Advertisement

A current algebra description of kaon-nucleus scattering lengths

  • P. M. Gensini
Article
  • 17 Downloads

Summary

Current algebra sum rules for kaon-nucleus elastic-scattering amplitudes are re-written as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the meson-nucleus continua and in the bound-state spectra, we produce a general formula for the dependence of the real parts of kaon-nucleus scattering lengths on the target quantum numbers. We introduce explicitly a shell-model description of nuclear ground-states, which was instrumental in reproducing with satisfactory accuracy the corresponding pion-nucleus data: most of the effects observed there (up to and including the 2s−1d shell) were consistent with a naive spherical-harmonic-oscillator picture. An output of this analysis is the (average) kaon-nucleon sigma-term: the value derived here stays as large as found in two previous estimates by ourselves, the first from a slightly less sophisticated analysis of (mostly) the same data, the second derived from the dispersion-relation evaluations of the zero-energy, fixed-t kaon-nucleon scattering amplitudes made by Oades. Such a large value (about 640 MeV) confirms the hypothesis, advanced by Donoghue and Nappi, of a large, nonperturbative, strange-quark scalar density in the nucleon.

PACS

11.30.Rd - Chiral symmetries 

PACS

11.50.Li - Sum rules 

PACS

25.80.Nv - Kaon-nucleus elastic scattering 

Описание с помощью алгебры токов длин рассеяния каонов на ядрах

Резюме

Мы занов записываем правила сумм алгебры токов для амплитуд упругого рассеяния каонов на ядрах в виде дисперсионных соотношений в направлении вперед, вне массовой поверхности. Насыщая последние с узкими уровнями, в непрерывном и дискретном мезон-qjдерных спектрах, мы воспроизводим обшую формулу для зависимости вещественных частей длин каон-ядерного рассеяния от квантовых чисел мишени. Мы явно вводим описание модели оболочек для основных состояний ядер, которое дает удовлетворительнуй точность для соответствующих пион-ядерных данных. Большинство наблюдаемых эффектов согласуется с картиной сферического гармонического осциллятора. Из нашего анализа получается (средний) каон-нуклонный сигма-член. Полученная величина является такой же большой, как и в случае двух предыдущих оценок, проведенных нами сначала из менее сложного анализа тех же данных, а затем из анализа дисперсионных соотношений для амплитуд каон-нуклонного рассеяния при фиксированномt, проведенного Оадсом. такая большая величина (около 600 МэВ) подтверждает гипотезу Донохью и Наппи о больмой, непертурбационной скалярной плотности странных кварков в нуклоне.

Riassunto

Si riscrivono le regole di somma dell'algebra delle correnti in forma di relazioni di dispersione su contorno finito per le ampiezze di diffusione in avanti, fuori del “mass-shell”. Saturando poi queste relazioni con livelli stretti, sia nel continuo che sotto soglia, troviamo una formula per esprimere la dipendenza dai numeri quantici del nucleo bersaglio delle parti reali delle lunghezze di diffusione K-nucleo. Viene esplicitamente introdotta una descrizione di modello “a strati” per gli stati fondamentali dei nuclei, rivelatasi essenziale per riprodurre accuratamente gli stessi dati per la diffusione π--nucleo: gran parte degli effetti osservati erano spiegati con un semplice modello di oscillatore armonico sferico fino allo strato 1d–2s incluso. Un risultato di questa analisi è il valore medio per i nucleoni del termine sigma KN: confermiamo qui il valore abbastanza grande trovato in analisi precedenti degli stessi dati, come pure in un'estrapolazione analitica delle ampiezze elastiche KN ad energia nulla. Un valore cosí grande (circa 640 MeV) conferma l'ipotesi avanzata da Donoghue e Nappi di una apprezzabile densità scalare (non perturbativa) di quark strani nel nucleone.

References

  1. [1]
    R. L. Jaffe andC. L. Kopra:comments Nucl. Part. Phys.,17, 163 (1987);R. L. Jaffe:Nucl. Phys. A,478, 3c (1988);K. K. Seth:Perspectives in Nuclear Physics at Intermediate Energies, 3rd Workshop, edited byS. Boffi, C. Ciofi Degli Atti andM. M. Giannini (Singapore, 1988), p. 37.Google Scholar
  2. [2]
    J. Gasser:Ann. Phys. (N. Y.),136, 62 (1981); Physics with Light Mesons and 2nd International Workshop on\(\pi \mathcal{N}\) Physics, edited byW. R. Gibbs andB. M. K. Nefkens (Los Alamos, NM, 1987), p. 266.CrossRefADSGoogle Scholar
  3. [3]
    J. F. Donoghue andC. R. Nappi:Phys. Lett. B,168, 105 (1986);J. F. Donoghue: Physics with Light Mesons and 2nd International Workshop on\(\pi \mathcal{N}\) physics, edited byW. R. Gibbs andB. M. K. Nefkens (Los Alamos, NM, 1987), p. 283.CrossRefADSGoogle Scholar
  4. [4]
    R. Koch:Z. Phys. C,15, 161 (1982);U. Wiedner, K. Göring, J. Jaki, U. Klein, W. Kluge, H. Matthäy, M. Metzler, E. Pedroni, W. Fetscher, H. J. Gerber andR. Koch:Phys. Rev. Lett.,58, 648 (1987);G. Höhler: Physics with Light Mesons and 2nd International Workshop on\(\pi \mathcal{N}\) Physics, edited byW. R. Gibbs andB. M. K. Nefkens (Los Alamos, NM, 1987), p. 296;W. Kluge:Pion-Nucleus Physics. Future Directions and New Facilities at LAMPF, edited byR. J. Peterson andD. D. Strottman (New York, N. Y., 1988), p. 247.CrossRefADSGoogle Scholar
  5. [5]
    D. B. Kaplan andA. E. Nelson:Phys. Lett. B,175, 57 (1986); Erratum:Phys. Lett. B,179, 409 (1986);Nucl. Phys. A,479, 273c (1988);A. E. Nelson andD. B. Kaplan:Phys. Lett. B,192, 193 (1987);Nucl. Phys. A,479, 285c (1988).CrossRefADSGoogle Scholar
  6. [6]
    G. E. Brown, K. Kubodera andM. Rho:Phys. Lett. B,192, 273 (1987);G. E. Brown, K. Kubodera, D. Page andP. Pizzochero:Phys. Rev. D,37, 2042 (1988);G. E. Brown, K. Kubodera, M. Prakash andM. Rho:Nucl. Phys. A,479, 175c (1988).CrossRefADSGoogle Scholar
  7. [7]
    V. M. Khatsymovsky, I. B. Kriplovich andA. R. Zhitnitsky:Z. Phys. C,36, 455 (1987);I. I. Balitsky, V. M. Braun andA. V. Kolesnichenko:Z. Phys. C,39, 225 (1988);P. M. Gensini: Università di Perugia report DFUPG-12-88 (Perugia, 1988), to be published inNuovo Cimento A.CrossRefADSGoogle Scholar
  8. [8]
    See ref. [3]J. F. Donoghue, andC. R. Nappi:Nuclear Chromodynamics. Quark and Gluons in Particles and Nuclei, edited byS. J. Brodsky andE. Moniz (Singapore, 1986), p. 405.Google Scholar
  9. [9]
    S. Fubini andG. Furlan:Ann. Phys. (N. Y.),48, 322 (1968);V. de Alfaro andC. Rossetti:Nuovo Cimento, Suppl.,6, 575 (1968);V. de Alfaro, S. Fubini, G. Furlan andC. Rossetti:Nuovo Cimento A,62, 497 (1969).CrossRefADSGoogle Scholar
  10. [10]
    S.-S. Shei andH.-S. Tsao:Phys. Rev. D,15, 3049 (1977).CrossRefADSGoogle Scholar
  11. [11]
    G. J. Komen:Nuovo Cimento A,19, 265 (1974). See also the original Weinberg's paper in ref. [21]S. Weinberg:Phys. Rev. Lett.,17, 616 (1966).CrossRefADSGoogle Scholar
  12. [12]
    M. Ericson andM. Rosa-Clot:Phys. Lett. B,188, 11 (1987).CrossRefADSGoogle Scholar
  13. [13]
    See the latest PDG compilation, byM. Aguilar-Benitez et al.:Phys. Lett. B,170, 1 (1986). For the pseudoscalar recurrences, see also the recent review by B. Diekmann:Phys. Rep.,159, 99 (1988).Google Scholar
  14. [14]
    P. M. Gensini:Nuovo Cimento A,17, 557 (1973);A,60, 234 (1980); Erratum:Nuovo Cimento A,63, 256 (1981).CrossRefADSGoogle Scholar
  15. [15]
    P. M. Gensini:Lett. Nuovo Cimento,1, 273 (1971);Nuovo Cimento A,6, 259 (1971); see alsoP. M. Gensini andG. Soliani:Lett. Nuovo Cimento,4, 329 (1970), and the appendix (p. 245-46) to the second paper in ref. [14].P. M. Gensini:Nuovo Cimento A,17, 557 (1973);A,60, 234 (1980); Erratum:Nuovo Cimento A,63, 256 (1981).CrossRefGoogle Scholar
  16. [16]
    C. A. Dominguez:Phys. Rev. D,27, 1572 (1983);Riv. Nuovo Cimento,8, 6 (1985).CrossRefADSGoogle Scholar
  17. [17]
    P. M. Gensini: Università di Perugia report DFUPG-13-88 (Perugia, 1988), to be published inNuovo Cimento A.Google Scholar
  18. [18]
    V. Flaminio, W. G. Moorhead, D. R. O. Morrison andN. Rivoire: CERNHERA report 83-02 (Geneva, 1983).Google Scholar
  19. [19]
    J. M. Eisenberg:Meson-Nuclear Physics 1976, edited byP. D. Barnes, R. A. Eisenstein andL. S. Kisslinger (New York, N. Y., 1976), p. 542;W. Weise andL. Tauscher:Phys. Lett. B,64, 424 (1976);R. Brockman, W. Weise andL. Tauscher:Nucl. Phys. A,308, 365 (1978).Google Scholar
  20. [20]
    B. Povh:Proceedings of the International Conference on Nuclear Physics, Florence, 1983, edited byP. Blasi andR. A. Ricci (Bologna, 1983), p. 455. For discussions of more recent results see,e.g.:H. Feshbach:Nucl. Phys. A,450, 339 (1986);R. E. Chrien, E. V. Hungerford andT. Kishimoto:Phys. Rev. C,35, 1589 (1987);N. Auerbach:Phys. Rev. C,35, 1798 (1987);M. Kohno, R. Hausmann, P. B. Siegel andW. Weise:Nucl. Phys. A,470, 609 (1987);R. Hausmann, P. B. Siegel, W. Weise andM. Kohno:Phys. Lett. B,199, 17 (1987).Google Scholar
  21. [21]
    S. Weinberg:Phys. Rev. Lett.,17, 616 (1966);Y. Tomozawa:Nuovo Cimento A,46, 707 (1966).CrossRefADSGoogle Scholar
  22. [22]
    P. M. Gensini:Lett. Nuovo Cimento,38, 620 (1983);Nuovo Cimento A,78, 471 (1983).CrossRefGoogle Scholar
  23. [23]
    C. J. Batty:Nucl. Phys. A,411, 399 (1983); see alsoC. J. Batty:Nucl. Phys. A,372, 418 (1981).CrossRefADSGoogle Scholar
  24. [24]
    We are grateful to R. Leonardi for clarifying discussions on this point.Google Scholar
  25. [25]
    N. Hoshi andT. Fujita:Meson-Nuclear Physics 1976, edited byP. D. Barnes, R. A. Eisenstein andL. S. Kisslinger (New York, 1976), p. 540;Y.-S. Zhang, Y.-G. Li, W.-W. Wang andT.-N. Ruan:Kexue Tongbao,28, 465 (1983).Google Scholar
  26. [26]
    J. Blomqvist andA. Molinari:Nucl. Phys. A,106, 545 (1968).CrossRefADSGoogle Scholar
  27. [27]
    S. V. Tolokonikov andS. A. Fayans:JETP Lett.,35, 499 (1982), (English translation ofPis'ma Ž. Eksp. Teor. Fiz. 35, 403 (1982)).ADSGoogle Scholar
  28. [28]
    B. Povh:Annu. Rev. Nucl. Part. Sci.,28, 1 (1978);W. Brückner:Nukleonika,25, 427 (1981);R. Bertini:Intermediate Energy Nuclear Physics, edited byR. Bergère, S. Costa andC. Schaerf (Singapore, 1982), p. 383;T. Bressani:Hadronic Physics at Intermediate Energy, edited byT. Bressani andR. A. Ricci (Amsterdam, 1986), p. 259.CrossRefADSGoogle Scholar
  29. [29]
    We thank S. Fantoni (private communication) for pointing out these features to us.Google Scholar
  30. [30]
    M. C. Birse andG. A. Miller:Phys. Rev. Lett.,52, 1938 (1984);B. Johnson et al.: Weak and Electromagnetic Interactions in Nuclei, edited byH. V. Klapdor (Berlin, 1986), p. 244.CrossRefADSGoogle Scholar
  31. [31]
    A. D. Martin:Nucl. Phys. B,179, 33 (1981);Intermediate and Low Energy Kaon-Nucleon Physics, edited byE. Ferrari andG. Violini (Reidel, Dordrecht, 1981), p. 97.CrossRefADSGoogle Scholar
  32. [32]
    P. M. Gensini:Z. Phys. C,14, 319 (1982).CrossRefADSGoogle Scholar
  33. [33]
    G. C. Oades:Low and Intermediate Energy Kaon-Nucleon Physics, edited byE. Ferrari andG. Violini (Reidel, Dordrecht, 1981), p. 53;N. M. Queen:Low and Intermediate Energy Kaon-Nucleon Physics, edited byE. Ferrari andG. Violini (Reidel, Dordrecht, 1981), p. 115;G. Violini:Low and Intermediate Energy Kaon-Nucleon Physics, edited byE. Ferrari andG. Violini (Reidel, Dordrecht, 1981), p. 161.CrossRefGoogle Scholar
  34. [34]
    P. M. Gensini:J. Phys. G,7, 1177 (1981);Nuovo Cimento A,84, 203 (1984); Physics with Light Mesons and 2nd International\(\pi \mathcal{N}\) Workshop, edited byW. R. Gibbs andB. M. K. Nefkens (Los Alamos, NM, 1987), p. 301.CrossRefADSGoogle Scholar
  35. [35]
    See also, forf π:S. A. Coon andM. D. Scadron:Phys. Rev. C,23, 1150 (1981).CrossRefADSGoogle Scholar
  36. [36]
    V. P. Efrosinin andD. A. Zaikin:Sov. J. Nucl. Phys.,46, 117 (1987) (English translation ofYad. Fiz.,46, 190 (1987)).Google Scholar
  37. [37]
    M. Ericson andM. Rho:Phys. Lett. B,36, 93 (1971);V. P. Efrosinin andD. A. Zaikin:Z. Phys. A,318, 357 (1984);Sov. J. Nucl. Phys.,39, 717 (1984) (English translation ofYad. Fiz.,39, 1135 (1984);Sov. J. Part. Nucl.,16, 593 (1985) (English translation ofFiz. Elem. Chastists At. Yadra,16, 1330 (1985)).CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1990

Authors and Affiliations

  • P. M. Gensini
    • 1
  1. 1.Dipartimento di Fisica dell'Università and I.N.F.N.Perugia

Personalised recommendations