Why is LaMET an effective field theory for partonic structure?

Abstract: Partons are effective degrees of freedom describing the structure of hadrons involved in high-energy collisions. Familiar theories of partons are QCD light-front quantization and soft-collinear effective theory, both of which are intrinsically Minkowskian and appear unsuitable for classical Monte Carlo simulations. A ``new'' form of the parton theory has been formulated in term of the old-fashioned, Feynman's infinite momentum frame, in which the parton degrees of freedom are filtered through infinite-momentum external states. The partonic structure of hadrons is then related to the matrix elements of static (equal-time) correlators in the state $|P^z=\infty\rangle$. This representation lays the foundation of large-momentum effective theory (LaMET) which approximates parton physics through a systematic $M/P^z$ expansion of the lattice QCD matrix elements at a finite but large momentum $P^z$, and removes the residual logarithmic-$P^z$ dependence by the standard effective-field-theory matching and running.