Access by Xinjiang University

Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering

Laboratory of Theoretical Physics, Sobolev Institute for Mathematics, Novosibirsk, 630090, Russia

^*Electronic address: achasov@math.nsc.ru
^†Electronic address: kiselev@math.nsc.ru

Phys. Rev. D 73, 054029 – Published 30 March, 2006Erratum Phys. Rev. D 74, 059902 (2006)

DOI: https://doi.org/10.1103/PhysRevD.73.054029

Abstract

The high-statistical KLOE data on the $ϕ \to π^{0} π^{0} γ$ decay are described simultaneously with the data on the $π π$ scattering and the $π π \to K \bar{K}$ reaction. The description is carried out taking into account the chiral shielding of the putative $σ (600)$ meson and its mixing with the well-established $f_{0} (980)$ meson. It is shown that the data do not contradict the existence of the $σ (600)$ meson and yield evidence in favor of the four-quark nature of the $σ (600)$ and $f_{0} (980)$ mesons.

Erratum

Erratum: Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering [Phys. Rev. D 73, 054029 (2006)]

N. N. Achasov and A. V. Kiselev

Phys. Rev. D 74, 059902 (2006)

Article Text

References (62)

S. Eidelman et al. (Particle Data Group-2004), Phys. Lett. B 592, 1 (2004).
The nontrivial nature of the well-established light scalar resonances $f_{0} (980)$ and $a_{0} (980)$ is no longer denied practically anybody. In particular, there exist numerous evidences in favor of the four-quark ( $q^{2} {\bar{q}}^{2}$ ) structure of these states (see, for example, Refs. [3,4], and references therein). As for the nonet as a whole, a look at Particle Data Group Review [1] gives an idea of the four-quark structure of the light scalar meson nonet, inverted in comparison with the classical two-quark ( $q \bar{q}$ ) vector and tensor meson nonets. Really, while such a nonet cannot be treated as the $q \bar{q}$ one in the naive quark model, it can be easily understood as the $q^{2} {\bar{q}}^{2}$ nonet, where $f_{0} (600)$ (or $σ$ ) has no strange quarks, $κ (700 - 900)$ has the $s$ -quark, and $f_{0} (980)$ , $a_{0} (980)$ have the $s \bar{s}$ pair (see Refs. [5,6]). To be on the safe side, notice that the linear $σ$ model is not contrary to the non- $q \bar{q}$ nature of the light scalars because quantum fields can contain different virtual particles in different regions of virtuality.
N. N. Achasov, Yad. Fiz. 65, 573 (2002) [Phys. At. Nucl. 65, 546 (2002)].
N. N. Achasov, Nucl. Phys. A728, 425 (2003); Yad. Fiz. 67, 1552 (2004) [Phys. At. Nucl. 67, 1529 (2004)].
R. L. Jaffe, Phys. Rev. D 15, 267 (1977); 15, 281 (1977).
D. Black, A. Fariborz, F. Sannino, and J. Schechter, Phys. Rev. D 59, 074026 (1999).
M. Gell-Mann and M. Levy, Nuovo Cimento 16, 705 (1960); S. Weinberg, Phys. Rev. Lett. 18, 188 (1967); B. W. Lee, Nucl. Phys. B9, 649 (1969); S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969); J. Schechter and Y. Ueda, Phys. Rev. D 3, 168 (1971); 3, 2874 (1971); C. Rosenzweig, J. Schechter, and C. G. Trahern, 21, 3388 (1980); P. Di Vecchia and G. Veneziano, Nucl. Phys. B171, 253 (1980); G.’t Hooft, hep-th/9903189.
N. N. Achasov and G. N. Shestakov, Phys. Rev. D 49, 5779 (1994); Yad. Fiz. 56, 206 (1993) [Phys. At. Nucl. 56, 1270 (1993)]; Int. J. Mod. Phys. A 9, 3669 (1994).
Note that after Ref. [8] a negative background in the $σ (600)$ energy region was introduced in R. Kamiński, L. Leśniak, and J.-P. Maillet, Phys. Rev. D 50, 3145 (1994) without a connection with chiral dynamics. For the sake of objectivity note that the resonance scattering (and production) with background was always known, see G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936). The classical example of such a case is the $f_{0} (980)$ resonance which is seen as the narrow deep in the elastic scattering because of its destructive interference with the large background and as the narrow peak in inelastic reactions, for example, in $J / ψ \to ϕ π π$ . In the case of a wide resonance similar to the putative $σ (600)$ resonance, the large background hinders us from a resonance identification in principle if the background nature is not known. The significance of Ref. [8] consists in revealing the chiral nature of background shielding the putative $σ (600)$ resonance.
N. A. Törnqvist, Z. Phys. C 68, 647 (1995); M. Ishida, S. Ishida, and T. Ishida, Prog. Theor. Phys. 99, 1031 (1998).
S. L. Adler, Phys. Rev. B 137, 1022 (1965); 139, 1638 (1965).
A few approximate nonperturbative solutions in the frame of the simplest linear $σ$ -model are found in Ref. [8].
N. N. Achasov, S. A. Devyanin, and G. N. Shestakov, Phys. Lett. 88B, 367 (1979).
N. N. Achasov, S. A. Devyanin, and G. N. Shestakov, Phys. Lett. 96B, 168 (1980).
N. N. Achasov, S. A. Devyanin, and G. N. Shestakov, Yad. Fiz. 32, 1098 (1980) [Sov. J. Nucl. Phys. 32, 566 (1980)].
N. N. Achasov, S. A. Devyanin, and G. N. Shestakov, Z. Phys. C 22, 53 (1984).
N. N. Achasov, S. A. Devyanin, and G. N. Shestakov, Usp. Fiz. Nauk 142, 361 (1984) [Sov. Phys. Usp. 27, 161 (1984)].
N. N. Achasov, in Proceedings of the 13th International Seminar QUARKS’2004, Pushkinogorie, Russia, edited by D. G. Levkov, V. A. Matveev, and V. A. Rubakov (Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 2005), Vol. 1, pp. 110–124; Phys. Part. Nucl. Suppl. 2, 36, 14 (2005).
N. N. Achasov and A. V. Kiselev, Phys. Rev. D 70, 111901 (2004).
This approach gave indirect evidences of the four-quark nature of the $f_{0} (980)$ and $a_{0} (980)$ mesons [14–17].
L. Montanet, Rep. Prog. Phys. 46, 337 (1983); L. G. Landsberg, Usp. Fiz. Nauk 160, 3 (1990) [Sov. Phys. Usp. 33, 169 (1990)]; M. R. Pennington, in Proceedings of the 6h International Conference on Hadron Spectroscopy (HADRON ’95), Manchester, UK, 1995, edited by M. C. Birse, G. D. Lafferty, and J. A. McGovern (World Scientific, Singapore, 1996), p. 3; T. Barnes, VII International Conference on Hadron Spectroscopy, Upton, New York, 1997, edited by S. U. Chung and H. J. Willutzki, AIP Conf. Proc. No. 432 (AIP, New York, 1998), p. 3; C. Amsler, Rev. Mod. Phys. 70, 1293 (1998); S. Godfrey and J. Napolitano, 71, 1411 (1999); P. Minkowski and W. Ochs, Eur. Phys. J. C 9, 283 (1999); K. Maltman, Phys. Lett. B 462, 14 (1999); H. Y. Cheng, Phys. Rev. D 67, 034024 (2003); F. E. Close and N. A. Törnqvist, J. Phys. G 28, R249 (2002); C. Amsler and N. A. Törnqvist, Phys. Rep. 389, 61 (2004); S. F. Tuan, AIP Conf. Proc. 619, 495 (2002); Proceedings of the International Symposium on Hadron Spectroscopy Chiral Symmetry and Relativistic Description of Bound Systems, Tokyo, 2003 [hep-ph/0303248); KEK Proceedings 2003-7 Nup-B-2003-1, 2003, H, edited by S. Ishida, K. Takamatsu, T. Tsuru, S. Y. Tsai, M. Ishida, and T. Komado, p. 319; S. Krewald, R. H. Lemmer, and F. P. Sassen, Phys. Rev. D 69, 016003 (2004); Yu. S. Kalashnikova et al., Eur. Phys. J. A 24, 437 (2005); A. E. Radzhabov, M. K. Volkov, and V. L. Yudichev, J. Phys. G 32, 111 (2006); S. Narison, hep-ph/0512256.
N. N. Achasov and G. N. Shestakov, Usp. Fiz. Nauk 161, 53 (1991) [Sov. Phys. Usp. 34, 471 (1991)]; N. N. Achasov, Nucl. Phys. B, Proc. Suppl. 21, 189 (1991); Usp. Fiz. Nauk 168, 1257 (1998) [Phys. Usp. 41, 1149 (1998)]; Nucl. Phys. A675, 279c (2000).
N. N. Achasov and V. N. Ivanchenko, Nucl. Phys. B315, 465 (1989); Report No. INP 87-129, 1987, Novosibirsk.
A. Bramon, A. Grau, and G. Pancheri, Phys. Lett. B 289, 97 (1992); F. E. Close, N. Isgur, and S. Kumano, Nucl. Phys. B389, 513 (1993); J. L. Lucio and M. Napsuciale, Phys. Lett. B 331, 418 (1994).
N. N. Achasov and V. V. Gubin, Phys. Rev. D 56, 4084 (1997); Yad. Fiz. 61, 274 (1998) [Phys. At. Nucl. 61, 224 (1998)].
N. N. Achasov, V. V. Gubin, and V. I. Shevchenko, Phys. Rev. D 56, 203 (1997); Int. J. Mod. Phys. A 12, 5019 (1997); Yad. Fiz. 60, 89 (1997) [Phys. At. Nucl. 60, 81 (1997)].
N. N. Achasov, V. V. Gubin, and E. P. Solodov, Phys. Rev. D 55, 2672 (1997); Yad. Fiz. 60, 1279 (1997) [Phys. At. Nucl. 60, 1152 (1997)].
N. N. Achasov and V. V. Gubin, Phys. Rev. D 57, 1987 (1998); Yad. Fiz. 61, 1473 (1998) [Phys. At. Nucl. 61, 1367 (1998)].
M. N. Achasov et al., Phys. Lett. B 438, 441 (1998).
M. N. Achasov et al., Phys. Lett. B 440, 442 (1998).
M. N. Achasov et al., Phys. Lett. B 479, 53 (2000).
M. N. Achasov et al., Phys. Lett. B 485, 349 (2000).
R. R. Akhmetshin et al., Phys. Lett. B 462, 380 (1999).
A. Aloisio et al. (KLOE Collaboration), Phys. Lett. B 536, 209 (2002).
A. Aloisio et al. (KLOE Collaboration), Phys. Lett. B 537, 21 (2002).
C. Bini, P. Gauzzi, S. Giovanella, D. Leone, and S. Miscetti, KlOE Note 173 06/02, http://www.lnf.infn.it/kloe/.
N. N. Achasov and V. V. Gubin, Phys. Rev. D 63, 094007 (2001); Yad. Fiz. 65, 1566 (2002) [Phys. At. Nucl. 65, 1528 (2002)].
N. N. Achasov and V. V. Gubin, Phys. Rev. D 64, 094016 (2001); Yad. Fiz. 65, 1939 (2002) [Phys. At. Nucl. 65, 1887 (2002)].
A. Bramon et al., Eur. Phys. J. C 26, 253 (2002).
N. N. Achasov, The Second $D A Φ N E$ Physics Handbook, edited by L. Maiani, G. Pancheri, and N. Paver (Laboratory Nazionali di Frascati, Frascati, Italy, 1995), Vol. II, p. 671.
N. N. Achasov, S. A. Devyanin, G. N. Shestakovand , Phys. Lett. 108B, 134 (1982); Z. Phys. C 16, 55 (1982).
N. N. Achasov and G. N. Shestakov, Z. Phys. C 41, 309 (1988).
N. N. Achasov and A. V. Kiselev, Phys. Lett. B 534, 83 (2002).
N. N. Achasov and A. V. Kiselev, Phys. Rev. D 68, 014006 (2003); Yad. Fiz. 67, 653 (2004) [Phys. At. Nucl. 67, 633 (2004)].
N. N. Achasov and G. N. Shestakov, Phys. Rev. Lett. 92, 182001 (2004); Pis’ma Zh. Eksp. Teor. Fiz. 79, 724 (2004) [JETP Lett. 79, 588 (2004)]; Phys. Rev. D 70, 074015 (2004); Yad. Fiz. 68, 2130 (2005) [Phys. At. Nucl. 68, 2068 (2005)]; Phys. Rev. D 72, 013006 (2005).
We are very thankful to the KLOE experimenters for the detailed constructive discussion of this question.
N. N. Achasov and A. A. Kozhevnikov, Phys. Rev. D 61, 054005 (2000); Yad. Fiz. 63, 2029 (2000) [Phys. At. Nucl. 63, 1936 (2000)].
M. N. Achasov et al., Phys. Rev. D 63, 072002 (2001).
D. E. Groom et al. (Particle Data Group-2000) Eur. Phys. J. C 15, 1 (2000).
S. I. Dolinsky et al., Z. Phys. C 42, 511 (1989).
M. N. Achasov et al., Phys. Lett. B 559, 171 (2003).
B. Hyams et al., Nucl. Phys. B64, 134 (1973).
P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974).
A. D. Martin, E. N. Ozmutlu, and E. J. Squires, Nucl. Phys. B121, 514 (1977).
V. Srinivasan et al., Phys. Rev. D 12, 681 (1975).
L. Rosselet et al., Phys. Rev. D 15, 574 (1977).
Note that $e^{2 i δ_{B}^{π π}}$ also should have no (simple) zeros, otherwise there are cuts in the amplitude [Eq. (2)]. Fortunately, in all obtained variants there are no such zeros.
G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001).
S. Pislak et al., Phys. Rev. Lett. 87, 221801 (2001).
A. Etkin et al., Phys. Rev. D 25, 1786 (1982).
D. Black, A. Fariborz, and J. Schechter, Phys. Rev. D 61, 074001 (2000).
J. L. Basdevant and B. V. Lee, Phys. Lett. B 29, 437 (1969); Phys. Rev. D 2, 1680 (1970).

Physical Review D

Export citation

Export citation

Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering

Abstract

Erratum

Erratum: Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering [Phys. Rev. D 73, 054029 (2006)]

Article Text

References (62)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Properties of the light scalar mesons face the experimental data on the ϕ→π0π0γ decay and the ππ scattering

Abstract

Erratum

Erratum: Properties of the light scalar mesons face the experimental data on the ϕ→π0π0γ decay and the ππ scattering [Phys. Rev. D 73, 054029 (2006)]

Article Text

References (62)

Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering

Erratum: Properties of the light scalar mesons face the experimental data on the $ϕ \to π^{0} π^{0} γ$ decay and the $π π$ scattering [Phys. Rev. D 73, 054029 (2006)]