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No-go theorem for critical phenomena in large-N(c) QCD
Yoshimasa Hidaka1, Naoki Yamamoto
1Mathematical Physics Laboratory, RIKEN Nishina Center, Saitama 351-0198, Japan.
Physical Review Letters
|May 1, 2012
Summary
Critical phenomena in Quantum Chromodynamics (QCD) are forbidden at finite temperatures and quark chemical potentials for non-zero quark masses. This study rules out a critical point in QCD under specific conditions related to pion condensation.
Area of Science:
- High Energy Physics
- Quantum Chromodynamics (QCD)
- Statistical Mechanics
Background:
- Understanding the phase transitions of Quantum Chromodynamics (QCD) is crucial for nuclear physics.
- The behavior of QCD at finite temperature and chemical potential is complex and not fully understood.
- Large-N(c) (number of colors) limits offer theoretical simplifications for QCD-like theories.
Purpose of the Study:
- To rigorously investigate the chiral phase transition in QCD and QCD-like theories.
- To determine the existence of critical phenomena and soft modes under specific conditions.
- To rule out the QCD critical point at finite baryon chemical potential under certain phase diagram constraints.
Main Methods:
- Application of QCD inequalities.
- Utilizing the large-N(c) orbifold equivalence.
- Analysis of flavor-symmetric QCD at finite temperature (T) and quark chemical potential (μ).
Main Results:
- Critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD for non-zero quark masses at finite T and μ.
- The critical point in QCD at finite baryon chemical potential (μ(B)=N(c)μ) is ruled out.
- These findings hold when the (T, μ) coordinate is outside the pion condensed phase in the QCD phase diagram at finite isospin chemical potential (μ(I)=2μ).
Conclusions:
- The chiral phase transition in QCD exhibits restricted critical behavior under the studied conditions.
- The absence of critical phenomena suggests a smoother transition in these regimes.
- The results provide rigorous constraints on the QCD phase diagram, particularly concerning the critical point.
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