Pionic atom as a probe of origin of the Hadron Mass. Quantitative evaluation of the chiral condensate in a nuclear medium

Spontaneous breaking of chiral symmetry is believed to be the mechanism which endows nucleus their large masses. The order parameter of the symmetry breaking is the chiral condensate, whose magnitude is predicted to decrease linearly as the nuclear density is increased. The reduction of quark condensate was quantitatively studied from recent precise measurement of deeply bound pionic 1s states on three tin (Sn) isotopes. We made use of the Gell-Mann-Oakes-Renner relation which connects the magnitude of quark-codensate to a pion decay constant, and then used the Tomozawa-Weinberg relation which relates the pion decay constant to an isovector strength of the pion-nucleus potential. The potential strength was determined by fitting the measured pionic 1s-state binding energies. The result shows that the quark-condensate strength is reduced by about 35% at normal nuclear density, compared with the ''vacuum'' value obtained from pionic hydrogen X-ray measurements. This is the first quantitative deduction of the quark condensate modification at finite nuclear density, and is an important step towards understanding the origin of hadron masses. (author)