Boosting QCD Studies with Bootstrap Tools

Introduction

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.

Physical Regime

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 perspective and might describe physics beyond the standard model.

Although significant progress has been made in studying QCD, its complete understanding remains a challenge.

Bootstrap Tools

In the last decade, there has been incredible development of bootstrap tools which we will use in this project to obtain a series of groundbreaking results about QCD that are difficult or impossible to obtain by other means.

1. We will use the S-matrix bootstrap to study QCD in the physical regime.
2. Our main goal is to find numerically crossing symmetric, analytic, and unitary expressions for scattering amplitudes of pions, protons, and neutrons.
3. We will perform spectral analysis of resonances described by complex energies.

Secondary Goals

As a secondary goal, we will compute non-perturbatively the scattering amplitude in the 3d phi4 model.

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

Model Independence

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.