<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mo>→</mo><mi>e</mi><mi>ν</mi><mi>γ</mi></math></span> decay and the SU(3) × SU(3) <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math></span> model

R. Montemayor; M. Moreno

doi:10.1103/PhysRevD.21.3144

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$π \to e ν γ$ decay and the SU(3) × SU(3) $σ$ model

R. Montemayor and M. Moreno

Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, México 20, D.F., México

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Phys. Rev. D 21, 3144 – Published 1 June, 1980

DOI: https://doi.org/10.1103/PhysRevD.21.3144

Abstract

With the purpose of taking scalar-meson mixing into account in the framework of the SU(3) × SU(3) $σ$ model of Lévy, we compute the ratio between the axial-vector form factor $F_{A}$ and the vector form factor $F_{V}$ for the $π \to e ν γ$ decay. Our results do not agree with previous calculations in this model even in the limit of no scalar-meson mixing. However, we find agreement with the experimental values of $\frac{F_{A}}{F_{V}}$ for uncolored integrally charged quarks, and disagreement with colored fractionally charged quarks. This in turn implies that one must discard the SU(3) × SU(3) $σ$ model or the quark-loop-dominance framework because this fits the meson radiative decays only for colored fractionally charged quarks.

References (19)

M. Lévy, Nuovo Cimento 52A, 23 (1967)
S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969) V. de Alfaro, S. Fubini, G. Furlan, and C. Rossetti, Currents in Hadron Physics (North-Holland, Amsterdam, 1973)
N. Chase and M. T. Vaughn, Phys. Lett. 61B, 175 (1976) Lai-Him Chan, Phys. Rev. Lett. 39, 1124 (1977)
R. Decker, Phys. Lett. 65B, 153 (1976)
D. A. Ortendahl, Lawrence Berkeley Laboratory Report No. LBL-5305 (unpublished) A. Stetz et al., Nucl. Phys. B138, 185 (1978)
M. Moreno and J. Pestieau, Phys. Rev. D 13, 175 (1976) M. Moreno, ibid. D 16, 720 (1977)
B. W. Lee, Nucl. Phys. B9, 649 (1969) S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969)
M. Gell-Mann and M. Lévy, Nuovo Cimento 16, 53 (1960)
M. Gell-Mann, Phys. Rev. 125, 1067 (1962)
J. Bjorken and S. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)
S. L. Adler, Phys. Rev. 139, B1638 (1965) M. Veltman, Phys. Rev. Lett. 17, 553 (1967) M. Nauenberg, Phys. Rev. 154, 1455 (1967)
S. Bludman and J. Young, Phys. Rev. 118, 602 (1960) D. Neville, ibid. 124, 2037 (1961) V. F. Muller, Z. Phys. 173, 438 (1963) P. De Baenst and J. Pestieau, Nuovo Cimento 53A, 407 (1968) ibid. 53A, 137 (1968) M. G. Smoes, Nucl. Phys. B20, 237 (1970) D. Bardin and S. Beleńkiĭ, Yad. Fiz. 16, 557 (1972) [Sov. J. Nucl. Phys. 16, 311 (1973)]
S. L. Adler, in Lectures on Elementary Particles and Quantum Field Theory, 1970 Brandeis Summer Institute in Theoretical Physics, edited by S. Deser, M. Grisaru, and H. Pendleton (MIT Press, Cambridge, Mass., 1970) R. Jackiw, in Lectures on Current Algebra and its Applications (Princeton Univ. Press, Princeton, 1970), p. 130
D. G. Sutherland, Nucl. Phys. B2, 433 (1967) M. Veltman, Proc. R. Soc. London A301, 107 (1967)
L. M. Chounet, J. M. Gaillard, and M. K. Gaillard, Phys. Rep. 4C, 201 (1972)
J. Bernabeü, R. Tarrach, and F. J. Ynduráin, Phys. Lett. 79B, 464 (1978) R. Montemayor and M. Moreno, Phys. Rev. D 20, 250 (1979)
R. Montemayor and M. Socolovski (in preparation)
Particle Data Group, Phys. Lett. 75B, 1 (1978)
P. Estabrooks et al., Nucl. Phys. B133, 490 (1978)

[c1] M. Lévy, Nuovo Cimento 52A, 23 (1967)

[c2] S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969) V. de Alfaro, S. Fubini, G. Furlan, and C. Rossetti, Currents in Hadron Physics (North-Holland, Amsterdam, 1973)

[c3] N. Chase and M. T. Vaughn, Phys. Lett. 61B, 175 (1976) Lai-Him Chan, Phys. Rev. Lett. 39, 1124 (1977)

[c4] R. Decker, Phys. Lett. 65B, 153 (1976)

[c5] D. A. Ortendahl, Lawrence Berkeley Laboratory Report No. LBL-5305 (unpublished) A. Stetz et al., Nucl. Phys. B138, 185 (1978)

[c6] M. Moreno and J. Pestieau, Phys. Rev. D 13, 175 (1976) M. Moreno, ibid. D 16, 720 (1977)

[c7] B. W. Lee, Nucl. Phys. B9, 649 (1969) S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969)

[c8] M. Gell-Mann and M. Lévy, Nuovo Cimento 16, 53 (1960)

[c9] M. Gell-Mann, Phys. Rev. 125, 1067 (1962)

[c10] J. Bjorken and S. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)

[c11] S. L. Adler, Phys. Rev. 139, B1638 (1965) M. Veltman, Phys. Rev. Lett. 17, 553 (1967) M. Nauenberg, Phys. Rev. 154, 1455 (1967)

[c12] S. Bludman and J. Young, Phys. Rev. 118, 602 (1960) D. Neville, ibid. 124, 2037 (1961) V. F. Muller, Z. Phys. 173, 438 (1963) P. De Baenst and J. Pestieau, Nuovo Cimento 53A, 407 (1968) ibid. 53A, 137 (1968) M. G. Smoes, Nucl. Phys. B20, 237 (1970) D. Bardin and S. Beleńkiĭ, Yad. Fiz. 16, 557 (1972) [Sov. J. Nucl. Phys. 16, 311 (1973)]

[c13] S. L. Adler, in Lectures on Elementary Particles and Quantum Field Theory, 1970 Brandeis Summer Institute in Theoretical Physics, edited by S. Deser, M. Grisaru, and H. Pendleton (MIT Press, Cambridge, Mass., 1970) R. Jackiw, in Lectures on Current Algebra and its Applications (Princeton Univ. Press, Princeton, 1970), p. 130

[c14] D. G. Sutherland, Nucl. Phys. B2, 433 (1967) M. Veltman, Proc. R. Soc. London A301, 107 (1967)

[c15] L. M. Chounet, J. M. Gaillard, and M. K. Gaillard, Phys. Rep. 4C, 201 (1972)

[c16] J. Bernabeü, R. Tarrach, and F. J. Ynduráin, Phys. Lett. 79B, 464 (1978) R. Montemayor and M. Moreno, Phys. Rev. D 20, 250 (1979)

[c17] R. Montemayor and M. Socolovski (in preparation)

[c18] Particle Data Group, Phys. Lett. 75B, 1 (1978)

[c19] P. Estabrooks et al., Nucl. Phys. B133, 490 (1978)

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$π \to e ν γ$ decay and the SU(3) × SU(3) $σ$ model

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π→eνγ decay and the SU(3) × SU(3) σ model

Abstract

References (19)

$π \to e ν γ$ decay and the SU(3) × SU(3) $σ$ model