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.
{ "_oai": { "updated": "2023-02-05T09:30:23Z", "id": "oai:repo.scoap3.org:63561", "sets": [ "EPJC" ] }, "authors": [ { "affiliations": [ { "country": "Spain", "value": "Departamento de F\u00edsica Te\u00f3rica and IPARCOS, Universidad Complutense, Madrid, 28040, Spain", "organization": "Universidad Complutense" } ], "surname": "G\u00f3mez Nicola", "email": "gomez@ucm.es", "full_name": "G\u00f3mez Nicola, A.", "given_names": "A." }, { "affiliations": [ { "country": "Switzerland", "value": "Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, Bern, 3012, Switzerland", "organization": "University of Bern" } ], "surname": "Ruiz de Elvira", "email": "elvira@itp.unibe.ch", "full_name": "Ruiz de Elvira, J.", "given_names": "J." }, { "affiliations": [ { "country": "Spain", "value": "Departamento de F\u00edsica Te\u00f3rica and IPARCOS, Universidad Complutense, Madrid, 28040, Spain", "organization": "Universidad Complutense" } ], "surname": "Vioque-Rodr\u00edguez", "email": "avioque@ucm.es", "full_name": "Vioque-Rodr\u00edguez, A.", "given_names": "A." }, { "affiliations": [ { "country": "Spain", "value": "Departamento de F\u00edsica Te\u00f3rica and IPARCOS, Universidad Complutense, Madrid, 28040, Spain", "organization": "Universidad Complutense" } ], "surname": "\u00c1lvarez-Herrero", "email": "davial06@ucm.es", "full_name": "\u00c1lvarez-Herrero, D.", "given_names": "D." } ], "titles": [ { "source": "Springer", "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" } ], "dois": [ { "value": "10.1140/epjc/s10052-021-09458-1" } ], "publication_info": [ { "page_end": "9", "journal_title": "European Physical Journal C", "material": "article", "journal_volume": "81", "artid": "s10052-021-09458-1", "year": 2021, "page_start": "1", "journal_issue": "7" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-02-05T09:30:22.406887", "source": "Springer", "method": "Springer", "submission_number": "a95ab70aa53711ed9a680e231c257137" }, "page_nr": [ 9 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "63561", "record_creation_date": "2021-07-21T12:30:15.991774", "_files": [ { "checksum": "md5:df4cf7845355cd4fad2f68590f45a8a5", "filetype": "xml", "bucket": "122ed606-f0e7-4850-994f-9dd42c7e0f34", "version_id": "3a44b827-ac3e-4d1b-86d2-1ff0b3de69ea", "key": "10.1140/epjc/s10052-021-09458-1.xml", "size": 23197 }, { "checksum": "md5:b4148617e7688bbabf51d0f5bd52a610", "filetype": "pdf/a", "bucket": "122ed606-f0e7-4850-994f-9dd42c7e0f34", "version_id": "53ed492e-8a73-4b09-b4d8-039a3ce01091", "key": "10.1140/epjc/s10052-021-09458-1_a.pdf", "size": 870874 } ], "collections": [ { "primary": "European Physical Journal C" } ], "abstracts": [ { "source": "Springer", "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." } ], "imprints": [ { "date": "2021-07-21", "publisher": "Springer" } ] }