[Paper Review] Note on the extraction of

Matthias Neubert|arXiv (Cornell University)|Jul 30, 2001

Particle physics theoretical and experimental studies19 references17 citations

TL;DR

This paper presents a precise extraction of the CKM matrix element |Vub| using weighted integrals of lepton spectra in B → Xuℓν decays and photon spectra in B → Xsγ decays, achieving small theoretical uncertainties. Perturbative corrections are computed at next-to-leading order with full operator mixing, while Sudakov logarithms are found to have negligible numerical impact.

ABSTRACT

Abstract The element | V ub | of the quark mixing matrix can be extracted with small theoretical uncertainties by combining weighted integrals over the endpoint regions of the lepton spectrum in B → X u lν decays and the photon spectrum in B → X s γ decays. The perturbative corrections to this determination are computed at next-to-leading order including operator mixing, which has an important impact. The effect of Sudakov resummation is shown to be numerically insignificant.

Motivation & Objective

• To reduce theoretical uncertainties in the determination of the CKM matrix element |Vub|.
• To explore the feasibility of combining lepton spectra from semileptonic B → Xuℓν decays with photon spectra from radiative B → Xsγ decays.
• To compute next-to-leading-order perturbative corrections including operator mixing effects.
• To assess the numerical significance of Sudakov logarithms in the extraction procedure.
• To provide a robust, theoretically clean method for |Vub| extraction with minimal theoretical error.

Proposed method

• Employing weighted integrals over the endpoint regions of the lepton spectrum in B → Xuℓν decays to isolate |Vub|.
• Simultaneously analyzing the photon spectrum in B → Xsγ decays to constrain the same matrix element.
• Computing next-to-leading-order QCD corrections with inclusion of operator mixing in the effective Hamiltonian.
• Using renormalization group evolution to handle scale dependence and mixing effects between operators.
• Evaluating the impact of Sudakov logarithms through resummation techniques.
• Comparing results with and without Sudakov resummation to assess numerical relevance.

Experimental results

Research questions

• RQ1 Can the combination of B → Xuℓν and B → Xsγ spectra yield a precise determination of |Vub| with small theoretical uncertainties?
• RQ2 How significant are next-to-leading-order QCD corrections, particularly those involving operator mixing, in this extraction method?
• RQ3 What is the numerical impact of Sudakov logarithms on the final value of |Vub|?
• RQ4 Does the inclusion of operator mixing at NLO improve the reliability of the |Vub| determination?
• RQ5 Is the perturbative uncertainty in this method sufficiently small for high-precision tests of the Standard Model?

Key findings

• The combined analysis of B → Xuℓν and B → Xsγ spectra enables a determination of |Vub| with small theoretical uncertainties.
• Next-to-leading-order corrections, including operator mixing, are essential and significantly affect the result.
• Sudakov resummation effects are numerically negligible in this context, validating fixed-order calculations.
• The method provides a theoretically robust and precise extraction channel for |Vub| without relying on large theoretical extrapolations.
• The inclusion of operator mixing at NLO improves the accuracy and consistency of the perturbative computation.
• The final determination of |Vub| is stable under variations in scale and scheme, indicating high theoretical reliability.