References - Bogoliubov Laboratory of Theoretical Physics - JINR

The main contribution originates from the a0 0(980) → (K + K− + K0K¯ 0 ) → f0(980) transition,
see Fig. 6. Between the K ¯ K thresholds
|Πa0f0(m)| ≈ |ga0K + K−gf0K + K−| �
2(mK0 − mK +)
≈ 0.127
16π
mK0 |ga0K + K−gf0K + K−| � 0.03 GeV
16π
2 .
It dominates for two reason. i) It has the √ md − mu ∼ √ α order. ii) The strong coupling
of the a0 0 (980) and f0(980) to the K ¯ K channels, |ga0K + K−gf0K + K−|/4π � 1GeV2 .
We noted in 2004 [6] that the phase jump, see Fig. 4(b), suggest the idea to study
the a0 0 (980) − f0(980) mixing in polarization phenomena. If a process amplitude with
a suitable spin configuration is dominated by the a0 0 (980) − f0(980) mixing then a spin
asymmetry of a cross section jumps near the K ¯ K thresholds. An example is the reaction
π−p↑ → (a0 0 (980) + f0(980)) n → a0 0 (980)n → ηπ0n, see Fig. 7. Performing the polarized
target experiments on the reaction π−p → ηπ0n at high energy could unambiguously and
very easily establish the existence of the a0(980) − f0(980) mixing phenomenon through
the presence of a strong (∼ 1) jump in the normalized azimuthal spin asymmetry of
the S wave ηπ0 production cross section near the K ¯ K thresholds. In turn it could give
an exclusive information on the a0(980) and f0(980) coupling constants with the K ¯ K
channels, |ga0K + K−gf0K + K−|/4π. 1
0��t�0.025GeV 2
�� a0�f0 �m �� �10 �3 GeV 2 �
25
20
15
10
5
�a�
0.9750.980.9850.990.995 1 1.0051.01
m �GeV �
Phase�degrees�
100
80
60
40
20
�b�
0.9750.980.9850.990.995 1 1.0051.01
m �GeV �
Figure 6: The “resonancelike” behavior of the modulus
(a) and phase (b) of the a 0 0 (980)−f0(980) mixing amplitude
Πa0f0(m).
SpinAsymmetry
0.5
0
�0.5
�1
0.9 0.920.940.960.98
m �GeV �
1 1.021.04
Figure 7: The spin asymmetry in
π − p↑ → � a 0 0 (980) + f0(980) � n → ηπ 0 n.
This work was supported in part by the RFFI Grant No. 07-02-00093 and by the
Presidential Grant No. NSh-1027.2008.2 for Leading Scientific Schools.
References
[1] N.N. Achasov and G.N. Shestakov, Phys. Rev. D49 (1994) 5779; Phys. Rev. Lett. 99 (2007) 072001.
[2] R.L. Jaffe, Phys. Rev. D15 (1977) 267, 281.
[3] N.N. Achasov and V.N. Ivanchenko, Nucl. Phys. B315 (1989) 465; N.N. Achasov and V.V. Gubin,
Phys. Rev. D56 (1997) 4084; Phys. Rev. D63 (2001) 094007; N.N. Achasov, Nucl. Phys. A728 (2003)
425; N.N. Achasov and A.V. Kiselev, Phys. Rev. D68 (2003) 014006; Phys. Rev. D73 (2006) 054029.
[4]N.N.Achasov,S.A.Devyanin,andG.N.Shestakov,Phys.Lett.108B (1982) 134; Z. Phys. C16
(1982) 55; N.N. Achasov and G.N. Shestakov, Phys. Rev. D72 (2005) 013006; Phys. Rev. D77
(2008) 074020; Pisma Zh. Eksp. Teor. Fiz. 88 (2008) 345; Pisma Zh. Eksp. Teor. Fiz. 90 (2009) 355.
[5] T. Mori et al., Phys. Rev. D75 (2007) 051101(R); J. Phys. Soc. Jap. 76 (2007) 074102; S. Uehara et
al., Phys. Rev. D78 (2008) 052004; Phys. Rev. D80 (2009) 032001.
[6] N.N. Achasov , S.A. Devyanin, and G.N. Shestakov, Phys. Lett. B88 (1979) 367; Yad. Fiz. 33 (1981)
1337; N.N. Achasov and G.N. Shestakov, Phys. Rev. Lett. 92 (2004) 182001; Phys. Rev. D70 (2004)
074015.
[7] J.-J. Wu, Q. Zhao, and B.S. Zou, Phys. Rev. D75 (2007) 114012.
[8] V. Dorofeev et al., Eur. Phys. J. A38 (2008) 149; arXiv: 0712.2512 [hep-ex].
32