sjtu-sai-agents/physmaster/lamet-asymptotic-expansion

LaMET Asymptotic Expansion

Apply this skill when the task involves quasi-distributions, quasi-TMD matrix elements, or other quasi-observables computed at finite hadron momentum and you need a leading-power relation to the corresponding light-cone quantity.

Goal

Relate quasi-observables computed at finite hadron momentum to their light-cone counterparts using the large-momentum effective theory (LaMET) asymptotic expansion.

Scope

• Hadron momentum P_z >> Lambda_QCD
• Leading-power LaMET only
• Neglect O(1 / P_z^2) power corrections unless the user explicitly asks to analyze them

Inputs

• quasi_observable: Renormalized quasi-distribution or quasi-TMD matrix element defined with spacelike Wilson lines
• hadron_momentum: Large hadron momentum component, usually P_z
• renormalization_scale: Renormalization scale mu

Outputs

• factorized_form: Leading-power factorized expression relating the quasi-observable to the corresponding light-cone quantity
• power_counting_statement: Explicit statement of neglected power corrections and their parametric scaling

Workflow

1. Identify the large-momentum variable.

Fix the reference frame and specify which hadron momentum component is taken to be asymptotically large.

1. Perform the power expansion.

Expand the quasi-observable in powers of 1 / P_z and keep the leading-power term.

1. Match operator structures.

Identify the light-cone operator corresponding to the leading term in the large-momentum expansion.

1. State the factorization formula.

Write the leading-power LaMET relation, including perturbative matching if required by the task.

Quality Checks

• The extracted leading contribution should be P_z independent up to higher-order corrections.
• Subleading terms should be explicitly described as parametrically suppressed, typically O(1 / P_z^2) or smaller.

Constraints

• Do not claim power-correction control beyond leading power unless it is derived or explicitly provided.
• Do not blur quasi-observables and their matched light-cone counterparts; keep the mapping explicit.
• If perturbative matching kernels are required but not given, state that they must be supplied or computed separately.