A new look at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mn></mn><mo>(</mo><mn>1280</mn><mo>)</mo><mn></mn></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mn></mn><mo>(</mo><mn>1400</mn><mo>)</mo><mn></mn></math> meson system. Derivation of mass formulas and selection rules

S. Oneda; Jung S. Rno

doi:10.1103/PhysRevD.22.155

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A new look at the $A_{1}$ , $B$ , $Q_{1} (1280)$ , and $Q_{2} (1400)$ meson system. Derivation of mass formulas and selection rules

S. Oneda

Jung S. Rno

Center for Theoretical Physics, University of Maryland, College Park, Maryland 20742

R. Walters College, University of Cincinnati, Cincinnati, Ohio 45236

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Phys. Rev. D 22, 155 – Published 1 July, 1980

DOI: https://doi.org/10.1103/PhysRevD.22.155

Abstract

A new study of the $A_{1}$ , $B$ , $Q_{1} (1280)$ , and $Q_{2} (1400)$ mesons is carried out in the presence of large SU(3) mixing between the $Q$ mesons. The theoretical framework used is a purely algebraic one which expresses the dynamics of confined quarks through chiral SU(3) ⊗ SU(3) charge algebras, related exotic-charge commutators characterizing symmetry breaking, asymptotic SU(3) symmetry, and asymptotic level realization of SU(3) in the chiral SU(2) ⊗ SU(2) charge algebra $[A_{π^{+}}, A_{π^{-}}] = 2 V_{π^{0}}$ . A simple mass formula ${Q_{2}}^{2} - B^{2} = {Q_{1}}^{2} - A^{2}$ is derived which predicts the mass of $A_{1}$ around 1.1 GeV with $Γ (A_{1} \to ρ π) ≃ 300$ MeV. The SU(3) mixing angle $θ$ of the $Q$ mesons is also derived in terms of the observable masses. The sum rules obtained exhibit a close interplay among the masses, $θ$ , and asymptotic axial-vector matrix elements. There exists an "ideal angle" $θ = 30 °$ for which the couplings $Q_{2} (1400) \to ρ K and ω K$ become forbidden as observed by experiment. $θ = 30 °$ is also found to be compatible with the mass spectrum of the $A_{1}$ , $B$ , $Q_{1}$ , and $Q_{2}$ system. The $Q_{2} (1400)$ , rather than the $Q_{1} (1280)$ , turns out to be the SU(3) counterpart of $A_{1} (1100)$ , suggesting that an inversion in the mass ordering took place through mixing.

References (33)

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Omitted endnote
H. L. Hallock and S. Oneda, Phys. Rev. 19, 347 (1979)
S. Okubo, Phys. Rev. D 16, 2336 (1977)
Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
C. Y. Huang, Ph.D. thesis, University of Maryland, 1973 (unpublished)
E. Takasugi and S. Oneda, Phys. Rev. Lett. 31, 1274 (1973)
Seisaku Matsuda and S. Oneda, Phys. Rev. 185, 1887 (1969)
[8]
Omitted endnote
Seisaku Matsuda and S. Oneda, Phys. Rev. 174, 2106 (1968)
S. Weinberg, Phys. Rev. Lett. 18, 507 (1967) T. Das, V. S. Mathur, and S. Okubo, ibid. 18, 761 (1967) F. J. Gilman and H. Harari, Phys. Rev. 165, 1803 (1969)
Omitted endnote

[c1] A. Jaros et al., Phys. Rev. Lett. 40, 1120 (1978) G. Alexander et al., Phys. Lett. 73B, 99 (1978)

[c2] J. L. Basdevant and E. L. Berger, Phys. Rev. Lett. 40, 994 (1978)

[c3] P. Gavillet et al., Phys. Lett. 78B, 158 (1978) ibid.69B, 119 (1977) ibid.76B, 517 (1978)

[c4] D. A. Geffen and Warren J. Wilson, Phys. Rev. D 18, 2488 (1978) H. Goldberg and R. Aaron, Phys. Rev. Lett. 42, 339 (1979) T. N. Pham, C. Roiesnel, and Tran N. Truong, École Polytechnique Report No. AA294, 1978 (unpublished)

[c5] G. W. Brandenburg et al., Phys. Rev. Lett. 36, 703 (1976) R. K. Carnegie et al., Nucl. Phys. B127, 509 (1977)

[c6] David W. G. S. Leith, in Experimental Meson Spectroscopy 1977, proceedings of the International Conference, Boston, edited by E. von Goeler and R. Weinstein (Northeastern University Press, Boston, 1978), p. 207

[c7] J. L. Basdevant and E. L. Berger, Phys. Rev. 19, 246 (1979)

[c8] M. Mazzucato et al., Nucl. Phys. B156, 532 (1979)

[c9] H. Lipkin, in Experimental Meson Spectroscopy 1977 ([6]), p. 388

[c10] S. Oneda, in Lecture Notes in Physics, No. 94, Group Theoretical Methods in Physics, edited by W. Beiglböck, A. Böhm, and E. Takasugi (Springer, Berlin, 1979), p. 334 in Proceedings of INS International Symposium on New Particles and the Structure of Hadrons, Tokyo, 1977, edited by K. Fujikawa (Institute for Nuclear Study, University of Tokyo, Tokyo, 1978), p. 94 S. Oneda and Seisaku Matsuda, in Fundamental Interaction in Physics, 1973 Coral Gables Conference, edited by B. Kursonoğlu and A. Perlmutter (Plenum, New York, 1973), p. 175

[c11] T. Laankan and S. Oneda, Phys. Lett. 46B, 77 (1973)

[c12] G. Fourez and S. Oneda, Nuovo Cimento 59A, 65 (1969)

[c13] Seisaku Matsuda and S. Oneda, Phys. Rev. 174, 1992 (1968)

[c14] E. Takasugi and S. Oneda, Phys. Rev. D 12, 198 (1975) H. L. Hallock, S. Oneda, and Milton D. Slaughter, ibid. 15, 884 (1977)

[c15] S. Oneda and Seisaku Matsuda, Phys. Lett. 37B, 105 (1971) Phys. Rev. D 5, 2287 (1972) T. Laankan, S. Oneda, and Seisaku Matsuda, ibid. 8, 4067 (1973)

[c16] Milton D. Slaughter and S. Oneda, Phys. Rev. D 14, 1314 (1976)

[c17] S. Oneda, Jung S. Rno, and Milton D. Slaughter, Phys. Rev. D 17, 1389 (1978)

[c18] S. Oneda, T. Tanuma, and Milton D. Slaughter, Phys. Lett. 88B, 343 (1979)

[c19] Omitted endnote

[c20] H. L. Hallock and S. Oneda, Phys. Rev. 19, 347 (1979)

[c21] S. Okubo, Phys. Rev. D 16, 2336 (1977)

[c22] Omitted endnote

[c23] Omitted endnote

[c24] Omitted endnote

[c25] Omitted endnote

[c26] C. Y. Huang, Ph.D. thesis, University of Maryland, 1973 (unpublished)

[c27] E. Takasugi and S. Oneda, Phys. Rev. Lett. 31, 1274 (1973)

[c28] Seisaku Matsuda and S. Oneda, Phys. Rev. 185, 1887 (1969)

[c29] [8]

[c30] Omitted endnote

[c31] Seisaku Matsuda and S. Oneda, Phys. Rev. 174, 2106 (1968)

[c32] S. Weinberg, Phys. Rev. Lett. 18, 507 (1967) T. Das, V. S. Mathur, and S. Okubo, ibid. 18, 761 (1967) F. J. Gilman and H. Harari, Phys. Rev. 165, 1803 (1969)

[c33] Omitted endnote

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A new look at the $A_{1}$ , $B$ , $Q_{1} (1280)$ , and $Q_{2} (1400)$ meson system. Derivation of mass formulas and selection rules

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A new look at the A1, B, Q1(1280), and Q2(1400) meson system. Derivation of mass formulas and selection rules

Abstract

References (33)

A new look at the $A_{1}$ , $B$ , $Q_{1} (1280)$ , and $Q_{2} (1400)$ meson system. Derivation of mass formulas and selection rules