QCD factorization for ${\Lambda }_b^0\to {\Lambda }_c^{+}{\pi }^{-}$

Abstract

We prove that in the limit $m_b,m_c\to \infty$ with $m_c/m_b$ fixed, factorization holds at order ${\alpha }_s$ for the decay ${\Lambda }_b^0\to {\Lambda }_c^{+}{\pi }^{-}$. This proof is done in the infinite-momentum frame in which the momenta of $\pi$, ${\Lambda }_c$, and ${\Lambda }_b$ go to infinity. Our result is renormalization scale and scheme independent at $\mathcal{O}({\alpha }_s)$. This is the same as QCD factorization for $B\to D\pi$.