Anomalous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mi>A</mml:mi> </mml:msub> </mml:math> couplings and the Columbia plot
Francesco Giacosa, Győző Kovács, Péter Kovács, Robert D. Pisarski, Fabian Rennecke
Abstract
When the quark masses are lighter than those in QCD, the standard lore is that a chiral transition of first order must emerge for three light flavors. Recently, however, numerical simulations on the lattice suggest that the chiral transition is of second order in the chiral limit. Using an extended linear sigma model in the mean field approximation, we study the relation between terms which break the anomalous, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mi>A</a:mi> </a:msub> </a:math> symmetry and the order of the chiral phase transition, especially how a chiral transition of second order can arise for three massless flavors. We note that in an (unphysical) region of the “Columbia” phase diagram, when the strange quark mass is light and negative, corresponding to topological angle <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>θ</e:mi> <e:mo>=</e:mo> <e:mi>π</e:mi> </e:math> , the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>C</g:mi> <g:mi>P</g:mi> </g:math> symmetry is spontaneously broken.