Periodic Reporting for period 1 - X-HEP (Exotic High Energy Phenomenology)
Período documentado: 2022-10-01 hasta 2025-03-31
CONTEXT
The X-HEP Project ("Exotic High Energy Phenomenology") aims to advance our understanding of quantum field theories (QFTs) and effective field theories (EFTs), two fundamental frameworks in theoretical physics. These frameworks are pivotal for describing the physics of fundamental particles, their interactions, and emergent phenomena at different scales, from the subatomic to the cosmological.
The key Background and Motivation:
1- Exploration of the Standard Model's Boundaries:
The Standard Model (SM) of particle physics is an incredibly successful theory but is known to be incomplete. It does not explain phenomena such as dark matter, neutrino masses, or the hierarchy problem.
Tools like EFTs are essential to parameterize deviations from the Standard Model and explore physics beyond it.
2- Strong Coupling Regimes in Quantum Field Theory:
Understanding quantum field theories at strong coupling is one of the most challenging and least understood areas of physics. It is essential for describing phenomena such as confinement in quantum chromodynamics (QCD) and emergent dynamics in strongly correlated systems.
3- Physical Predictions from Fundamental Constraints:
The scattering S-matrix, a fundamental observable in physics, encodes the probability of particle interactions. Understanding the constraints on the S-matrix from first principles (such as causality, unitarity, and symmetry) is crucial for deriving physically consistent theories.
OVERALL OBJECTIVES
The X-HEP project is centered on two primary themes, each addressing distinct yet interconnected problems in high-energy physics.
Theme 1: Constraining Relativistic Effective Field Theories
1- Develop techniques to impose consistency conditions on low-energy EFTs, using the scattering S-matrix as a primary tool.
2.-Extract physical predictions for the Standard Model and beyond, emphasizing:
Higgs physics (e.g. constraints on dimension-six operators and trilinear couplings).
Extending positivity bounds and S-matrix bootstrap methodologies.
3.-Bridge the gap between theoretical constraints and experimentally measurable observables, potentially impacting collider physics and other areas.
Theme 2: Studying Quantum Field Theories at Strong Coupling
1.-Extend and refine Hamiltonian Truncation methods to study renormalization group flows and strongly coupled QFTs in higher dimensions.
2.-Apply theoretical advancements to practical scenarios, such as the QCD equation of state and thermal effects in confining flux tubes.
3.- Explore novel phenomena, such as non-unitary UV completions and unexpected violations of positivity bounds.
The X-HEP Project ("Exotic High Energy Phenomenology") aims to advance our understanding of quantum field theories (QFTs) and effective field theories (EFTs), two fundamental frameworks in theoretical physics. These frameworks are pivotal for describing the physics of fundamental particles, their interactions, and emergent phenomena at different scales, from the subatomic to the cosmological.
The key Background and Motivation:
1- Exploration of the Standard Model's Boundaries:
The Standard Model (SM) of particle physics is an incredibly successful theory but is known to be incomplete. It does not explain phenomena such as dark matter, neutrino masses, or the hierarchy problem.
Tools like EFTs are essential to parameterize deviations from the Standard Model and explore physics beyond it.
2- Strong Coupling Regimes in Quantum Field Theory:
Understanding quantum field theories at strong coupling is one of the most challenging and least understood areas of physics. It is essential for describing phenomena such as confinement in quantum chromodynamics (QCD) and emergent dynamics in strongly correlated systems.
3- Physical Predictions from Fundamental Constraints:
The scattering S-matrix, a fundamental observable in physics, encodes the probability of particle interactions. Understanding the constraints on the S-matrix from first principles (such as causality, unitarity, and symmetry) is crucial for deriving physically consistent theories.
OVERALL OBJECTIVES
The X-HEP project is centered on two primary themes, each addressing distinct yet interconnected problems in high-energy physics.
Theme 1: Constraining Relativistic Effective Field Theories
1- Develop techniques to impose consistency conditions on low-energy EFTs, using the scattering S-matrix as a primary tool.
2.-Extract physical predictions for the Standard Model and beyond, emphasizing:
Higgs physics (e.g. constraints on dimension-six operators and trilinear couplings).
Extending positivity bounds and S-matrix bootstrap methodologies.
3.-Bridge the gap between theoretical constraints and experimentally measurable observables, potentially impacting collider physics and other areas.
Theme 2: Studying Quantum Field Theories at Strong Coupling
1.-Extend and refine Hamiltonian Truncation methods to study renormalization group flows and strongly coupled QFTs in higher dimensions.
2.-Apply theoretical advancements to practical scenarios, such as the QCD equation of state and thermal effects in confining flux tubes.
3.- Explore novel phenomena, such as non-unitary UV completions and unexpected violations of positivity bounds.
The X-HEP Project has undertaken a comprehensive and multi-faceted approach to advance the study of Effective Field Theories (EFTs) and Quantum Field Theories (QFTs). This section outlines the major activities and technical achievements, emphasizing the significant scientific advancements achieved during the project.
WORK PERFORMED
Theme 1: Constraining Relativistic Effective Field Theories
1.-S-Matrix Constraints on EFTs:
Developed methods to impose consistency constraints on EFTs via the scattering S-matrix.
Simplified the analysis of scattering amplitudes in weak and strong coupling regimes.
Linked the vacuum S-matrix to finite-temperature partition functions, broadening EFT applications.
2.-Positivity Bounds and Bootstrap Techniques:
Improved numerical optimization in the S-matrix bootstrap, refining primal and dual formulations.
Extended positivity bounds to include dimension-six operators relevant to Higgs physics.
3.-Applications to the Standard Model:
Used the tools to constrain Wilson coefficients of dimension-six operators in Higgs scattering.
Explored connections between EFT descriptions and high-energy constraints for realistic scenarios.
4.-Thermodynamics of Relativistic Systems:
Improved the Dashen-Ma-Bernstein formalism to link scattering amplitudes with thermodynamics.
Applied the framework to QCD, enabling more precise computations of the equation of state.
Theme 2: Quantum Field Theories at Strong Coupling
1.-Development of Hamiltonian Truncation Methods:
Enhanced Hamiltonian Truncation (HT) techniques to address UV divergences and renormalization.
Incorporated conformal perturbation theory to broaden the method’s applicability.
2.-Applications to Renormalization Group Flows:
Studied renormalization group flows in two-dimensional QFTs, confirming predictions and exploring new scenarios.
Used HT to analyze strongly coupled systems and compute effective Hamiltonians.
MAIN ACHIEVEMENTS (up to December 2024)
Theme 1 Achievements
1.- S-Matrix Bootstrap Innovations:
Published "Bridging Positivity and S-Matrix Bootstrap Bounds," introducing significant advancements in optimizing the S-matrix bootstrap and extending positivity bounds.
Elucidated the physical and mathematical assumptions required for realistic applications of the S-matrix bootstrap to the Standard Model.
2.- Higgs Physics Contributions:
Demonstrated new bounds on Higgs couplings, including trilinear form factors and Wilson coefficients of dimension-six operators, with implications for collider experiments.
Published results in Physical Review D and presented findings at major international venues.
3.- Thermodynamic Applications:
Showcased the potential of the Dashen-Ma-Bernstein framework to compute the QCD equation of state, addressing long-standing challenges in thermal QFT.
Theme 2 Achievements
1.- Hamiltonian Truncation for UV-Divergent QFTs:
Developed a robust renormalization framework for HT, enabling its application to realistic QFTs with UV divergences.
Applied the method to study complex RG flows, confirming predictions and uncovering new fixed points.
2.- Unexpected Outcomes:
Discovered a UV-complete theory that violates positivity bounds, challenging conventional wisdom and opening new research directions.
Thus far the project has successfully achieved its scientific objectives, laying the foundation for continued exploration of EFTs, QFTs, and their applications to particle physics and beyond.
These outcomes have advanced the state-of-the-art in theoretical high-energy physics and will significantly impact future research.
WORK PERFORMED
Theme 1: Constraining Relativistic Effective Field Theories
1.-S-Matrix Constraints on EFTs:
Developed methods to impose consistency constraints on EFTs via the scattering S-matrix.
Simplified the analysis of scattering amplitudes in weak and strong coupling regimes.
Linked the vacuum S-matrix to finite-temperature partition functions, broadening EFT applications.
2.-Positivity Bounds and Bootstrap Techniques:
Improved numerical optimization in the S-matrix bootstrap, refining primal and dual formulations.
Extended positivity bounds to include dimension-six operators relevant to Higgs physics.
3.-Applications to the Standard Model:
Used the tools to constrain Wilson coefficients of dimension-six operators in Higgs scattering.
Explored connections between EFT descriptions and high-energy constraints for realistic scenarios.
4.-Thermodynamics of Relativistic Systems:
Improved the Dashen-Ma-Bernstein formalism to link scattering amplitudes with thermodynamics.
Applied the framework to QCD, enabling more precise computations of the equation of state.
Theme 2: Quantum Field Theories at Strong Coupling
1.-Development of Hamiltonian Truncation Methods:
Enhanced Hamiltonian Truncation (HT) techniques to address UV divergences and renormalization.
Incorporated conformal perturbation theory to broaden the method’s applicability.
2.-Applications to Renormalization Group Flows:
Studied renormalization group flows in two-dimensional QFTs, confirming predictions and exploring new scenarios.
Used HT to analyze strongly coupled systems and compute effective Hamiltonians.
MAIN ACHIEVEMENTS (up to December 2024)
Theme 1 Achievements
1.- S-Matrix Bootstrap Innovations:
Published "Bridging Positivity and S-Matrix Bootstrap Bounds," introducing significant advancements in optimizing the S-matrix bootstrap and extending positivity bounds.
Elucidated the physical and mathematical assumptions required for realistic applications of the S-matrix bootstrap to the Standard Model.
2.- Higgs Physics Contributions:
Demonstrated new bounds on Higgs couplings, including trilinear form factors and Wilson coefficients of dimension-six operators, with implications for collider experiments.
Published results in Physical Review D and presented findings at major international venues.
3.- Thermodynamic Applications:
Showcased the potential of the Dashen-Ma-Bernstein framework to compute the QCD equation of state, addressing long-standing challenges in thermal QFT.
Theme 2 Achievements
1.- Hamiltonian Truncation for UV-Divergent QFTs:
Developed a robust renormalization framework for HT, enabling its application to realistic QFTs with UV divergences.
Applied the method to study complex RG flows, confirming predictions and uncovering new fixed points.
2.- Unexpected Outcomes:
Discovered a UV-complete theory that violates positivity bounds, challenging conventional wisdom and opening new research directions.
Thus far the project has successfully achieved its scientific objectives, laying the foundation for continued exploration of EFTs, QFTs, and their applications to particle physics and beyond.
These outcomes have advanced the state-of-the-art in theoretical high-energy physics and will significantly impact future research.
The X-HEP Project has yielded significant scientific advancements, many of which have transformative potential for theoretical physics. Below is an outline of the results, their potential impacts, and the critical steps needed to maximize their uptake and success.
RESULTS BEYOND THE STATE OF THE ART (as of December 2024)
Scientific Advancements:
- Refined S-matrix bootstrap and positivity bounds, improving constraints on Effective Field Theories (EFTs) and Standard Model extensions.
- Developed Hamiltonian Truncation methods to handle UV-divergent Quantum Field Theories (QFTs) and renormalization group flows.
- Constrained Higgs physics parameters, aiding experimental collider studies.
The X-HEP Project has advanced EFT and QFT methodologies, produced impactful publications, and identified novel theoretical phenomena. These results provide a foundation for future research and experimental exploration.
RESULTS BEYOND THE STATE OF THE ART (as of December 2024)
Scientific Advancements:
- Refined S-matrix bootstrap and positivity bounds, improving constraints on Effective Field Theories (EFTs) and Standard Model extensions.
- Developed Hamiltonian Truncation methods to handle UV-divergent Quantum Field Theories (QFTs) and renormalization group flows.
- Constrained Higgs physics parameters, aiding experimental collider studies.
The X-HEP Project has advanced EFT and QFT methodologies, produced impactful publications, and identified novel theoretical phenomena. These results provide a foundation for future research and experimental exploration.