In this talk I will consider asymptotically free gauge theories with gauge group $SU(N_c)$ and $N_f$ quarks with mass $m_q <<\Lambda_{QCD}$ that undergo chiral symmetry breaking and confinement. I will described a proposal for a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of $N_c=3$, $N_f=2$, a numerical implementation of the method gives the phase shifts of the $S0$, $P1$ and $S2$ waves in good agreement with experimental results. The method incorporates gauge theory information ($N_c$, $N_f$, $m_q$, $\Lambda_{QCD}$) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. This requires, in addition, the values of the quark and gluon condensates. At low energy we impose constraints from chiral symmetry breaking which additionally require knowing the pion mass $m_\pi$.

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.

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.

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.

The charm sector provides new and unique insights into flavor and BSM physics, complementing longstanding programs with kaons and B-mesons. We report status and  progress in null test searches from theory on rare decays of charm mesons and baryons into invisibles, photons and leptons, and where flavor experiments are currently pushing this frontier. We also discuss CP-violation together with sizable U-spin violation seen in hadronic 2-body decays at the LHCb-experiment. A stunning explanation of this puzzle is given by a light, hadrophilic Z-prime that can also resolve issues with the pion-form factor in J/psi-decays.