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

Abstract

I compute the hard spectator interaction amplitude in $B\to \pi \pi$ at NLO i.e. at O(α_s^2). This special part of the amplitude, whose LO starts at O(α_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 ${\alpha }_s$. In this calculation it is necessary to obtain an expansion of Feynman integrals in powers of ${\Lambda }_{\text{QCD}}/m_b$. I will present a general method to obtain this expansion in a systematic way once the leading power is given as an input. This method is based on differential equation techniques and easy to implement in a computer algebra system. The numerical impact on amplitudes and branching ratios is considered. The NLO contributions of the hard spectator interactions are important but small enough for perturbation theory to be valid.

Publication based on my PhD thesis, 41 pages, 12 figures, Changed affiliation and other minor changes, corrected misprint in eq.(44)

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Cited by in corpus (40)

• Flavor Physics in the Quark Sector
• B, D and K decays
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• Three-Body Non-Leptonic B Decays and QCD Factorization
• Revisiting Charmless Hadronic B_{u,d} Decays in QCD Factorization
• NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
• Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude
• Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region
• $B_c$ Exclusive Decays to Charmonium and a Light Meson at Next-to-Leading Order Accuracy
• NNLO vertex corrections in charmless hadronic B decays: Real part
• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• Possible resolution of the B -> pi pi, pi K puzzles
• Master integrals for the two-loop penguin contribution in non-leptonic B-decays
• B- -> pi- pi0/rho- rho0 to NNLO in QCD factorization
• Factorization in exclusive quarkonium production
• Analysis of the $B_q\to D_q(D_q^{\ast })P$ and $B_q\to D_q(D_q^{\ast })V$ decays within the factorization approach in QCD
• Resolving B-CP Puzzles in QCD Factorization
• QCD Factorization for $B\to \pi \pi \ell \nu$ Decays at Large Dipion Masses
• Glauber gluons in spectator amplitudes for $B\to \pi M$ decays
• Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators
• Two-loop non-leptonic penguin amplitude in QCD factorization
• Three-Body Non-Leptonic Heavy-to-heavy $B$ Decays at NNLO in QCD
• Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
• Order alpha_s^2 magnetic penguin correction for B decay to light mesons
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• A Possible Solution to the $B\to \pi \pi$ Puzzle Using the Principle of Maximum Conformality
• Reinvestigating the $B$ $\to$ $PV$ decays by including the contributions from ${\varphi }_{B2}$ with the perturbative QCD approach
• Collider-Flavour Complementarity from the bottom to the top
• Measurement of the branching fraction and $CP$ asymmetry of $B^0\to {\pi }^0{\pi }^0$ decays using $198\times 10^6$ $B\overline{B}$ pairs in Belle II data
• B Physics Theory for Hadron Colliders
• $B_u$ $\to$ $\psi M$ decays and $S$-$D$ wave mixing effects
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• Soft-collinear factorization in B decays
• Non-Leptonic Heavy Meson Decays - Theory Status
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• NNLO corrections to charmless hadronic B decays
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• Theory of charmless hadronic B-decays
• NNLO corrections to semileptonic and hadronic B decays
• Constraining New Physics in B-->pi+pi- with Reparametrization Invariance and QCD Factorization