[Paper Review] Angular distribution of the rare decay $\Lambda_b o \Lambda( o N \pi) \ell^+\ell^-$

Han Yan|arXiv (Cornell University)|Nov 26, 2019

Particle physics theoretical and experimental studies67 references4 citations

TL;DR

This paper presents the first complete angular distribution for the rare decay Λb → Λ(→ Nπ)ℓ⁺ℓ⁻, including full contributions from tensor operators and massive leptons in the effective Hamiltonian framework. It reveals significant sensitivity of angular observables to tensor operators, indicating that New Physics effects in b → sℓ⁺ℓ⁻ transitions cannot be ignored, especially in light of deviations from Standard Model predictions and potential signals in the S1 + S3 leptoquark model.

ABSTRACT

We provide a determination of the complete angular distribution for the four body rare decay $\Lambda_b o \Lambda( o N \pi) \ell^+\ell^-$, with unpolarized $\Lambda_b$ baryons and massive leptons, in the operator basis approach which includes the scalar, pseudo-scalar, vector, axial-vector and tensor operators. Especially, the contributions of tensor operators have been calculated for the first time in this work. Since the lepton mass is retained in our calculations, the lepton flavour universality and the decay mode $\Lambda_b o \Lambda( o N \pi) au^+ au^-$ can be investigated in detail. For comparison with the experiment, we study the numerical results of observables within the Standard Model and the $S_1+S_3$ Leptoquark model. Significant deviation can be found between experiment data and the Standard Model predictions. The $S_1+S_3$ Leptoquark model can be further explored with the experimental progresses. In addition, we demonstrate the sensitivity of various angular observables to tensor operators contributions firstly, and find out that the potential New Physics effects of tensor operators can not be ignored in $b o s\ell^+\ell^-$ transitions.

Motivation & Objective

• To provide a complete angular distribution for the four-body decay Λb → Λ(→ Nπ)ℓ⁺ℓ⁻ with unpolarized Λb baryons and massive leptons.
• To include and analyze the contributions of tensor operators in the effective Hamiltonian for b → sℓ⁺ℓ⁻ transitions for the first time.
• To investigate lepton flavour universality violations via detailed numerical analysis in the Standard Model and the S1 + S3 leptoquark model.
• To assess the sensitivity of angular observables to tensor operator contributions, identifying potential New Physics signals.

Proposed method

• Formalism based on the effective Hamiltonian in the operator basis, including scalar, pseudo-scalar, vector, axial-vector, and tensor operators.
• Use of helicity amplitudes for both hadronic and leptonic currents, with explicit expressions derived in the Dirac representation.
• Employment of the narrow-width approximation to handle the intermediate Λ resonance in the four-body decay.
• Numerical evaluation using lattice QCD form factors for Λb → Λ transition, extrapolated via BCL parametrization.
• Calculation of differential decay rates and angular observables, including forward-backward asymmetries and polarization asymmetries.
• Comparison of results in the Standard Model and the S1 + S3 leptoquark model, with emphasis on massive lepton effects and LFU ratios.

Experimental results

Research questions

• RQ1 How do tensor operators contribute to the angular distribution of Λb → Λ(→ Nπ)ℓ⁺ℓ⁻, and what is their sensitivity in angular observables?
• RQ2 To what extent do massive lepton effects alter predictions for lepton flavour universality ratios in this decay?
• RQ3 Can the S1 + S3 leptoquark model explain the observed deviations from Standard Model predictions in this decay mode?
• RQ4 Are the angular observables in this decay sensitive enough to detect New Physics beyond the Standard Model?
• RQ5 How do the results compare with experimental data, particularly in light of LHCb measurements?

Key findings

• Tensor operators contribute significantly to the angular distribution and are detectable through specific angular observables, indicating that their effects cannot be neglected in b → sℓ⁺ℓ⁻ transitions.
• The inclusion of massive leptons reveals stronger deviations from Standard Model predictions, especially in the τ⁺τ⁻ final state, enhancing sensitivity to lepton flavour universality violation.
• Numerical results show significant discrepancies between experimental data and Standard Model predictions, particularly in forward-backward asymmetries and polarization observables.
• The S1 + S3 leptoquark model provides a viable framework to explain the observed deviations, suggesting it as a promising New Physics candidate.
• The study demonstrates that angular observables such as the forward-backward asymmetry and polarization asymmetries are highly sensitive to tensor operator contributions, offering a clean probe for New Physics.