Higher order QCD corrections in exclusive charmless B decays

TL;DR

The work provides a rigorous NNLO exploration of exclusive charmless B decays within QCD Factorization, focusing on the imaginary part of hadronic two-body amplitudes and the real part's partial NNLO treatment. It develops and applies advanced multi-loop techniques (IBP reduction, differential equations, Mellin-Barnes, sector decomposition) to compute master integrals and demonstrates that the NNLO corrections are perturbatively well-defined, with notable strong-phase implications for CP violation. The thesis also investigates heavy-to-light form factors in a non-relativistic setting to test factorization concepts (including soft-overlap ξ) and to analyze endpoint and Sudakov logarithms, providing insights into the structure and resummation of large logs. Collectively, the work advances the precision frontier in exclusive B decays, tests factorization, and furnishes new NRQCD-based inputs for heavy-to-light transitions. The results reinforce QCD Factorization as a robust framework while highlighting remaining power-suppressed uncertainties and the need for further all-order proofs and phenomenological input refinement.

Abstract

We discuss exclusive charmless B decays within the Standard Model of particle physics. In particular, we consider hadronic two-body decays as B -> pi pi and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B -> pi l nu. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. We present results for the imaginary part of the topological tree amplitudes and a partial calculation of the real part of the amplitudes which is technically more involved. In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we consider form factors between non-relativistic bound states. We perform a NLO analysis and compute the so-called soft-overlap contribution which is calculable in our set-up. As a byproduct of our analysis, we calculate leading-twist light-cone distribution amplitudes for non-relativistic bound states which can be applied for B_c or eta_c mesons.

Figures (32)

• Figure 1: Global fit of the unitarity triangle (status September 2006) CKMfitter.
• Figure 2: Running of strong coupling constant runningas.
• Figure 3: Factorization of short- and long distance effects in heavy-to-heavy transitions. The former are contained in a coefficient function $H$, the latter in a soft-overlap contribution $S$. The double lines denote heavy quarks with $m_Q\gg\Lambda_\text{QCD}$.
• Figure 4: Collinear factorization of short- and long distance effects. The former give rise to a hard-scattering kernel $T$, the latter to light-cone distribution amplitudes $\phi_\pi$. The dashed lines denote collinear quarks.
• Figure 5: QCD Factorization of short- and long distance effects in exclusive $B$ decays into heavy-light final states. All related quantities have already been introduced in Figure \ref{['fig:FFtype1']} and \ref{['fig:FFtype2']}.