Brown–Rho scaling

In quantum chromodynamics (QCD), Brown–Rho (BR) scaling is an approximate scaling law for hadrons in an ultra-hot, ultra-dense medium, such as hadrons in the quark epoch during the first microsecond of the Big Bang or within neutron stars.^[1]

According to Gerald E. Brown and Mannque Rho in their 1991 publication in Physical Review Letters:^[2]

By using effective chiral Lagrangians with a suitable incorporation of the scaling property of QCD, we establish the approximate in-medium scaling law, m^*
_σ/m
_σ ≈ m^*
_N/m
_N ≈ m^*
_ρ/m
_ρ ≈ m^*
_ω/m
_ω ≈ f^*
_π/f
_π. This has a highly nontrivial implication for nuclear processes at or above nuclear-matter density.

m
_ρ refers to the pole mass of the ρ meson, whereas m^*
_ρ refers to the in-medium mass^[3] (or running mass in the medium) of the ρ meson according to QCD sum rules.^[4] The omega meson, sigma meson, and neutron are denoted by ω, σ, and N, respectively. The symbol f
_π denotes the free-space pion decay constant. (Decay constants have a "running time" and a "pole time" similar to the "running mass" and "pole mass" concepts, according to special relativity.) The symbol F
_π is also used to denote the pion decay constant.^[5]

For hadrons, a large part of their masses are generated by the chiral condensate. Since the chiral condensate may vary significantly in hot and/or dense matter, hadron masses would also be modified. ... Brown–Rho scaling ... suggests that the partial restoration of the chiral symmetry can be experimentally accessible by measuring in-medium hadron masses, and triggered many later theoretical and experimental works. Theoretically, a similar behavior is also found in the NJL model ... and the QCD sum rule ...^[6]

The hypothesis of Brown–Rho scaling is supported by experimental evidence on beta decay of ¹⁴C to the ¹⁴N ground state.^[3]

See also

• Quantum chromodynamics
• QCD matter
• Pion decay constant