Summary
An analysis of the energy of the\(\overline K \mathcal{N}\) S-wave scattering lengths near the threshold is performed with the following hypotheses: the Y* can be regarded as an unstable particle with complex mass, which is coupled to the states having its same quantum numbers, dominating the nearby energy regions. The spin of the Y* is assumed to be 1/2. For simplicity’s sake only theI=0 isospin state is discussed.
Riassunto
Si analizza il comportamento energetico vicino alla soglia delle lunghezze di scattering in ondaS del\(\overline K \mathcal{N}\) con le seguenti ipotesi: l’Y* può essere considerato come una particella instabile con massa complessa accoppiata agli stati che hanno i suoi stessi numeri quantici, dominando il circostante intervallo energetico. Lo spin dell’Y* è assunto eguale a 1/2. Per semplicità si discute solo lo stato di spin isotopicoI=0.
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References
For the experimental status of the Y* seeF. T. Solmitz:The Aix en Provence Intern. Conf. on Elementary Particles, vol.2 (C.E.N. Saclay, 1961), p. 177, and for a review of the theoretical discussions seeA. Salam:The Aix en Provence Intern. Conf. on Elementary Particles, vol.2 (C.E.N. Saclay, 1961), p. 191. The Y*s pins are up today rather uncertain, but here we shall assume that the Y*0 have spin 1/2. The [ΣΛ] parity is assumed to be even.
See, for example,R. Zumino: inLectures on Field Theory, edited byE. R. Caianiello (New York, 1961), p. 37.
For a derivation of the partial waves in the many-channel case see, for example,F. Ferrari, G. Frye andM. Pusterla:Phys. Rev.,123, 308 (1961).
R. H. Dalitz: quoted in footnote (2). Other details on the scattering lengths can be found in the review ofDalitz inAix en Provence Proc., quoted in (1), p. 151.R. Ross: UCRL-9749 (June 1961);W. E. Humphrey: UCRL-9752 (June 1961).
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Pagiola, E. Effects of the Y* on the\(\overline K - \mathcal{N}\) low energyS-wave parameterslow energyS-wave parameters. Nuovo Cim 25, 169–174 (1962). https://doi.org/10.1007/BF02733321
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DOI: https://doi.org/10.1007/BF02733321