Production representation of partial wave scattering amplitudes and the f₀(600) particle

Abstract

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.

Keywords

scalar mesons / chiral symmetry / unitarization

References

[1] M. H. Johnson and E. Teller, Classical field theory of nuclear forces, Phys. Rev., 1955, 98(3): 783

[2] M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cim., 1960, 16(4): 705

[3] S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (I), Phys. Rev., 1969, 177(5): 2239

[4] C. G. Callan, S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (II), Phys. Rev., 1969, 177(5): 2247

[5] Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity (I), Phys. Rev., 1961, 122(1): 345

[6] K. C. Chou, On the pseudovector current and lepton decays of baryons and mesons, Soviet Physics JETP, 1961, 12: 492

[7] S. Weinberg, Phenomenological Lagrangians, Physica A, 1979, 96(1-2): 327

[8] J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys., 1984, 158(1): 142

[9] 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.

[10] 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

[11] 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 π-p→π-π+n: Apparatus, method of analysis, and general features of results at 17 GeV/c, Nucl. Phys. B, 1974, 75(2): 189

[12] W. Ochs, Ph.D. thesis, Munich University, 1974

[13] 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

[14] 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

[15] S. Pislak, . [The E865 Collaboration], High statistics measurement of Ke4 decay properties, Phys. Rev. D, 2003, 67(7): 072004

[16] 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

[17] Z. G. Xiao and H. Q. Zheng, Further analysis of scattering dispersion relations, Chin. Phys. Lett., 2003, 20(3): 342

[18] E. M. Aitala, . [E791 Collaboration], Experimental evidence for a light and broad scalar resonance in DD+→π-π+π+decay, Phys. Rev. Lett., 2001, 86(5): 770

[19] M. Ablikim, . [BESII Collaboration], The sigma pole in J/ψ→ωπ+π-J/ψ→ωπ+π-,Phys. Lett. B, 2004, 598(3-4): 149

[20] M. Ablikim, . [BES Collaboration], Evidence for κ meson production in process, Phys. Lett. B, 2006, 633(6): 681

[21] D. V. Bugg, The kappa in J/ψ↦K+πEur. Phys. J. A, 2005, 25(1): 107; Erratum-ibid, 2005, 26(1):

[22] E. M. Aitala, . [E791 Collaboration], Dalitz plot analysis of the decay D+→K-π+π+ and indication of a low-mass scalar Kπ resonance, Phys. Rev. Lett., 2002, 89(12): 121801

[23] J. M. Link, . [The FOCUS Collaboration], Evidence for new interference phenomena in the decay D+→K-π+μ+v,Phys. Lett. B, 2002, 535(1-4): 43

[24] 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

[25] Z. G. Xiao and H. Q. Zheng, Further analysis of scattering dispersion relations, Chin. Phys. Lett., 2003, 20(3): 342

[26] 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

[27] 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

[28] 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

[29] 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

[30] 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

[31] 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

[32] 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

[33] 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

[34] Z. H. Guo and J. J. Sanz-Cillero, ππ-scattering lengths at O(p6) revisited, Phys. Rev. D, 2009, 79(9): 096006

[35] I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett., 2006, 96(13): 132001

[36] D. Aston, . [LASS Collaboration], A study of K-π+ scattering in the reaction K-p→K-π+n at 11 GeV/c, Nucl. Phys. B, 1988, 296(3): 493

[37] 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

[38] 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

[39] 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):

[40] 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

[41] 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

[42] 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

[43] 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 γγ→π+π-,π0π0 processes, Phys. Rev. D, 2009, 79(11): 116008

[44] G. Mennessier, S. Narison, and W. Ochs, Glueball nature of the from pp and γγ scatterings, Phys. Lett. B, 2008, 665(4): 205

[45] 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 γγ→ππ process, arXiv: 0910.0341; talk given at Conference Chiral Dynamics 09, PoS CD, 2009, 09: 084

[46] M. R. Pennington, T. Mori, S. Uehara, and Y. Watanabe, Amplitude analysis of high statistics results on γγ→π+π- and the two photon width of isoscalar states, Eur. Phys. J. C, 2008, 56(1): 1

[47] See for example the compilation in: M. Hoferichter, D. R. Phillips, and C. Schat, Roy-Steiner equations for γγ→ππ, Eur. Phys. J. C, 2011, 71: 1743

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