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Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances \(\sigma /f_0(500) \) and \(\kappa /K_0^*(700) \)

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Abstract

For several decades, the \(\sigma /f_0(500)\) and \(\kappa /K_0^*(700)\) resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review, we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons \(\sigma /f_0(500) \) and \(\kappa /K_0^*(700) \). Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.

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Notes

  1. Although we have quoted the last RPP edition, all previous ones can be found in the Particle Data Group web-page at https://pdg.lbl.gov/rpp-archive/.

  2. Literally, the authors of that compilation wrote: “We are beginning to think that \(\kappa \) should be classified along with flying saucers, the Loch Ness Monster, and the Abominable Snowman”.

  3. See reference 15 in [41].

  4. C. Hanhart. Private communication.

  5. On top of that even with the same method and data there were several ambiguities leading to different possible solutions, like for instance the so-called up or down solutions [13, 14]. Over the years it has been possible to disentangle those ambiguities with other input or dispersion relations [93]. We omit this discussion here and refer the reader to the review in [36] and references therein.

  6. In the literature these are also written as \(\delta _{I\ell },\delta ^{(I)}_\ell \) and \(\eta _{I\ell },\eta ^{(I)}_\ell \) as we will see in several figures of this review.

  7. The only exception is the \(\eta '\) whose huge mass is due to another well-understood effect, which is the chiral anomaly, beyond the scope of this tutorial review.

  8. While this work was in the referee process a review has appeared, where large-\(N_c\) behavior of tetraquarks is reviewed in great detail [212].

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Acknowledgements

We acknowledge J.A. Oller for encouraging us to write a tutorial review on this topic. We thank I. Danilkin for his corrections on the manuscript. This project has received funding from the Spanish Ministerio de Ciencia e Innovación grant PID2019-106080GB-C21 and the European Union’s Horizon 2020 research and innovation program under grant agreement No 824093 (STRONG2020). AR acknowledges the financial support of the U.S. Department of Energy contract DE-SC0018416 at William & Mary, and contract DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab. JRE acknowledges financial support from the Swiss National Science Foundation under Project No. PZ00P2 174228.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad Complutense and IPARCOS, 28040, Madrid, Spain

    José R. Peláez

  2. Department of Physics, College of William and Mary, Williamsburg, VA, 23187, USA

    Arkaitz Rodas

  3. Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA, 23606, USA

    Arkaitz Rodas

  4. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Jacobo Ruiz de Elvira

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  1. José R. Peláez
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  2. Arkaitz Rodas
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  3. Jacobo Ruiz de Elvira
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Correspondence to José R. Peláez.

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Peláez, J.R., Rodas, A. & Ruiz de Elvira, J. Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances \(\sigma /f_0(500) \) and \(\kappa /K_0^*(700) \). Eur. Phys. J. Spec. Top. 230, 1539–1574 (2021). https://doi.org/10.1140/epjs/s11734-021-00142-9

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