Unitary model analysis of f0(500) pole positions by continuously varying mπ</mml:…

Resonance, bound-state, and virtual-state pole positions of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>f</a:mi><a:mn>0</a:mn></a:msub><a:mo stretchy="false">(</a:mo><a:mn>500</a:mn><a:mo stretchy="false">)</a:mo></a:math> scalar meson are computed as a continuous function of pion mass in the framework of a unitarized and analytic coupled-channel model for scalar mesons, described as dynamical quark-antiquark states. The <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>f</e:mi><e:mn>0</e:mn></e:msub><e:mo stretchy="false">(</e:mo><e:mn>500</e:mn><e:mo stretchy="false">)</e:mo></e:math> is modeled with both light and strange <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>q</i:mi><i:mover accent="true"><i:mi>q</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math> seeds, mixing with each other through the common <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>S</m:mi></m:math>-wave <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>π</o:mi><o:mi>π</o:mi></o:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>K</q:mi><q:mover accent="true"><q:mi>K</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math>, and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>η</u:mi><u:mi>η</u:mi></u:math> meson-meson decay channels. The few model parameters are fitted to experimental <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>S</w:mi></w:math>-wave <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>π</y:mi><y:mi>π</y:mi></y:math> phase shifts up to 1 GeV. In the case of the physical <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msup><ab:mi>π</ab:mi><ab:mo>±</ab:mo></ab:msup></ab:math> mass of 139.57 MeV, resonance poles at <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mo stretchy="false">(</cb:mo><cb:mn>460</cb:mn><cb:mo>−</cb:mo><cb:mi>i</cb:mi><cb:mn>222</cb:mn><cb:mo stretchy="false">)</cb:mo><cb:mtext> </cb:mtext><cb:mtext> </cb:mtext><cb:mi>MeV</cb:mi></cb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mo stretchy="false">(</gb:mo><gb:mn>978</gb:mn><gb:mo>−</gb:mo><gb:mi>i</gb:mi><gb:mn>37.2</gb:mn><gb:mo stretchy="false">)</gb:mo><gb:mtext> </gb:mtext><gb:mtext> </gb:mtext><gb:mi>MeV</gb:mi></gb:math> are found for the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msub><kb:mi>f</kb:mi><kb:mn>0</kb:mn></kb:msub><kb:mo stretchy="false">(</kb:mo><kb:mn>500</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>f</ob:mi><ob:mn>0</ob:mn></ob:msub><ob:mo stretchy="false">(</ob:mo><ob:mn>980</ob:mn><ob:mo stretchy="false">)</ob:mo></ob:math>, respectively. Resonance, bound-state, and virtual-state pole trajectories are computed and plotted as a function of pion masses up to 500 MeV, both in the complex-energy and complex-momentum planes. The results are discussed and compared to the most advanced lattice QCD computations employing interpolators that correspond to the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>q</sb:mi><sb:mover accent="true"><sb:mi>q</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover></sb:math> and meson-meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations. Published by the American Physical Society 2024