Production representation of partial wave scattering amplitudes and the <italic>f</italic><sub>0</sub>(600) particle

doi:10.1007/s11467-013-0387-8

Frontiers of Physics

2013, Vol. 8

Issue (5): 540-547 https://doi.org/10.1007/s11467-013-0387-8

REVIEW ARTICLE

本期目录

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

Han-Qing Zheng(

)

Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China

全文: PDF(245 KB) HTML

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.

Key words： scalar mesons chiral symmetry unitarization

收稿日期: 2013-08-12 出版日期: 2013-10-01

Corresponding Author(s): Zheng Han-Qing,Email:zhenghq@pku.edu.cn

引用本文:

. Production representation of partial wave scattering amplitudes and the f₀(600) particle[J]. Frontiers of Physics, 2013, 8(5): 540-547.
Han-Qing Zheng. Production representation of partial wave scattering amplitudes and the f₀(600) particle. Front. Phys. , 2013, 8(5): 540-547.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-013-0387-8
https://academic.hep.com.cn/fop/CN/Y2013/V8/I5/540

1	M. H. Johnson and E. Teller, Classical field theory of nuclear forces, Phys. Rev. , 1955, 98(3): 783 doi: 10.1103/PhysRev.98.783
2	M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cim. , 1960, 16(4): 705 doi: 10.1007/BF02859738
3	S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (I), Phys. Rev. , 1969, 177(5): 2239 doi: 10.1103/PhysRev.177.2239
4	C. G. Callan, S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians (II), Phys. Rev. , 1969, 177(5): 2247 doi: 10.1103/PhysRev.177.2247
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 doi: 10.1103/PhysRev.122.345
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 doi: 10.1016/0378-4371(79)90223-1
8	J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Ann. Phys. , 1984, 158(1): 142 doi: 10.1016/0003-4916(84)90242-2
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, 12-14Jun. 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 doi: 10.1016/j.nuclphysbps.2007.08.111
11	G. Grayer, B. Hyams, C. Jones, P. Schlein, P. Weilhammer, W. Blum, H. Dietl, W. Koch, E. Lorenz, G. Lütjens, W. M?nner, 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 doi: 10.1103/PhysRevD.15.574
15	S. Pislak, . [The E865 Collaboration], High statistics measurement of Ke4 decay properties, Phys. Rev. D , 2003, 67(7): 072004 doi: 10.1103/PhysRevD.67.072004
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 doi: 10.1016/S0375-9474(01)01100-9
17	Z. G. Xiao and H. Q. Zheng, Further analysis of scattering dispersion relations, Chin. Phys. Lett. , 2003, 20(3): 342 doi: 10.1088/0256-307X/20/3/308
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 doi: 10.1016/j.physletb.2005.12.062
21	D. V. Bugg, The kappa in J/ψ?K+π,Eur. 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
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 doi: 10.1016/j.nuclphysa.2003.12.021
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 doi: 10.1016/j.nuclphysa.2006.06.170
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 doi: 10.1103/PhysRev.74.131
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 doi: 10.1088/0253-6102/48/4/024
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 doi: 10.1142/S0217732307020713
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 doi: 10.1016/j.physletb.2008.01.073
34	Z. H. Guo and J. J. Sanz-Cillero, ππ-scattering lengths at O(p6) revisited, Phys. Rev. D , 2009, 79(9): 096006 doi: 10.1103/PhysRevD.79.096006
35	I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. , 2006, 96(13): 132001 doi: 10.1103/PhysRevLett.96.132001
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 doi: 10.1140/epjc/s10052-006-0036-2
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 doi: 10.1142/S021773230802906X
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): doi: 10.1016/j.nuclphysa.2007.06.004
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 doi: 10.1142/S0217732307023304
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 doi: 10.1016/j.physletb.2008.06.018
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

Viewed

Full text

Abstract

Cited

Shared

Discussed