[Paper Review] Exclusive and Semi-inclusive B Decays in QCD Factorization

Hai-Yang Cheng|ArXiv.org|Oct 2, 2001

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper applies QCD factorization to exclusive and semi-inclusive B decays, computing branching ratios for processes like $B\to\phi K$, $B\to VV$, and $B\to J/\psi K(K^*)$, while extending the framework to semi-inclusive decays $B\to MX$. It shows that nonfactorizable corrections and hard spectator interactions are crucial for accurate predictions, with results in good agreement with experimental data, especially for $B\to J/\psi X_s$ and $B\to \phi K$ modes.

ABSTRACT

Applications of QCD factorization to $B oϕK$, charmless $B o VV$, $B o J/ψK(K^*)$ and semi-inclusive decays $B o MX$ are discussed.

Motivation & Objective

• To compute exclusive and semi-inclusive $B$ decay branching ratios using QCD factorization, addressing nonfactorizable and hard spectator contributions.
• To resolve discrepancies between theoretical predictions and experimental data in $B\to\phi K$ and $B\to VV$ decays by including higher-twist and nonfactorizable corrections.
• To extend the QCD factorization framework to semi-inclusive decays $B\to MX$, avoiding form factor uncertainties and infrared divergences.
• To identify promising modes for direct CP violation measurement with large asymmetries and accessible branching ratios.
• To compare QCD factorization predictions with pQCD and experimental results, highlighting differences due to scale dependence and operator contributions.

Proposed method

• Applies QCD factorization to compute amplitudes for exclusive $B\to\phi K$, $B\to VV$, and $B\to J/\psi K(K^*)$ decays, including vertex-type and penguin-type corrections at $\mathcal{O}(\alpha_s)$.
• Incorporates nonfactorizable corrections via effective parameters $a_i$, with $a_4$ made renormalization-scale and $\gamma_5$-scheme independent by including $\mathcal{O}(\alpha_s)$ corrections.
• Treats power-suppressed annihilation contributions via $X_A$, accounting for $(S-P)(S+P)$ penguin operators not subject to helicity suppression.
• Generalizes the factorization formula to semi-inclusive decays $B\to MX$ by excluding spectator quark contributions and form factors, using $\int du\, T^I(u)\Phi_M(u) + \int d\xi du\, T^{II}(\xi,u)\Phi_B(\xi)\Phi_M(u)$.
• Imposes kinematic cuts ($p_M > 2.1$ GeV) and excludes $B\to M$ form factors to avoid endpoint divergences and reduce background.
• Considers bremsstrahlung and fragmentation processes as subleading corrections, suppressed by $\alpha_s/\pi \approx 7\%$, and focuses on vertex and hard spectator interactions for reliability.

Experimental results

Research questions

• RQ1 How do nonfactorizable corrections and hard spectator interactions affect the branching ratios of $B\to\phi K$ decays, and can they resolve discrepancies with experiment?
• RQ2 Why do pQCD and QCD factorization yield different predictions for $B\to\phi K$ decays, and what role do Wilson coefficients and chromomagnetic dipole operators play?
• RQ3 To what extent do form factor models (LCSR vs. BSW) influence $B\to VV$ decay rates, and which is favored by current data?
• RQ4 Can the QCD factorization framework be reliably extended to semi-inclusive $B\to MX$ decays, and what advantages does it offer over exclusive decays?
• RQ5 Which semi-inclusive $B\to MX$ modes offer the best prospects for measuring direct CP violation with large asymmetries and accessible branching ratios?

Key findings

• The predicted branching ratio for $B^{-}\to\phi K^{-}$ is $(4.6^{+3.2}_{-1.5})\times 10^{-6}$ and for $B^{0}\to\phi K^{0}$ is $(4.2^{+3.0}_{-1.3})\times 10^{-6}$, in agreement with experimental data within uncertainties.
• The $B\to VV$ decay rates strongly depend on the form factor ratio $A_2/A_1$, with LCSR predictions ($\sim9.3\times 10^{-6}$) favoring experimental data over BSW model ($\sim4.3\times 10^{-6}$).
• For $B\to J/\psi K(K^*)$, the predicted branching ratio is too small by a factor of 5 in leading-twist factorization, indicating the need for nonfactorizable corrections.
• The semi-inclusive decay $B\to J/\psi X_s$ is predicted at $9.6\times 10^{-3}$, in excellent agreement with CLEO ($8.0\pm 0.8)\times 10^{-3}$ and BaBar ($7.89\pm 0.10\pm 0.40)\times 10^{-3}$.
• Modes such as $\overline{B}^{0}_{s}\to\rho^{0}X_{s\bar{s}}$, $B^{-}\to K^{*-}X_s$, and $\overline{B}^{0}\to K^{*-}X$ show CP rate asymmetries of $10\sim40\%$ and branching ratios of $10^{-6}\sim10^{-4}$, making them ideal for direct CP violation searches.
• With $1\times 10^7$ $B\overline{B}$ pairs, the $K^{*-}$ channel asymmetry becomes accessible; with $7\times 10^7$ events, other modes become feasible for asymmetry measurements.