# What is a sigma meson? [duplicate]

I have seen some articles talking about the role of sigma meson in nuclear force, but more articles omit it and only mention pion, rho and omega (e.g., Wikipedia). What is this sigma meson?

## marked as duplicate by Cosmas Zachos, Qmechanic♦Sep 16 '16 at 17:20

• If I am not mistaken $\sigma$ refers to scalar mesons (total spin 0 and even parity $JP=0^+$) in general. As @annav pointed out one candidate is $f_0(500)$. Especially in effective theories of the nuclear force mesons are quiet important since there are many models describing the nuclear force with the exchange of those mesons: exchange models (see Pion-exchange model, Yukawa potential,...). How ever I think in a more modern view one uses chiral EFT with multiple pion exchanges to model the nuclear interaction. – M. J. Steil Sep 16 '16 at 14:04
• Related to 241162. – Cosmas Zachos Sep 16 '16 at 14:14
• @Cosmas Zachos Yes that one is asking the same thing. I did not find that question probably because it did not mention the word "meson." And it seems sigma may not be a meson. – Fan Sep 16 '16 at 15:46
• Well, it is a spinless state, and the PDG lists it under mesons when it does. It may not be wise to jam states through a narrow filter according to their quark interpretation. Their internal logic almost always runs on symmetry. – Cosmas Zachos Sep 16 '16 at 16:54
• @Cosmas Zachos Could you mark this as duplicate? – Fan Sep 16 '16 at 16:58

For example.

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: f0(500).

Here it is as f_0 (500).

The dominant decay mode is pi-pi . I expect it is used in nuclear physics as one of the particle exchanges in the models.

Abstract from arXiv:1205.6606

On the size of the sigma meson and its nature

In this work the nature of the $\sigma$ or $f_0(600)$ resonance is discussed by evaluating its quadratic scalar radius, $r^2$. This allows one to have a quantitative estimate for the size of this resonance. We obtain that the $\sigma$ resonance is a compact object with $r^2=(0.19\pm0.02)-i(0.06\pm 0.02)$ $fm^2$. Within our approach, employing unitary chiral perturbation theory, the $\sigma$ is a dynamically generated resonance that stems from the pion-pion interactions. Given its small size we conclude that the two pions inside the resonance are merged. A four-quark picture is then more appropriate. However, when the pion mass increases, for pion masses somewhat above 400 MeV, the picture of a two-pion molecule is the appropriate one. The $\sigma$ is then a spread $\pi\pi$ bound state.

• The link does not seem to be available. So this reference thinks sigma is a tetraquark instead of a meson? – Fan Sep 16 '16 at 15:40
• Hi Fan, sorry, link is ok now. To come straight to it, anna v or any of the other people who provide you with an answer would help you far better than me, ( I self study), so rather than waste your time with my ignorance , you could ask them. Sorry for not being of more help. – user108787 Sep 16 '16 at 15:47
• But having said that, yes I would intrepret A four-quark picture is then more appropriate as agreeing with you, subject to the caveat in the line below that in the abstract above. Best of luck with your question. – user108787 Sep 16 '16 at 15:50
• I believe that Ernest Sternglass [book: BEFORE THE BIG BANG (1997)] says of this mysterious little rascal that it's composed of four pi-mesons, but is "stable against decay into four pi-mesons" because its mass [500 Mev] is slightly less than the mass of four pi-mesons. He says that, however, it can decay into two pi-mesons, because the other two can annihilate and give their energy to the two which survive, which then use this additional energy to speed away from the decay-site at a very-rapid rate. If I can find a proper reference for this bold statement, then I will post it here. :-) – PERFESSER CREEK-WATER Mar 15 '18 at 4:50
• The reference which relates to my previous comment: In his presentation at 1965's Second Topical Conference on Resonant Particles, Athens, Ohio, Sternglass says: "The pi+ pi- decay of the 4-pi [tetrahedral] system is ... energetically stable against decay into 4 pions of total mass 560 MeV. Decay into 2 pions is possible since the remaining pair can annihilate each other, the energy being given to the other 2 pions" {pages 39 and 41} file:///home/chronos/u-5d5d965f442b7fd0c946a20071f8247ac34924d7/Downloads/Sternglass%20Proceedings%202nd%20top%20conf%20Resonant%20Particles%201965.PDF – PERFESSER CREEK-WATER Mar 26 '18 at 19:31