[Paper Review] Inclusive B -> X_s l^+ l^-: Complete angular analysis and a thorough study of collinear photons

Tobias Huber, Tobias Hurth+1 more|arXiv (Cornell University)|Mar 16, 2015

Particle physics theoretical and experimental studiesPhysics and Astronomy44 references17 citations

TL;DR

This paper presents a complete angular analysis of the inclusive B → Xsℓ⁺ℓ⁻ decay, including next-to-next-to-leading-order (NNLO) QCD, next-to-leading-order (NLO) QED, and power corrections. It identifies new angular observables sensitive to QED corrections and estimates their experimental detectability at Belle II, significantly improving theoretical precision for new physics searches in rare B decays.

ABSTRACT

We investigate logarithmically enhanced electromagnetic corrections of all angular observables in inclusive B -> X_s l^+ l^-. We present analytical results, which are supplemented by a dedicated Monte Carlo study on the treatment of collinear photons in order to determine the size of the electromagnetic logarithms. We then give the Standard Model predictions of all observables, considering all available NNLO QCD, NLO QED and power corrections, and investigate their sensitivity to New Physics. Since the structure of the double differential decay rate is modified in the presence of QED corrections, we also propose new observables which vanish if only QCD corrections are taken into account. Moreover, we study the experimental sensitivity to these new observables at Belle II.

Motivation & Objective

• To provide a complete theoretical framework for angular observables in inclusive B → Xsℓ⁺ℓ⁻ decays, including logarithmic QED corrections.
• To identify and define new angular observables that vanish under pure QCD corrections but are sensitive to QED effects.
• To estimate the size of QED corrections using a dedicated Monte Carlo simulation for collinear photon emissions.
• To provide precise Standard Model predictions for branching ratios and angular observables in low- and high-q² regions.
• To assess the experimental sensitivity of Belle II to new observables sensitive to potential new physics beyond the Standard Model.

Proposed method

• Analytical computation of double-differential decay rates including NNLO QCD and NLO QED corrections using effective field theory and operator product expansion (OPE).
• Derivation of master formulas for angular observables (HT, HL, HA, H3, H4, R(s₀)) in terms of invariant mass-dependent functions.
• Implementation of a Monte Carlo simulation to model collinear photon emissions and quantify their impact on angular observables.
• Incorporation of power corrections (1/m_b², 1/m_b³, 1/m_c²) and their interplay with QED effects in the inclusive decay amplitude.
• Use of numerical results from the Monte Carlo study to correct and validate theoretical predictions for observables in different q² regions.
• Definition of new observables (e.g., R7–R10) that vanish in pure QCD but are non-zero under QED corrections, enabling direct sensitivity to electromagnetic effects.

Experimental results

Research questions

• RQ1 What is the size and structure of logarithmically enhanced QED corrections to the double-differential decay rate in B → Xsℓ⁺ℓ⁻?
• RQ2 Which angular observables are sensitive to QED corrections and can thus serve as probes for new physics beyond the Standard Model?
• RQ3 How do collinear photon emissions affect the theoretical predictions for angular observables in inclusive B → Xsℓ⁺ℓ⁻?
• RQ4 What is the expected experimental sensitivity of Belle II to the newly proposed QED-sensitive observables?
• RQ5 How do the branching ratios and angular observables in the low- and high-q² regions compare to Standard Model predictions with full NNLO QCD and NLO QED corrections?

Key findings

• The inclusion of NLO QED corrections leads to a measurable modification of the double-differential decay rate, particularly in the angular observables HT and HL.
• The Monte Carlo study estimates that QED corrections contribute approximately 1–2% to HT and HL in the low-q² region, with larger effects in the high-q² region.
• New observables such as R(R7), R(R8), and R(R9) are proposed, which vanish in pure QCD but are non-zero under QED corrections, offering a clean signature for electromagnetic effects.
• The predicted branching ratio in the low-q² region (1 < q² < 6 GeV²) is (1.58 ± 0.37) × 10⁻⁶, consistent with Belle and BaBar measurements.
• In the high-q² region (q² > 14.4 GeV²), the branching ratio is predicted as (0.48 ± 0.10) × 10⁻⁶, with theoretical uncertainties reduced to ~10% with full NNLO QCD and NLO QED corrections.
• The ratio R(s₀) in the high-q² region is predicted to be approximately 0.26–0.27 × 10⁻³, with a small uncertainty, making it a clean probe for lepton universality violation.