# Kaonic Atoms to Investigate Global Symmetry Breaking

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{9}

^{*}

## Abstract

**:**

## 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

## References

- Guaraldo, C. The DEAR physics programme. Phys. Detect. DAΦNE
**1999**, XVI, 643–658. [Google Scholar] - Reya, C. Chiral symmetry breaking and meson-nucleon sigma commutators: A Review. Rev. Mod. Phys.
**1974**, 46, 545–580. [Google Scholar] [CrossRef] - Cheng, T.P.; Dashen, R.T. Experimental test of time-reversal invariance in the reaction np → γd. Phys. Rev. Lett.
**1971**, 26, 1659–1662. [Google Scholar] - Altarelli, G.; Cabibbo, N.; Maiani, L. The sigma term and low-energy π-n scattering. Nucl. Phys. B
**1971**, 34, 621–631. [Google Scholar] [CrossRef] - Gasser, J.; Sainio, M.E. Sigma term physics. Phys. Detect. DADAΦNE
**1999**, XVI, 659. [Google Scholar] - Pavan, M.M.; Arndt, R.A.; Strakovsky, I.I.; Workman, R.I. New Result for the Pion-Nucleon Sigma Term from an Updated VPI/GW Pion-Nucleon Partial-Wave and Dispersion Relation Analysis. PiN Newslett.
**1999**, 15, 118–192. [Google Scholar] - Bottino, A.; Donato, F.; Fornengo, N.; Scopel, S. Size of the neutralino nucleon cross-section in the light of a new determination of the pion nucleon sigma term. Astropart. Phys.
**2002**, 18, 205–211. [Google Scholar] [CrossRef][Green Version] - Koch, R. A New Determination of the πN Sigma Term Using Hyperbolic Dispersion Relations in the (ν
^{2}, t) plane. Z. Phys. C**1982**, 15, 161–168. [Google Scholar] [CrossRef] - Jaffe, R.L. The Sigma Term Revisited. Phys. Rev. D
**1980**, 21, 3215–3224. [Google Scholar] [CrossRef] - Pagels, H.J.; Pardee, W.J. Nonanalytic behavior of the sigma term in π-n scattering. Phys. Rev. D
**1971**, 4, 3335–3337. [Google Scholar] [CrossRef] - Jaffe, R.L.; Korpa, C.L. The Pattern of Chiral Symmetry Breaking and the Strange Quark Content of the Proton. Comments Nucl. Part. Phys.
**1987**, 17, 163–175. [Google Scholar] - Di Claudio, B.; Violini, G.; Rodríguez-Vergas, A.M. Uncertainties on the Determination of KNΣ Term Due to K
^{−}N Unphysical and Low-energy Region. Lett. Nuovo Cimento**1979**, 26, 555–561. [Google Scholar] [CrossRef] - Di Claudio, B.; Rodríguez-Vergas, A.M.; Violini, G. The Adler-Weisberger sum rule and the σ-commutator for the kaon-proton system. Z. Phys. C
**1979**, 3, 75–82. [Google Scholar] [CrossRef] - Rodríguez-Vergas, A.M.; Violini, G. The Adler-Weisberger sum rule and the σ-commutator for the kaon-neutron system. Z. Phys. C
**1980**, 4, 135–139. [Google Scholar] [CrossRef] - Martin, A.D.; Violini, G. The Zero Energy Kp Scattering Amplitude and the Evaluation of the Kaon-Nucleon Σ Terms. Lett. Nuovo Cimento
**1981**, 30, 105–110. [Google Scholar] [CrossRef] - Chen, H.-X.; Dimitrasinovic, V.; Hosaka, A. Baryon fields with U
_{L}(3) × U_{R}(3) chiral symmetry: Axial currents of nucleons and hyperons. Phys. Rev. D**2010**, 81. [Google Scholar] [CrossRef][Green Version] - Chen, H.-X.; Dimitrasinovic, V.; Hosaka, A. Baryon fields with U
_{L}(3) × U_{R}(3) chiral symmetry. IV. Interactions with chiral (8,1) ⨁ (1,8) vector and axial-vector mesons and anomalous magnetic moments. Phys. Rev. C**2012**, 85, 055205(1)–055205(10). [Google Scholar] [CrossRef][Green Version] - Chen, H.-X.; Dimitrasinovic, V.; Hosaka, A.; Nagata, K.; Zhu, S.-L. Chiral properties of baryon fields with flavor SU(3) symmetry. Phys. Rev. D
**2008**, 78. [Google Scholar] [CrossRef][Green Version] - Alexandrou, C.; Drach, V.; Jansen, K.; Kallidonis, C.; Koutsou, G. Baryon spectrum with N
_{f}= 2 + 1 + 1 twisted mass fermions. Phys. Rev. D**2014**, 90, 074501(1)–074501(29). [Google Scholar] [CrossRef][Green Version] - Torrero, C. Computing the nucleon sigma terms at the physical point. In Proceedings of the 32nd International Symposium on Lattice Field Theory, New York, NY, USA, 23–28 June 2014. [Google Scholar]
- Dalitz, R.H.; McGinley, J.; Belyea, C.; Anthony, S. Theory of Low-energy Kaon-Nucleon Scattering. In Proceedings of the International Conference on Hypernuclear and Kaon Physics, Heidelberg, Germany, 20–24 June 1982; pp. 201–214. [Google Scholar]
- Zmeskal, J. From kaonic atoms to kaonic nuclei: A search for antikaon-mediated bound nuclear systems. Part. Nucl. Phys.
**2008**, 61, 512–550. [Google Scholar] [CrossRef] - Iwasaki, M.; Bartlett, K.; Beer, G.A.; Gill, D.R.; Hayano, R.S.; Ito, T.M.; Lee, L.; Mason, G.; Nakamura, S.N.; Olin, A.; et al. Discovery of the repulsive energy shift of the kaonic hydrogen 1s state. Nucl. Phys. A
**1998**, 639, 501c–510c. [Google Scholar] [CrossRef] - Deser, S.; Goldberger, M.L.; Baumann, K.; Thirring, W. Energy Level Displacements in Pi-Mesonic Atoms. Phys. Rev.
**1954**, 96, 774–776. [Google Scholar] [CrossRef] - Trueman, T.L. Energy level shifts in atomic states of strongly-interacting particles. Nucl. Phys.
**1961**, 26, 57–67. [Google Scholar] [CrossRef] - Meißner, U.-G.; Raha, U.; Rusetsky, A. Kaon-nucleon scattering lengths from kaonic deuterium experiments. Eur. Phys. J. C
**2006**, 47, 473–480. [Google Scholar] [CrossRef][Green Version] - Meißner, U.-G.; Raha, U.; Rusetsky, A. Spectrum and decays of kaonic hydrogen. Eur. Phys. J. C
**2004**, 35, 349–357. [Google Scholar] [CrossRef][Green Version] - Bazzi, M.; Beer, G.; Bombelli, L.; Bragadireanu, A.; Cargnelli, M.; Corradi, G.; Curceanu (Petrascu), C.; d’Uffizi, A.; Fiorini, C.; Frizzi, T.; et al. A new measurement of kaonic hydrogen X-rays. Phys. Lett. B
**2011**, 704, 113–117. [Google Scholar] [CrossRef][Green Version] - Beer, G.; Bragadireanu, A.M.; Cargnelli, M.; Curceanu-Petrascu, C.; Egger, J.P.; Fuhrmann, H.; Guaraldo, C.; Iliescu, M.; Ishiwatari, T.; Itahashi, K.; et al. Measurement of the kaonic hydrogen X-ray spectrum. Phys. Rev. Lett.
**2005**, 94, 212302. [Google Scholar] [CrossRef][Green Version] - Hashimoto, T.; Ajimura, S.; Beer, G.; Bhang, H.; Bragadireanu, M.; Busso, L.; Cargnelli, M.; Choi, S.; Curceanu, C.; Enomoto, S.; et al. Search for the deeply bound K
^{−}pp state from the semi-inclusive forward-neutron spectrum in the in-flight K^{−}reaction on helium-3. Prog. Theor. Exp. Phys.**2015**, 2015. [Google Scholar] [CrossRef][Green Version]

**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.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Curceanu, C.; Guaraldo, C.; Sirghi, D.; Amirkhani, A.; Baniahmad, A.; Bazzi, M.; Bellotti, G.; Bosnar, D.; Bragadireanu, M.; Cargnelli, M.; Carminati, M.; Clozza, A.; De Paolis, L.; Del Grande, R.; Fiorini, C.; Iliescu, M.; Iwasaki, M.; King, P.; Levi Sandri, P.; Marton, J.; Miliucci, M.; Moskal, P.; Niedźwiecki, S.; Okada, S.; Piscicchia, K.; Scordo, A.; Silarski, M.; Sirghi, F.; Skurzok, M.; Spallone, A.; Tüchler, M.; Utica, G.; Vazquez Doce, O.; Zmeskal, J. 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, Carminati M, Clozza A, De Paolis L, Del Grande R, Fiorini C, Iliescu M, Iwasaki M, King P, Levi Sandri P, Marton J, Miliucci M, Moskal P, Niedźwiecki S, Okada S, Piscicchia K, Scordo A, Silarski M, Sirghi F, Skurzok M, Spallone A, Tüchler M, Utica G, Vazquez Doce O, Zmeskal J. 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, Marco Carminati, Alberto Clozza, Luca De Paolis, Raffaele Del Grande, Carlo Fiorini, Mihail Iliescu, Masahiko Iwasaki, Pietro King, Paolo Levi Sandri, Johann Marton, Marco Miliucci, Paweł Moskal, Szymon Niedźwiecki, Shinji Okada, Kristian Piscicchia, Alessandro Scordo, Michał Silarski, Florin Sirghi, Magdalena Skurzok, Antonio Spallone, Marlene Tüchler, Gianlorenzo Utica, Oton Vazquez Doce, and Johann Zmeskal. 2020. "Kaonic Atoms to Investigate Global Symmetry Breaking" *Symmetry* 12, no. 4: 547.
https://doi.org/10.3390/sym12040547