In-medium pion and partial restoration of chiral symmetry

Abstract

The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation qq * / qq = (F t π /Fπ)Z * 1/2 π with the in-medium quark condensate qq * , in-medium pion decay constant F t π and in-medium pion wave-function renormalization Z * π . Calculating Z * π at low density from the iso-scalar pion-nucleon scattering data and relating F t π to the isovector pion-nucleus scattering length b * 1 , it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleus interaction observed in the deeply bound pionic atoms directly implies the reduction of the in-medium quark condensate. The knowledge of the in-medium pion mass m * π is not necessary to reach this conclusion.

Mesonic and nucleon fluctuation effects at finite baryon density

“…If so, it would affect the mesonic spectrum, and, in particular, the mass of the η meson could decrease by a significant amount. It is also argued that in nuclear medium, the chiral condensate drops about 30% at the normal nuclear density [3], which could also imply a partial restoration of the U A (1) symmetry.…”

Spectroscopy of Pionic Atoms Via (p, 2He) Reaction

“…m π , M and µ are the mass of the pion, the nucleus and the reduced mass respectively. The isovector b 1 parameter is theoretically known to be related to the order parameter of spontaneous chiral syemmmtry breaking, chiral condensate [1][2][3][4]. In the deeply bound pionic atoms, the pion is partly embeded inside the nucleus and in-medium b 1 parameter is deduced from the binding energy and the width.…”

“…Thus, we can investigate the in-medium value of chiral condensate. The deeply pionic atoms were studied in GSI by using missing-mass spectroscopy of the (d, 3 He) reactions. Pionic states with 205,207 Pb [5][6][7][8] and 115,119,123 Sn [9] were measured and it was concluded that b f ree 1 /b med 1 = 0.78 ± 0.05, where b med…”

“…In addition, the method of dispersion-matched optics is adopted in that facility [12]. Since the deuteron beam energy available in RCNP is too low to satisfy the recoilless condition in the (d, 3 He) reaction, the (p, 2 He) reaction will be adopted.…”

Search for η′ Mesic Nuclei in GSI/FAIR

“…A successful example is high precision spectroscopy of pionic atoms [14,15], and an advanced experiment in conjunction with theoretical investigations [16][17][18][19] provided quantitative information on the chiral symmetry breaking and its partial restoration in a nuclear medium based on the precision data [20]. The deduced order parameter of the chiral symmetry, chiral condensate ⟨qq⟩, at the nuclear saturation density ρ 0 presented reduction of ∼ 30% compared to that in the vacuum.…”