NNLO corrections to charmless hadronic B decays
We report on the status of the perturbative calculation in the QCD factorization framework to charmless hadronic B meson decays and present a compilation of available NNLO results.
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arXiv subjects
Guido Bell
Publications and source records attributed to Guido Bell.
B- -> pi- pi0/rho- rho0 to NNLO in QCD factorization
The approximate tree decays B- -> pi- pi0/rho- rho0 may serve as benchmark channels for testing the various theoretical descriptions of the strong interaction dynamics in hadronic B meson decays. The ratios of hadronic and differential semileptonic B -> pi l nu/rho l nu decay rates at maximum recoil provide particularly clean probes of the QCD dynamics. We confront the recent NNLO calculation in the QCD factorization framework with experimental data and find support for the factorization assumption. A detailed analysis of all tree-dominated B -> pi pi/pi rho/rho rho decay modes seems to favour somewhat enhanced colour-suppressed amplitudes, which may be accommodated in QCD factorization by a small value of the first inverse moment of the B meson light-cone distribution amplitude, lambda_B ~ 250 MeV. Precise measurements of the B -> rho l nu spectrum could help to clarify this point.
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NNLO corrections to inclusive semileptonic B decays in the shape-function region
We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B -> X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO corrections and include a discussion on charm mass effects.
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NNLO vertex corrections in charmless hadronic B decays: Real part
We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced at NNLO. We in particular do not find an enhancement of the phenomenologically important ratio |C/T| from the perturbative calculation.
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Higher order QCD corrections in exclusive charmless B decays
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.
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Modelling light-cone distribution amplitudes from non-relativistic bound states
We calculate light-cone distribution amplitudes for non-relativistic bound states, including radiative corrections from relativistic gluon exchange to first order in the strong coupling constant. We distinguish between bound states of quarks with equal (or similar) mass, m_1 ~ m_2, and between bound states where the quark masses are hierarchical, m_1 >> m_2. For both cases we calculate the distribution amplitudes at the non-relativistic scale and discuss the renormalization-group evolution for the leading-twist and 2-particle distributions. Our results apply to hard exclusive reactions with non-relativistic bound states in the QCD factorization approach like, for instance, (B_c -> eta_c l nu) or (e^+ e^- -> J/psi eta_c). They also serve as a toy model for light-cone distribution amplitudes of light mesons or heavy B and D mesons, for which certain model-independent properties can be derived. In particular, we calculate the anomalous dimension for the B meson distribution amplitude phi_B^-(w) in the Wandzura-Wilczek approximation and derive the according solution of the evolution equation at leading logarithmic accuracy.
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NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B -> pi pi. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quark mass. The numerical impact of the NNLO corrections is found to be significant, in particular they lead to an enhancement of the strong phase of the colour-suppressed tree amplitude.
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