  We outline the many physics opportunities offered by a multi-purpose
fixed-target experiment using the LHC proton and Pb beams extracted by a bent
crystal. In a proton run with the LHC 7-TeV beam, one can analyze pp, pd and pA
collisions at sqrt(s_NN)~115 GeV and even higher using the Fermi motion in a
nuclear target. In a Pb run with a 2.76 TeV-per-nucleon beam, sqrt(s_NN) is as
high as 72 GeV. Bent crystals can be used to extract about 5x10^8 protons/s;
the integrated luminosity over a year reaches 0.5fb-1 on a typical 1 cm-long
target without species limitation. Such an extraction mode does not alter the
performance of the collider experiments at the LHC. By instrumenting the
target-rapidity region, gluon and heavy-quark proton and neutron PDFs can be
accessed at large x and even at x larger than 1 in the nuclear case. Single
diffractive physics and, for the first time, the large negative-xF domain can
be accessed. The nuclear target-species versatility provides a unique
opportunity to study nuclear matter vs. the features of the hot and dense
matter formed in heavy-ion collisions, which can be studied in PbA collisions
over the full range of target-rapidity domain with a large variety of nuclei.
The polarization of hydrogen and nuclear targets allows an ambitious spin
program, including measurements of the QCD lensing effects which underlie the
Sivers single-spin asymmetry, the study of transversity distributions and
possibly of polarized PDFs. We also emphasize the potential offered by pA
ultra-peripheral collisions where the nucleus target A is used as a coherent
photon source, mimicking photoproduction processes in ep collisions. Finally,
we note that W and Z bosons can be produced and detected in a fixed-target
experiment and in their threshold domain for the first time, providing new ways
to probe the partonic content of the proton and the nucleus.
