Measuring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>|</mi><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>td</mi></mrow></msub></mrow><mrow><msub><mrow><mo>/</mo><mi>V</mi></mrow><mrow><mi>ub</mi></mrow></msub></mrow><mi>|</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>(</mo><mo>=</mo><mi mathvariant="normal">sin</mi><mi></mi><mi>γ</mi><mo>/</mo><mi mathvariant="normal">sin</mi><mi></mi><mi>β</mi></math> within the SM) through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow></mrow><mi>M</mi><mi>ν</mi><mrow><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mi>¯</mi></mrow></mover></mrow></mrow><mi> </mi><mo>(</mo><mi>M</mi><mo>=</mo><mi>π</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>ρ</mi><mrow><msup><mrow><mo>,</mo><mi>K</mi></mrow><mrow><mi>*</mi></mrow></msup></mrow><mo>)</mo></math> decays

T. M. Aliev; C. S. Kim

doi:10.1103/PhysRevD.58.013003

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Measuring $| V_{td} {/ V}_{ub} |$ $(= \sin γ / \sin β$ within the SM) through $\vec{B} M ν \bar{ν} (M = π, K, ρ {, K}^{*})$ decays

T. M. Aliev^*

C. S. Kim^†

Physics Department, Girne American University, Girne, Cyprus

Physics Department, Yonsei University, Seoul 120-749, Korea

^*Email address: taliev@cc.emu.edu.tr
^†Email address: kim@cskim.yonsei.ac.kr, cskim@kekvax.kek.jp, http://phya.yonsei.ac.kr/ $\tilde{}$ cskim/

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Phys. Rev. D 58, 013003 – Published 15 May, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.013003

Abstract

We propose a new method for the precise determination of $| V_{td} {/ V}_{ub} |$ from the ratios of branching ratios $B (\vec{B} ρ ν \bar{ν}) / B (\vec{B} ρ l ν)$ and $B (\vec{B} π ν \bar{ν}) / B (\vec{B} π l ν) .$ These ratios depend only on the ratio of the Cabibbo-Kobayashi-Maskawa (CKM) elements $| V_{td} {/ V}_{ub} |$ with little theoretical uncertainty, when very small isospin breaking effects are neglected. As is well known, $| V_{td} {/ V}_{ub} |$ equals $(\sin γ / \sin β)$ for the CKM version of $CP$ violation within the standard model. We also give in detail analytical and numerical results on the differential decay width $d Γ (\vec{B} K^{*} ν \bar{ν} {) / d q}^{2}$ and the ratio of the differential rates $d B (\vec{B} ρ ν \bar{ν} {) / d q}^{2} / d B (\vec{B} K^{*} ν \bar{ν} {) / d q}^{2}$ as well as $B (\vec{B} ρ ν \bar{ν}) / B (\vec{B} K^{*} ν \bar{ν})$ and $B (\vec{B} π ν \bar{ν}) / B (\vec{B} K ν \bar{ν}) .$

References (21)

G. Buchalla, A. Buras, and M. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).
V. Barger, C.S. Kim, and R.J.N. Phillips, Phys. Lett. B 235, 187 (1990); ibid.251, 629 (1990); C.S. Kim, D.S. Hwang, P. Ko, and W. Namgung, in CP Violation, Its Implications to Particle Physics and Cosmology, Proceedings of the Topical Conference, Tsuhuba, Japan, 1993, edited by Y. Kuno and Y. Okada [Nucl. Phys. B (Proc. Suppl.) 37A, 69 (1994)]; Phys. Rev. D 50, 5762 (1994).
C.S. Kim, Phys. Lett. B 414, 347 (1997); in Fourth Topical Conference on Flavor Physics, Tsuhuba, Japan, 1996, edited by Y. Kuno and M. Nojiri [Nucl. Phys. B (Proc. Suppl.) 59, 114 (1997)], hep-ph/9701316; A.F. Falk, Z. Ligeti, and M.B. Wise, Phys. Lett. B 406, 225 (1997); I. Bigi, R.D. Dikeman, and N. Uraltsev, hep-ph/9706520, presented at 3rd BaBar Physics Workshop, Orsay, France, 1997; P. Ball, hep-ph/9709407, talk given at 7th International Symposium on Heavy Flavor Physics, Santa Barbara, CA, 1997.
A.O. Bouzas and D. Zappalà, Phys. Lett. B 333, 215 (1994); A. Falk, M. Luke, and M. Savage, Phys. Rev. D 53, 2491 (1996).
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APE Collaboration, C.R. Allton et al., Phys. Lett. B 345, 513 (1995); Z. Ligeti and M.B. Wise, Phys. Rev. D 53, 4937 (1996).
C.S. Kim, T. Morozumi, and A.I. Sanda, Phys. Rev. D 56, 7240 (1997); talk given at 2nd Conference on B Physics and CP Violation, Honolulu, HI, 1997 (hep-ph/9706380).
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[c1] G. Buchalla, A. Buras, and M. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).

[c2] V. Barger, C.S. Kim, and R.J.N. Phillips, Phys. Lett. B 235, 187 (1990); ibid.251, 629 (1990); C.S. Kim, D.S. Hwang, P. Ko, and W. Namgung, in CP Violation, Its Implications to Particle Physics and Cosmology, Proceedings of the Topical Conference, Tsuhuba, Japan, 1993, edited by Y. Kuno and Y. Okada [Nucl. Phys. B (Proc. Suppl.) 37A, 69 (1994)]; Phys. Rev. D 50, 5762 (1994).

[c3] C.S. Kim, Phys. Lett. B 414, 347 (1997); in Fourth Topical Conference on Flavor Physics, Tsuhuba, Japan, 1996, edited by Y. Kuno and M. Nojiri [Nucl. Phys. B (Proc. Suppl.) 59, 114 (1997)], hep-ph/9701316; A.F. Falk, Z. Ligeti, and M.B. Wise, Phys. Lett. B 406, 225 (1997); I. Bigi, R.D. Dikeman, and N. Uraltsev, hep-ph/9706520, presented at 3rd BaBar Physics Workshop, Orsay, France, 1997; P. Ball, hep-ph/9709407, talk given at 7th International Symposium on Heavy Flavor Physics, Santa Barbara, CA, 1997.

[c4] A.O. Bouzas and D. Zappalà, Phys. Lett. B 333, 215 (1994); A. Falk, M. Luke, and M. Savage, Phys. Rev. D 53, 2491 (1996).

[c5] A.I. Sanda and A. Yamada, Phys. Rev. Lett. 75, 2807 (1995).

[c6] APE Collaboration, C.R. Allton et al., Phys. Lett. B 345, 513 (1995); Z. Ligeti and M.B. Wise, Phys. Rev. D 53, 4937 (1996).

[c7] C.S. Kim, T. Morozumi, and A.I. Sanda, Phys. Rev. D 56, 7240 (1997); talk given at 2nd Conference on B Physics and CP Violation, Honolulu, HI, 1997 (hep-ph/9706380).

[c8] G. Buchalla and A. Buras, Phys. Rev. D 54, 6782 (1996).

[c9] G. Buchalla and A. Buras, Nucl. Phys. B400, 225 (1993).

[c10] T. Inami and C.S. Lim, Prog. Theor. Phys. 65, 297 (1981).

[c11] R. Casalbuoni et al., Phys. Rep. 281, 145 (1997).

[c12] P. Colangelo, F. De Fazio, P. Santorelli, and E. Scrimieri, Phys. Rev. D 53, 3672 (1996); Phys. Lett. B 395, 339 (1997).

[c13] W. Jaus and D. Wyler, Phys. Rev. D 41, 3405 (1991); D. Melikhov, N. Nikitin, and S. Simula, Phys. Lett. B 410, 290 (1997).

[c14] W. Roberts, Phys. Rev. D 54, 863 (1996).

[c15] T.M. Aliev, A. Ozpineci, M. Savci, and H. Koru, Phys. Lett. B 400, 194 (1997).

[c16] T.M. Aliev, A. Ozpineci, and M. Savci, Phys. Rev. D 56, 4260 (1997).

[c17] P. Ball and V.M. Braun, Phys. Rev. D 55, 5561 (1997).

[c18] W. Marciano and Z. Parsa, Phys. Rev. D 53, R1 (1996).

[c19] C.S. Kim, D. London, and T. Yoshikawa, Phys. Rev. D 57, 4010 (1998).

[c20] V.M. Belyaev, V.M. Braun, A. Khodjamirian, and R. Rückl, Phys. Rev. D 51, 6177 (1995).

[c21] Particle Data Group, R.M. Barnett et al., Phys. Rev. D 54, 1 (1996).

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Measuring $| V_{td} {/ V}_{ub} |$ $(= \sin γ / \sin β$ within the SM) through $\vec{B} M ν \bar{ν} (M = π, K, ρ {, K}^{*})$ decays

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Measuring |Vtd/Vub| (=sinγ/sinβ within the SM) through B→Mνν¯ (M=π,K,ρ,K*) decays

Abstract

References (21)

Measuring $| V_{td} {/ V}_{ub} |$ $(= \sin γ / \sin β$ within the SM) through $\vec{B} M ν \bar{ν} (M = π, K, ρ {, K}^{*})$ decays