QCD vacuum

The QCD vacuum is the quantum vacuum state of quantum chromodynamics, known as QCD. In physics, a vacuum is not just empty space. In QCD, the vacuum is a complex state characterized by non-vanishing condensates. These include the gluon condensate and the quark condensate. These condensates define the confined phase of quark matter. This phase is where quarks are trapped inside larger particles. Understanding the vacuum helps scientists explain how the strong force works.

To understand the vacuum, we must look at symmetry. A system has symmetry if its rules remain the same under certain changes. The QCD Lagrangian, which contains the rules for QCD, has several symmetries. It has Poincaré symmetry and CPT invariance. It also has local SU(3) gauge symmetry. There is also an approximate global flavor and chiral symmetry. One specific part, the baryon number symmetry, is exact. However, some symmetries are broken in the vacuum. For example, the scale or conformal symmetry is broken by the scale anomaly. This breaking leads to a phenomenon called asymptotic freedom.

A major concept in the vacuum is spontaneous symmetry breaking, or SSB. This occurs when the underlying rules of a system are symmetric, but the vacuum state is not. A good example is a ferromagnetic material. At high temperatures, the atoms act like tiny magnets pointing in random directions. The system is symmetric because there is no preferred direction. At low temperatures, the magnets all align in one direction. This creates a net magnetization. The rotational symmetry of the system is now broken. In QCD, the chiral flavor symmetry is spontaneously broken in the vacuum.

When a continuous symmetry is broken, new particles appear. These are called Goldstone bosons. In the QCD vacuum, the breaking of chiral flavor symmetry creates pseudoscalar mesons. These mesons are the Goldstone bosons of the theory. If we only consider up and down quarks as massless, we see three pions. If we include the strange quark as massless, we see eight pseudoscalar mesons. In the real world, quarks have small masses. This makes the pions "pseudo-Goldstone bosons" instead of perfectly massless particles. Scientists use chiral perturbation theory to calculate their actual masses.

History shows how our understanding of the vacuum has grown. Evidence for QCD condensates came from two different eras. From 1950 to 1973, researchers established the existence of the quark chiral condensate. After 1974, new results proved the existence of the gluon condensate. Scientists like Yoichiro Nambu and Jeffrey Goldstone explained the Nambu-Goldstone non-linear symmetry realization. They showed that the pion field is a Goldstone boson. Later, Steven Weinberg used these ideas to calculate amplitudes for particle collisions. These discoveries built the foundation for modern strong interaction physics.

There are surprising mathematical links in the vacuum. One is the Goldberger-Treiman relation. This relates the strong interaction coupling of pions to nucleons with the weak decay rate of the neutron. This relation is accurate to within 2.5%. It suggests that pions act as surrogates for axial weak currents. Another important idea is the partially conserved axial current, or PCAC, hypothesis. This hypothesis explains how a broken symmetry current can still be nearly conserved. It helps describe how pions are emitted during particle interactions.

Researchers also use advanced tools to study these complex states. One method is the operator product expansion, or OPE. This allows scientists to write the vacuum expectation value of an operator as a sum of local condensates. Another powerful tool is lattice QCD. This uses computers to perform numerical computations of the theory. Scientists can vary the quark mass in these simulations. They then check if the results match chiral perturbation theory. This provides direct evidence for the structure of the QCD vacuum.