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.

In the preceding equation, 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

References
  1. Brown, Gerald Edward; Rho, Mannque (2002). "On the manifestation of chiral symmetry in nuclei and dense nuclear matter". Physics Reports. 363 (2): 85–171. arXiv:hep-ph/0103102. Bibcode:2002PhR...363...85B. doi:10.1016/S0370-1573(01)00084-9. arXiv preprint
  2. Gerald E. Brown, Mannque Rho (1991). "Scaling effective Lagrangians in a dense medium". Phys. Rev. Lett. 66 (21): 2720–2723. Bibcode:1991PhRvL..66.2720B. doi:10.1103/PhysRevLett.66.2720. PMID 10043599.
  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. arXiv:0710.0310. doi:10.1103/PhysRevLett.100.062501. PMID 18352465. arXiv preprint
  4. 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". Phys Rev C. 73 (3): 034907. arXiv:hep-ph/0509134. Bibcode:2006PhRvC..73c4907R. doi:10.1103/PhysRevC.73.034907. arXiv preprint
  5. Bernstein, A. M.; Holstein, Barry R. (2013). "Neutral pion lifetime measurements and the QCD chiral anomaly". Reviews of Modern Physics. 85 (1): 49. arXiv:1112.4809. Bibcode:2013RvMP...85...49B. doi:10.1103/RevModPhys.85.49. arXiv preprint
  6. Ohnishi,A.; Kawamoto, N.; Miura, K. (2008). "Brown-Rho Scaling in the Strong Coupling Lattice QCD". Mod Phys Lett A. 23 (27–30): 2459–2464. arXiv:0803.0255. Bibcode:2008MPLA...23.2459O. doi:10.1142/S0217732308029587. arXiv preprint
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