Once more about the KK̄ molecule approach to the light scalars

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 76, Issue 7, 2007, Pages

  Achasov, N N ^a   Kiselev, A V ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

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Indexed keywords

EID: 35448950308     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.76.077501     Document Type: Article

References (17)

1. Yu.S. Kalashnikova, A.E. Kudryavtsev, A.V. Nefediev, C. Hanhart, and J. Haidenbauer, Eur. Phys. J. A 24, 437 (2005). EPJAFV 1434-6001 10.1140/epja/i2005-10008-4
2. As it follows from Ref., this set of β corresponds to the set of the nonrelativistic average momentum square of a K meson in the molecule, k2/mK2: 0.056, 0.084, and 0.224.
3. Notice that |ReI(a,b;Γ)/ImI(a,b;Γ)|2 1 at β≤0.2GeV, so that |I(a,b;Γ)| is dominated by ImI(a,b;Γ) which is caused certainly by real intermediate nonrelativistic kaons. But (a-b)ImI(a,b;Γ) can explain not greater than 20% of branching ratios of decays under consideration even for the pointlike interaction and leads to an over-narrow resonance structure to fit data.
4. Notice that there is another sloppily built place in Ref.. The authors of Ref. calculate A((p)→γ(q)S(p′)) at q=0, p2=m 2, and (p′)2=mS2 (mS-2m<0), that is, at p p′+q. The point is that a question of principle for them is an interpretation of 1/(ES-k2m+i0) as a nonrelativistic two-particle (KK̄) Green function. But gauge invariance forces the authors of Ref. to replace mS by the invariant mass [minv2=(p′)2] of decay products in the physical region p=p′+q, the actual interval of which is quite large. The typical values lie in the range -100MeV
5. N.N. Achasov and V.V. Gubin, Phys. Rev. D 63, 094007 (2001); PRVDAQ 0556-2821 10.1103/PhysRevD.63.094007
6. N.N. Achasov V.V. Gubin Yad. Fiz. 65, 1566 (2002) IDFZA7 0044-0027
7. [N.N. Achasov V.V. Gubin Phys. At. Nucl. 65, 1528 (2002)]; PANUEO 1063-7788 10.1134/1.1501665
8. N.N. Achasov, Nucl. Phys. NUPABL 0375-9474 A728, 425 (2003); 10.1016/j.nuclphysa.2003.09.002
9. N.N. Achasov Yad. Fiz. 67, 1552 (2004) IDFZA7 0044-0027
10. [N.N. Achasov Phys. At. Nucl. 67, 1529 (2004)]. PANUEO 1063-7788 10.1134/1.1788044
11. N.N. Achasov and V.N. Ivanchenko, Nucl. Phys. NUPBBO 0550-3213 B315, 465 (1989). 10.1016/0550-3213(89)90364-7
12. N.N. Achasov and A.V. Kiselev, Phys. Rev. D 68, 014006 (2003); PRVDAQ 0556-2821 10.1103/PhysRevD.68.014006
13. N.N. Achasov A.V. Kiselev Yad. Fiz. 67, 653 (2004) IDFZA7 0044-0027
14. [N.N. Achasov A.V. Kiselev Phys. At. Nucl. 67, 633 (2004)]; PANUEO 1063-7788 10.1134/1.1690073
15. N.N. Achasov A.V. Kiselev Phys. Rev. D 73, 054029 (2006). PHRVAO 0031-899X 10.1103/PhysRevD.73.054029
16. N.N. Achasov, Yad. Fiz. 70, 896 (2007) IDFZA7 0044-0027
17. [N.N. Achasov Phys. At. Nucl. 70, 862 (2007)]. PANUEO 1063-7788 10.1134/S1063778807050080