Nonrelativistic bound states lie at the core of quantum physics,

permeating the fabric of nature across diverse realms, spanning particle

to nuclear physics, and from condensed matter to astrophysics. These

systems are pivotal in addressing contemporary challenges at the forefront

of particle physics. Characterized by distinct energy scales, they serve

as unique probes of complex environments. Historically, their

incorporation into quantum field theory was fraught with difficulty until

the emergence of nonrelativistic effective field theories (NREFTs).



In this talk, we delve into the construction of a potential NREFT

(pNREFT), a framework that directly tackles bound state dynamics

reimagining quantum mechanics from field theory.

Focusing on heavy quarkonia, pNRQCD facilitates systematic definitions and

precise calculations for high-energy collider

observables. At the cutting edge, we investigate nonrelativistic bound

states in intricate environments, like the newly discovered exotics X, Y,

Z  above the strong decay threshold and the behavior in out-of-equilibrium

scenarios, such as quarkonium suppression in a Quark Gluon Plasma or dark

matter interactions in the early universe.



Our ability to achieve precision calculations and control strongly

interacting systems is closely linked to bridging perturbative methods

with nonperturbative tools, notably numerical lattice gauge theories.