Brown–Rho scaling explained

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]

refers to the pole mass of the ρ meson, whereas 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 byω, σ, and N, respectively. The symbol 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 is also used to denote the pion decay constant.^[5]

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

Notes and References

1. Brown, Gerald Edward. Rho, Mannque. On the manifestation of chiral symmetry in nuclei and dense nuclear matter. Physics Reports. 363. 2. 2002. 85–171. 10.1016/S0370-1573(01)00084-9. 2002PhR...363...85B. hep-ph/0103102. arXiv preprint
2. Gerald E. Brown, Mannque Rho. Scaling effective Lagrangians in a dense medium. Physical Review Letters. 66. 21. 2720–2723. 1991. 10.1103/PhysRevLett.66.2720. 10043599. 1991PhRvL..66.2720B.
3. Holt, J. W.. Brown, G. E.. Kuo, T. T. S.. Holt, J. D.. Machleidt, R.. 2008. Shell Model Description of the ¹⁴C Dating β Decay with Brown-Rho-Scaled NN Interactions. Physical Review Letters. 100. 6. 062501. 10.1103/PhysRevLett.100.062501. 18352465. 0710.0310. arXiv preprint
4. Ruppert, Jörg. Renk, Thorsten. Müller, Berndt. Mass and Width of the Rho Meson in a Nuclear Medium from Brown-Rho Scaling and QCD Sum Rules. Physical Review C . 73. 3. 15 March 2006. 034907. 10.1103/PhysRevC.73.034907. 2006PhRvC..73c4907R. hep-ph/0509134. arXiv preprint
5. Bernstein, A. M.. Holstein, Barry R.. Neutral pion lifetime measurements and the QCD chiral anomaly. Reviews of Modern Physics. 85. 1. 49. 2013. 2013RvMP...85...49B. 1112.4809. 10.1103/RevModPhys.85.49. arXiv preprint