Matching the QCD and hadron sectors and medium-dependent meson masses; hadronization in relativistic heavy ion collisions

Abstract

The recent developments on the "vector manifestation" of chiral symmetry by Harada and Yamawaki provide a compelling evidence for, and "refine," the in-medium scaling of hadronic properties in dense/hot matter (call it "BR scaling") proposed by the authors in 1991. We reinterpret the Harada-Yamawaki result obtained in a Wilsonian renormalization-group approach to hidden local symmetry theory matched to QCD at near the chiral scale in terms of the Nambu-Jona-Lasinio model and predict that the vector meson mass in medium should scale m ⋆ ρ /m ρ ∼ ( qq ⋆ / qq ) 1/2 from n = 0 up to ∼ n = n 0 (where n 0 is nuclear matter density) and then go over to the linear scaling m ⋆ ρ /m ρ ∼ qq ⋆ / qq up to the chiral transition density n c at which the mass is to vanish (in the chiral limit) according to the vector manifestation fixed point. In the regime of the linear scaling above n 0 , the (vector) gauge coupling constant should fall linearly in qq ⋆ , vanishing at the critical point, with the width of the vector meson becoming steeply narrower. We suggest the in-medium vector meson mass, both parametric and pole, which goes smoothly to zero with increasing density, to be an order parameter for chiral symmetry restoration. Some issues related to recent RHIC observations are qualitatively discussed in the appendices. Our main conclusion that follows from these considerations is that the movement towards chiral restoration can be reliably described in Nambu-Jona-Lasinio mean field, with constituent quarks as variables, although there is probably density discontinuity following chiral restoration.

Double decimation and sliding vacua in the nuclear many-body system

“…As we have explained in a series of recent papers [14,15,16,17], a candidate effective field theory relevant in the hadronic sector matched to QCD at a scale near the chiral scale Λ χ is hidden local symmetry (HLS) theory with the vector manifestation (VM) found by Harada and Yamawaki [6,7]. This theory, denoted HLS/VM in short, with the vector mesons 2 , ρ, ω etc.…”

“…One is to incorporate the ratio [61] f ⋆ π /f π ≈ qq ⋆ / qq ≈ 0.78 at n = n 0 which enters into the Weinberg-Tomozawa isovector term in the pion-nucleon scattering amplitude 9 . This scaling can be identified [17] as the "intrinsic" density dependence required by matching to QCD. The other medium modification Friedman needs goes back to the relativistic impulse approximation used by Birbrair and collaborators [63] which gives small components of the Dirac wave functions for the nucleon enhanced by the factor F = m N /M (r) (29) where M (r) = m N + 1 2 [S(r) − V (r)] with S(r) and V (r) the vector mean fields.…”

“…As noted[17], the vector coupling and associated constants are presumed to be non-scaling up to nuclear matter density.…”

Matter-induced modification of resonances at RHIC freezeout

“…Here and below in-matter quantities are marked by the asterisk. Brown and Rho have proposed another scaling ( see the latest work [10] for earlier references and explanations)…”

“…This is to be compared to -10 MeV in average low energy hadroproduction reactions (10) and to a shift of about -30 MeV in preliminary STAR pp data [1] mention in the Introduction.…”