Transverse-momentum-dependent wave functions with Glauber gluons in $B\to \pi \pi$, $\rho \rho$ decays

Abstract

We investigate the Glauber-gluon effect on the $B\to \pi \pi$ and $\rho \rho$ decays, which is introduced via a convolution of a universal Glauber phase factor with transverse-momentum-dependent(TMD) meson wave functions in the $k_T$ factorization theorem. For an appropriate parametrization of the Glauber phase, it is observed that a TMD wave function for the pion ($\rho$ meson) with a weak (strong) falloff in parton transverse momentum $k_T$ leads to significant (moderate) modification of the $B^0\to {\pi }^0{\pi }^0$ ($B^0\to {\rho }^0{\rho }^0$) branching ratio: the former (latter) is enhanced (reduced) by about a factor of 2 (15\%). This observation is consistent with the dual role of the pion as a massless Nambu-Goldstone boson and as a $q\bar{q}$ bound state, which requires a tighter spatial distribution of its leading Fock state relative to higher Fock states. The agreement between the theoretical predictions and the data for all the $B\to \pi \pi$ and ${\rho }^0{\rho }^0$ branching ratios is then improved simultaneously, and it is possible to resolve the $B\to \pi \pi$ puzzle.

arXiv commentRevTex file, 11 pages, 4 figures, and 1 table, contents improved and references added; matching the published version

References in corpus (44)

• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• Fat penguins and imaginary penguins in perturbative QCD
• Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach
• Calculating the Jet Quenching Parameter from AdS/CFT
• Higher Twist Distribution Amplitudes of Vector Mesons in QCD: Formalism and Twist Three Distributions
• Final State Interactions in Hadronic B Decays
• Theoretical Update of Pseudoscalar Meson Distribution Amplitudes of Higher Twist: The Nonsinglet Case
• Wilson loops in heavy ion collisions and their calculation in AdS/CFT
• Leading-power contributions to $B\to \pi ,\rho$ transition form factors
• Branching fractions, polarisation and asymmetries of B -> VV decays
• B->V gamma Beyond QCD Factorisation
• k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
• Resolution to the B -> pi K puzzle
• Transverse Momentum Broadening and the Jet Quenching Parameter, Redux
• Next-to-leading-order corrections to $B\to \pi$ form factors in $k_T$ factorization
• 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
• Updating B --> PP, VP decays in the framework of flavor symmetry
• Final State Interactions and New Physics in B -> pi K Decays
• Gauge invariant definition of the jet quenching parameter
• Possible resolution of the B -> pi pi, pi K puzzles
• The perturbative pion-photon transition form factors with transverse momentum corrections
• Implication of the B -> rho rho data on the B -> pi pi puzzle
• The NLO twist-3 contributions to $B\to \pi$ form factors in $k_T$ factorization
• Final State Rescattering and Color-suppressed \bar B^0-> D^{(*)0} h^0 Decays
• SCET Analysis of B -> K pi, B -> K Kbar, and B -> pi pi Decays
• Universality of the rho-meson coupling in effective field theory
• Spectator Scattering and Annihilation Contributions as a Solution to the $\pi K$ and $\pi \pi$ Puzzles within QCD Factorization Approach
• Space-like and time-like pion-rho transition form factors in the light-cone formalism
• Pion Form Factor in the $k_T$ Factorization Formalism
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• Glauber gluons in spectator amplitudes for $B\to \pi M$ decays
• Indication for Large Rescatterings in Charmless Rare B Decays
• Rescattering effects in charmless B_{u,d,s} to P P decays
• The puzzles in $B\to \pi \pi$ and $\pi K$ decays: possible implications for R-parity violating supersymmetry
• On the $\pi$ and $K$ as $q\bar{q}$ Bound States and Approximate Nambu-Goldstone Bosons
• Power corrections in e+ e- --> pi+ pi-, K+ K- and B --> K pi, pi pi
• Measurements of New Physics in B -> pi pi Decays
• To the origin of the difference of FSI phases in $B\to \pi \pi$ and $B\to \rho \rho$ decays
• Three-parton contribution to the $B\to \pi$ form factors in $k_T$ factorization
• Restoration of $k_T$ factorization for low $p_T$ hadron hadroproduction
• Looking for Delta I = 5/2 amplitude components in B -> pi pi and B -> rho rho experiments
• Jet Quenching Parameter via Soft Collinear Effective Theory (SCET)
• Implications for new physics from ${\bar{B}}^0\to {\pi }^0{\pi }^0$ and ${\bar{B}}^0\to {\bar{K}}^0{K}^0$

Cited by in corpus (17)

• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Hochschild homology, trace map and $\zeta$-cycles
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• Resolving the $B\to K\pi$ puzzle by Glauber-gluon effects
• Reinvestigating the $B$ $\to$ $PP$ decays by including the contributions from ${\varphi }_{B2}$
• The PQCD approach towards to next-to-leading order: a short review
• Nonleptonic decays of $B\to (f_1(1285),f_1(1420))V$ in the perturbative QCD approach
• Large non-factorizable contributions in $B\to a_0{a}_0$ decays
• The perturbative QCD factorization of $\rho {\gamma }^{\star }\to \rho$
• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• The next-to-leading order corrections to $B\to \rho$ transition in the $k_T$ factorization
• Hadronic decays of $B\to a_1(1260)b_1(1235)$ in the perturbative QCD approach
• Glauber gluons in pion-induced Drell-Yan processes revisited
• Glauber gluons in annihilation amplitudes for heavy meson decays