Toward a direct measurement of partial restoration of chiral symmetry at J-PARC E16 via density-induced chiral mixing

The degeneracy of chiral partners is an ideal signal for measuring the restoration of the spontaneously broken chiral symmetry in QCD. In this work we investigate the observability of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>ϕ</a:mi></a:math> - <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>f</b:mi><b:mn>1</b:mn></b:msub><b:mrow><b:mo>(</b:mo><b:mn>1420</b:mn><b:mo>)</b:mo></b:mrow></b:mrow></b:math> degeneracy in the J-PARC E16 experiment, which measures dielectrons emitted from 30-GeV pA collisions. We for this purpose make use of an effective Lagrangian approach, which naturally incorporates the broken charge-conjugation symmetry in nuclear matter and the ensuing anomaly-induced mixing between vector and axial-vector mesons, to compute the spectral function relevant for the experimental measurement. The real-time dynamics of the pA collision is obtained from a transport simulation. Including experimental background and resolution effects on top of that, we find that a signal of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>ϕ</c:mi></c:math> - <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>f</d:mi><d:mn>1</d:mn></d:msub><d:mrow><d:mo>(</d:mo><d:mn>1420</d:mn><d:mo>)</d:mo></d:mrow></d:mrow></d:math> mixing can be observed at around 2.5 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>σ</e:mi></e:math>, with the Run2 statistics planned for the J-PARC E16 experiment with an ideal mixing strength.