  In this work we discuss an analytic bootstrap approach [1,2] in the context
of spinning 4D conformal blocks [3,4]. As an example we study the simplest
spinning case, the scalar-fermion correlator
$\langle\phi\psi\phi\bar\psi\rangle$. We find that to every pair of primary
scalar $\phi$ and fermion $\psi$ correspond two infinite towers of fermionic
large spin primary operators. We compute their twists and products of OPE
coefficients using both s-t and u-t bootstrap equations to the leading and
sub-leading orders. We find that the leading order is represented by the
scalar-fermion generalized free theory and the sub-leading order is governed by
the minimal twist bosonic (light scalars, currents and the energy-momentum
tensor) and fermionic (light fermions and the suppersymmetric current)
operators present in the spectrum.
