We report on the opportunities for spin physics and Transverse-Momentum Dependent distribution (TMD) studies at a future multi-purpose fixed-target experiment using the proton or lead ion LHC beams extracted by a bent crystal. The LHC multi-TeV beams
allow for the most energetic fixed-target experiments ever performed, opening new domains of particle and nuclear physics and complementing that of collider physics, in particular that of RHIC and the EIC projects. The luminosity achievable with AFTER@LHC using typical targets would surpass that of RHIC by more that 3 orders of magnitude in a similar energy region. In unpolarised proton-proton collisions, AFTER@LHC allows for measurements of TMDs such as the Boer-Mulders quark distributions, the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using the polarisation of hydrogen and nuclear targets, one can measure transverse single-spin asymmetries of quark and gluon sensitive probes, such as, respectively, Drell-Yan pair and quarkonium production. The fixed-target mode has the advantage to allow for measurements in the target-rapidity region, namely at large x^uparrow in the polarised nucleon. Overall, this allows for an ambitious spin program which we outline here.
We outline the opportunities to study with high precision the interface between nuclear and particle physics, which are offered by a next generation and multi-purpose fixed-target experiment exploiting the proton and ion LHC beams extracted by a bent crystal.
We summarise the perspectives on heavy-quarkonium production at the LHC, both for proton-proton and heavy-ion runs, as emanating from the round table held at the HLPW 2008 Conference. The main topics are: present experimental and theoretical knowledg
e, experimental capabilities, open questions, recent theoretical advances and potentialities linked to some new observables.
We report on our recent evaluation of the s-channel cut contribution to J/psi hadroproduction. We show that it is likely significantly larger than the usual cut contribution of the colour-singlet model (CSM), which is known to underestimate the exper
imental measurements. Here the s-channel cut develops for configurations with off-shell quarks in the bound state. A correct treatment of its contribution requires the introduction of a four point function, partially constrained by gauge invariance and limiting behaviours at small and large momenta. When the unconstrained degrees of freedom are fixed to reproduce the Tevatron data, we show that RHIC data are remarkably well reproduced down to very low transverse momenta P_T without need of resummation of initial-state gluon effects. This unique feature might be typical of s-channel cut contribution.
We update the theoretical predictions for direct Y(nS) hadroproduction in the framework of NRQCD. We show that the next-to-leading order corrections in alpha_s to the color-singlet transition significantly raise the differential cross section at high
pT and substantially affect the polarization of the Upsilon. Motivated by the remaining gap between the NLO yield and the cross section measurements at the Tevatron, we evaluate the leading part of the alpha_s^5 contributions, namely those coming from Y(nS) associated with three light partons. The differential color-singlet cross section at alpha_s^5 is in substantial agreement with the data, so that there is no evidence for the need of color-octet contributions. Furthermore, we find that the polarization of the Y(nS) is longitudinal. We also present our predictions for Y(nS) production at the LHC.
