$B\to \pi \pi$ Decay in QCD

Abstract

A new method is suggested to calculate the $B\to \pi \pi$ hadronic matrix elements from QCD light-cone sum rules. To leading order in ${\alpha }_s$ and $1/m_b$, the sum rule reproduces a factorizable matrix element, in accordance with the prediction of the QCD factorization approach. Whereas the QCD factorization can only take into account the nonfactorizable corrections induced by hard-gluon exchanges, the method suggested here also allows a systematic inclusion of soft-gluon effects. In this paper, I concentrate on the latter aspect and present a calculation of the nonfactorizable soft-gluon exchange contributions to $B\to \pi \pi$. The result, including twist 3 and 4 terms, is suppressed by one power of $1/m_b$ with respect to the factorizable amplitude. Despite its numerical smallness, the soft effect is at the same level as the $O({\alpha }_s)$ correction to the QCD factorization formula for $B\to \pi \pi$. The method suggested here can be applied to matrix elements of different topologies and operators and to various other B-decay channels. I also comment on the earlier applications of QCD sum rules to nonleptonic decays of heavy mesons.

20 pages, 2 figures, Latex, epsfig.sty, a few sentences reworded, two comments added, version to appear in Nucl. Phys. B

Cited by in corpus (49)

• Generalized Parton Distributions
• QCD factorization for B->PP and B->PV decays
• Charm-loop effect in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }\gamma$
• B->V gamma Beyond QCD Factorisation
• Unbiased analysis of CLEO data at NLO and pion distribution amplitude
• B, D and K decays
• CP Violation in the B System and Relations to $K\to \pi \nu \bar{\nu }$ Decays
• Nonfactorizable contributions to $B\to D^{(\ast )}M$ decays
• Isospin asymmetries in $B\to (K^{\ast },\rho )\gamma /l^{+}{l}^{-}$ and $B\to K{l}^{+}{l}^{-}$ in and beyond the Standard Model
• Direct CP asymmetry in $D\to {\pi }^{-}{\pi }^{+}$ and $D\to K^{-}{K}^{+}$ in QCD-based approach
• Comments on Color-Suppressed Hadronic B Decays
• B->gamma e nu Transitions from QCD Sum Rules
• Twist-3 distribution amplitudes of scalar mesons from QCD sum rules
• Exclusive Chromomagnetism in heavy-to-light FCNCs
• $\Delta A_{CP}$ within the Standard Model and beyond
• Nonleptonic $B_s$ to charmonium decays: analyses in pursuit of determining the weak phase ${\beta }_s$
• Flavour SU(3) Symmetry in Charmless B Decays
• Scalar mesons in weak semileptonic decays of $B_{(s)}$
• Light-cone QCD sum rules for the semileptonic decay Lambda_b --> p lepton anti-neutrino
• New Aspects of B -> pi pi, pi K and their Implications for Rare Decays
• Annihilation effects in $B\to \pi \pi$ from QCD Light-Cone Sum Rules
• Probing Non-leptonic Two-body Decays of $B_c$ meson
• QCD Light-Cone Sum Rule Estimate of Charming Penguin Contributions in B -> pi pi
• LCSR analysis of exclusive two-body B decay into charmonium
• Hochschild homology, trace map and $\zeta$-cycles
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• Nonfactorizable corrections to B -> J/psi K
• Nonfactorizable soft contributions in the $B⟶{\eta }_{c}K,{\chi }_{c0}K$ decays with the light-cone sum rules approach
• Strong Couplings of Heavy Mesons to A Light Vector Meson in QCD
• $B\to K_0^{\ast }(1430)l^{+}{l}^{-}$ decays in supersymmetric theories
• Gluonic Penguins in $B\to \pi \pi$ from QCD Light-Cone Sum Rules
• Global Analysis of hadronic two-body B decays in the perturbative QCD approach
• Higher-Order Corrections to QCD Factorization in B->pi K,pi pi Decays
• Three-parton contribution to pion form factor in kT factorization
• A gluonic mechanism for B --> D eta'
• QCD aspects of exclusive B meson decays
• Exclusive non-leptonic B meson decays from QCD
• The PQCD approach towards to next-to-leading order: a short review
• $Z\to {\pi }^{+}{\pi }^{-},K^{+}{K}^{-}$: A touchstone of the PQCD approach
• W-exchange contribution to the decays ${\Xi }_{cc}^{++}\to {\Xi }_c^{+(\prime )}{\pi }^{+}$ using light-cone sum rules
• Three-parton contribution to the $B\to \pi$ form factors in $k_T$ factorization
• Family Non-universal $Z^{\prime }$ Effects on $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ Decays in Perturbative QCD Approach
• $B\to K\pi$ Decays with $1/m_b$ Corrections in $QCD$ Factorization
• Theory of CP Violation in the B-Meson System
• W-exchange/Annihilation amplitudes in LCSR - $B_d^0\to D_s^{-}{K}^{+}$ as an example
• Analysis of the decay $B^0\to {\chi }_{c1}{\pi }^0$ with light-cone QCD sum rules
• Two-body modes of B mesons and the CP-b triangle
• Exclusive Charmless $B$ Decays in QCD
• Non-factorization contributions in $D\to \pi K,KK$ decay