Determining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>ub</mi></mrow></msub></mrow></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mo>→</mo><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>*</mi><mo>+</mo></mrow></msubsup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mi>−</mi></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mo>→</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mi>−</mi></mrow></msup></mrow></math>

David H. Evans; Benjamín Grinstein; Detlef R. Nolte

doi:10.1103/PhysRevD.60.057301

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Determining $V_{ub}$ from $B^{+} \to D_{s}^{* +} e^{+} e^{-}$ and $B^{+} \to D^{* +} e^{+} e^{-}$

David H. Evans^*, Benjamín Grinstein^†, and Detlef R. Nolte^‡

Department of Physics, University of California at San Diego, La Jolla, California 92093

^*Electronic address: daevans@physics.ucsd.edu
^†Electronic address: bgrinstein@ucsd.edu
^‡Electronic address: dnolte@ucsd.edu

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Phys. Rev. D 60, 057301 – Published 28 July, 1999

DOI: https://doi.org/10.1103/PhysRevD.60.057301

Abstract

It was recently pointed out that the decays $B^{+} \to D_{s}^{* +} γ$ and $B^{+} \to D^{* +} γ$ can be used for an extraction of $| V_{ub} | .$ The theory of these decays is poorly understood. It was shown that in a world of almost degenerate b and c quarks the decay would be computable. The severe difficulties that are encountered in the realistic calculation stem primarily from the very hard photon produced in the two body decay. We point out that in the decays $B^{+} \to D_{s}^{* +} e^{+} e^{-}$ and $B^{+} \to D^{* +} e^{+} e^{-}$ the photon vertex is soft when the charmed meson is nearly at rest (in the $B^{+}$ rest frame). This allows us to compute with some confidence the decay rate in a restricted but interesting kinematic regime. Given enough data the extraction of $V_{ub}$ with reasonably small uncertainties could proceed through an analysis of these exclusive decays much as is done in the determination of $V_{cb} .$

References (9)

J. Chay, H. Georgi, and B. Grinstein, Phys. Lett. B 247, 399 (1990); I. I. Bigi, M. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Phys. Rev. Lett. 71, 496 (1993); B. Blok, L. Koyrakh, M. Shifman, and A. I. Vainshtein, Phys. Rev. D 49, 3356 (1994); ibid.50, 3572(E) (1994); ibid.A. V. Manohar and M. B. Wise, 49, 1310 (1994).
I. I. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Int. J. Mod. Phys. A 9, 2467 (1994); Phys. Lett. B 328, 431 (1994); T. Mannel and M. Neubert, Phys. Rev. D 50, 2037 (1994); ibid.M. Neubert, 49, 3392 (1994); ibid.49, 4623 (1994).
V. Barger, Phys. Lett. B 251, 629 (1990); ibid.J. Dai, 333, 212 (1994); ibid.A. F. Falk, Z. Ligeti, and M. B. Wise, 406, 225 (1997).
B. Grinstein and R. Lebed, Phys. Rev. D 60, 031302 (1999).
M. B. Wise, Phys. Rev. D 45, R2188 (1992); G. Burdman and J. F. Donoghue, Phys. Lett. B 280, 287 (1992); T.-M. Yan et al., Phys. Rev. D 46, 1148 (1992); ibid.T.-M. Yan55, 5851(E) (1997).
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B. Grinstein, E. Jenkins, A. V. Manohar, M. J. Savage, and M. B. Wise, Nucl. Phys. B380, 369 (1992).

[c1] J. Chay, H. Georgi, and B. Grinstein, Phys. Lett. B 247, 399 (1990); I. I. Bigi, M. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Phys. Rev. Lett. 71, 496 (1993); B. Blok, L. Koyrakh, M. Shifman, and A. I. Vainshtein, Phys. Rev. D 49, 3356 (1994); ibid.50, 3572(E) (1994); ibid.A. V. Manohar and M. B. Wise, 49, 1310 (1994).

[c2] I. I. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Int. J. Mod. Phys. A 9, 2467 (1994); Phys. Lett. B 328, 431 (1994); T. Mannel and M. Neubert, Phys. Rev. D 50, 2037 (1994); ibid.M. Neubert, 49, 3392 (1994); ibid.49, 4623 (1994).

[c3] V. Barger, Phys. Lett. B 251, 629 (1990); ibid.J. Dai, 333, 212 (1994); ibid.A. F. Falk, Z. Ligeti, and M. B. Wise, 406, 225 (1997).

[c4] B. Grinstein and R. Lebed, Phys. Rev. D 60, 031302 (1999).

[c5] M. B. Wise, Phys. Rev. D 45, R2188 (1992); G. Burdman and J. F. Donoghue, Phys. Lett. B 280, 287 (1992); T.-M. Yan et al., Phys. Rev. D 46, 1148 (1992); ibid.T.-M. Yan55, 5851(E) (1997).

[c6] A. F. Falk, Phys. Lett. B 305, 268 (1993).

[c7] N. Isgur and M. B. Wise, Phys. Lett. B 232, 113 (1989); ibid.237, 527 (1990); ibid.E. Eichten and B. Hill, 234, 511 (1990).

[c8] J. F. Amundson et al., Phys. Lett. B 296, 415 (1992).

[c9] B. Grinstein, E. Jenkins, A. V. Manohar, M. J. Savage, and M. B. Wise, Nucl. Phys. B380, 369 (1992).

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Determining $V_{ub}$ from $B^{+} \to D_{s}^{* +} e^{+} e^{-}$ and $B^{+} \to D^{* +} e^{+} e^{-}$

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Determining Vub from B+→Ds*+e+e− and B+→D*+e+e−

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Determining $V_{ub}$ from $B^{+} \to D_{s}^{* +} e^{+} e^{-}$ and $B^{+} \to D^{* +} e^{+} e^{-}$