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Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
We report the results of a study of the exclusive charmless semileptonic
decays, B^0 --> pi^- l^+ nu, B^+ --> pi^0 l^+ nu, B^+ --> omega l^+ nu, B^+ -->
eta l^+ nu and B^+ --> eta^' l^+ nu, (l = e or mu) undertaken with
approximately 462x10^6 B\bar{B} pairs collected at the Upsilon(4S) resonance
with the BABAR detector. The analysis uses events in which the signal B decays
are reconstructed with a loose neutrino reconstruction technique. We obtain
partial branching fractions in several bins of q^2, the square of the momentum
transferred to the lepton-neutrino pair, for B^0 --> pi^- l^+ nu, B^+ --> pi^0
l^+ nu, B^+ --> omega l^+ nu and B^+ --> eta l^+ nu. From these distributions,
we extract the form-factor shapes f_+(q^2) and the total branching fractions
BF(B^0 --> pi^- l^+ nu) = (1.45 +/- 0.04_{stat} +/- 0.06_{syst})x10^-4
(combined pi^- and pi^0 decay channels assuming isospin symmetry), BF(B^+ -->
omega l^+ nu) = (1.19 +/- 0.16_{stat} +/- 0.09_{syst})x10^-4 and BF(B^+ --> eta
l^+ nu) = (0.38 +/- 0.05_{stat} +/- 0.05_{syst})x10^-4. We also measure BF(B^+
--> eta^' l^+ nu) = (0.24 +/- 0.08_{stat} +/- 0.03_{syst})x10^-4. We obtain
values for the magnitude of the CKM matrix element V_{ub} by direct comparison
with three different QCD calculations in restricted q^2 ranges of B --> pi l^+
nu decays. From a simultaneous fit to the experimental data over the full q^2
range and the FNAL/MILC lattice QCD predictions, we obtain |V_{ub}| = (3.25 +/-
0.31)x10^-3, where the error is the combined experimental and theoretical
uncertainty.Comment: 35 pages, 14 figures, submitted to PR
Gr\"obner-Shirshov bases for -algebras
In this paper, we firstly establish Composition-Diamond lemma for
-algebras. We give a Gr\"{o}bner-Shirshov basis of the free -algebra
as a quotient algebra of a free -algebra, and then the normal form of
the free -algebra is obtained. We secondly establish Composition-Diamond
lemma for -algebras. As applications, we give Gr\"{o}bner-Shirshov bases of
the free dialgebra and the free product of two -algebras, and then we show
four embedding theorems of -algebras: 1) Every countably generated
-algebra can be embedded into a two-generated -algebra. 2) Every
-algebra can be embedded into a simple -algebra. 3) Every countably
generated -algebra over a countable field can be embedded into a simple
two-generated -algebra. 4) Three arbitrary -algebras , , over a
field can be embedded into a simple -algebra generated by and if
and , where is the free product of
and .Comment: 22 page
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