$B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist (1811.00983v2)

Abstract: We provide results for the full set of form factors describing semileptonic $B$-meson transitions to pseudoscalar mesons $\pi$, $K$, $\bar{D}$ and vector mesons $\rho$, $K^*$, $\bar{D}^*$. Our results are obtained within the framework of QCD Light-Cone Sum Rules with $B$-meson distribution amplitudes. We recalculate and confirm the results for the leading-twist two-particle contributions in the literature. Furthermore, we calculate and provide new expressions for the two-particle contributions up to twist four. Following new developments for the three-particle distribution amplitudes, we calculate and provide new results for the complete set of three-particle contributions up to twist four. The form factors are computed numerically at several phase space points using up-to-date input parameters, including correlations across phase space points and form factors. We use a model ansatz for all contributing $B$-meson distribution amplitudes that is self-consistent up to twist-four accuracy. We find that the higher-twist two-particle contributions have a substantial impact on the results, and dominate over the three-particle contributions. Our numerical results, including correlations, are provided as machine-readable ancillary files. We discuss the qualitative phenomenological impact of our results on the present $b$ anomalies.

• The paper significantly extends B-meson LCSR analysis by incorporating twist-four corrections in both two- and three-particle states.
• It employs a robust numerical framework that confirms dominant higher-twist two-particle contributions over three-particle effects in form factor predictions.
• The study constrains b anomalies and sets the stage for further exploration of heavy quark effective theory and radiative corrections in semileptonic decays.

Analytical and Numerical Advancements in $B$-Meson Form Factor Calculation

The paper "$B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist" presents a detailed paper on the computation of form factors associated with semileptonic $B$-meson decays. This research encompasses transitions to both pseudoscalar ($P$) and vector ($V$) mesons, utilizing Quantum Chromodynamics (QCD) Light-Cone Sum Rules (LCSRs) with $B$-meson distribution amplitudes. The paper explores both theoretical frameworks and numerical implementation, contributing significantly to the ongoing discourse on $B$-meson decays and their associated anomalies.

Numerical Framework and Strong Results

The researchers re-evaluate form factors from $B$-meson decays, extending beyond leading-twist contributions to include calculations up to twist four for two-particle states and twist four for three-particle states. Notably, the paper identifies substantial contributions from higher-twist two-particle terms that surpass those from three-particle states, reinforcing their dominance in influencing the results. The numerical computation is conducted at various phase space points using contemporary input parameters, ensuring robust results that are machine-readable.

Analytical Enhancements

Analytically, the paper advances the framework for $B$-meson LCSRs by considering three-particle distribution amplitudes in addition to the traditionally calculated two-particle contributions. Through a comprehensive recalibration, the authors provide updated expressions and numerical assessments, improving the theoretical underpinnings of form factor computation. Model ansatzes are introduced for the contributing $B$-meson distribution amplitudes, maintaining consistency to twist-four precision.

Impact on $b$ Anomalies and Future Directions

Phenomenological applications of the research are evident in its analysis of the $B\to K^*\mu^+\mu^-$ anomaly. The paper clarifies the symmetry relations at large kaon energies and correlates these findings with prior lattice QCD and LCSR results. This analysis indicates no significant deviation from symmetry limits, thereby constraining potential new physics explanations for existing anomalies. Moreover, the paper addresses Standard Model and New Physics considerations for $B\to D^{(*)}\ell\bar\nu$ decays, supplying predictions for lepton flavor universality (LFU) ratios $R(D)$ and $R(D^*)$.

The future trajectory of this research may involve integrating radiative corrections to leading-twist contributions, as well as addressing the inclusion of dynamic factors such as the $B$-meson's LCDA in modeling extrapolations. This paper underpins the need for continued exploration into heavy quark effective theory (HQET) and the intricacies of sum rule techniques for an enhanced understanding of form factor dynamics.

Conclusion

In summary, this paper contributes significantly to the computation and understanding of $B$-meson form factors through advanced analytical techniques and rigorous numerical validation. The research impacts ongoing investigations into $b$ anomalies, providing clarity and direction for future studies. By incorporating higher-twist contributions and modern computational methods, this paper sets a foundation for future enhancements in $B$-meson decay predictions and the resolution of phenomenological discrepancies.