics.

Abstract

A systematic study of all relevant in-medium effects on the total $K^-$-nuclear potential is presented in this work. The $K^-N$ scattering amplitudes, including Pauli blocking effects and hadron self-energies (hyperons, nucleons, pions and kaons), are derived within a next-to-leading order chiral meson-baryon coupled-channel interaction model. These amplitudes are employed in a microscopic model of the $K^-$-nuclear potential in symmetric nuclear matter that includes one-, two- and, when the kaons and pions are dressed, also multinucleon absorption processes. The potential is then applied in calculations of the strong energy shifts and widths of 64 measured kaonic atom levels. The comparison of the results of the full model that includes Pauli correlations and hadron self-energies with data provides $χ^2 /d.p=1.5$, the lowest value obtained by a theoretical model to date and comparable with that of the best fitted phenomenological potentials. Furthermore, the calculated branching ratios for mesonic and non-mesonic absorption channels in kaonic carbon and kaonic neon are in good agreement with available data.

Antikaon absorption in the nuclear medium: the role of hadron self-energies and implications for kaonic atoms

TL;DR

This work develops a fully microscopic description of the -nuclear potential by embedding next-to-leading-order chiral, coupled-channel amplitudes within a nuclear medium that includes Pauli blocking and self-energies for nucleons, hyperons, kaons, and pions, as well as multinucleon absorption channels. The authors solve the in-medium Bethe–Salpeter equation to obtain and optical potentials and apply them to kaonic atoms via a Klein–Gordon framework with subthreshold kinematics, achieving a fit to 64 kaonic-atom data points with , on par with the best phenomenological multi-nucleon potentials. They find that self-energies soften the amplitudes and reduce the potential depth at saturation density ( to MeV, to MeV for the Pauli+YNKπ model), while multinucleon absorption remains substantial (≈60 MeV at ). The calculated mesonic and non-mesonic branching ratios in C and Ne are in fair agreement with data, though results are sensitive to final-state corrections, highlighting the importance of a fully microscopic, self-consistent treatment for interpreting kaonic-atom observables and high-density kaon-nucleus dynamics.

Abstract

A systematic study of all relevant in-medium effects on the total -nuclear potential is presented in this work. The scattering amplitudes, including Pauli blocking effects and hadron self-energies (hyperons, nucleons, pions and kaons), are derived within a next-to-leading order chiral meson-baryon coupled-channel interaction model. These amplitudes are employed in a microscopic model of the -nuclear potential in symmetric nuclear matter that includes one-, two- and, when the kaons and pions are dressed, also multinucleon absorption processes. The potential is then applied in calculations of the strong energy shifts and widths of 64 measured kaonic atom levels. The comparison of the results of the full model that includes Pauli correlations and hadron self-energies with data provides , the lowest value obtained by a theoretical model to date and comparable with that of the best fitted phenomenological potentials. Furthermore, the calculated branching ratios for mesonic and non-mesonic absorption channels in kaonic carbon and kaonic neon are in good agreement with available data.

Paper Structure

This paper contains 7 sections, 33 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Model
  3. $K^-N$ amplitudes with hadron self-energies
  4. $K^-N$ and $K^-NN$ absorption model including hadron self-energies
  5. Kaonic atoms
  6. Results
  7. Conclusions

Figures (10)

  • Figure 1: Real part (solid lines) and imaginary part (dashed lines) of the $K^-p\rightarrow K^-p$ free-space amplitude, $f_{K^-p}$ (left panel), and the $K^-n\rightarrow K^-n$ free-space amplitude, $f_{K^-n}$ (right panel), for the BCN model (black lines) and the Oset-Ramos model (red lines).
  • Figure 2: Real (left) and imaginary (right) parts of the $K^-p\rightarrow K^-p$ amplitude, $f_{K^-p}$, with Pauli blocking (black), Pauli+YN SE (red), Pauli + YNK SE (green) and Pauli + YNK$\pi$ SE (magenta) calculated at $\rho=0.17$ fm$^{-3}$. The corresponding free-space amplitude (blue) is shown for comparison.
  • Figure 3: Real (left) and imaginary (right) parts of the $K^-n\rightarrow K^-n$ amplitude, $f_{K^-n}$, with Pauli blocking (black), Pauli+YN SE (red), Pauli + YNK SE (green) and Pauli + YNK$\pi$ SE (magenta) calculated at $\rho=0.17$ fm$^{-3}$. The corresponding free-space amplitude (blue) is shown for comparison.
  • Figure 4: Absolute value of the $K^-n\rightarrow \pi^- \Lambda$ amplitude in the Pauli+YN SE (red), Pauli + YNK SE (green) and Pauli + YNK$\pi$ SE (magenta) models, evaluated at $\rho = 0.3\rho_0$ as a function of the centre-of-mass energy $\sqrt{s}$ compared with the measurement by the AMADEUS collaboration amadeus2018. For comparison there is also the corresponding free-space amplitude (blue) above threshold (vertical line) compared with the amplitude extracted from cross section data kim_exp.
  • Figure 5: Feynman diagram corresponding to the $K^-N\rightarrow \pi Y$ ($Y=\Sigma, \Lambda$) absorption channel in nuclear matter with dressed hyperon and nucleon.
  • ...and 5 more figures