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We present the analytic expressions for the color-planar contributions to theheavy-light form factors at three loops in perturbative QCD. These form factorsplay an important role in the precision predictions of various observables intop quark and flavour physics. We compute the master integrals using the methodof differential equations. We perform the ultraviolet renormalization for allthe appearing fields and parameters. The analytic results for the renormalizedform factors are expressed in terms of generalized harmonic polylogarithms. Wealso study the Sudakov behaviour of these form factors in the asymptotic limit,which enables us to obtain the complete logarithmic three-loop and partialfour-loop contributions.

Three loop QCD corrections to the heavy-light form factors in the color-planar limit