Approximate scaling law for hadrons in extreme environments
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]
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]
