Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x -> 1. In the Drell-Yan process \pi N -> \mu^- mu^+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries x_F > 0.6 of the pion. I define and study the Berger-Brodsky limit of Q^2 -> \infty with Q^2(1-x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |e\gamma> Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, \gamma^*(q)+i -> f, may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.

Elliptic flow of thermal photons in heavy-ion collisions at Relativistic Heavy Ion Collider and Large Hadron Collider

We calculate the thermal photon transverse momentum spectra and elliptic flow in $\sqrt{s_{NN}} = 200$ GeV Au+Au collisions at RHIC and in $\sqrt{s_{NN}} = 2.76$ TeV Pb+Pb collisions at the LHC, using an ideal-hydrodynamical framework which is constrained by the measured hadron spectra at RHIC and LHC. The sensitivity of the results to the QCD-matter equation of state and to the photon emission rates is studied, and the photon $v_2$ is discussed in the light of the photonic $p_T$ spectrum measured by the PHENIX Collaboration. In particular, we make a prediction for the thermal photon $p_T$ spectra and elliptic flow for the current LHC Pb+Pb collisions.