  We study the transverse target spin dependence of the cross section for
inclusive electron-nucleon scattering with unpolarized beam. Such dependence is
absent in the one-photon exchange approximation (Christ-Lee theorem) and arises
only in higher orders of the QED expansion, from the interference of one-photon
and absorptive two-photon exchange amplitudes as well as from real photon
emission (bremsstrahlung). We demonstrate that the transverse spin-dependent
two-photon exchange cross section is free of QED infrared and collinear
divergences. We argue that in DIS kinematics the transverse spin dependence
should be governed by a "parton-like" mechanism in which the two-photon
exchange couples mainly to a single quark. We calculate the normal spin
asymmetry in an approximation where the dominant contribution arises from quark
helicity flip due to interactions with non-perturbative vacuum fields
(constituent quark picture) and is proportional to the quark transversity
distribution in the nucleon. Such helicity-flip processes are not significantly
Sudakov-suppressed if the infrared scale for gluon emission in the photon-quark
subprocess is of the order of the chiral symmetry breaking scale, mu_chiral^2
>> Lambda_QCD^2. We estimate the asymmetry in the kinematics of the planned
Jefferson Lab Hall A experiment to be of the order 10^{-4}, with different sign
for proton and neutron. We also comment on the spin dependence in the limit of
soft high-energy scattering.
