Radiative decay of the resonant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>K</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mi>π</mml:mi></mml:math> amplitude from lattice QCD
Archana Radhakrishnan, Jo Dudek, Robert G. Edwards
Abstract
We present the first calculation in lattice QCD of the process $\ensuremath{\gamma}K\ensuremath{\rightarrow}K\ensuremath{\pi}$ in which the narrow ${K}^{*}$ vector resonance appears. Using a lattice on which the pion has a mass of 284 MeV, we determine the transition amplitude at 128 points in the $({Q}^{2},{E}_{K\ensuremath{\pi}})$ plane, and find suitable resonant scattering descriptions. We demonstrate the need to account for $S$-wave $K\ensuremath{\pi}$ elastic scattering when converting the finite-volume matrix elements computed in lattice QCD to the physically relevant infinite-volume matrix elements, even when we are primarily interested in the $P$-wave amplitude. Analytically continuing parametrizations of the $\ensuremath{\gamma}K\ensuremath{\rightarrow}K\ensuremath{\pi}$ amplitude to the ${K}^{*}$ resonance pole, we obtain the ${K}^{*+}\ensuremath{\rightarrow}{K}^{+}\ensuremath{\gamma}$ transition form factor and compare the ${Q}^{2}=0$ value to the corresponding value extracted from the experimental partial decay width.