Lattice QCD Strategy Calculates Complex Amplitudes in Lepton Decays Accurately

The subtle decay of certain subatomic particles holds clues to the fundamental laws of physics, and accurately predicting these decays presents a significant challenge to theoretical models. Roberto Frezzotti, Sachrajda (University of Southampton), Francesco Sanfilippo and Silvano Simula (Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre), along with Luca Silvestrini (INFN, Sezione di Roma), present a new theoretical framework for calculating the rates of these decays using lattice quantum chromodynamics. Their work addresses a long-standing problem in these calculations, specifically the complex contributions arising from intermediate particles that are difficult to model with standard techniques. By employing advanced spectral-density methods, the researchers demonstrate a way to account for these “charming penguin” diagrams and other complex effects, paving the way for more precise predictions and a deeper understanding of particle interactions.

Researchers develop a strategy for computing the decay rates of B mesons into kaons and leptons using lattice quantum chromodynamics (QCD). These calculations are challenging because of complex contributions arising from intermediate particles that propagate within the decay process, introducing uncertainties into standard predictions. Existing methods struggle to accurately account for these effects, often relying on approximations and model-dependent assumptions. This research aims to address these challenges by employing lattice QCD, a non-perturbative approach that allows for first-principles calculations of hadronic properties and decay processes, providing a robust framework for investigating these decays and improving the precision of Standard Model predictions.

Lattice QCD Calculations of Hadron Properties

A comprehensive body of research focuses on applying lattice QCD to understand the fundamental properties of hadrons and their interactions. This work covers the core methodologies and techniques used in lattice QCD calculations, including the formulation of fermion actions, renormalization procedures, and the maintenance of chiral symmetry. Researchers are continually refining these techniques to reduce computational errors and improve the accuracy of predictions. A significant portion of this research focuses on calculating decay rates, form factors, and contributions to quantities like the muon anomalous magnetic moment.

Studies explore the decay of kaons, pions, and B mesons, calculating form factors essential for understanding weak decays and CP violation. Calculations of D-meson decays are also prominent, alongside investigations into the role of charming penguins in B and D decays. This research also addresses the calculation of hadronic contributions to the muon anomalous magnetic moment and decay rates for pseudoscalar mesons. Furthermore, studies focus on flavor physics and Standard Model precision tests, including calculations of CP-violating asymmetries and searches for rare decays sensitive to new physics. This body of work represents a comprehensive overview of the current state of lattice QCD calculations in hadron physics and flavor physics, demonstrating the progress made in recent years.

B Meson Decay Rates via Spectral Functions

Researchers have developed a new strategy for calculating the rates of certain particle decays, specifically those involving the decay of B mesons into kaons and leptons. These calculations are challenging because of the presence of complex contributions arising from intermediate particles that can propagate within the decay process, introducing uncertainties into standard predictions. This new approach combines lattice quantum chromodynamics (QCD) with a method called spectral function reconstruction. This allows researchers to determine both the real and imaginary parts of the decay amplitudes, overcoming the difficulties associated with complex intermediate states.

The team successfully applied this method to calculate contributions from “charming penguins”, diagrams involving loops of charm quarks, and the chromomagnetic operator, which previously required estimations. The significance of this work lies in its ability to reduce uncertainties in predicting decay rates. Charming penguin contributions, in particular, can be comparable in size to leading-order effects, potentially mimicking new physics if not accurately calculated. By providing a robust, first-principles calculation of these contributions, researchers can more confidently search for deviations from the Standard Model in experimental data. The method extends to scenarios with multiple interacting particles, demonstrating its versatility and paving the way for more precise calculations of complex decay processes. Furthermore, the team addressed a subtle issue related to ultraviolet divergences, mathematical infinities that arise in quantum field theory, and demonstrated a method for separating these divergences from the long-distance contributions, ensuring the accuracy of the calculations.

Spectral Densities Resolve Decay Amplitudes

This research presents a strategy for calculating the amplitudes of certain particle decays using lattice quantum chromodynamics (QCD). The study addresses complex contributions to these decays, arising from intermediate particles that are difficult to calculate with standard lattice QCD techniques. Researchers successfully demonstrate that these contributions, including those from “charming penguins” and the chromomagnetic operator, can be determined using spectral density methods. The team focused on calculating the matrix elements of specific operators within the effective Hamiltonian governing these decays, achieving results for the dominant contributions to the decay amplitude. Importantly, the methods developed are not limited to these operators and can, in principle, be extended to calculate contributions from other, previously neglected, terms. This work provides a pathway for more precise calculations of decay amplitudes, reducing uncertainties in predictions for these processes.