Speaker
Description
We analyze the factorization to subleading power in the flavor changing neutral current processes $\bar B\rightarrow X_{s} \ell^+ \ell^-$ and $\bar B\rightarrow X_{d} \ell^+ \ell^-$. In particular, we compute the so-called resolved contributions and explore the numerical impact on observables. In these contributions the virtual photon couples to light partons instead of connecting directly to the effective weak-interaction vertex.
As distinctive feature, the resolved contributions remain nonlocal when the hadronic mass cut is released. Therefore, they reflect an irreducible uncertainty not dependent on the hadronic mass cut. They factorize in hard functions describing physics at the high scale $m_b$, in so-called jet functions characterizing the physics at the hadronic final state $X_s$ which corresponds to an invariant mass of order $\sqrt{m_b \Lambda_{\rm QCD}}$, and in soft functions, so-called shape functions, parametrizing the hadronic physics at the scale $\Lambda_{\rm QCD}$. Knowing the explicit form of the latter, one can derive general properties of such shape functions which allow for precise estimates of the corresponding uncertainties.
