The $Λ_{b} \to Λ$ transition form factors in perturbative QCD approach

TL;DR

Problem addressed: compute the Λ_b → Λ transition form factors for b to s FCNC decays within a perturbative QCD framework. Approach: combine low-q^2 PQCD results with high-q^2 lattice QCD by performing a z-series expansion to cover the full kinematic range and include higher-twist LCDAs up to twist-6. Key findings: high twist LCDAs dominate the form factors, the predictions are consistent with lattice and other methods, and the analysis provides differential branching fraction and angular observables for Λ_b → Λ mu+ mu- decays. Significance: this work strengthens SM tests in baryon decays, clarifies the role of higher-twist effects, and informs the interpretation of current and future experiments.

Abstract

In this work, we investigate the $Λ_b \to Λ$ transition form factors in the perturbative QCD (PQCD) approach, incorporating higher-twist light-cone distribution amplitudes (LCDAs). The resulted form factors show that higher-twist LCDAs are dominant numerically. By combining our PQCD predictions at low-$q^2$ with lattice QCD results at high-$q^2$, $z$-series expansion fits are performed to parametrize the form factors over the full kinematic range. We also provide the prediction for physical observables in the rare decay $Λ_b \to Λμ^+ μ^-$, including the differential branching fraction, dilepton longitudinal polarization fraction, and forward-backward asymmetries (lepton-side, hadron-side, and combined lepton-hadron). Our obtained form factors are consistent with those in other theoretical methods within the uncertainties.

Figures (5)

• Figure 1: The leading order Feynman diagrams for the $\Lambda_b\to\Lambda$ transition form factors in the PQCD approach. The green $\otimes$ denote the weak interaction currents.
• Figure 2: Dependencies of the $\Lambda_b$ baryon LCDAs $\psi_2$, $\psi_3^{+-}$, $\psi_3^{-+}$ and $\psi_4$ on the momentum fractions $x_i$ in the exponential model Bell:2013tfa. Each point inside the triangles satisfies the relation $x_1+x_2+x_3=1$.
• Figure 3: Form factors at the full kinematic range.
• Figure 4: Differential branching fraction of the $\Lambda_b \to \Lambda \mu^+\mu^-$ decay. The cyan curve and the lighter band correspond to the central values and theoretical uncertainties obtained in this work, respectively, compared with the experimental data from LHCb LHCb:2015tgy.
• Figure 5: Angular observables of the $\Lambda_b \to \Lambda(\to p^+ \pi^-)\mu^+\mu^-$ decay obtained in this work, where the bands represent the corresponding theoretical uncertainties, compared with the experimental data from LHCb LHCb:2015tgy.