Confined but chirally and chiral spin symmetric hot matter

Abstract We investigate properties of the quark–antiquark mesons at zero and finite temperature in the framework of a solvable chirally symmetric quark model. The interquark linearly rising interaction is reminiscent of that derived in Coulomb gauge QCD, with the string tension being the only model parameter. We demonstrate that while the confining interaction induces spontaneous breaking of chiral symmetry at $$T=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , it gets restored at a temperature $$T_\textrm{ch}\simeq 90$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> <mml:mo>≃</mml:mo> <mml:mn>90</mml:mn> </mml:mrow> </mml:math> MeV for the string tension fixed to provide the phenomenological value of the quark condensate. This temperature is similar to $$T_\textrm{ch}\simeq 130$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> <mml:mo>≃</mml:mo> <mml:mn>130</mml:mn> </mml:mrow> </mml:math> MeV observed on the lattice in the chiral limit for $$N_c=3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . The physical mechanism responsible for chiral symmetry restoration in the confining regime is Pauli blocking of the quark levels, required for the existence of a nonvanishing quark condensate, by thermal excitations of the quarks and antiquarks. Thus, above the chiral restoration temperature, meson-like states are chirally symmetric and approximately chiral spin symmetric. A crucial property of the confined meson-like light-light states above $$T_\textrm{ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> </mml:math> is their size that exceeds drastically that in the chirally broken phase below $$T_\textrm{ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> </mml:math> . Heavy-heavy mesons nearly preserve their size irrespective of the temperature. Furthermore, the root-mean-square radius of the states with $$J=0,1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> diverges in the chiral limit. This unexpected property must be a key to understanding unusual features of the hot QCD matter as observed at RHIC and LHC. Consequently, the confining but chirally symmetric matter above $$T_\textrm{ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> </mml:math> can be considered as a dense system of very large and strongly overlapping meson-like states (“strings”).