On low-energy pion-pion scattering lengths

C. S. Lai

doi:10.1007/bf02731801

The kaonic atoms research program at DAΦNE: from SIDDHARTA to SIDDHARTA-2

EPJ Web of Conferences ◽

10.1051/epjconf/201818101004 ◽

2018 ◽

Vol 181 ◽

pp. 01004 ◽

Cited By ~ 2

Author(s):

A. Scordo ◽

A. Amirkhani ◽

M. Bazzi ◽

G. Bellotti ◽

C. Berucci ◽

...

Keyword(s):

Energy Shift ◽

Theoretical Work ◽

Research Field ◽

Low Energy ◽

Kaonic Hydrogen ◽

Nucleon Scattering ◽

X Ray ◽

Kaonic Atoms ◽

Kaonic Deuterium ◽

Scattering Lengths

The interaction of antikaons with nucleons and nuclei in the low-energy regime represents an active research field in hadron physics with still many important open questions. The investigation of light kaonic atoms, in which one electron is replaced by a negatively charged kaon, is a unique tool to provide precise information on this interaction; the energy shift and the broadening of the low-lying states of such atoms, induced by the kaon-nucleus hadronic interaction, can be determined with high precision from the atomic X-ray spectroscopy, and this experimental method provides unique information to understand the low energy kaon-nucleus interaction at the production threshold. The lightest atomic systems, like the kaonic hydrogen and the kaonic deuterium deliver, in a model-independent way, the isospin-dependent kaon-nucleon scattering lengths. The most precise kaonic hydrogen measurement to-date, together with an exploratory measurement of kaonic deuterium, were carried out in 2009 by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN, combining the excellent quality kaon beam delivered by the collider with new experimental techniques, as fast and very precise X-ray detectors, like the Silicon Drift Detectors. The SIDDHARTA results triggered new theoretical work, which achieved major progress in the understanding of the low-energy strong interaction with strangeness reflected by the antikaon-nucleon scattering lengths calculated with the antikaon-proton amplitudes constrained by the SIDDHARTA data. The most important open question is the experimental determination of the hadronic energy shift and width of kaonic deuterium; presently, a major upgrade of the setup, SIDDHARTA-2, is being realized to reach this goal. In this paper, the results obtained in 2009 and the proposed SIDDHARTA-2 upgrades are presented.

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Relative entropy in scattering and the S-matrix bootstrap

SciPost Physics ◽

10.21468/scipostphys.9.5.081 ◽

2020 ◽

Vol 9 (5) ◽

Author(s):

Anjishnu Bose ◽

Parthiv Haldar ◽

Aninda Sinha ◽

Pritish Sinha ◽

Shaswat Tiwari

Keyword(s):

Relative Entropy ◽

Cross Sections ◽

High Energy ◽

Quantum Field Theories ◽

Superstring Theory ◽

Information Theoretic ◽

Pion Scattering ◽

S Matrix ◽

Information Theoretic Measures ◽

Scattering Lengths

We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include \phi^4ϕ4 theory, chiral perturbation theory (\chi PTχPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In \chi PTχPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the \rhoρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop \chi PTχPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin.

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