Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Glauber gluons in spectator amplitudes for $B \to \pi M$ decays   We extract the Glauber divergences from the spectator amplitudes for two-body
hadronic decays $B \to M_1 M_2$ in the $k_T$ factorization theorem, where $M_2$
denotes the meson emitted at the weak vertex. Employing the eikonal
approximation, the divergences are factorized into the corresponding Glauber
phase factors associated with the $M_1$ and $M_2$ mesons. It is observed that
the latter factor enhances the spectator contribution to the color-suppressed
tree amplitude by modifying the interference pattern between the two involved
leading-order diagrams. The first factor rotates the enhanced spectator
contribution by a phase, and changes its interference with other tree diagrams.
The above Glauber effects are compared with the mechanism in elastic
rescattering among various $M_1 M_2$ final states, which has been widely
investigated in the literature. We postulate that only the Glauber effect
associated with a pion is significant, due to its special role as a $q \bar q$
bound state and as a pseudo Nambu-Goldstone boson simultaneously. Treating the
Glauber phases as additional inputs in the perturbative QCD (PQCD) approach, we
find a good fit to all the $B \to \pi\pi$, $\pi\rho$, $\pi\omega$, and $\pi K$
data, and resolve the long-standing $\pi\pi$ and $\pi K$ puzzles. The
nontrivial success of this modified PQCD formalism is elaborated.

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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph