59,986 research outputs found
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 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 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 boson production in polarized pp and 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
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