Quantum Defect Theory for High Partial Wave Cold Collisions

We extend Multichannel Quantum Defect Theory (MQDT) to ultracold collisions involving high partial wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\le 2$ Fano-Feshbach resonances in the range 0-1000 G for the scattering of ${}^{40}$K + ${}^{87}$Rb in their lowest hyperfine states.