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Bayesian Extraction of HQET Parameters from Inclusive Semi-Leptonic Decay of the $Λ_{c}^{+}$ Baryon

Kangkang Shao, Dong Xiao

TL;DR

The paper develops a Bayesian, data-driven framework to extract rest-frame electron-energy moments from inclusive Λ_c^+ → X e^+ ν_e decays, where the laboratory spectrum is a superposition of many boosted configurations. Using a Monte Carlo–driven iterative inference, the authors unfold the Λ_c^+ rest-frame spectrum and obtain the first four electron-energy moments, complete with statistical and systematic uncertainties. They then perform a global fit within the Heavy Quark Expansion in the 1S mass scheme, including NNLO perturbative corrections and power corrections up to O(1/m_c^3), to determine the non-perturbative HQET parameters μ_π^2(Λ_c^+) and ρ_D^3(Λ_c^+) and the weak annihilation term τ_WA(Λ_c^+). The results show μ_π^2(Λ_c^+) ≈ 0.133 GeV^2, ρ_D^3(Λ_c^+) ≈ -0.000295 GeV^3, and τ_WA(Λ_c^+) ≈ -0.269 GeV^3 with quantified uncertainties, highlighting a data-driven path to charm-baryon HQET parameter extraction and potential implications for inclusive charm phenomenology and CKM determinations.

Abstract

We extract the non-perturbative Heavy Quark Effective Theory (HQET) parameters from the inclusive semi-leptonic decay $Λ_c^+ \to X e^+ ν_e$. Unlike charmed mesons produced near threshold, $Λ_c^+$ baryons produced in $e^+e^-$ annihilation exhibit a complex momentum distribution, making the transformation of the electron energy spectrum from the laboratory frame to the $Λ_c^+$ rest frame non-trivial. To address this, we develop a novel Bayesian inference method to reconstruct the electron energy moments in the $Λ_c^+$ rest frame. By performing a global fit of theoretical predictions in the 1S mass scheme to these extracted moments, we determine the HQET parameters $μ_π^2(Λ_c^+)$ and $ρ_D^3(Λ_c^+)$ for the first time using a purely data-driven approach.

Bayesian Extraction of HQET Parameters from Inclusive Semi-Leptonic Decay of the $Λ_{c}^{+}$ Baryon

TL;DR

The paper develops a Bayesian, data-driven framework to extract rest-frame electron-energy moments from inclusive Λ_c^+ → X e^+ ν_e decays, where the laboratory spectrum is a superposition of many boosted configurations. Using a Monte Carlo–driven iterative inference, the authors unfold the Λ_c^+ rest-frame spectrum and obtain the first four electron-energy moments, complete with statistical and systematic uncertainties. They then perform a global fit within the Heavy Quark Expansion in the 1S mass scheme, including NNLO perturbative corrections and power corrections up to O(1/m_c^3), to determine the non-perturbative HQET parameters μ_π^2(Λ_c^+) and ρ_D^3(Λ_c^+) and the weak annihilation term τ_WA(Λ_c^+). The results show μ_π^2(Λ_c^+) ≈ 0.133 GeV^2, ρ_D^3(Λ_c^+) ≈ -0.000295 GeV^3, and τ_WA(Λ_c^+) ≈ -0.269 GeV^3 with quantified uncertainties, highlighting a data-driven path to charm-baryon HQET parameter extraction and potential implications for inclusive charm phenomenology and CKM determinations.

Abstract

We extract the non-perturbative Heavy Quark Effective Theory (HQET) parameters from the inclusive semi-leptonic decay . Unlike charmed mesons produced near threshold, baryons produced in annihilation exhibit a complex momentum distribution, making the transformation of the electron energy spectrum from the laboratory frame to the rest frame non-trivial. To address this, we develop a novel Bayesian inference method to reconstruct the electron energy moments in the rest frame. By performing a global fit of theoretical predictions in the 1S mass scheme to these extracted moments, we determine the HQET parameters and for the first time using a purely data-driven approach.

Paper Structure

This paper contains 15 sections, 6 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Calculation of Electron Energy Moments in $\Lambda_c^+$ Rest Frame
  3. Iterative Bayesian Inference Methodology
  4. Monte Carlo Simulation
  5. The Iterative Procedure
  6. Low-Momentum Theoretical Constraint
  7. Electron Momentum Distribution
  8. Nominal Results of Electron Energy Moments
  9. Statistical Uncertainty
  10. Systematic Uncertainties
  11. Final Result of Electron Energy Moment
  12. Phenomenological Analysis of Inclusive $\Lambda_c^+$ Decays
  13. Theoretical formulas
  14. Towards an extraction of the kinetic energy and Darwin terms
  15. Conclusion

Figures (3)

  • Figure 1: A flowchart illustrating the iterative Bayesian inference method. The process starts with an arbitrary assumption for the electron momentum probability density function (PDF) in the $\Lambda_c^+$ rest frame, which is refined by comparing the resulting simulated lab-frame PDF with experimental data. Here $f$ is the one dimensional normalized PDF of electron momentum, while $\phi$ denotes the PDF in the three momentum vector space. The $p$ and $\vec{p}$ represent the variables in the laboratory frame, whereas $p^*$ and $\vec{p}\,^*$ stand for the variables in the $\Lambda_c^+$ rest frame.
  • Figure 2: Result of the electron momentum distribution of $\Lambda_c^+ \to X e^+ \nu_e$.
  • Figure 3: Final result of the electron momentum distribution of $\Lambda_c^+ \to X e^+ \nu_e$ in the $\Lambda_c^+$ rest frame.