Production representation of partial wave scattering amplitudes and the
Han-Qing Zheng
Production representation of partial wave scattering amplitudes and the
The establishment of production representation of partial wave scattering amplitudes is reviewed in the context of quantum field theory. Its relation to the production representation, or Ning Hu representation in quantum mechanical scattering theory is pointed out. One of the most important application of the production representation is the physics of the f0(600) and K(700) scalar hadron resonances, on which we also give a brief review. It is emphasized that all evidences accumulated so far are consistent with the picture that the f0(600) meson is the chiral partner of the Nambu-Goldstone bosons in a linear realization of chiral symmetry.
scalar mesons / chiral symmetry / unitarization
[ait1] |
M. H. Johnson and E. Teller, Classical field theory of nuclear forces, Phys. Rev., 1955, 98(3): 783
CrossRef
ADS
Google scholar
|
[ait2] |
M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cim., 1960, 16(4): 705
CrossRef
ADS
Google scholar
|
[ait3] |
S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (I), Phys. Rev., 1969, 177(5): 2239
CrossRef
ADS
Google scholar
|
[ait4] |
C. G. Callan, S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (II), Phys. Rev., 1969, 177(5): 2247
CrossRef
ADS
Google scholar
|
[ait5] |
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity (I), Phys. Rev., 1961, 122(1): 345
CrossRef
ADS
Google scholar
|
[ait6] |
K. C. Chou, On the pseudovector current and lepton decays of baryons and mesons, Soviet Physics JETP, 1961, 12: 492
|
[ait7] |
S. Weinberg, Phenomenological Lagrangians, Physica A, 1979, 96(1-2): 327
CrossRef
ADS
Google scholar
|
[ait8] |
J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys., 1984, 158(1): 142
CrossRef
ADS
Google scholar
|
[ait9] |
For a review, see, N. A. Tornqvist, Invited talk at YITP Workshop on Possible Existence of the Sigma Meson and Its Implications to Hadron Physics, Kyoto, Japan, <day>12-14</day><month>Jun</month>. 2000, arXiv: hep-ph/0008135, and reference therein.
|
[ait10] |
L. Y. Xiao, H. Q. Zheng, and Z. Y. Zhou, Lightest scalars as chiral partners of the Nambu-Goldstone bosons, Nucl. Phys. Proc., 2007, 174(Suppl. 174): 142
CrossRef
ADS
Google scholar
|
[ait11] |
G. Grayer, B. Hyams, C. Jones, P. Schlein, P. Weilhammer, W. Blum, H. Dietl, W. Koch, E. Lorenz, G. Lütjens, W. Männer, J. Meissburger, W. Ochs, and U. Stierlin, High statistics study of the reaction
|
[ait12] |
W. Ochs, Ph.D. thesis, Munich University, 1974
|
[ait13] |
W. Maenner, in: Experimental Meson Spectroscopy-1974 (Boston), Proceedings of the fourth International Conference on Meson Spectroscopy, edited by D. A. Garelick, AIP Conf. Proc. 21, 1974
|
[ait14] |
L. Rosselet, P. Extermann, J. Fischer, O. Guisan, R. Mermod, R. Sachot, A. Diamant-Berger, P. Bloch, G. Bunce, B. Devaux, N. Do-Duc, G. Marel, and R. Turlay, Experimental study of 30000 Ke4 decays, Phys. Rev. D, 1977, 15(3): 574
CrossRef
ADS
Google scholar
|
[ait15] |
S. Pislak,
CrossRef
ADS
Google scholar
|
[ait16] |
Z. G. Xiao and H. Q. Zheng, Left-hand singularities, hadron form factors and the properties of the sigma meson, Nucl. Phys. A, 2001, 695(1-4): 273
CrossRef
ADS
Google scholar
|
[ait17] |
Z. G. Xiao and H. Q. Zheng, Further analysis of scattering dispersion relations, Chin. Phys. Lett., 2003, 20(3): 342
CrossRef
ADS
Google scholar
|
[ait18] |
E. M. Aitala,
|
[ait19] |
M. Ablikim,
|
[ait20] |
M. Ablikim,
CrossRef
ADS
Google scholar
|
[ait21] |
D. V. Bugg, The kappa in
|
[ait22] |
E. M. Aitala,
|
[ait23] |
J. M. Link,
|
[ait24] |
J. Y. He, Z. G. Xiao, and H. Q. Zheng, The constraints of unitary on pi pi scattering dispersion relations, Phys. Lett. B, 2002, 536(1-2): 59; Erratum-ibid, 2002, 549(3-4): 362
|
[ait25] |
Z. G. Xiao and H. Q. Zheng, Further analysis of scattering dispersion relations, Chin. Phys. Lett., 2003, 20(3): 342
CrossRef
ADS
Google scholar
|
[ait26] |
Z.-Y. Zhou, G.-Y. Qin, P. Zhang, Z.-G. Xiao, H.-Q. Zheng, and N. Wu, The pole structure of the unitary, crossing symmetric low energy ππ scattering amplitudes, J. High Energy Phys., 2005, 0502: 043
|
[ait27] |
H. Q. Zheng, Z. Y. Zhou, G. Y. Qin, Z. G. Xiao, J. J. Wang, and N. Wu, The k resonance in s wave pK scatterings, Nucl. Phys. A, 2004, 733(3-4): 235
CrossRef
ADS
Google scholar
|
[ait28] |
Z. Y. Zhou and H. Q. Zheng, An improved study of the kappa resonance and the non-exotic s wave pK scatterings up to of LASS data, Nucl. Phys. A, 2006, 775(3-4): 212
CrossRef
ADS
Google scholar
|
[ait29] |
N. Hu, On the application of Heisenberg’s theory of S-matrix to the problems of resonance scattering and reactions in nuclear physics, Phys. Rev., 1948, 74(2): 131
CrossRef
ADS
Google scholar
|
[ait30] |
Z. G. Xiao and H. Q. Zheng, Use of dispersion relations in pp and K [unknown entity & Kmacr] coupled-channel system, Commun. Theor. Phys., 2007, 48(4): 685
CrossRef
ADS
Google scholar
|
[ait31] |
Z. G. Xiao and H. Q. Zheng, Analyticity and the Nc counting rule of S matrix poles, Mod. Phys. Lett. A, 2007, 22(01): 55
CrossRef
ADS
Google scholar
|
[ait32] |
Z. H. Guo, J. J. Sanz-Cillero, and H. Q. Zheng, Partial waves and large Nc resonance sum rules, J. High Energy Phys., 2007, 0706: 030, arXiv: hep-ph/0701232
|
[ait33] |
Z. H. Guo, J. J. Sanz-Cillero, and H. Q. Zheng, extension of the large-partial wave dispersion relations, Phys. Lett. B, 2008, 661(5): 342
CrossRef
ADS
Google scholar
|
[ait34] |
Z. H. Guo and J. J. Sanz-Cillero, ππ-scattering lengths at O(p6) revisited, Phys. Rev. D, 2009, 79(9): 096006
CrossRef
ADS
Google scholar
|
[ait35] |
I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett., 2006, 96(13): 132001
CrossRef
ADS
Google scholar
|
[ait36] |
D. Aston,
|
[ait37] |
S. Descotes-Genon and B. Moussallam, The K* 0(800) scalar resonance from Roy-Steiner representations of πK scattering, Eur. Phys. J. C, 2006, 48(2): 553
CrossRef
ADS
Google scholar
|
[ait38] |
For an incomplete list of early references, see for example, H. Q. Zheng, Plenary talk given at conference Chiral 07, Mod. Phys. Lett. A, 2008, 23: 2218
CrossRef
ADS
Google scholar
|
[ait39] |
M. X. Su, L. Y. Xiao, and H. Q. Zheng, On the scalar nonet in the extended Nambu-Jona-Lasinio model, Nucl. Phys.A, 2007, 792(3-4):
CrossRef
ADS
Google scholar
|
[ait40] |
Z. X. Sun, L. Y. Xiao, Z. G. Xiao, and H. Q. Zheng, Model dependent analyses on the Nc dependence of the sigma pole trajectory, Mod. Phys. Lett. A, 2007, 22: 711
CrossRef
ADS
Google scholar
|
[ait41] |
Z. G. Xiao and H. Q. Zheng, Analyticity and the Nc counting rule of S matrix poles, Mod. Phys. Lett. A, 2007, 22(01): 55
CrossRef
ADS
Google scholar
|
[ait42] |
Z. H. Guo, L. Y. Xiao, and H. Q. Zheng, Is the f0(600) meson a dynamically generated resonance? A lesson learned from the O(N) model and beyond, Int. J. Mod. Phys. A, 2007, 22(26): 4603
|
[ait43] |
Y. Mao, X. G. Wang, O. Zhang, H. Q. Zheng, and Z. Y. Zhou, Dispersive analysis on the f0(600) and f0(980) resonances in
|
[ait44] |
G. Mennessier, S. Narison, and W. Ochs, Glueball nature of the from pp and γγ scatterings, Phys. Lett. B, 2008, 665(4): 205
CrossRef
ADS
Google scholar
|
[ait45] |
X. G. Wang, O. Zhang, L. C. Jin, H. Q. Zheng, and Z. Y. Zhou, Investigations on the property of f0(600) and f0(980) resonances in
|
[ait46] |
M. R. Pennington, T. Mori, S. Uehara, and Y. Watanabe, Amplitude analysis of high statistics results on
|
[ait47] |
See for example the compilation in: M. Hoferichter, D. R. Phillips, and C. Schat, Roy-Steiner equations for
|
/
〈 | 〉 |