The Regularized Siegel-Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula

In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis

Semileptonic BB Meson Decays Into A Highly Excited Charmed Meson Doublet

We study the heavy quark effective theory prediction for semileptonic $B$ decays into an orbital excited $F$-wave charmed doublet, the ($2^{+}$, $3^{+}$) states ($D^{*'}_{2}$, $D_{3}$), at the leading order of heavy quark expansion. The corresponding universal form factor is estimated by using the QCD sum rule method. The decay rates we predict are $\Gamma_{B\to D^{*'}_{2}\ell\overline{\nu}}=1.85\times10^{-19} {GeV}$ and $\Gamma_{B\to D_{3}\ell\overline{\nu}}=1.78\times10^{-19} {GeV}$. The branching ratios are $\mathcal {B}(B\to D_{2}^{*'}\ell\overline{\nu})=4.6\times10^{-7}$ and $\mathcal {B}(B\to D_{3}\ell\overline{\nu})=4.4\times10^{-7}$, respectively.Comment: 6 pages,2 figure