Hard spectator interactions in B to pi pi at order alpha_s^2

Understand

In the present thesis I discuss the hard spectator interaction amplitude in $B\to\pi\pi$ at NLO i.e.

• at $\mathcal{O}(\alpha_s^2)$.
• This special part of the amplitude, whose LO starts at $\mathcal{O}(\alpha_s)$, is defined in the framework of QCD factorization.
• QCD factorization allows to separate the short- and the long-distance physics in leading power in an expansion in $\lqcd/m_b$, where the short-distance physics can be calculated in a perturbative expansion in $\alpha_s$.