Updated NNLO QCD predictions for the weak radiative B-meson decays (1503.01789v2)

Abstract: Weak radiative decays of the B mesons belong to the most important flavor changing processes that provide constraints on physics at the TeV scale. In the derivation of such constraints, accurate standard model predictions for the inclusive branching ratios play a crucial role. In the current Letter we present an update of these predictions, incorporating all our results for the O(alpha_s^2) and lower-order perturbative corrections that have been calculated after 2006. New estimates of nonperturbative effects are taken into account, too. For the CP- and isospin-averaged branching ratios, we find B_{s gamma} = (3.36 +_ 0.23) * 10^-4 and B_{d gamma} = 1.73^{+0.12}_{-0.22} * 10^-5, for E_gamma > 1.6GeV. Both results remain in agreement with the current experimental averages. Normalizing their sum to the inclusive semileptonic branching ratio, we obtain R_gamma = ( B_{s gamma} + B_{d gamma})/B_{c l nu} = (3.31 +_ 0.22) * 10^-3. A new bound from B_{s gamma} on the charged Higgs boson mass in the two-Higgs-doublet-model II reads M_{H^+} > 480 GeV at 95%C.L.

• The paper refines previous NNLO QCD predictions by integrating four-loop anomalous dimensions and replacing the BLM approximation.
• It provides precise branching ratios for radiative decays, notably Bₛγ = (3.36 ± 0.23)×10⁻⁴ and B_dγ = 1.73^(+0.12)_(-0.22)×10⁻⁵ for Eγ > 1.6 GeV.
• The analysis constrains beyond-SM physics by setting a charged Higgs mass bound of Mₕ₊ > 480 GeV at a 95% confidence level.

Updated NNLO QCD Predictions for the Weak Radiative B-Meson Decays

The paper of weak radiative decays of B mesons provides a significant contribution to understanding flavor physics and the potential constraints on theories beyond the Standard Model (SM). The paper under discussion presents an update to the Next-to-Next-to-Leading Order (NNLO) Quantum Chromodynamics (QCD) predictions for inclusive radiative B-meson decays, specifically focusing on $B \rightarrow X_s \gamma$ and $B \rightarrow X_d \gamma$. These processes are pivotal in constraining the parameter space of new physics scenarios, particularly those featuring additional Higgs bosons and supersymmetric particles.

Summary of Contributions

This research provides an enhancement over previous predictions by incorporating all results for the NNLO and lower-order perturbative corrections accumulated post-2006. The key numerical results reported are:

1. For the branching ratios with photon energy $E_\gamma > 1.6 \, \text{GeV}$:
   • $B_{s\gamma} = (3.36 \pm 0.23) \times 10^{-4}$
   • $B_{d\gamma} = 1.73^{+0.12}_{-0.22} \times 10^{-5}$
2. When normalized to the inclusive semileptonic branching ratio:
   • $$\mathcal{R}_\gamma = (B_{s\gamma} + B_{d\gamma}) / B_{c\ell \nu} = (3.31 \pm 0.22) \times 10^{-3}$$

Such predictions play a crucial role in corroborating theoretical precision with experimental data and provide benchmark constraints on the mass of the charged Higgs boson within the Two-Higgs-Doublet Model Type II (THDM II). The updated bound is $M_{H^\pm} > 480 \, \text{GeV}$ at a 95% confidence level.

Theoretical and Methodological Advances

The analysis includes several advancements:

• It completes the NNLO Wilson coefficient calculations by integrating four-loop anomalous dimensions pertinent to operator mixing under renormalization.
• Updated evaluations of charm and bottom quark mass effects in multi-loop diagrams are included.
• The research replaces the previous Boundary-Layer Matching (BLM) approximation with explicit calculations of the charm quark mass boundary condition, enhancing precision and reliability.

The inclusion of these contributions represents a substantial refinement over prior results, most explicitly reflected in the altered central values of the radiative decay branching ratios.

Implications and Future Directions

The implications of these results are profound for beyond-SM physics, allowing for stronger constraints on theoretical models, particularly regarding the contributions to Wilson coefficients $\Delta C_7$ and $\Delta C_8$ from new physics effects. The updated calculations ensure improved control over theoretical uncertainties and pave the way for potential reductions in previously dominant sources of error.

Future prospects include further reduction of uncertainties through more precise determinations of subleading shape functions or advanced lattice QCD techniques. Additionally, extending the calculations to address arbitrary values of the charm quark mass $m_c$ could further refine interpolations and reduce associated uncertainties.

Conclusion

This paper significantly extends the field of precision QCD calculations within the standard framework of flavor physics. By achieving enhanced theoretical predictions, it charts a promising course for harmonizing theoretical advances with observational precision, thereby aligning with more comprehensive searches for novel physical phenomena. As collider experiments such as Belle II progress, improved determinations of the branching ratios envisioned here will offer more stringent tests for SM extensions and potentially unveil new dynamics underpinning the fabric of particle interactions.