NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part

Abstract

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.

28 pages, 6 figures. v2: minor changes in Section 4.3, results unchanged, version accepted for publication in Nuclear Physics B

References in corpus (36)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• Harmonic Polylogarithms
• Differential Equations for Two-Loop Four-Point Functions
• QCD factorization for B->PP and B->PV decays
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• Differential Equations for Feynman Graph Amplitudes
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• The B-Meson Distribution Amplitude in QCD
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• The B Meson Decay Constant from Unquenched Lattice QCD
• Evanescent Operators, Scheme Dependences and Double Insertions
• Moments of pseudoscalar meson distribution amplitudes from the lattice
• f_B and f_B_s from QCD sum rules
• |Delta F| = 1 Nonleptonic Effective Hamiltonian in a Simpler Scheme
• Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors
• Model-Independent Properties of the B-Meson Distribution Amplitude
• Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes
• Heavy-to-light B meson form factors at large recoil energy -- spectator-scattering corrections
• $B$-Meson Distribution Amplitude from the $B\to \pi$ Form Factor
• The Evolution of the Pion Distribution Amplitude in Next-to-Leading Order
• Heavy-Light Meson Decay Constant from QCD Sum Rules in Three-Loop Approximation
• Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes
• |V_ub| and Constraints on the Leading-Twist Pion Distribution Amplitude from B->pi l nu
• Hard spectator interactions in B to pi pi at order alpha_s^2
• Loop Corrections to Heavy-to-Light Form Factors and Evanescent Operators in SCET
• Higher order QCD corrections in exclusive charmless B decays
• Decay constants of charm and beauty pseudoscalar heavy-light mesons on fine lattices
• Asymptotics of QCD Factorization in Exclusive Hadronic Decays of B Mesons
• Phenomenology of B -> pi pi, pi K Decays at O(alpha^2 beta_0) in QCD Factorization

Cited by in corpus (59)

• The Physics of the B Factories
• 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
• Anatomy of the pQCD Approach to the Baryonic Decays ${\Lambda }_b\to p\pi ,pK$
• Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region
• Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude
• Model-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesons
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• NNLO vertex corrections in charmless hadronic B decays: Real part
• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• Hard spectator interactions in B to pi pi at order alpha_s^2
• Possible resolution of the B -> pi pi, pi K puzzles
• NNLO corrections to B --> X_u l nu in the shape-function region
• Master integrals for the two-loop penguin contribution in non-leptonic B-decays
• B- -> pi- pi0/rho- rho0 to NNLO in QCD factorization
• Heavy-to-light currents at NNLO in SCET and semi-inclusive anti-B ---> X(s) l+ l- decay
• CP violation in the B system
• 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
• Higher order QCD corrections in exclusive charmless B decays
• Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators
• On a two-loop crossed six-line master integral with two massive lines
• QED factorization of non-leptonic $B$ decays
• Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel
• Two-loop non-leptonic penguin amplitude in QCD factorization
• Three-Body Non-Leptonic Heavy-to-heavy $B$ Decays at NNLO in QCD
• Two-loop master integrals for non-leptonic heavy-to-heavy decays
• Anomalies in Hadronic $B$ Decays
• Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
• ${\bar{B}}_{d,s}\to D_{d,s}^{\ast }V$ and ${\bar{B}}_{d,s}^{\ast }\to D_{d,s}V$ decays within QCD Factorization and Possible Puzzles
• The effects of a family non-universal Z-prime boson on B--->pipi decays
• Order alpha_s^2 magnetic penguin correction for B decay to light mesons
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• CP Asymmetries in B->K pi, K*pi, rho K Decays
• Disentangling weak and strong interactions in $B\to K^{\ast }(\to K\pi )\pi$ Dalitz-plot analyses
• A Possible Solution to the $B\to \pi \pi$ Puzzle Using the Principle of Maximum Conformality
• Collider-Flavour Complementarity from the bottom to the top
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• B Physics Theory for Hadron Colliders
• Anomalies in Hadronic $B$ Decays: an Update
• $B_u$ $\to$ $\psi M$ 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
• Charmless Non-Leptonic Multi-Body 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
• Isospin-based EWP-tree Relations
• Non-leptonic B-decays at two loops in QCD Factorization
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• Recent Development of QCD Factorization for B-> M1 M2
• Theory of charmless hadronic B-decays
• Constraining New Physics in B-->pi+pi- with Reparametrization Invariance and QCD Factorization
• A possible solution of $B$ arrow $\pi \pi$ puzzle in Z' model