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Physical Review D

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$B \to D^{*} l ν$ and $B \to D l ν$ form factors in staggered chiral perturbation theory

Jack Laiho and Ruth S. Van de Water

Theoretical Physics Department, Fermilab, Batavia, Illinois 60510, USA

Phys. Rev. D 73, 054501 – Published 2 March, 2006

DOI: https://doi.org/10.1103/PhysRevD.73.054501

Abstract

We calculate the $B \to D$ and $B \to D^{*}$ form factors at zero recoil in staggered chiral perturbation theory. We consider heavy-light mesons in which only the light ( $u$ , $d$ , or $s$ ) quark is staggered; current lattice simulations generally use a highly improved action such as the Fermilab or nonrelativistic QCD action for the heavy ( $b$ or $c$ ) quark. We work to lowest nontrivial order in the heavy-quark expansion and to one-loop order in the chiral expansion. We present results for a partially quenched theory with three sea quarks in which there are no mass degeneracies (the “ $1 + 1 + 1$ ” theory) and for a partially quenched theory in which the $u$ and $d$ sea quark masses are equal (the “ $2 + 1$ ” theory). We also present results for full ( $2 + 1$ ) QCD, along with a numerical estimate of the size of staggered discretization errors. Finally, we calculate the finite volume corrections to the form factors and estimate their numerical size in current lattice simulations.

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References (23)

S. Hashimoto et al., Phys. Rev. D 61, 014502 (2000).
S. Hashimoto, A. S. Kronfeld, P. B. Mackenzie, S. M. Ryan, and J. N. Simone, Phys. Rev. D 66, 014503 (2002).
M. Okamoto et al., Nucl. Phys. B, Proc. Suppl. 140, 461 (2005).
A. D. Kennedy, Nucl. Phys. B, Proc. Suppl. 140, 190 (2005).
C. Aubin et al. (MILC), Phys. Rev. D 70, 114501 (2004).
W.-J. Lee and S. R. Sharpe, Phys. Rev. D 60, 114503 (1999).
C. Aubin and C. Bernard, Phys. Rev. D 68, 034014 (2003).
C. Aubin and C. Bernard, Phys. Rev. D 68, 074011 (2003).
S. R. Sharpe and R. S. Van de Water, Phys. Rev. D 71, 114505 (2005).
C. Aubin and C. Bernard, Phys. Rev. D 73, 014515 (2006).
C. Aubin et al., Phys. Rev. Lett. 95, 122002 (2005).
J. Laiho, Proc. Sci., LAT2005 (2005) 221 [hep-lat/0510058].
D. Arndt and C. J. D. Lin, Phys. Rev. D 70, 014503 (2004).
A. S. Kronfeld, Phys. Rev. D 62, 014505 (2000).
A. S. Kronfeld, Nucl. Phys. B, Proc. Suppl. 129, 46 (2004).
G. Burdman and J. F. Donoghue, Phys. Lett. B 280, 287 (1992).
M. B. Wise, Phys. Rev. D 45, R2188 (1992).
S. R. Sharpe and Y. Zhang, Phys. Rev. D 53, 5125 (1996).
N. Isgur and M. B. Wise, Phys. Lett. B 232, 113 (1989).
M. E. Luke, Phys. Lett. B 252, 447 (1990).
S. Dürr, Proc. Sci., LAT2005 (2005) 021 [hep-lat/0509026].
M. J. Savage, Phys. Rev. D 65, 034014 (2002).
L. Randall and M. B. Wise, Phys. Lett. B 303, 135 (1993).