Lattice NRQCD calculation of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mo>−</mo><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math></span> mixing parameter <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></math></span>

S. Hashimoto; K-I. Ishikawa; H. Matsufuru; T. Onogi; N. Yamada

doi:10.1103/PhysRevD.60.094503

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Lattice NRQCD calculation of the $B^{0} - B^{0}$ mixing parameter $B_{B}$

S. Hashimoto and K-I. Ishikawa

H. Matsufuru, T. Onogi, and N. Yamada

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

Department of Physics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

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Phys. Rev. D 60, 094503 – Published 27 September, 1999

DOI: https://doi.org/10.1103/PhysRevD.60.094503

Abstract

We present a lattice calculation of the B meson B parameter $B_{B}$ using the NRQCD action. The heavy quark mass dependence is explicitly studied over a mass range between $m_{b}$ and ${4 m}_{b}$ with the ${O (1 / m}_{Q})$ and ${O (1 / m}_{Q}^{2})$ actions. We find that the ratios of lattice matrix elements $〈 O_{N}^{lat} 〉 / 〈 A_{0}^{lat} 〉^{2}$ and $〈 O_{S}^{lat} 〉 / 〈 A_{0}^{lat} 〉^{2},$ which contribute to $B_{B}$ through mixing, have significant ${1 / m}_{Q}$ dependence while that of the leading operator $〈 O_{L}^{lat} 〉 / 〈 A_{0}^{lat} 〉^{2}$ has little ${1 / m}_{Q}$ effect. The combined result for $B_{B} {(m}_{b})$ has small but nonzero mass dependence, and the $B_{B} {(m}_{b})$ becomes smaller by 10% with the ${1 / m}_{Q}$ correction compared to the static result. Our result in the quenched approximation at $β = 5.9$ is $B_{B_{d}} (5$ GeV) = 0.75(3)(12), where the first error is statistical and the second is a systematic uncertainty.

References (31)

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[c1] For a review of the constraints on the CKM matrix, see, for example, Particle Data Group, C. Caso et al., Eur. Phys. J. C 3, 1 (1998).

[c2] LEP B Oscillations Working Group, LEPBOSC 98/3, available from http://www.cern.ch/LEPBOSC/

[c3] T. Draper, plenary talk given at the XII International Symposium, Boulder, Colorado, hep-lat/9810065.

[c4] B.A. Thacker and G.P. Lepage, Phys. Rev. D 43, 196 (1991); ibid.G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, and K. Hornbostel, 46, 4052 (1992).

[c5] K-I. Ishikawa, H. Matsufuru, T. Onogi, N. Yamada, and S. Hashimoto, Phys. Rev. D 56, 7028 (1997).

[c6] A.X. El-Khadra, A.S. Kronfeld, and P.B. Mackenzie, Phys. Rev. D 55, 3933 (1997).

[c7] JLQCD Collaboration, S. Aoki et al., Phys. Rev. Lett. 80, 5711 (1998); A. El-Khadra et al., Phys. Rev. D 58, 014506 (1998); MILC Collaboration, C. Bernard et al., Phys. Rev. Lett. 81, 4812 (1998).

[c8] JLQCD Collaboration, K-I. Ishikawa et al., talk given at the XII International Symposium, Boulder, Colorado [3], hep-lat/9809152; for previous calculations of $f_{B}$ using the NRQCD action, see [5] and S. Collins et al., Phys. Rev. D 55, 1630 (1997); ibid.A. Ali Khan et al., 56, 7012 (1997); , Phys. Lett. B 427, 132 (1998).

[c9] UKQCD Collaboration, A.K. Ewing et al., Phys. Rev. D 54, 3526 (1996).

[c10] V. Giménez and G. Martinelli, Phys. Lett. B 398, 135 (1997).

[c11] J. Christensen, T. Draper, and C. McNeile, Phys. Rev. D 56, 6993 (1997).

[c12] C. Bernard, T. Blum, and A. Soni, Phys. Rev. D 58, 014501 (1998).

[c13] UKQCD Collaboration, L. Lellouch and C.-J.D. Lin, talk given at the XII International Symposium, Boulder, Colorado, [3], hep-lat/9809018.

[c14] J.M. Flynn, O.F. Hernandez, and B.R. Hill, Phys. Rev. D 43, 3709 (1991).

[c15] A. Borrelli and C. Pittori, Nucl. Phys. B385, 502 (1992); an error in $D_{R}$ is corrected in [16][17][18].

[c16] UKQCD Collaboration, M. Di Pierro and C.T. Sachrajda, Nucl. Phys. B534, 373 (1998).

[c17] V. Giménez and J. Reyes, Nucl. Phys. B545, 576 (1999).

[c18] K-I. Ishikawa, T. Onogi, and N. Yamada, Phys. Rev. D 60, 034501 (1999).

[c19] N. Yamada et al., talk given at the XII International Symposium, Boulder, Colorado [3], hep-lat/9809156.

[c20] G. Buchalla, A.J. Buras, and M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996), and references therein.

[c21] B. Sheikholeslami and R. Wohlert, Nucl. Phys. B259, 572 (1985).

[c22] M. Golden and B. Hill, Phys. Lett. B 354, 225 (1991).

[c23] A. Duncan et al., Phys. Rev. D 51, 5101 (1995), and references therein.

[c24] G.P. Lepage and P.B. Mackenzie, Phys. Rev. D 48, 2250 (1993).

[c25] C.T.H. Davies and B.A. Thacker, Phys. Rev. D 45, 915 (1992).

[c26] C.J. Morningstar, Phys. Rev. D 48, 2265 (1993).

[c27] G.P. Lepage, Nucl. Phys. B (Proc. Suppl.) 26, 45 (1992).

[c28] S. Hashimoto, Phys. Rev. D 50, 4639 (1994).

[c29] V. Giménez, Nucl. Phys. B401, 116 (1993).

[c30] M. Ciuchini, E. Franco, and V. Giménez, Phys. Lett. B 388, 167 (1996).

[c31] G. Buchalla, Phys. Lett. B 395, 364 (1997).

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Lattice NRQCD calculation of the $B^{0} - B^{0}$ mixing parameter $B_{B}$

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Lattice NRQCD calculation of the B0−B0 mixing parameter BB

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References (31)

Lattice NRQCD calculation of the $B^{0} - B^{0}$ mixing parameter $B_{B}$