Quark Matter at Four Loops: Hardships and How to Overcome Them

Area of Science:

• Nuclear Physics
• Quantum Chromodynamics
• Astrophysics

Background:

• The equation of state for neutron-star matter is essential for understanding neutron star internal structure.
• Accurate calculations of cold and dense quark matter pressure are key constraints for this equation of state.
• Previous calculations were limited in precision, necessitating further theoretical advancements.

Purpose of the Study:

• To determine the next-to-next-to-next-to-leading order contribution to the pressure of cold, dense quark matter.
• To address the final unknown term required for a more complete theoretical description.
• To validate theoretical frameworks and numerical methods for high-precision calculations in quantum chromodynamics.

Main Methods:

• Calculation of all four-loop vacuum diagrams in dense quantum chromodynamics.
• Demonstration of covariant gauge parameter and infrared divergence cancellation.
• Application of the dense loop tree duality method for infrared-finite four-loop integrals.

Main Results:

• Significant progress has been made in calculating the pressure of cold quark matter at the next-to-next-to-next-to-leading order.
• The cancellation of gauge parameters and infrared divergences was successfully demonstrated.
• The dense loop tree duality method proved effective for complex multiloop calculations.

Conclusions:

• Completing the next-to-next-to-next-to-leading order pressure calculation for cold quark matter is now within reach.
• These advancements provide crucial data for refining neutron star equation of state models.
• The study highlights the power of effective-field-theory and novel numerical techniques in theoretical physics.