Physics: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/mσ ≈ m*N/mN ≈ m*ρ/mρ ≈ m*ω/mω ≈ f*π/fπ. This has a highly nontrivial implication for nuclear processes at or above nuclear-matter density.
mρ 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 fπ 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 Fπ 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
References
- ↑ Brown, Gerald Edward; Rho, Mannque (2002). "On the manifestation of chiral symmetry in nuclei and dense nuclear matter". Physics Reports 363 (2): 85–171. doi:10.1016/S0370-1573(01)00084-9. Bibcode: 2002PhR...363...85B. arXiv preprint
- ↑ Gerald E. Brown, Mannque Rho (1991). "Scaling effective Lagrangians in a dense medium". Physical Review Letters 66 (21): 2720–2723. doi:10.1103/PhysRevLett.66.2720. PMID 10043599. Bibcode: 1991PhRvL..66.2720B.
- ↑ 3.0 3.1 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. doi:10.1103/PhysRevLett.100.062501. PMID 18352465. arXiv preprint
- ↑ Ruppert, Jörg; Renk, Thorsten; Müller, Berndt (15 March 2006). "Mass and Width of the Rho Meson in a Nuclear Medium from Brown-Rho Scaling and QCD Sum Rules". Physical Review C 73 (3): 034907. doi:10.1103/PhysRevC.73.034907. Bibcode: 2006PhRvC..73c4907R. arXiv preprint
- ↑ Bernstein, A. M.; Holstein, Barry R. (2013). "Neutral pion lifetime measurements and the QCD chiral anomaly". Reviews of Modern Physics 85 (1): 49. doi:10.1103/RevModPhys.85.49. Bibcode: 2013RvMP...85...49B. arXiv preprint
- ↑ Ohnishi,A.; Kawamoto, N.; Miura, K. (2008). "Brown-Rho Scaling in the Strong Coupling Lattice QCD". Modern Physics Letters A 23 (27–30): 2459–2464. doi:10.1142/S0217732308029587. Bibcode: 2008MPLA...23.2459O. arXiv preprint
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