Elastic nucleon-pion scattering amplitudes in the Δ channel at physical pion mass from lattice QCD

We present an investigation of pion-nucleon elastic scattering in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>I</a:mi><a:mo stretchy="false">(</a:mo><a:msup><a:mi>J</a:mi><a:mi>P</a:mi></a:msup><a:mo stretchy="false">)</a:mo><a:mo>=</a:mo><a:mfrac><a:mn>3</a:mn><a:mn>2</a:mn></a:mfrac><a:mo stretchy="false">(</a:mo><a:msup><a:mfrac><a:mn>3</a:mn><a:mn>2</a:mn></a:mfrac><a:mo>+</a:mo></a:msup><a:mo stretchy="false">)</a:mo></a:math> channel using lattice QCD with degenerate up and down, strange and charm quarks with masses tuned to their physical values. We use an ensemble of twisted mass fermions with box size <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>L</g:mi><g:mo>=</g:mo><g:mn>5.1</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>fm</g:mi></g:math> and lattice spacing <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>a</i:mi><i:mo>=</i:mo><i:mn>0.08</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>fm</i:mi></i:math> and we consider the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>π</k:mi><k:mi>N</k:mi></k:math> system in rest and moving frames up to total momentum <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msup><m:mrow><m:mover accent="true"><m:mrow><m:mi>P</m:mi></m:mrow><m:mrow><m:mo stretchy="false">→</m:mo></m:mrow></m:mover></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup><m:mo>=</m:mo><m:mn>3</m:mn><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>π</m:mi><m:mo>/</m:mo><m:mi>L</m:mi><m:msup><m:mrow><m:mo stretchy="false">)</m:mo></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup><m:mo>=</m:mo><m:mn>0.17</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:msup><m:mrow><m:mi>GeV</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup></m:mrow></m:math>. We take into account the finite volume symmetries and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>S</s:mi></s:math>- and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>P</u:mi></u:math>-wave mixing, and use the Lüscher formalism to simultaneously constrain the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>J</w:mi><w:mo>=</w:mo><w:mn>1</w:mn><w:mo>/</w:mo><w:mn>2</w:mn><w:mo>,</w:mo><w:mo>ℓ</w:mo><w:mo>=</w:mo><w:mn>0</w:mn></w:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>J</y:mi><y:mo>=</y:mo><y:mn>3</y:mn><y:mo>/</y:mo><y:mn>2</y:mn><y:mo>,</y:mo><y:mo>ℓ</y:mo><y:mo>=</y:mo><y:mn>1</y:mn></y:math> scattering amplitudes. We estimate the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="normal">Δ</ab:mi></ab:math> resonance pole in the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>P</db:mi></db:math>-wave channel as well as the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>S</fb:mi></fb:math>-wave isospin-<hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mrow><hb:mn>3</hb:mn><hb:mo>/</hb:mo><hb:mn>2</hb:mn></hb:mrow></hb:math> scattering length. Published by the American Physical Society 2024