Il Nuovo Cimento A (1965-1970)

, Volume 41, Issue 1, pp 73–95 | Cite as

Meson-meson scattering amplitudes in the modifiedK-matrix formalism

  • C. B. Lang


On the basis of a modified definition of theK-matrix we construct amplitudes for low-energy ππ, K\(\overline {\text{K}} \) and πK scatterings. An iteration scheme allows us to account for crossing symmetry and coupled-channel unitarity. We find that we have to include information on the masses and widths of the possible resonances—they cannot be predicted in this framework. As a result we present partial-wave amplitudes that agree well with experiments. Conclusions on several features of meson-meson scattering can be drawn.

Амплитуда рассеяния меэона на меэоне в формалиэме модифицированнойK-матрицы


На основе модифицированного определенияK-матрицы мы кон?струируем амплитуды для ππ, K\(\overline {\text{K}} \) и πK рассеяния при ниэких знергиях. Схема итераций поэволяет общяснить кроссинг-симметрию и инвариантность свяэанных каналов. Мы находим, что необходимо включить информацию о массах и щиринах воэможных реэонансов, т.к. зти величины не могут быть предскаэаны в зтом подходе. Мы приводим парциальные амплитуды, которые хорощо согласуются с зкспериментами. На основе зтих реэультатов можно сделать ряд эаключений о некоторых особенностях меэон-меэонного рассеяния.


Si costruiscono le ampiezze degli scattering a bassa energia ππ, K\(\overline {\text{K}} \) e πK sulla base di una definizione modificata della matriceK. Uno schema di iterazione ci permette di spiegare la simmetria d’incrocio e l’unitarietà dei canali accoppiati. Si trova che bisogna includere informazioni sulle masse e le ampiezze delle possibili risonanze — esse non possono essere predette in questo contesto. Come risultato si presentano ampiezze dell’onda parziale che sono in buon accordo con gli esperimenti. Si possono trarre delle conclusioni riguardo a molte caratteristiche dello scattering mesone-mesone.


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  1. (1).
    J. L. Basdevant, C. D. Froggatt andJ. L. Petersen:Nucl. Phys.,72 B, 413 (1974).CrossRefADSGoogle Scholar
  2. (2).
    F. Steiner:Fortschr. Phys.,18, 43 (1970);19, 115 (1971);S. M. Roy:Phys. Lett.,36 B, 353 (1971).CrossRefGoogle Scholar
  3. (3).
    D. Morgan:Phys. Lett.,51 B, 71 (1974);B. R. Martin, D. Morgan andG. Shaw:Pion-Pion Interactions in Particle Physics (New York, N. Y., 1976).CrossRefADSGoogle Scholar
  4. (4).
    H. Nielsen andG. C. Oades:Nucl. Phys.,55 B, 301 (1973).ADSGoogle Scholar
  5. (5).
    N. O. Johannesson andJ. L. Petersen:Nucl. Phys.,68 B, 397 (1974).CrossRefADSGoogle Scholar
  6. (6).
    N. Hedegaard-Jensen:Nucl. Phys.,77 B, 173 (1974).CrossRefADSGoogle Scholar
  7. (7).
    C. B. Lang:Nucl. Phys.,93 B, 429 (1975).CrossRefADSGoogle Scholar
  8. (8).
    D. Atkinson:Nucl. Phys.,7 B, 375 (1968);8 B, 377 (1968);13 B, 415 (1969);23 B, 397 (1970);D. Atkinson, P. W. Johnson andR. L. Warnock:Phys. Rev. D,6, 2966 (1972).CrossRefADSGoogle Scholar
  9. (9).
    C. B. Lang:Nucl. Phys.,93 B, 415 (1975).CrossRefADSGoogle Scholar
  10. (10).
    W. Zimmermann:Nuovo Cimento,21, 249 (1961);D. Branson:Ann. of Phys.,35, 351 (1965);S. Humble:Phys. Rev.,183, 1335 (1969).CrossRefGoogle Scholar
  11. (*).
    This is correct only in the limit in which we have included all possible intermediate and external states. In our model we treat only a small number of allowed states and τ then describes in principle all that is left,i.e. higher cuts, poles, etc. Therefore it is related to the « driving terms » of the Roy equations as discussed by BFP (1). We include thed-waves and some coupled-channel effects explicitly; this justifies the assumptions discussed above.Google Scholar
  12. (11).
    H. P. Jakob andF. Steiner:Zeits. Phys.,228, 353 (1969);H. Nielsen, J. L. Petersen andE. Pietarinen:Nucl. Phys.,22 B, 525 (1970).CrossRefADSGoogle Scholar
  13. (12).
    H. Nielsen:Nucl. Phys.,30 B, 317 (1971);H. Nielsen andG. C. Oades:Nucl. Phys.,49 B, 573, 586 (1972).CrossRefADSGoogle Scholar
  14. (13).
    M. J. Matison, A. Barbaro-Galtieri, M. Alston-Garnjost, S. M. Flatté, J. H. Friedmann, G. R. Lynch, M. S. Rabin andF. T. Solmitz:Phys. Rev. D,9, 1872 (1974);H. H. Bingham, W. M. Dunwoodie, D. Drijard, D. Linglin, Y. Goldschmidt-Clermont, F. Muller, T. Trippe, F. Grard, P. Herquet, J. Naisse, R. Windmolders, E. Colton, P. E. Schlein andW. E. Slater:Nucl. Phys.,41 B, 1 (1972);R. Mercer, P. Antich, A. Callahan, C.-Y. Chien, B. Cox, R. Carson, D. Denegri, L. Ettlinger, D. Feiock, G. Goodmann, J. Haynes, A. Pevsner, R. Sekulin, V. Sreedhar andR. Zdanis:Nucl. Phys.,32 B, 381 (1972);A. Firestone G. Goldhaber, D. Lissauer andG. H. Trilling:Phys. Rev. D,5, 2188 (1972).CrossRefADSGoogle Scholar
  15. (14).
    G. C. Fox andM. L. Griss:Nucl. Phys.,80 B, 403 (1974).CrossRefADSGoogle Scholar
  16. (15).
    S. Weinberg:Phys. Rev. Lett.,17, 616 (1966);R. W. Griffith:Phys. Rev.,176, 1705 (1968);J. L. Petersen:Phys. Rep.,2, 155 (1971).CrossRefADSGoogle Scholar
  17. (16).
    E. Colton, E. Malamud, P. E. Schlein, A. D. Johnson, V. J. Stenger andP. G. Wohlmut:Phys. Rev. D,3, 2028 (1971);D. Cohen, T. Ferbel, P. Slattery andB. Werner:Phys. Rev. D,7, 661 (1973);M. J. Losty, V. Chaloupka, A. Ferrando, L. Montanet, E. Paul, D. Yaffe, A. Zieminski, J. Alitti, B. Gandois andJ. Louie:Nucl. Phys.,69 B, 185 (1974);W. Hoogland, G. Grayer, B. Hyams, C. Jones, P. Weilhammer, W. Blum, H. Dietl, W. Koch, E. Lorenz, G. Lütjens, W. Männer, J. Meissburger andU. Stierlin:Nucl. Phys.,69 B, 266 (1974).CrossRefADSGoogle Scholar
  18. (17).
    A. M. Bakker, W. Hoogland, J. C. Kluyver, G. Giacomelli, P. Lugaresi-Serra, A. M. Rossi, D. Merrill, J. C. Scheuer, G. Lamidey, A. Rougé, A. Shapira andU. Karshon:Nucl. Phys.,24 B, 211 (1970);Y. Cho, M. Derrick, D. Johnson, B. Musgrave, T. Wangler, J. Wong, R. Davis, B. Werner, R. Ammar, W. Kropac andH. Yarger:Phys. Lett.,32 B, 409 (1970);P. Antich, A. Callahan, R. Carson, C.-Y. Chien, B. Cox, D. Denegri, L. Ettlinger, D. Feiock, G. Goodman, J. Haynes, R. Mercer, A. Pevsner, L. Resvanis, R. Sekulin, V. Sreedhar andR. Zdanis:Nucl. Phys.,29 B, 305 (1971);A. R. Kirschbaum, E. Colton, P. M. Dauber, J. H. Friedman andP. E. Schlein:Phys. Rev. D,4, 3254 (1971);D. Linglin:Nucl. Phys.,55 B, 408 (1973);D. Linglin, B. Chaurand, B. Drévillon, G. Labrosse, R. Lestienne, R. A. Salmeron, R. J. Miller, K. Paler, J. J. Phelan, T. P. Shah, R. Barloutaud, A. Borg, C. Louedec, F. Pierre andM. Spiro:Nucl. Phys.,57 B, 64 (1973);B. Jongejans, R. A. van Meurs, A. G. Tenner, H. Voorthuis, P. M. Heinen, W. J. Metzger, H. G. J. M. Tiecke andR. T. Van de Walle:Nucl. Phys.,67 B, 381 (1973).CrossRefADSGoogle Scholar
  19. (18).
    S. D. Protopopescu, M. Alston-Garnjost, A. Barbaro-Galtieri, S. M. Flatté, J. H. Friedman, T. A. Lasinski, G. R. Lynch, M. S. Rabin andF. T. Solmitz:Phys. Rev. D,7, 1279 (1973);B. Hyams, C. Jones, P. Weilhammer, W. Blum, H. Dietl, G. Grayer, W. Koch, E. Lorenz, G. Lütjens, W. Männer, J. Meissburger, W. Ochs, U. Stierlin andF. Wagner:Nucl. Phys.,64 B, 134 (1973);P. Estabrooks andA. D. Martin:Nucl. Phys.,79 B, 301 (1974);W. Männer: contribution to theXVII International Conference on High-Energy Physics (London, 1974);C. D. Froggatt andJ. L. Petersen:Nucl. Phys.,91 B, 454 (1975).CrossRefADSGoogle Scholar
  20. (19).
    S. M. Flatté:Phys. Lett.,63 B, 228 (1976).CrossRefADSGoogle Scholar
  21. (20).
    M. Gell-Mann: Caltech Report (TSL-20/1961), unpublished;S. Okubo:Prog. Theor. Phys.,27, 949 (1967).Google Scholar
  22. (21).
    P. Estabrooks andA. D. Martin:Nucl. Phys.,95 B, 322 (1975);B. Hyams, C. Jones, P. Weilhammer, W. Blum, H. Dietl, G. Grayer, W. Koch, E. Lorenz, G. Lütjens, W. Männer, J. Meissburger, W. Ochs andU. Stierlin:Nucl. Phys.,100 B, 205 (1975);W. Wetzel, K. Freudenreich, F. X. Gentit, P. Mühlemann, W. Beusch, A. Birman, D. Websdale, P. Astbury, A. Harckham andM. Letheren:Nucl. Phys.,115 B, 208 (1976).CrossRefADSGoogle Scholar
  23. (22).
    P. Extermann, J. Fischer, O. Guisan, R. Mermod, L. Rosselet, R. Sachot, P. Bloch, G. Bunce, B. Devaux, A. M. Diamant-Berger, N. Do-Duc, G. Marcel andR. Turlay: contribution to theXVIII International Conference on High-Energy Physics, Palermo, June 1975.Google Scholar
  24. (23).
    J. L. Petersen:The ππ interaction, CERN 77-04, lecture given at CERN (April 1976).Google Scholar
  25. (24).
    B. Bonnier andN. Johannesson:Nucl. Phys.,101 B, 72 (1975).CrossRefADSGoogle Scholar
  26. (25).
    M. M. Nagels, J. J. de Swart, H. Nielsen, G. C. Oades, J. L. Petersen, B. Tromborg, G. Gustafson, A. C. Irving, C. Jarlskog, W. Pfeil, H. Pilkuhn, F. Steiner andL. Tauscher:Nucl. Phys.,109 B, 1 (1976).MATHCrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1977

Authors and Affiliations

  • C. B. Lang
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GrazGrazAustria

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