[Paper Review] Non-factorizable contributions in B decays revisited

K. Terasaki|ArXiv.org|Nov 29, 2000

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper re-evaluates non-factorizable contributions in exclusive B decays by decomposing amplitudes into factorizable (naive factorization) and non-factorizable (hard pion approximation in infinite momentum frame) components. It finds that while factorizable amplitudes dominate in color-favored decays like $\bar{B}\to D\pi$ and $D^*\pi$, non-factorizable contributions are non-negligible and crucial for interference; in color-suppressed decays like $\bar{B}\to J/\psi\bar{K}$, they are dominant and essential for reproducing experimental branching ratios.

ABSTRACT

Two-body decays of B mesons are studied by decomposing their amplitude into a sum of factorizable and non-factorizable ones. The former is estimated by using the naive factorization while the latter is calculated by using a hard pion (or kaon) approximation in the infinite momentum frame. It is seen that the non-factorizable contribution is small but not negligible in color favored decays while it is more important in color mismatched decays.

Motivation & Objective

• To assess the role of non-factorizable (long-distance) contributions in exclusive B decays beyond naive factorization.
• To resolve inconsistencies in measured branching ratios for $\bar{B}\to D\pi$ and $D^*\pi$ decays by estimating phenomenologically allowed lower bounds.
• To evaluate the importance of final-state interactions and non-leading large-$N_c$ effects in charm and B meson decays.
• To determine whether non-factorizable amplitudes can improve agreement with experimental branching ratios, especially in color-suppressed modes.
• To examine the sensitivity of results to model-dependent form factors and $B_H$ parameters.

Proposed method

• Decomposes decay amplitudes into factorizable (naive factorization) and non-factorizable (hard pion approximation) components.
• Applies the hard pion approximation in the infinite momentum frame (IMF) to compute non-factorizable contributions.
• Uses the BSW Hamiltonian with $a_1 \simeq 1.024$ and phenomenological $a_2 \simeq 0.21$ for factorized amplitudes.
• Estimates phenomenologically allowed branching ratios by excluding unphysical values of phase differences ($\cos\delta > 1$).
• Compares sum of factorized and non-factorized amplitudes with experimental data and phenomenological estimates.
• Evaluates sensitivity of results to $B_H$ and $B_H'$ parameters and model-dependent form factors.

Experimental results

Research questions

• RQ1 How significant are non-factorizable contributions in $\bar{B}\to D\pi$ and $D^*\pi$ decays, and do they improve agreement with experimental branching ratios?
• RQ2 Can the observed branching ratios for $\bar{B}\to D\pi$ and $D^*\pi$ decays be consistently explained by a sum of factorized and non-factorized amplitudes?
• RQ3 Why do measured branching ratios for $\bar{B}^0\to D^{0}\pi^0$ and $D^{*0}\pi^0$ remain unmeasured, and what lower bounds can be phenomenologically derived?
• RQ4 How do non-factorizable contributions affect color-suppressed decays such as $\bar{B}\to J/\psi\bar{K}$ and $J/\psi\pi$?
• RQ5 To what extent are the results sensitive to the values of form factors and the $B_H$ parameters?

Key findings

• Non-factorizable contributions are small but non-negligible in color-favored $\bar{B}\to D\pi$ and $D^*\pi$ decays, and can still interfere significantly with the dominant factorized amplitude.
• Phenomenologically allowed lower bounds for ${\cal B}(\bar{B}^0\to D^{0}\pi^0)$ and ${\cal B}(\bar{B}^0\to D^{*0}\pi^0)$ are derived from consistency with measured branching ratios of other modes.
• In color-suppressed decays $\bar{B}\to J/\psi\bar{K}$ and $J/\psi\pi$, non-factorizable contributions are dominant and essential for reproducing experimental branching ratios.
• The sum of factorized and non-factorized amplitudes improves agreement with data compared to naive factorization alone, but results remain sensitive to model-dependent form factors.
• With $a_2 \simeq 0.125$, even the sum of amplitudes fails to reproduce experimental rates unless $B_H'$ is significantly larger than $B_H \simeq 0.17$, indicating sensitivity to hadronic matrix elements.
• The non-factorizable amplitude is proportional to asymptotic matrix elements $B_H$ and $B_H'$, highlighting the importance of long-distance dynamics in exclusive B decays.