[Paper Review] Order {alpha}{sub s}{sup 2}{beta}{sub 0} correction to the charged lepton spectrum in b{r_arrow}cscr(l){bar {nu}}{sub scr(l)} decays

Martin Gremm, Iain W. Stewart|arXiv (Cornell University)|Feb 1, 1997

Particle physics theoretical and experimental studies21 citations

TL;DR

This paper computes the αₛ²β₀ two-loop QCD corrections to the charged lepton spectrum in b→cℓν̄ₗ decays, finding these corrections to be approximately 50% of the leading-order contributions across most lepton energies. Including these corrections, the authors extract central values of ȞΛ = 0.33 GeV and λ₁ = -0.17 GeV², which are used to determine the b and c quark masses in the MS̄ scheme and the CKM matrix element |Vcb|.

ABSTRACT

We compute the ${\ensuremath{\alpha}}_{s}^{2}{\ensuremath{\beta}}_{0}$ part of the two-loop QCD corrections to the charged lepton spectrum in $b\ensuremath{ ightarrow}c\mathcal{l}{\overline{\ensuremath{ u}}}_{\mathcal{l}}$ decays and find them to be about 50% of the first order corrections at all lepton energies, except those close to the end point. Including these corrections we extract the central values $\overline{\ensuremath{\Lambda}}=0.33 \mathrm{GeV}$ and ${\ensuremath{\lambda}}_{1}=\ensuremath{-}0.17{\mathrm{ }\mathrm{GeV}}^{2}$ for the HQET matrix elements and use them to determine the $\overline{\mathrm{MS}}$ $b$ and $c$ quark masses, and $|{V}_{\mathrm{cb}}|$.

Motivation & Objective

• To compute the αₛ²β₀ contribution to the two-loop QCD corrections in b→cℓν̄ₗ decays.
• To assess the impact of these corrections on the charged lepton spectrum across the energy spectrum.
• To extract reliable values for the HQET matrix elements ȞΛ and λ₁ from the corrected spectrum.
• To determine the MS̄ b and c quark masses and the CKM matrix element |Vcb| using the extracted HQET parameters.

Proposed method

• The calculation employs two-loop QCD field theory techniques to compute the αₛ²β₀ term in the decay amplitude.
• The corrections are evaluated in the heavy quark effective theory (HQET) framework to handle the heavy b and c quark dynamics.
• The lepton spectrum is computed as a function of energy, with the full αₛ²β₀ contribution included in the differential decay rate.
• The extracted HQET parameters are used as input to determine the MS̄ b and c quark masses and |Vcb| via theoretical matching procedures.

Experimental results

Research questions

• RQ1 What is the magnitude and energy dependence of the αₛ²β₀ two-loop QCD correction to the charged lepton spectrum in b→cℓν̄ₗ decays?
• RQ2 How do these two-loop corrections affect the determination of the HQET parameters ȞΛ and λ₁?
• RQ3 What are the resulting values of the MS̄ b and c quark masses and |Vcb| when the αₛ²β₀ corrections are included in the analysis?
• RQ4 How do the extracted HQET parameters compare with previous determinations in light of the improved QCD corrections?

Key findings

• The αₛ²β₀ correction contributes approximately 50% of the leading-order correction across most of the lepton energy spectrum, except near the endpoint.
• The central value for the HQET matrix element ȞΛ is determined to be 0.33 GeV.
• The central value for the HQET parameter λ₁ is found to be -0.17 GeV².
• Using these parameters, the MS̄ b quark mass and c quark mass are extracted consistently within the theoretical framework.
• The CKM matrix element |Vcb| is determined using the corrected spectrum and the extracted HQET parameters.
• The results indicate a significant impact of two-loop QCD corrections on precision determinations in inclusive B→clν̄ decays.