[Paper Review] Polarized $\\Lambda_{b} \ o X_{c} \ au \ u$ in the SM and THDM

Chao-Shang Huang, Hua-Gang Yan|arXiv (Cornell University)|Aug 1, 1997

Particle physics theoretical and experimental studies1 references4 citations

TL;DR

This paper computes the inclusive semileptonic decay Λb → Xcτν in the Standard Model (SM) and Two-Higgs-Doublet Model (THDM), including O(αs) QCD corrections and spin-dependent effects up to 1/m²b order. It finds that τ lepton polarization and spectrum are sensitive to new physics, especially charged Higgs contributions in THDM, with significant deviations from SM predictions at high tanβ and light H± masses, providing a probe for new physics beyond the SM.

ABSTRACT

The inclusive rate and $\ au$ spectrum for a polarized $\\Lambda_b$ -baryon to decay to charm hadronic final states and leptons $\ au \ u$ in the SM and a two-Higgs doublet model are computed.The $O(\\alpha_s)$ QCD corrections to

Motivation & Objective

• To compute the inclusive decay rate and τ lepton spectrum for polarized Λb → Xcτν in the Standard Model with non-zero τ mass.
• To extend the SM results to include spin-dependent form factors up to 1/m²b order in Heavy Quark Effective Theory (HQET).
• To compute the inclusive decay rate and τ spectrum in the Two-Higgs-Doublet Model (THDM), including O(αs) QCD corrections and nonperturbative 1/m²b effects.
• To assess the sensitivity of the τ spectrum and polarization to new physics, particularly charged Higgs bosons in THDM.
• To provide a quantitative framework for testing THDM parameters via future experimental measurements of Λb semileptonic decays.

Proposed method

• Uses Heavy Quark Effective Theory (HQET) to compute hadronic tensor structure functions Wμν up to 1/m²b order, including spin-dependent contributions.
• Derives the differential decay rate in terms of kinematic variables: x = 2Eτ / mb, y = 2Eν / mb, t = q²/m²b, η = m²τ / m²b, and cosθ (angle between τ and Λb spin).
• Computes the τ energy spectrum as dΓ/dxdcosθ = AW(x,η,ε) + BW(x,η,ε)cosθ in the SM, and includes additional contributions AH, BH, AI, BI in the THDM.
• Incorporates O(αs) QCD corrections to the τ spectrum in the THDM using perturbative QCD calculations.
• Introduces parameters Kb and ǫb to parametrize nonperturbative 1/m²b effects in Λb decays.
• Analyzes the dependence on tanβ and mH± in THDM, showing that large tanβ enhances charged Higgs contributions.

Experimental results

Research questions

• RQ1 How do 1/m²b corrections affect the τ lepton spectrum and polarization in Λb → Xcτν in the SM when the τ mass is non-zero?
• RQ2 What are the contributions of charged Higgs bosons to the inclusive decay rate and τ spectrum in the THDM?
• RQ3 How do O(αs) QCD corrections modify the τ spectrum in the THDM?
• RQ4 How sensitive is the τ spectrum and polarization to the charged Higgs mass and tanβ in the THDM?
• RQ5 Can the Λb → Xcτν decay serve as a clean probe for new physics beyond the SM, particularly in the THDM?

Key findings

• The SM τ spectrum with non-zero τ mass and spin-dependent 1/m²b corrections deviates from the massless limit, with explicit expressions for AW and BW provided in the appendix.
• In the THDM, the charged Higgs contribution to the decay rate becomes dominant at high tanβ, with the total width increasing significantly when tanβ > 50.
• For mH± = 200 GeV, the THDM total width exceeds the SM width by up to 30% at tanβ = 100, indicating strong sensitivity to new physics.
• The O(αs) QCD corrections to the τ spectrum in the THDM are non-negligible and modify the spectrum shape, especially at high x (high τ energy).
• The angular distribution of the τ lepton, characterized by the cosθ dependence, shows a strong enhancement in the forward-backward asymmetry in the THDM at high tanβ, making it a sensitive probe for new physics.
• In the large tanβ limit, the THDM contributions scale as r⁴ tan²β, with dominant effects in the AH and BH terms, leading to observable deviations from the SM prediction.