Brown–Rho scaling
{{Short description|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.{{cite journal|author=Brown, Gerald Edward|author2=Rho, Mannque|title=On the manifestation of chiral symmetry in nuclei and dense nuclear matter|journal=Physics Reports|volume=363|issue=2|year=2002|pages=85–171|doi=10.1016/S0370-1573(01)00084-9|bibcode=2002PhR...363...85B|arxiv=hep-ph/0103102}} [https://arxiv.org/abs/hep-ph/0103102 arXiv preprint]
According to Gerald E. Brown and Mannque Rho in their 1991 publication in Physical Review Letters:{{cite journal|author=Gerald E. Brown, Mannque Rho| title=Scaling effective Lagrangians in a dense medium| journal=Physical Review Letters| volume=66| issue=21| pages=2720–2723| year=1991| doi=10.1103/PhysRevLett.66.2720| pmid=10043599| bibcode=1991PhRvL..66.2720B}}
{{blockquote|By using effective chiral Lagrangians with a suitable incorporation of the scaling property of QCD, we establish the approximate in-medium scaling law, {{nowrap|m{{su|p=*|b=σ}}}}/{{nowrap|m{{su|p=|b=σ}}}} ≈ {{nowrap|m{{su|p=*|b=N}}}}/{{nowrap|m{{su|p=|b=N}}}} ≈ {{nowrap|m{{su|p=*|b=ρ}}}}/{{nowrap|m{{su|p=|b=ρ}}}} ≈ {{nowrap|m{{su|p=*|b=ω}}}}/{{nowrap|m{{su|p=|b=ω}}}} ≈ {{nowrap|f{{su|p=*|b=π}}}}/{{nowrap|f{{su|p=|b=π}}}}. This has a highly nontrivial implication for nuclear processes at or above nuclear-matter density.}}
{{nowrap|m{{su|p=|b=ρ}}}} refers to the pole mass of the ρ meson, whereas {{nowrap|m{{su|p=*|b=ρ}}}} refers to the in-medium mass{{cite journal|author=Holt, J. W.|author2=Brown, G. E.|author3=Kuo, T. T. S.|author4=Holt, J. D.|author5=Machleidt, R.|year=2008|title=Shell Model Description of the 14C Dating β Decay with Brown-Rho-Scaled NN Interactions|journal=Physical Review Letters|volume=100|issue=6|page=062501|doi=10.1103/PhysRevLett.100.062501|pmid=18352465|arxiv=0710.0310}} [https://arxiv.org/abs/0710.0310 arXiv preprint] (or running mass in the medium) of the ρ meson according to QCD sum rules.{{cite journal|author=Ruppert, Jörg|author2=Renk, Thorsten|author3=Müller, Berndt|title=Mass and Width of the Rho Meson in a Nuclear Medium from Brown-Rho Scaling and QCD Sum Rules|journal=Physical Review C |volume=73|issue=3|date=15 March 2006|page=034907|doi=10.1103/PhysRevC.73.034907|bibcode=2006PhRvC..73c4907R|arxiv=hep-ph/0509134}} [https://arxiv.org/abs/hep-ph/0509134 arXiv preprint] The omega meson, sigma meson, and neutron are denoted by
ω, σ, and N, respectively. The symbol {{nowrap|f{{su|p=|b=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 {{nowrap|F{{su|p=|b=π}}}} is also used to denote the pion decay constant.{{cite journal|author=Bernstein, A. M.|author2=Holstein, Barry R.|title=Neutral pion lifetime measurements and the QCD chiral anomaly|journal=Reviews of Modern Physics|volume=85|issue=1|page=49|year=2013|bibcode=2013RvMP...85...49B|arxiv=1112.4809|doi=10.1103/RevModPhys.85.49}} [https://arxiv.org/abs/1112.4809 arXiv preprint]
{{blockquote|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 ...{{cite journal|author=Ohnishi,A.|author2=Kawamoto, N.|author3=Miura, K.|title=Brown-Rho Scaling in the Strong Coupling Lattice QCD|journal=Modern Physics Letters A|volume=23|issue=27–30|pages=2459–2464|year=2008|bibcode=2008MPLA...23.2459O|arxiv=0803.0255|doi=10.1142/S0217732308029587}} [https://arxiv.org/abs/0803.0255 arXiv preprint]}}
The hypothesis of Brown–Rho scaling is supported by experimental evidence on beta decay of 14C to the 14N ground state.