On interpretation of fluctuations of conserved charges at high T

Abstract Fluctuations of conserved charges calculated on the lattice which can be measured experimentally, are well reproduced by a hadron resonanse gas model at temperatures below $$T_{ch} \sim 155$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>ch</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>155</mml:mn> </mml:mrow> </mml:math> MeV and radically deviate from the hadron resonance gas predictions above the chiral restoration crossover. This behaviour is typically interpreted as an indication of deconfinement in the quark-gluon plasma regime. We present an argument that this interpretation may be too simple. The argument is based on the scaling of quantities with the number of colors: demonstration of deconfinement and QGP requires observable that is sensitive to $$\sim N_c^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> gluons while the conserved charges are sensitive only to quarks and above $$T_{ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>ch</mml:mi> </mml:mrow> </mml:msub> </mml:math> scale as $$N_c^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> <mml:mn>1</mml:mn> </mml:msubsup> </mml:math> . The latter scaling is consistent with the existence of an intermediate regime characterized by restored chiral symmetry and by approximate chiral spin symmetry which is a symmetry of confining interaction. In this regime the energy density, pressure and entropy density scale as $$N_c^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> <mml:mn>1</mml:mn> </mml:msubsup> </mml:math> . In the large $$N_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> limit this regime might become a distinct phase separated from the hadron gas and from QGP by phase transitions. A natural observable that associates with deconfinement and is directly sensitive to deconfined $$N_c^2-1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> gluons is the Polyakov loop; in the $$N_c=3$$ <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> world it remains very close to 0 at temperatures well above chiral crossover, reaches the value $$\sim 0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> around $$\sim 3T_{ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>3</mml:mn> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>ch</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and the value close to 1 at temperatures $$\sim 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> GeV.