Boosting QCD Studies with Bootstrap Tools

In this project we are embarking on the ambitious and exciting journey to advance our understanding of Quantum Chromodynamics (QCD) in 4d, a fundamental theory that describes interactions among quarks and gluons.

Our primary focus will be on studying QCD in two different regimes: in the physical regime with two flavours of quarks and in the conformal window.

In the physical regime QCD is the theory of Strong interactions responsible for the existence of mesons, baryons and nuclei.

QCD in the conformal window holds significant relevance from the purely theoretical prospective and might describe physics beyond the standard model. Although significant progress has been made in studying QCD, its complete understanding remains a challenge.

In the last decade there has been an incredible development of bootstrap tools which we will use in this project to obtain a series of groundbreaking results about QCD which are difficult or impossible to obtain by other means. We will use the S-matrix bootstrap to study QCD in the physical regime.

Our main goal is to find numerically crossing symmetric, analytic and unitary expressions for scattering amplitudes of pions, protons and neutrons, and perform spectral analysis of resonances described by complex energies. As a secondary goal we will compute non-perturbatively the scattering amplitude in the 3d phi4 model.

We will use the conformal bootstrap to study QCD in the left part of the conformal window and perturbation theory to study QCD in the right part of the conformal window in the Veneziano limit. We will attempt to determine the spectrum of Caswell-Banks-Zaks fixed points on both sides. As a secondary goal we will also obtain rigorous bounds on the trace anomalies in generic 4d conformal field theories.

Since the bootstrap tools are model independent, in order to study QCD we will augment them with QCD model dependent data which comes from experiments, numerical simulations and ('t Hooft and trace) anomalies.