EigenGP: Gaussian Process Models with Adaptive Eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements--eigenfunctions of a GP prior--and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements--eigenfunctions--and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machine.Comment: Accepted by IJCAI 201

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

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

Energy Evolution for the Sivers Asymmetries in Hard Processes

We investigate the energy evolution of the azimuthal spin asymmetries in semi-inclusive hadron production in deep inelastic scattering (SIDIS) and Drell-Yan lepton pair production in pp collisions. The scale dependence is evaluated by applying an approximate solution to the Collins-Soper-Sterman (CSS) evolution equation at one-loop order which is adequate for moderate Q^2 variations. This describes well the unpolarized cross sections for SIDIS and Drell-Yan process in the $Q^2$ range of 2.4-100GeV^2. A combined analysis of the Sivers asymmetries in SIDIS from HERMES and COMPASS experiments, and the predictions for the Drell-Yan process at RHIC at \sqrt{S}=200GeV are presented. We further extend to the Collins asymmetries and find, for the first time, a consistent description for HERMES/COMPASS and BELLE experiments with the evolution effects. We emphasize an important test of the evolution effects by studying di-hadron azimuthal asymmetry in e^+e^- annihilation at moderate energy range, such as at BEPC at \sqrt{S}=4.6GeV.Comment: 8 pages, 4 figures; references added, presentation improve

Uniformly expanding vacuum: a possible interpretation of the dark energy

Following the spirit of the equivalence principle, we take a step further to recognize the free fall of the observer as a method to eliminate causes that would lead the perceived vacuum to change its original state. Thus, it is expected that the vacuum should be in a rigid Minkowski state or be uniformly expanding. By carefully investigating the impact on measurement caused by the expansion, we clarify the exact meaning of the uniformly expanding vacuum and find that this proposal may be able to explain the current observations of an accelerating universe.Comment: 5 pages, accepted by Physics of the Dark Univers

Resummation of High Order Corrections in ZZ Boson Plus Jet Production at the LHC

We study the multiple soft gluon radiation effects in $Z$ boson plus jet production at the LHC. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of the $Z$ boson plus jet final state system, are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm(NLL). We also compare the prediction of our resummation calculation to the CMS data by employing a reweighting procedure to estimate the effect from imposing kinematic cuts on the leptons from $Z$ boson decay, and find good agreement for both the imbalance transverse momentum and the azimuthal angle correlation of the final state $Z$ boson and jet system, for $pp\to Z+jet$ production at the LHC.Comment: 7 pages, published versio