Challenges and Opportunities for LaMET in Lattice QCD

While LaMET has enabled significant progress in accessing parton physics from lattice QCD, several challenges remain. At the same time, new opportunities are emerging as computational and theoretical techniques advance.

Main Challenges

1. Achieving Large Hadron Momenta

Lattice calculations require hadrons to be boosted to large momenta, but this is technically demanding due to discretization effects, signal-to-noise degradation, and finite volume artifacts.

2. Renormalization and Mixing

Nonlocal operators in LaMET are subject to ultraviolet divergences and operator mixing. Developing robust nonperturbative renormalization methods is an active area of research.

3. Control of Systematic Uncertainties

Systematic effects such as excited-state contamination, finite volume, and discretization errors must be carefully controlled to ensure reliable results.

4. Matching and Factorization

The matching between quasi-distributions and light-cone PDFs involves perturbative calculations and power corrections. Improving the precision of these steps is crucial for accurate phenomenology.

Opportunities

• Algorithmic Advances: New algorithms and increased computational power are enabling calculations at higher momenta and with better control of systematics.
• Broader Applications: LaMET is being applied to a wider range of observables, including GPDs, TMDs, and more.
• Synergy with Experiments: Results from LaMET are increasingly relevant for interpreting data from current and future experiments, such as the EIC.

Conclusion

LaMET continues to be a vibrant area of research, with ongoing efforts to overcome challenges and seize new opportunities in the study of hadron structure from first principles.