Small X Physics PDF Download

In this thesis we study the dynamics of quark and gluon distributions inside a proton, allowing for the proton and its constituent quarks to be polarized transversely with respect to the momentum of the proton (or the beam axis in a scattering experiment). We call such a polarization transverse spin, and the interactions between the orbital motion of quarks within a proton and this transverse spin of both the proton and the quarks themselves lead to a variety of fascinating effects in nuclear physics, including the existence of time-reversal odd observables and the violation of traditional wisdom that transverse spin-dependent effects should diminish rapidly at high energy. We consider the dynamics of transverse spin in the context of high energy collisions, which probe the quarks and gluons carrying the smallest fraction x (called Bjorken x) of the proton’s momentum. As the collision energy is increased and consequently lower values of x are probed, the population of quarks and gluons grows and turns the proton into an extremely dense cloud of gluons. Tightly packing the proton or a nucleus as in this dense regime yields effects like nuclear shadowing and saturation as non-linear gluon recombination effects slow the growth of the gluon distributions toward very small values of x. In this work we study some features of transverse spin dynamics at small values of x, beginning with an investigation of the transverse spin asymmetry in collisions of transversely polarized protons off unpolarized proton or nucleus targets AN. Here we use a model calculation to see how a final state interaction between the constituents of the polarized proton (after scattering off the unpolarized target) can give a qualitative explanation of several puzzling features of this asymmetry. Next, we study the small-x asymptotics of the time reversal (T)-odd, leading-twist quark TMDs, the quark Sivers function f1T⊥ and the Boer-Mulders function h1⊥ . In order to derive these asymptotics, we first construct the full S-matrix for a quark scattering off the background quark and gluon fields of a target proton to sub-sub-eikonal order (suppressed by two inverse powers of center of mass energy for the scattering). We call this object the Polarized Wilson line, and it accounts for interactions between a quark with arbitrary polarization scattering off a target proton of arbitrary polarization, allowing us to construct small-x asymptotics for all the leading-twist quark TMDs. Employing this Polarized Wilson line, we derive closed small-x evolution equations for both the quark Sivers function and the Boer-Mulders function in the large-Nc limit, where we take the number of quark colors to be large. For the Sivers function we obtain two contributions, an eikonal (not suppressed by energy) contribution coming from the spin-dependent odderon and a novel sub-eikonal contribution. Combining the known small-x evolution for the odderon with the numerical solutions for the sub-eikonal contribution, we find the small-x asymptotics for the quark Sivers function as the spin-dependent odderon contribution and the new sub-eikonal correction. For the Boer-Mulders we obtain the new sub-sub-eikonal contribution.