We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ( $$\chi _S^\kappa $$ , $$\chi _P^K$$ ) in the isospin 1/2 channel. We show that $$\chi _S^\kappa $$ develops a maximum above the QCD chiral transition, after which it degenerates with $$\chi _P^K$$ . We also obtain $$\chi _S^\kappa $$ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $$K_0^*(700)$$ (or $$\kappa $$ ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $$\pi K$$ scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $$\chi _S^\kappa $$ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $$m_l/m_s$$ ratio that allows one studying $$K-\kappa $$ degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for $$O(4)\times U(1)_A$$ restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $$U(1)_A$$ restoration.
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"surname": "Vioque-Rodr\u00edguez",
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"surname": "\u00c1lvarez-Herrero",
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"title": "The role of strangeness in chiral and $$U(1)_A$$ <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>A</mi> </msub> </mrow> </math> restoration"
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"value": "We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ( $$\\chi _S^\\kappa $$ <math> <msubsup> <mi>\u03c7</mi> <mi>S</mi> <mi>\u03ba</mi> </msubsup> </math> , $$\\chi _P^K$$ <math> <msubsup> <mi>\u03c7</mi> <mi>P</mi> <mi>K</mi> </msubsup> </math> ) in the isospin 1/2 channel. We show that $$\\chi _S^\\kappa $$ <math> <msubsup> <mi>\u03c7</mi> <mi>S</mi> <mi>\u03ba</mi> </msubsup> </math> develops a maximum above the QCD chiral transition, after which it degenerates with $$\\chi _P^K$$ <math> <msubsup> <mi>\u03c7</mi> <mi>P</mi> <mi>K</mi> </msubsup> </math> . We also obtain $$\\chi _S^\\kappa $$ <math> <msubsup> <mi>\u03c7</mi> <mi>S</mi> <mi>\u03ba</mi> </msubsup> </math> within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $$K_0^*(700)$$ <math> <mrow> <msubsup> <mi>K</mi> <mn>0</mn> <mo>\u2217</mo> </msubsup> <mrow> <mo>(</mo> <mn>700</mn> <mo>)</mo> </mrow> </mrow> </math> (or $$\\kappa $$ <math> <mi>\u03ba</mi> </math> ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $$\\pi K$$ <math> <mrow> <mi>\u03c0</mi> <mi>K</mi> </mrow> </math> scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $$\\chi _S^\\kappa $$ <math> <msubsup> <mi>\u03c7</mi> <mi>S</mi> <mi>\u03ba</mi> </msubsup> </math> dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $$m_l/m_s$$ <math> <mrow> <msub> <mi>m</mi> <mi>l</mi> </msub> <mo>/</mo> <msub> <mi>m</mi> <mi>s</mi> </msub> </mrow> </math> ratio that allows one studying $$K-\\kappa $$ <math> <mrow> <mi>K</mi> <mo>-</mo> <mi>\u03ba</mi> </mrow> </math> degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for $$O(4)\\times U(1)_A$$ <math> <mrow> <mi>O</mi> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>\u00d7</mo> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>A</mi> </msub> </mrow> </math> restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $$U(1)_A$$ <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>A</mi> </msub> </mrow> </math> restoration."
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