Information on $B\to \pi \pi$ Provided by the Semileptonic Process $B\to \pi l\nu$

Abstract

Analysis of the present data on the semileptonic process $B\to \pi \ell \nu$ indicates that they have not yet reached the precision to provide adequate information on the $B\to \pi$ form factor $F_{+}(q^2)$, which for $q^2=m_{\pi }^2$ is known to be related to the factorized color-favored (``$T$'', or ``tree'') contribution to $B^0\to {\pi }^{+}{\pi }^{-}$. It is shown here that with around 500 $B\to \pi \ell \nu$ events in which rate and spectrum are measured one can improve the accuracy of $T$ by a significant amount. A recent CLEO determination of the $D^{\ast }D\pi$ coupling constant is compared with an earlier prediction, and its role in the description of the $B\to \pi$ form factors is noted. When combined with an estimate of the penguin amplitude (``$P$'') obtained using flavor SU(3) symmetry from $B\to K\pi$ decays, information on $T$ allows one to gauge the effects of the penguin amplitude on extraction of the weak phase $\alpha ={\varphi }_2$ from the time-dependent CP-violating rate asymmetry in $B^0\to {\pi }^{+}{\pi }^{-}$. The constraint on $\alpha$ implied by a recent experimental result on this asymmetry is described.

17 pages, LaTeX, 7 figures, revised version resubm. to Phys. Rev. D. Further modifications in abstract, text, and references

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Cited by in corpus (11)

• Two-Body Charmless B Decays Involving eta and eta'
• Strong and Weak Phases from Time-Dependent Measurements of $B\to \pi \pi$
• Evidence for CP-Violating Asymmetries in B0->pi+pi- Decays and Constraints on the CKM Angle phi2
• Updated Analysis of Some Two-Body Charmless B Decays
• Convention-independent study of CP-violating asymmetries in $B\to \pi \pi$
• Weak Phase $\gamma$ from $B_s(t)\to K^{+}{K}^{-}$
• The factorizable amplitude in $B^0\to {\pi }^{+}{\pi }^{-}$
• Charming penguins in B -> PP decays and the extraction of gamma
• Remarks on Semileptonic B and D Decays into Orbitally Excited Mesons
• Conference Summary (5th Int. Conf. on Hyperons, Charm, and Beauty Hadrons)
• $B\to D_s\pi$ and the tree amplitude in $B\to {\pi }^{+}{\pi }^{-}$