The decay <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo>→</mo><mi>sgg</mi></math></span> in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem

Jiang Liu; York-Peng Yao

doi:10.1103/PhysRevD.41.2147

Access by Xinjiang University

The decay $b \to sgg$ in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem

Jiang Liu and York-Peng Yao

Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109

PDF

Phys. Rev. D 41, 2147 – Published 1 April, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.2147

Abstract

An extension to the low-energy theorem for a flavor-changing two-gluon decay is discussed. It is shown that in cases where external momenta are much smaller than $M_{W}$ but not small compared with the mass of the decaying particle, contributions with the lowest powers of external momenta are only proportional to the corresponding one-gluon decay dipole-moment form factor. In particular, contributions from the color charge-radius form factor must cancel by gauge invariance. As an illustration, an explicit calculation for the decay $b \to sgg$ is carried out in the standard model. The result of the calculation agrees with our theorem. We estimate that the branching ratio $B (b \to s g g)$ is roughly ≲ $10^{- 4}$ and hence completely negligible in the study of nonleptonic inclusive charmless $B$ decays. This differs from other estimates.

References (11)

L. G. Lin, J. Liu, and Y. P. Yao, University of Michigan Report No. UM-Th-89-16 (unpublished) Michigan report (in preparation)
F. W. Low, Phys. Rev. 110, 974 (1958)
Wei-Shu Hou, Nucl. Phys. B308, 561 (1988) Wei-Shu Hou, A. Soni, and Herbert Steger, Phys. Rev. Lett. 59, 1521 (1987)
R. Grigjanis, P. J. O'Donnell, M. Sutherland, and H. Navelet, Phys. Lett. B 224, 209 (1989)
T. Inami and C. S. Lim, Prog. Theor. Phys. 65, 297 (1981) ibid.65, 1772(E) (1981)
S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970)
N. G. Deshpande, G. Eilam, A. Soni, and G. L. Kane, Phys. Rev. Lett. 57, 1106 (1986) Jean-Marc Gérard and Wei-Shu Hou, ibid. 62, 855 (1989)
L. Rosenberg, Phys. Rev. 129, 2786 (1963)
S. L. Adler, Phys. Rev. 177, 2426 (1969)
M. K. Gaillard and B. W. Lee, Phys. Rev. D 10, 897 (1974) E. Ma and A. Pramudita, ibid. 24, 2476 (1981)
Nilendra G. Deshpande and B. Gad Eilam, Phys. Rev. D 26, 2463 (1982)

[c1] L. G. Lin, J. Liu, and Y. P. Yao, University of Michigan Report No. UM-Th-89-16 (unpublished) Michigan report (in preparation)

[c2] F. W. Low, Phys. Rev. 110, 974 (1958)

[c3] Wei-Shu Hou, Nucl. Phys. B308, 561 (1988) Wei-Shu Hou, A. Soni, and Herbert Steger, Phys. Rev. Lett. 59, 1521 (1987)

[c4] R. Grigjanis, P. J. O'Donnell, M. Sutherland, and H. Navelet, Phys. Lett. B 224, 209 (1989)

[c5] T. Inami and C. S. Lim, Prog. Theor. Phys. 65, 297 (1981) ibid.65, 1772(E) (1981)

[c6] S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970)

[c7] N. G. Deshpande, G. Eilam, A. Soni, and G. L. Kane, Phys. Rev. Lett. 57, 1106 (1986) Jean-Marc Gérard and Wei-Shu Hou, ibid. 62, 855 (1989)

[c8] L. Rosenberg, Phys. Rev. 129, 2786 (1963)

[c9] S. L. Adler, Phys. Rev. 177, 2426 (1969)

[c10] M. K. Gaillard and B. W. Lee, Phys. Rev. D 10, 897 (1974) E. Ma and A. Pramudita, ibid. 24, 2476 (1981)

[c11] Nilendra G. Deshpande and B. Gad Eilam, Phys. Rev. D 26, 2463 (1982)

Physical Review D

Export citation

Export citation

The decay $b \to sgg$ in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem

Abstract

References (11)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

The decay b→sgg in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem

Abstract

References (11)

The decay $b \to sgg$ in the standard model and a nonsoft bremsstrahlung extension of the low-energy theorem