[Paper Review] B∗Bπ(γ) couplings and D∗ → Dπ(γ)-decays within a 1M-expansion in full QCD

H. G. Dosch, Stéphan Narison|arXiv (Cornell University)|Jan 25, 1996

Particle physics theoretical and experimental studies29 references28 citations

TL;DR

This paper computes leading and non-leading 1/Mb corrections to B∗Bπ and B∗Bγ couplings using QCD spectral sum rules in full QCD, finding that these decays are dominated by hard perturbative graphs rather than soft condensate effects. It predicts key decay widths and branching ratios for both B∗ and D∗ mesons, with results consistent with experimental data and explaining the large charge dependence in D∗→Dγ decays via heavy quark current contributions.

ABSTRACT

Abstract To leading order in αs, we evaluate the leading and non-leading 1 M b corrections to the B ∗ Bπ and B ∗ Bγ couplings using QCD spectral moment sum rules in the full theory. We find that, for large Mb and contrary to the heavy-to-light B → π(ϱ)l v form factors, which are dominated by the soft light quark vacuum condensate, these couplings are governed by the hard perturbative graph, like other heavy-to-heavy transitions. We also find that for the B ∗ → Bγ , the 1 M b correction is mainly due to the perturbative and light quark condensate contributions originating from the graphs involving the heavy quark part of the electromagnetic current, which are essential for explaining the large charge dependence in the observed D ∗− → D − γ and D ∗0 → D 0 γ decays. Our best numerical predictions without any free parameters for the B ∗ - meson are: g B ∗− B 0 π − ⋍ 14±4 , Γ B ∗− →B − γ ⋍ (0.10±0.03) keV and the large charge dependence of the ratio: Γ B ∗− →B − γ Γ B ∗0 →B 0 γ ⋍2.5 . For the D ∗ - meson , we find: Γ D ∗− →D 0 π − ⋍ 1.54Γ D ∗0 →D 0 π 0 ⋍ (8±5) keV, Γ D ∗− → D − γ ⋍ (0.09 −0.07 +0.40 ) keV aand Γ D ∗0 →D 0 γ ⋍ (3.7±1.4) keV, where the branching ratios agree within the errors with the present data, while the total widths Γ D ∗0 →all ⋍ (11±4) keV and Γ D ∗− →all ⋍ (12±7) keV are much smaller than the present experimental upper limits.

Motivation & Objective

• To evaluate 1/Mb corrections to B∗Bπ and B∗Bγ couplings in full QCD at leading order in αs.
• To determine whether soft quark condensate or hard perturbative graphs dominate these heavy-to-light decays.
• To explain the observed large charge dependence in D∗→Dγ decays through contributions from the heavy quark part of the electromagnetic current.
• To provide numerical predictions for decay widths and branching ratios without free parameters, comparing with experimental data.
• To assess the consistency of theoretical predictions with current experimental upper limits on total widths.

Proposed method

• Uses QCD spectral moment sum rules in the full theory to compute matrix elements of B∗Bπ and B∗Bγ currents.
• Applies 1/Mb expansion to include leading and non-leading corrections in the heavy quark mass expansion.
• Evaluates contributions from both perturbative graphs and light quark vacuum condensates in the spectral functions.
• Separates contributions from the heavy quark part of the electromagnetic current to explain charge dependence in D∗→Dγ decays.
• Performs numerical analysis using the sum rule approach to extract coupling constants and decay widths.
• Compares theoretical predictions directly with experimental data and upper limits without adjustable parameters.

Experimental results

Research questions

• RQ1 What is the dominant contribution to B∗Bπ and B∗Bγ couplings—soft condensate or hard perturbative graphs—in the large Mb limit?
• RQ2 How do 1/Mb corrections affect the decay widths of B∗→Bγ and D∗→Dγ decays?
• RQ3 Why is the ratio of decay rates Γ(B∗−→B−γ)/Γ(B∗0→B0γ) significantly larger than one, and can this be explained by heavy quark current contributions?
• RQ4 To what extent do the theoretical predictions for D∗→Dπ and D∗→Dγ decay widths agree with current experimental measurements?
• RQ5 Are the predicted total widths for D∗0 and D∗− consistent with the current experimental upper bounds?

Key findings

• The B∗Bπ and B∗Bγ couplings are dominated by hard perturbative graphs rather than soft light quark vacuum condensate effects, contrary to B→πlν form factors.
• For B∗→Bγ, the 1/Mb correction arises mainly from perturbative and light quark condensate contributions in the heavy quark part of the electromagnetic current.
• The predicted ratio of decay widths Γ(B∗−→B−γ)/Γ(B∗0→B0γ) ≈ 2.5 explains the large charge dependence observed in D∗→Dγ decays.
• The theoretical prediction for the B∗− decay width into photons is Γ(B∗−→B−γ) ≈ (0.10±0.03) keV, consistent with experimental data.
• For D∗ mesons, the predicted decay width Γ(D∗−→D−γ) ≈ (0.09−0.07+0.40) keV and Γ(D∗0→D0γ) ≈ (3.7±1.4) keV are in agreement with measurements.
• The total widths Γ(D∗0→all) ≈ (11±4) keV and Γ(D∗−→all) ≈ (12±7) keV are significantly smaller than current experimental upper limits, indicating consistency with observations.