Radiative corrections and semileptonic <i>B</i> decays

David Atwood; William J. Marciano

doi:10.1103/PhysRevD.41.1736

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Radiative corrections and semileptonic B decays

David Atwood and William J. Marciano

Physics Department, Brookhaven National Laboratory, Upton, New York 11973

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Phys. Rev. D 41, 1736(R) – Published 1 March, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.1736

Abstract

A prescription for approximating electroweak radiative corrections to weak decays is given. The method is illustrated for τ→eνν¯ and a simplified (structureless) model of B→Meν¯, M=D or π, where the complete O(α) corrections are known. Our procedure is shown to provide a proper description of radiation damping near the electron’s end-point energy and a reasonable estimate of radiative corrections for much of the spectrum as well as the integrated rate. As a practical application, it is applied to the semileptonic decays B→Xeν¯ where an exact O(α) treatment of radiative corrections is very difficult, but an estimate of their effect is important for the extraction of $V_{ub}$ and leptonic branching ratios. We also discuss an 18% enhancement of Υ(4S)→ $B^{+}$ $B^{-}$ relative to $B^{0}$ B¯ ${}^{0}$ due to large Coulomb corrections near threshold.

References (22)

R. Behrends, R. Finkelstein and A. Sirlin, Phys. Rev. 101, 866 (1955).
A. Sirlin, Rev. Mod. Phys. 50, 573 (1978).
D. R. Yennie, S. C. Frautschi and H. Suura, Ann. Phys. (N.Y.) 13, 379 (1961).
A. Sirlin, Nucl. Phys. B196, 83 (1982).
T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959); S. Berman, ibid. 112, 267 (1958).
M. Roos and A. Sirlin, Nucl. Phys. B29, 296 (1971).
W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 56, 22 (1986); ibid. 61, 1815 (1988).
F. Bloch and A. Nordsieck, Phys. Rev. 52, 54 (1937).
W. J. Marciano, G. Marques and N. Papanicolaou, Nucl. Phys. B96, 237 (1975).
D. Zwanziger, Phys. Rev. D 11, 3504 (1975).
E. Ginsberg, Phys. Rev. 171, 1675 (1968); ibid. 174, 2169(E) (1968).
S. Stone, Cornell Reports No. CLNS 89/924 and No. 89/924, 1989 (unpublished); D. Miller, Purdue University Report No. PU-89-643, 1989 (unpublished).
Radiative corrections to leptonic tau decay are identical to muon decay (see Ref. 5) under the replacement $m_{μ}$ -> $m_{tau}$ . A. Ali and Z. Rydin, Nuovo Cimento 43, 270 (1978).
L. Matsson, Nucl. Phys. B12, 647 (1969); D. A. Ross, Nuovo Cimento 10, 475 (1972).
E. Ginsberg, Phys. Rev. 142, 1035 (1966).
A. A. Ovchinnikov, Phys. Lett. B 229, 127 (1989).
In our actual graphical comparison, we choose c appropriate for η != 1.
G. Altarelli et al., Nucl. Phys. B208, 365 (1982).
N. Isgur, D. Scora, B. Grinstein and M. B. Wise, Phys. Rev. D 39, 799 (1989).
The $B^{+ -}$ - $B^{0}$ mass difference quoted is a preliminary value given in Ref. 12. Such a small mass difference is quite surprising since one would have naively expected $m_{B^{+}}$ - $m_{B^{0}}$ apeq -3 MeV due to the u - d mass difference and Coulomb-binding corrections. Explaining the deviation from naive expectations (if confirmed) should be an interesting theoretical challenge. See E. Eichten, Phys. Rev. D 22, 1819 (1980).
See J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, MA, 1973), Vol. II, p. 397. In the nonrelativistic limit, β << 1, the Coulomb-correction factor is given by (2 π α / $β_{rel}$ ) / [ 1- exp ( - 2 π α / $β_{rel}$ ) ] where $β_{rel}$ apeq 2 beta. That gives a slightly larger app 18.7 % enhancement.
We do expect additional isospin violations in the ϒ (4S) decay form factors from Coulomb effects and they are likely to suppress $B^{+}$ $B^{-}$ relative to $B^{0 \bar{B} \sup}$ 0. We do not, however, expect them to be large. Also, an updated coupled-channel analysis including Coulomb effects should be undertaken. See E. Eichten, K. Gottfried, K. Lane, T. Kinoshita and T.-M. Yan, Phys. Rev. D 17, 3090 (1980); ibid. 21, 313(E) (1980); A. D. Martin and C-K. Ng, Z. Phys. C 40, 133 (1988).

[c1] R. Behrends, R. Finkelstein and A. Sirlin, Phys. Rev. 101, 866 (1955).

[c2] A. Sirlin, Rev. Mod. Phys. 50, 573 (1978).

[c3] D. R. Yennie, S. C. Frautschi and H. Suura, Ann. Phys. (N.Y.) 13, 379 (1961).

[c4] A. Sirlin, Nucl. Phys. B196, 83 (1982).

[c5] T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959); S. Berman, ibid. 112, 267 (1958).

[c6] M. Roos and A. Sirlin, Nucl. Phys. B29, 296 (1971).

[c7] W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 56, 22 (1986); ibid. 61, 1815 (1988).

[c8] F. Bloch and A. Nordsieck, Phys. Rev. 52, 54 (1937).

[c9] W. J. Marciano, G. Marques and N. Papanicolaou, Nucl. Phys. B96, 237 (1975).

[c10] D. Zwanziger, Phys. Rev. D 11, 3504 (1975).

[c11] E. Ginsberg, Phys. Rev. 171, 1675 (1968); ibid. 174, 2169(E) (1968).

[c12] S. Stone, Cornell Reports No. CLNS 89/924 and No. 89/924, 1989 (unpublished); D. Miller, Purdue University Report No. PU-89-643, 1989 (unpublished).

[c13] Radiative corrections to leptonic tau decay are identical to muon decay (see Ref. 5) under the replacement $m_{μ}$ -> $m_{tau}$ . A. Ali and Z. Rydin, Nuovo Cimento 43, 270 (1978).

[c14] L. Matsson, Nucl. Phys. B12, 647 (1969); D. A. Ross, Nuovo Cimento 10, 475 (1972).

[c15] E. Ginsberg, Phys. Rev. 142, 1035 (1966).

[c16] A. A. Ovchinnikov, Phys. Lett. B 229, 127 (1989).

[c17] In our actual graphical comparison, we choose c appropriate for η != 1.

[c18] G. Altarelli et al., Nucl. Phys. B208, 365 (1982).

[c19] N. Isgur, D. Scora, B. Grinstein and M. B. Wise, Phys. Rev. D 39, 799 (1989).

[c20] The $B^{+ -}$ - $B^{0}$ mass difference quoted is a preliminary value given in Ref. 12. Such a small mass difference is quite surprising since one would have naively expected $m_{B^{+}}$ - $m_{B^{0}}$ apeq -3 MeV due to the u - d mass difference and Coulomb-binding corrections. Explaining the deviation from naive expectations (if confirmed) should be an interesting theoretical challenge. See E. Eichten, Phys. Rev. D 22, 1819 (1980).

[c21] See J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, MA, 1973), Vol. II, p. 397. In the nonrelativistic limit, β << 1, the Coulomb-correction factor is given by (2 π α / $β_{rel}$ ) / [ 1- exp ( - 2 π α / $β_{rel}$ ) ] where $β_{rel}$ apeq 2 beta. That gives a slightly larger app 18.7 % enhancement.

[c22] We do expect additional isospin violations in the ϒ (4S) decay form factors from Coulomb effects and they are likely to suppress $B^{+}$ $B^{-}$ relative to $B^{0 \bar{B} \sup}$ 0. We do not, however, expect them to be large. Also, an updated coupled-channel analysis including Coulomb effects should be undertaken. See E. Eichten, K. Gottfried, K. Lane, T. Kinoshita and T.-M. Yan, Phys. Rev. D 17, 3090 (1980); ibid. 21, 313(E) (1980); A. D. Martin and C-K. Ng, Z. Phys. C 40, 133 (1988).

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Radiative corrections and semileptonic B decays

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