| Popis: |
In this thesis we study the dynamics of quark and gluon distributions inside a proton, allowing forthe proton and its constituent quarks to be polarized transversely with respect to the momentumof the proton (or the beam axis in a scattering experiment). We call such a polarization transversespin, and the interactions between the orbital motion of quarks within a proton and this transversespin of both the proton and the quarks themselves lead to a variety of fascinating effects in nuclearphysics, including the existence of time-reversal odd observables and the violation of traditionalwisdom that transverse spin-dependent effects should diminish rapidly at high energy. We considerthe dynamics of transverse spin in the context of high energy collisions, which probe the quarksand gluons carrying the smallest fraction x (called Bjorken x) of the proton’s momentum. As thecollision energy is increased and consequently lower values of x are probed, the population of quarksand gluons grows and turns the proton into an extremely dense cloud of gluons. Tightly packingthe proton or a nucleus as in this dense regime yields effects like nuclear shadowing and saturationas non-linear gluon recombination effects slow the growth of the gluon distributions toward verysmall values of x. In this work we study some features of transverse spin dynamics at small valuesof x, beginning with an investigation of the transverse spin asymmetry in collisions of transverselypolarized protons off unpolarized proton or nucleus targets AN. Here we use a model calculation tosee how a final state interaction between the constituents of the polarized proton (after scatteringoff the unpolarized target) can give a qualitative explanation of several puzzling features of thisasymmetry. Next, we study the small-x asymptotics of the time reversal (T)-odd, leading-twistquark TMDs, the quark Sivers function f1T⊥ and the Boer-Mulders function h1⊥. In order to derivethese asymptotics, we first construct the full S-matrix for a quark scattering off the backgroundquark 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 protonof arbitrary polarization, allowing us to construct small-x asymptotics for all the leading-twistquark TMDs. Employing this Polarized Wilson line, we derive closed small-x evolution equationsfor both the quark Sivers function and the Boer-Mulders function in the large-Nc limit, where wetake 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 anda novel sub-eikonal contribution. Combining the known small-x evolution for the odderon with thenumerical solutions for the sub-eikonal contribution, we find the small-x asymptotics for the quarkSivers 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. |
