# Kaonic Atoms to Investigate Global Symmetry Breaking

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## Abstract

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## 1. Introduction

## 2. Low-Energy Strong Interaction Dynamics

#### 2.1. Global Symmetries

#### 2.2. Meson-Nucleon Sigma Terms

- There are channels opened below the threshold.
- There is a resonance, $\mathsf{\Lambda}\left(1405\right)$, just below threshold of $\overline{K}N\to \overline{K}N$.
- Uncertainties in the extrapolation procedure are present: the difference ${\mathsf{\Sigma}}_{KN}\left(2{M}_{K}^{2}\right)-{\mathsf{\Sigma}}_{KN}\left(0\right)$ is larger than in the $\pi N$ case, introducing additional uncertainty in the quantity of interest ${\mathsf{\Sigma}}_{KN}\left(0\right)$. In quantitative terms: let us refer to the $\pi N$ case, where the “experimental” value ${\mathsf{\Sigma}}_{\pi N}\left(0\right)$ is based on solid experimental data [9]. Here, ${\mathsf{\Sigma}}_{\pi N}\left(2{m}_{\pi}^{2}\right)$ at the C–D point is $(65\pm 5)\phantom{\rule{3.33333pt}{0ex}}MeV$. The estimated difference ${\mathsf{\Sigma}}_{\pi N}\left(2{m}_{\pi}^{2}\right)-{\mathsf{\Sigma}}_{\pi N}\left(0\right)=14\phantom{\rule{3.33333pt}{0ex}}MeV$ [10] gives ${\mathsf{\Sigma}}_{\pi N}\left(0\right)=(51\pm 5)\phantom{\rule{3.33333pt}{0ex}}MeV$ [11]; i.e., an uncertainty of about 10%.

## 3. Antikaon-Nucleon Scattering Lengths

#### 3.1. Formation of a Kaonic Atom

#### 3.2. Antikaon-Nucleon Scattering Lengths

## 4. The SIDDHARTA Kaonic Hydrogen Measurement

## 5. Kaonic Deuterium Experiments

#### 5.1. The SIDDHARTA-2 Experiment at LNF-INFN

#### 5.2. The E57 Experiment at J-PARC

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Procedure for the determination of the sigma term from experimental $\overline{K}N$ scattering amplitudes.

**Figure 2.**Kaonic hydrogen cascade processes, down to the ground state 1s. The ground state is shifted and broadened by the strong interaction [22].

**Figure 3.**The global simultaneous fit for the X-ray energy spectra for hydrogen and deuterium data (see text for details) [28].

**Figure 4.**Simulation of the SIDDHARTA-2 kaonic deuterium spectrum, assuming ${\epsilon}_{1s}$ = −800 eV and ${\mathsf{\Gamma}}_{1s}$ = 750 eV, as well as a K${}_{\alpha}$ yield of 10${}^{-3}$. Simulation for an integrated luminosity of 800 pb${}^{-1}$.

**Figure 5.**E57 simulated kaonic deuterium spectrum, assuming ${\epsilon}_{1s}$ = −800 eV and ${\mathsf{\Gamma}}_{1s}$ = 750 eV and a K${}_{\alpha}$ yield of 10${}^{-3}$. Simulation for four weeks of beam time and 40 kW proton beam power.

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**MDPI and ACS Style**

Curceanu, C.; Guaraldo, C.; Sirghi, D.; Amirkhani, A.; Baniahmad, A.; Bazzi, M.; Bellotti, G.; Bosnar, D.; Bragadireanu, M.; Cargnelli, M.;
et al. Kaonic Atoms to Investigate Global Symmetry Breaking. *Symmetry* **2020**, *12*, 547.
https://doi.org/10.3390/sym12040547

**AMA Style**

Curceanu C, Guaraldo C, Sirghi D, Amirkhani A, Baniahmad A, Bazzi M, Bellotti G, Bosnar D, Bragadireanu M, Cargnelli M,
et al. Kaonic Atoms to Investigate Global Symmetry Breaking. *Symmetry*. 2020; 12(4):547.
https://doi.org/10.3390/sym12040547

**Chicago/Turabian Style**

Curceanu, Catalina, Carlo Guaraldo, Diana Sirghi, Aidin Amirkhani, Ata Baniahmad, Massimiliano Bazzi, Giovanni Bellotti, Damir Bosnar, Mario Bragadireanu, Michael Cargnelli,
and et al. 2020. "Kaonic Atoms to Investigate Global Symmetry Breaking" *Symmetry* 12, no. 4: 547.
https://doi.org/10.3390/sym12040547