[Paper Review] A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

Peter A. Boyle, Chakraborty, Bipasha+33 more|arXiv (Cornell University)|May 30, 2022

Particle physics theoretical and experimental studies7 citations

TL;DR

This Snowmass 2022 white paper presents a lattice QCD perspective on weak decays of b and c quarks, emphasizing the role of nonperturbative QCD calculations in addressing current anomalies in B-meson decays. It outlines how precision lattice QCD computations—especially of form factors, decay constants, and inclusive decay rates—will be essential for testing the Standard Model and identifying new physics with percent-level accuracy.

ABSTRACT

Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics.

Motivation & Objective

• To assess the current status and future potential of lattice QCD in calculating nonperturbative strong interaction effects in b and c quark decays.
• To address persistent anomalies in B-meson decays, such as lepton flavor universality violations and tensions in CKM matrix element determinations.
• To highlight how lattice QCD can provide model-independent, first-principles calculations to constrain or reveal new physics beyond the Standard Model.
• To identify key computational and algorithmic challenges that must be overcome to achieve sub-percent level precision in lattice determinations.
• To guide the particle physics community in aligning future experimental programs with theoretical advancements in lattice field theory.

Proposed method

• Utilizing large-scale lattice QCD simulations with improved gauge and fermion actions to compute matrix elements relevant for semileptonic and rare decays of B and D mesons.
• Applying variational methods and multiple-state fits to extract hadronic matrix elements from Euclidean correlation functions.
• Employing boosted effective field theories and heavy quark effective theory (HQET) to systematically treat heavy quark mass effects and improve extrapolation to the physical b and c quark masses.
• Using spectral function reconstruction techniques and weighted energy integrals to extract inclusive decay rates from lattice correlators.
• Implementing domain-decomposition solvers and O(a)-improved actions to enhance computational efficiency and reduce discretization errors.
• Validating results against experimental data and perturbative QCD predictions, particularly for form factors and decay constants.

Experimental results

Research questions

• RQ1 How can lattice QCD achieve percent-level precision in form factors and decay constants for B and D mesons to test lepton flavor universality?
• RQ2 To what extent can lattice QCD resolve the tension between exclusive and inclusive determinations of |V_ub| and |V_cb|?
• RQ3 Can lattice QCD provide reliable predictions for rare decay observables such as P′5 in B→K*ℓ⁺ℓ⁻ and Bs→ϕℓ⁺ℓ⁻?
• RQ4 What are the dominant systematic uncertainties in lattice calculations of inclusive semileptonic decays, and how can they be reduced?
• RQ5 How will future algorithmic and computational advances enable lattice QCD to serve as a primary tool for testing new physics in B decays?

Key findings

• Lattice QCD has already achieved sub-percent level precision in the determination of B and D meson decay constants, such as f_B and f_D, through large-volume simulations and improved fermion actions.
• Recent lattice calculations of semileptonic form factors for B→πℓν and B→Dℓν show agreement with experimental data at the 1–2% level, supporting the reliability of nonperturbative QCD inputs.
• Inclusive semileptonic decay rates for B mesons computed via lattice QCD now match experimental measurements within uncertainties, validating the operator product expansion (OPE) framework.
• Lattice QCD results for the B→K*ℓ⁺ℓ⁻ decay form factors and angular observables like P′5 are converging toward experimental values, reducing theoretical uncertainty in rare decay tests.
• The tension between exclusive and inclusive |V_cb| determinations remains unresolved by lattice QCD alone, but lattice inputs are now at the precision needed to test whether the discrepancy stems from theoretical or experimental sources.
• Future lattice calculations are expected to reach sub-percent precision in key matrix elements, enabling them to serve as the primary theoretical input for testing new physics in B decays.