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

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.

💡 Research Summary

In this work the authors present a comprehensive study of the Λ_b → Λ transition form factors using the perturbative QCD (PQCD) approach with explicit inclusion of higher‑twist light‑cone distribution amplitudes (LCDAs) for both the initial Λ_b baryon and the final Λ baryon. The motivation stems from the need for precise hadronic inputs in rare b → s flavor‑changing neutral current processes, which have shown intriguing tensions between Standard Model predictions and LHCb measurements in both mesonic and baryonic channels. While lattice QCD provides reliable results at high momentum transfer (large q²) and light‑cone sum rules (LCSR) are applicable at low to intermediate q², the PQCD framework is uniquely suited to describe the fast‑recoil region where the Λ baryon carries large energy.

The paper first defines the ten independent form factors associated with vector, axial‑vector, tensor and pseudo‑tensor currents, both in the helicity basis and in the Weinberg classification, and derives the relations between the two parameterizations. Within the k_T‑factorization formalism the transition amplitude is expressed as a convolution of the hard scattering kernel H (computed at leading order O(α_s²) with two hard gluon exchanges) and the non‑perturbative LCDAs of the Λ_b and Λ. The authors adopt an exponential model for the Λ_b LCDAs, characterized by a shape parameter ω₀≈0.7 GeV, and use lattice‑determined normalization constants together with QCD‑sum‑rule inspired parameters for the Λ LCDAs up to twist‑6.

A detailed analysis shows that the higher‑twist LCDAs dominate the numerical values of the form factors, contributing roughly 60–70 % of the total amplitude. This resolves the longstanding underestimation of the form factors in earlier PQCD studies that retained only leading‑twist contributions. The computed form factors at low q² (0 ≤ q² ≲ 12 GeV²) are found to be of order 0.1–0.3, in good agreement with results from LCSR, SCET and lattice calculations once the higher‑twist effects are accounted for.

To obtain a description valid over the full kinematic range, the authors perform a combined z‑expansion fit. They use their PQCD results in the low‑q² region together with recent lattice QCD data at high q², imposing unitarity bounds and the known endpoint constraints. The fit up to third order in the conformal variable z yields a set of coefficients that smoothly interpolate between the two regimes, providing a unified parametrization of all ten form factors.

Armed with these form factors, the paper proceeds to phenomenological predictions for the rare decay Λ_b → Λ μ⁺μ⁻. Differential branching fractions dℬ/dq², the longitudinal polarization fraction of the dimuon system (F_L), and three forward‑backward asymmetries—lepton‑side (A_FB^ℓ), hadron‑side (A_FB^h), and the combined lepton‑hadron asymmetry (A_FB^{ℓh})—are calculated. The integrated branching fraction is ℬ(Λ_b → Λ μ⁺μ⁻) = (1.8 ± 0.4) × 10⁻⁶, consistent with the latest LHCb measurement. The shape of F_L(q²) and the magnitude of A_FB^{ℓh} are particularly sensitive to the higher‑twist contributions, underscoring their phenomenological relevance.

The authors conclude that (i) higher‑twist LCDAs are essential for a realistic description of heavy‑to‑light baryon transitions, (ii) the PQCD approach, when supplemented with accurate non‑perturbative inputs, provides reliable predictions in the large‑recoil region, and (iii) the combined PQCD‑lattice z‑fit offers a robust tool for future studies of rare baryonic decays. They suggest extensions to other channels such as Λ_b → Λ τ⁺τ⁻ or Λ_b → Λ νν̄, and note that the derived form factors can be employed to probe new‑physics scenarios (e.g., Z′ bosons or leptoquarks) through precise angular analyses. The paper thus delivers both a methodological advance in the treatment of baryonic form factors and concrete phenomenological predictions that can be tested with upcoming LHCb data.