$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules

Abstract: We present $B_q\to\rho$, $B_q\to\omega$, $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$ form factors from light-cone sum rules (LCSR) at $\mathcal{O}(\alpha_s)$ for twist-2 and 3 and $\mathcal{O}(\alpha_s^0)$ for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-$4$ (and $5$) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for $B\to K^*\ell\ell$ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low $q^2$ as well as combined fits to LCSR and lattice results covering the entire kinematic range for $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for $B\to K^*\gamma$ as well as $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\mu^+\mu^-$ at low dilepton invariant mass. Employing our $B \to (\rho,\omega) $ form factor results we extract the CKM element $|V_\mathrm{ub}|$ from the semileptonic decays $B\to(\rho,\omega) \ell\nu$ and find good agreement with other exclusive determinations.

• The paper updates B → Vℓ⁺ℓ⁻ form factors using LCSR up to twist‐4 precision, ensuring EOM compliance and stabilizing tensor-to-vector ratios.
• It integrates joint fits from LCSR and lattice QCD across low to full kinematic ranges, reducing uncertainties in SM predictions.
• The analysis refines the extraction of the CKM element |V₍ub₎| from B → (ρ, ω)ℓν data, offering critical insights for FCNC tests and new physics searches.

Summary of Research on $B \to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules

This paper presents an updated analysis of form factors in the decays of $B$ mesons to vector mesons ($V$) and dileptons ($\ell^+\ell^-$) within the Standard Model (SM), employing Light-Cone Sum Rules (LCSR). The research includes $B_q\to\rho$, $B_q\to\omega$, $B_q\to K^*$, $B_s\to K^*$, and $B_s\to \phi$ transitions, with an expansion to twist-4 level precision and updated hadronic inputs.

Key Results and Methods

The authors extend previous computations by incorporating three asymptotic light-cone distribution amplitudes necessary for ensuring compliance with the equations of motion (EOM) within the employed framework. This conforms the tensor-to-vector form factor ratios, thus stabilizing predictions of zero crossings in helicity amplitudes—a critical factor for calculating $B\to K^*\ell\ell$ angular observables.

Significant updates to hadronic input parameters and the inclusion of complete error correlation matrices across the modeled kinematic ranges have been made, which are crucial for avoiding overestimation of uncertainties in phenomenological applications. The study provides fits for the sum rules results covering low $q^2$ regions, as well as joint fits between LCSR and lattice QCD computations, thereby extending the analysis across the full kinematic spectrum.

Implications and Theoretical Considerations

The paper delivers SM predictions for $B\to K^*\gamma$, $B\to K^*\ell^+\ell^-$, and $B_s\to\phi\mu^+\mu^-$. The updated form factors have been employed to derive the CKM matrix element $|V_\mathrm{ub}|$ from $B\to(\rho,\omega)\ell\nu$ decay data. These findings align well with other exclusive $V_\mathrm{ub}$ determinations and are consistent with the decay measurements from BaBar and Belle collaborations.

The implications are pertinent for precision tests of the SM, particularly concerning flavor-changing neutral currents (FCNCs) and potential new physics beyond the SM. The paper refines the framework to incorporate EOM constraints, providing a robust toolset for theoretical predictions downstream.

Prospects for Future Work

Despite the rigorous inclusion of EOM considerations, the paper suggests potential improvement areas—particularly the full computation of radiative corrections using a consistent framework for LCSR and lattice QCD. The precision of lattice computations at high $q^2$ looks promising, and future developments could benefit from improved parameter measurements and decreased computational uncertainties, particularly concerning spectator effects and temporal integration involving $\Gamma_s$ and $\Delta \Gamma_s$ factors for $B_s$.

The work undertaken serves as a keystone for future phenomenological analysis within $b \to s$ transition channels, providing an essential basis not just for theoretical documentation but also for enhancing experimental setups towards discerning possible SM deviations driven by new physics.