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We extend Multichannel Quantum Defect Theory (MQDT) to ultracold collisionsinvolving high partial wave quantum numbers $L$. This requires a carefulstandardization of the MQDT reference wave functions at long range to ensuretheir linear independence. To illustrate the simplicity and accuracy of theresulting 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.

Quantum Defect Theory for High Partial Wave Cold Collisions