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Brief history of the pion–nucleon sigma term

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Abstract

The pion–nucleon sigma term is a quantity involved in many important aspects of particle and nuclear physics. In this review, I show its origin and how it is connected to important questions as the origin of mass of the ordinary matter, studies of dark matter detection and nucleosynthesis. I mention the most common methods used to obtain the sigma term, and comment on the extracted values. As it is shown, the accepted value of the sigma term has been moving from relatively low (\(\sim 40\) MeV) to larger ones (\(\sim 60\) MeV) until today, where this controversy still persist.

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Notes

  1. In the previous equation the \(2 m_N\) in the denominator appears because I used the normalization \(\langle N(p')| N(p)\rangle = (2\pi )^3 2E\, \delta ({\mathbf {p}\,' - \mathbf {p}})\), what will be customary for the rest of the article. Notice also that \(\hat{m}\) arises because we are working in the SU(2) symmetric limit.

  2. Note that the \(1/2m_N\) factor comes from the normalization of the nucleon states.

  3. The other matrix element, \(\langle N(p) | m_s\bar{s}s | N(p)\rangle \) can be estimated with the help of \(\sigma _{\pi N}\), as is shown later.

  4. Only in a relativistic formulation of chiral EFT with baryons the analytic structure is completely preserved. However, since the problematic parts in non-relativistic approaches are the Born terms, and they are subtracted in the Cheng-Dashen theorem, one can still apply it in these versions of the EFT.

  5. The last equality is valid only in a two-flavor approach.

  6. In this section, t refers always to time.

  7. The author provides the value of \(\varSigma \). This number considers the reduction by \(\varDelta _\sigma \).

  8. Notice that the approach of [43] is much closer to [42] than to [30].

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Acknowledgements

I would like to thank C. Alexandrou and N. Kaiser for allowing me to use the Figs. 4 and 2. I want to thank also J. A. Oller for a careful reading of the manuscript.

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  1. University of Alcalá, Nuclear and Particle Physics Group, Department of Physics and Mathematics, 28805, Alcalá de Henares, Madrid, Spain

    J. M. Alarcón

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Alarcón, J.M. Brief history of the pion–nucleon sigma term. Eur. Phys. J. Spec. Top. 230, 1609–1622 (2021). https://doi.org/10.1140/epjs/s11734-021-00145-6

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