Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization

Abstract

We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays ${\bar{B}}_{(s)}\to D_{(s)}^{(\ast )+}{L}^{-}$ and ${\Lambda }_b\to {\Lambda }_c^{+}{L}^{-}$, where $L$ is a light meson from the set $\{\pi ,\rho ,K^{(\ast )},a_1\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop $\mathcal{O}({\alpha }_s^2)$ correction to the leading-power hard scattering kernels, and give the results for the convoluted kernels almost completely analytically. Our newly computed contribution amounts to a positive shift of the magnitude of the tree amplitude by $\sim 2$\%. We then perform an extensive phenomenological analysis to NNLO in QCD factorization, using the most recent values for non-perturbative input parameters. Given the fact that the NNLO perturbative correction and updated values for form factors increase the theory prediction for branching ratios, while experimental central values have at the same time decreased, we reanalyze the role and potential size of power corrections by means of appropriately chosen ratios of decay channels.

38 pages, 5 tables, 4 figures. v2: Added explicit numbers for semi-leptonic rates that enter the factorization test, plus a few more minor adjustments. Matches version accepted by JHEP

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• Global Analysis of hadronic two-body B decays in the perturbative QCD approach
• Quasi-two-body decays $B\to D{K}^{\ast }(892)\to DK\pi$ in the perturbative QCD approach
• Using $B_s^0\to D_s^{\mp }{K}^{\pm }$ Decays as a Portal to New Physics
• Revealing New Physics in $B_s^0\to D_s^{\mp }{K}^{\pm }$ Decays
• Study of the weak annihilation contributions in charmless $B_s\to VV$ decays
• Study of ${\bar{B}}_{u,d,s}^{\ast }\to D_{u,d,s}^{\ast }V(V=D_{d,s}^{\ast -},K^{\ast -},{\rho }^{-})$ weak decays
• Diquark Explanation of $b\to s{\ell }^{+}{\ell }^{-}$
• Study of $\overline{B}{}^0\to D^{+}{h}^{-}(h=K/\pi )$ decays at Belle
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• Determinations of $|V_{cb}|$ and $|V_{ub}|$ from baryonic ${\Lambda }_b$ decays
• Collider-Flavour Complementarity from the bottom to the top
• Probing new physics in class-I $B$-meson decays into heavy-light final states
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• HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Charmless Non-Leptonic Multi-Body B decays
• Towards a Global Analysis of the $b\to c\bar{u}q$ Puzzle
• The $b$ quark fragmentation fractions at LHCb and meson decays with heavy quark spectators
• Possibility of experimental study on nonleptonic $B_c^{\ast }$ weak decays
• QED factorization of two-body non-leptonic and semi-leptonic $B$ to charm decays
• Testing the Standard Model with CP-asymmetries in flavour-specific non-leptonic decays
• Theory Motivation: What measurements are needed?
• Study of the two-body nonleptonic $B_c(2S)$ weak decays with the QCD factorization approach
• Measurement of B meson production fraction ratios in proton-proton collisions at $\sqrt{s}$ = 13 TeV using open-charm and charmonium decays
• Observation of ${\Lambda }_b^0\to D^{+}p{\pi }^{-}{\pi }^{-}$ and ${\Lambda }_b^0\to D^{\ast +}p{\pi }^{-}{\pi }^{-}$ decays