Physical-mass calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>770</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="ht

We present our study of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ρ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>770</a:mn><a:mo stretchy="false">)</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>K</e:mi><e:mo>*</e:mo></e:msup><e:mo stretchy="false">(</e:mo><e:mn>892</e:mn><e:mo stretchy="false">)</e:mo></e:math> resonances from lattice quantum chromodynamics (QCD) employing domain-wall fermions at physical quark masses. We determine the finite-volume energy spectrum in various momentum frames and obtain phase-shift parametrizations via the Lüscher formalism and as a final step the complex resonance poles of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>π</i:mi><i:mi>π</i:mi></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>K</k:mi><k:mi>π</k:mi></k:math> elastic scattering amplitudes via an analytical continuation of the models. By sampling a large number of representative sets of underlying energy-level fits, we also assign a systematic uncertainty to our final results. This is a significant extension to data-driven analysis methods that have been used in lattice QCD to date, due to the two-step nature of the formalism. Our final pole positions, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>M</m:mi><m:mo>+</m:mo><m:mi>i</m:mi><m:mi mathvariant="normal">Γ</m:mi><m:mo>/</m:mo><m:mn>2</m:mn></m:math>, with all statistical and systematic errors exposed, are <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msub><p:mrow><p:mi>M</p:mi></p:mrow><p:mrow><p:msup><p:mrow><p:mi>K</p:mi></p:mrow><p:mrow><p:mo>*</p:mo></p:mrow></p:msup></p:mrow></p:msub><p:mo>=</p:mo><p:mn>893</p:mn><p:mo stretchy="false">(</p:mo><p:mn>2</p:mn><p:mo stretchy="false">)</p:mo><p:mo stretchy="false">(</p:mo><p:mn>8</p:mn><p:mo stretchy="false">)</p:mo><p:mo stretchy="false">(</p:mo><p:mn>54</p:mn><p:mo stretchy="false">)</p:mo><p:mo stretchy="false">(</p:mo><p:mn>2</p:mn><p:mo stretchy="false">)</p:mo><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>MeV</p:mi></p:mrow></p:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi mathvariant="normal">Γ</z:mi><z:msup><z:mi>K</z:mi><z:mo>*</z:mo></z:msup></z:msub><z:mo>=</z:mo><z:mn>51</z:mn><z:mo stretchy="false">(</z:mo><z:mn>2</z:mn><z:mo stretchy="false">)</z:mo><z:mo stretchy="false">(</z:mo><z:mn>11</z:mn><z:mo stretchy="false">)</z:mo><z:mo stretchy="false">(</z:mo><z:mn>3</z:mn><z:mo stretchy="false">)</z:mo><z:mo stretchy="false">(</z:mo><z:mn>0</z:mn><z:mo stretchy="false">)</z:mo><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi>MeV</z:mi></z:math> for the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msup><kb:mi>K</kb:mi><kb:mo>*</kb:mo></kb:msup><kb:mo stretchy="false">(</kb:mo><kb:mn>892</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math> resonance and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mrow><ob:msub><ob:mrow><ob:mi>M</ob:mi></ob:mrow><ob:mrow><ob:mi>ρ</ob:mi></ob:mrow></ob:msub><ob:mo>=</ob:mo><ob:mn>796</ob:mn><ob:mo stretchy="false">(</ob:mo><ob:mn>5</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mo stretchy="false">(</ob:mo><ob:mn>15</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mo stretchy="false">(</ob:mo><ob:mn>48</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mo stretchy="false">(</ob:mo><ob:mn>2</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mtext> </ob:mtext><ob:mtext> </ob:mtext><ob:mi>MeV</ob:mi></ob:mrow></ob:math> and <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msub><yb:mi mathvariant="normal">Γ</yb:mi><yb:mi>ρ</yb:mi></yb:msub><yb:mo>=</yb:mo><yb:mn>192</yb:mn><yb:mo stretchy="false">(</yb:mo><yb:mn>10</yb:mn><yb:mo stretchy="false">)</yb:mo><yb:mo stretchy="false">(</yb:mo><yb:mn>28</yb:mn><yb:mo stretchy="false">)</yb:mo><yb:mo stretchy="false">(</yb:mo><yb:mn>12</yb:mn><yb:mo stretchy="false">)</yb:mo><yb:mo stretchy="false">(</yb:mo><yb:mn>0</yb:mn><yb:mo stretchy="false">)</yb:mo><yb:mtext> </yb:mtext><yb:mtext> </yb:mtext><yb:mi>MeV</yb:mi></yb:math> for the <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mi>ρ</jc:mi><jc:mo stretchy="false">(</jc:mo><jc:mn>770</jc:mn><jc:mo stretchy="false">)</jc:mo></jc:math> resonance. The four differently grouped sources of uncertainties are, in the order of occurrence: statistical, data-driven systematic, an estimation of systematic effects beyond our computation (dominated by the fact that we employ a single lattice spacing), and the error from the scale-setting uncertainty on our ensemble.