Physical-mass calculation of ρ(770) and K*(892) resonance parameters via ππ and Kπ scattering amplitudes from lattice QCD

We present our study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mn>770</mn> <mo stretchy="false">)</mo> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msup> <mi>K</mi> <mo>*</mo> </msup> <mo stretchy="false">(</mo> <mn>892</mn> <mo stretchy="false">)</mo> </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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>π</mi> <mi>π</mi> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>K</mi> <mi>π</mi> </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, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>M</mi> <mo>+</mo> <mi>i</mi> <mi mathvariant="normal">Γ</mi> <mo>/</mo> <mn>2</mn> </math> , with all statistical and systematic errors exposed, are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <msup> <mrow> <mi>K</mi> </mrow> <mrow> <mo>*</mo> </mrow> </msup> </mrow> </msub> <mo>=</mo> <mn>893</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>8</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>54</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mtext> </mtext> <mtext> </mtext> <mi>MeV</mi> </mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msub> <mi mathvariant="normal">Γ</mi> <msup> <mi>K</mi> <mo>*</mo> </msup> </msub> <mo>=</mo> <mn>51</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>11</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mtext> </mtext> <mtext> </mtext> <mi>MeV</mi> </math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msup> <mi>K</mi> <mo>*</mo> </msup> <mo stretchy="false">(</mo> <mn>892</mn> <mo stretchy="false">)</mo> </math> resonance and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mi>ρ</mi> </mrow> </msub> <mo>=</mo> <mn>796</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>15</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>48</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mtext> </mtext> <mtext> </mtext> <mi>MeV</mi> </mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msub> <mi mathvariant="normal">Γ</mi> <mi>ρ</mi> </msub> <mo>=</mo> <mn>192</mn> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>28</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>12</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mtext> </mtext> <mtext> </mtext> <mi>MeV</mi> </math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mn>770</mn> <mo stretchy="false">)</mo> </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.