An elementary approach for the phase retrieval problem

If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such a method which is recursive but highly non-linear in nature, based on a close look at the Fourier spectrum of the square of the function norm. In a one dimensional problem it takes $O(N^2)$ steps of calculation to recover the phases of an N component complex vector. This method could work in 1, 2 or even higher dimensional finite Fourier analysis without changes in the behavior of time complexity. For one dimensional problem the performance of an algorithm based on this method is shown, where the limitations are discussed too, especially when subject to random noises which contains significant high frequency components.Comment: 4 pages, 4 figure

Transverse Momentum Resummation for Dijet Correlation in Hadronic Collisions

We study the transverse momentum resummation for dijet correlation in hadron collisions based on the Collins-Soper-Sterman formalism. The complete one-loop calculations are carried out in the collinear factorization framework for the differential cross sections at low imbalance transverse momentum between the two jets. Important cross checks are performed to demonstrate that the soft divergences cancelled out between different diagrams, and in particular, those associated with final state jets. The leading and sub-leading logarithms are identified. All order resummation is derived following the transverse momentum dependent factorization at this order. Its phenomenological applications are also presented.Comment: 51 pages, 10 figure

TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production

We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high Q can describe well the transverse momentum distribution of the unpolarized cross sections in the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established between our evolution and the Collins-Soper-Sterman resummation with b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative form factors, which are formulated to describe the Drell-Yan lepton pair and W/Z boson production in hadronic collisions. With these results, we present the predictions for the Sivers single transverse spin asymmetries in Drell-Yan lepton pair production and $W^\pm$ boson production in polarized pp and $\pi^- p$ collisions for several proposed experiments. We emphasize that these experiments will not only provide crucial test of the sign change of the Sivers asymmetry, but also provide important opportunities to study the QCD evolution effects.Comment: 46 pages, 15 figure

Long Range Correlation in Higgs Boson Plus Two Jets Production at the LHC

We study Higgs boson plus two high energy jets production at the LHC in the kinematics where the two jets are well separated in rapidity. The partonic processes are dominated by the t-channel weak boson fusion (WBF) and gluon fusion (GF) contributions. We derive the associated QCD resummation formalism for the correlation analysis where the total transverse momentum q_\perp of the Higgs boson and two jets is small. Because of different color structures, the resummation results lead to distinguished behaviors: the WBF contribution peaks at relative low q_\perp while all GF channel contributions are strongly de-correlated and spread to a much wider q_\perp range. By applying a kinematic cut on q_\perp, one can effectively increase the WBF signal to the GF background by a significant factor. This greatly strengthens the ability to investigate the WBF channel in Higgs boson production and study the couplings of Higgs to electroweak bosons.Comment: 9 pages, 2 figure