Nlo Analysis Achieves Progress in Subleading-Power Interference at Large Energies with One-Loop Anomalous Dimension

Understanding the fundamental forces governing particle interactions requires increasingly precise theoretical calculations, and a team led by Riccardo Bartocci from Johannes Gutenberg University, Philipp Böer from CERN, and Tobias Hurth from Johannes Gutenberg University now presents progress towards achieving this precision in the study of interactions at high energies. The researchers calculate next-to-leading order radiative corrections to a key formula describing interference effects, incorporating the one-loop anomalous dimension of a specific shape function and two-loop corrections to a jet function containing an internal charm loop. This work simplifies the renormalization of a three-particle light-cone distribution amplitude with non-aligned light-like separations, representing a significant step towards more accurate predictions in particle physics, although the calculations remain limited to this specific configuration. The team’s insights refine theoretical models and pave the way for improved analysis of experimental data from high-energy collisions.

B-meson decays and Standard Model precision tests

Scientists are undertaking precise calculations of B-meson decays to rigorously test the Standard Model of particle physics and search for evidence of new phenomena. These investigations focus on understanding how B-mesons, unstable particles containing a bottom quark, break down into other particles, particularly those involving the emission of photons. Accurate theoretical predictions are essential for comparing with experimental data and identifying any discrepancies that might signal physics beyond the Standard Model. A cornerstone of this research is the technique of factorization, which simplifies complex decay processes by breaking them down into more manageable components.

Scientists employ sophisticated frameworks like soft-collinear effective theory (SCET) and operator product expansion (OPE) to systematically calculate decay rates and account for the complex interactions between particles. Understanding the internal structure of hadrons, the composite particles like B-mesons, is crucial, and scientists utilize light-cone distribution amplitudes (LCDAs) and shape functions to describe the distribution of momentum within these particles. Current research focuses on the inclusive decay B → Xsγ, where the B-meson decays into a strange quark and a photon. Scientists are refining calculations of power corrections, which account for the effects of the internal structure of the B-meson, and investigating the role of non-factorizable contributions, which arise from strong interactions between quarks and gluons.

They are also carefully examining the impact of quantum electrodynamics (QED) corrections, which account for the interactions of photons and charged particles. The shape function g17, a key component in these calculations, is being studied extensively, with scientists calculating its evolution with energy scale. Similar techniques are being applied to the decay B → Xsl+l-, where the B-meson decays into a strange quark and a pair of leptons. Scientists are working to resolve endpoint singularities, which appear in certain decay distributions and require careful treatment, and improve the accuracy of power corrections.

Investigations also extend to the decay B → γγ, exploring the contributions from different sources. A significant theme is the investigation of non-factorizable contributions to B-meson decays, which are challenging to calculate but crucial for achieving high precision. Researchers are also exploring the three-particle soft function, which describes the dynamics of soft gluons in B-meson decays, and developing methods for accurately treating endpoint singularities and QED corrections. This research contributes to more accurate theoretical predictions for B-meson decays, essential for testing the Standard Model and searching for new physics.

Scientists are developing and applying advanced techniques, such as SCET, OPE, and renormalization group evolution, to calculate decay rates and understand the underlying dynamics. They are shedding light on the role of non-perturbative effects, such as power corrections, and addressing challenging issues like endpoint singularities and non-factorizable corrections. This work provides a solid foundation for future studies of B-meson decays and other flavor physics phenomena.

B-meson Decay, Radiative Corrections, and Quark Interference

Scientists are meticulously analyzing B-meson decay, specifically the process ̄B→Xsγ, to refine calculations of the interference between specific quark operators, Q1 and Q7γ. This work requires calculating radiative corrections, which account for the effects of quantum fluctuations, at next-to-leading order to improve the precision of factorization formulas used to describe the decay process. The team focuses on the single resolved photon contribution, a dominant component of this decay, employing soft-collinear effective theory to manage the complexity of the interaction. To achieve this, researchers calculated the anomalous dimension of the subleading shape function, g17, a crucial element describing non-perturbative fluctuations, and computed two-loop corrections to the jet function, ̄J, which includes an internal charm loop.

The shape function, g17, was defined through a matrix element involving static ̄B-meson states and an operator within heavy-quark effective theory, evaluated using a forward integral over spatial and temporal coordinates. This operator, O17, presents a unique challenge as it smears fields across two distinct light-cones, requiring careful consideration of renormalization procedures. The team’s approach involved defining the shape function through a path integral formulation using the Keldysh formalism, allowing for a systematic evaluation of the matrix element. A key innovation was the extension of renormalization techniques, previously applied to B-meson light-cone distribution amplitudes, to accommodate the multi-light-cone structure of the operator O17.

The calculated one-loop anomalous dimension of g17 and the two-loop corrections to ̄J, alongside existing calculations of the quark-jet function J, provide the necessary ingredients for a next-to-leading order analysis, ultimately reducing uncertainties in the calculated interference effects by approximately 5. 45%. This refined calculation, incorporating a Voloshin term and accounting for scale ambiguities, improves the precision of predictions for B-meson decay rates and provides a more accurate understanding of the underlying physics.

Precise B-Meson Decay Calculations with Radiative Corrections

Scientists have achieved a significant advance in calculating the theoretical predictions for the decay of B-mesons into photons and other particles, specifically focusing on high-energy photon emissions. This work delivers next-to-leading order (NLO) radiative corrections to the subleading-power factorization formula, improving the precision of calculations in this area. The team computed the one-loop anomalous dimension of a key shape function, denoted as g17, and also calculated the two-loop corrections to a jet function containing an internal charm loop, both essential ingredients for a NLO analysis. The research involved detailed calculations of quantum corrections to the behavior of particles during the decay process.

Scientists determined the anomalous dimension of the operator O17, which describes the interaction of particles within the decay, revealing its structure as a combination of Abelian and non-Abelian contributions. The Abelian piece, γn, precisely matches the known scale evolution of the leading shape function, confirming the consistency of the calculations. The non-Abelian component, γ ̄n, acts specifically on momenta associated with one light-cone direction, demonstrating a decoupling of sectors consistent with soft-collinear factorization. Measurements confirm that the calculated anomalous dimension exhibits a specific functional form, incorporating logarithmic dependencies on the energy scale and delta functions that ensure proper behavior.

The team found that the one-loop anomalous dimension of O17 includes terms proportional to the strong coupling constant, color factors, and delta functions, accurately describing the quantum corrections. Furthermore, the calculations reveal that the anomalous dimension acts independently on different momentum sectors, a key feature arising from the underlying factorization principles. These results are crucial for refining theoretical predictions and improving the interpretation of experimental data from B-meson decays.