QCD Factorization for Quarkonium Production in Hadron Collions at Low Transverse Momentum

Inclusive production of a quarkonium $\eta_{c,b}$ in hadron collisions at low transverse momentum can be used to extract various Transverse-Momentum-Dependent(TMD) gluon distributions of hadrons, provided the TMD factorization for the process holds. The factorization involving unpolarized TMD gluon distributions of unpolarized hadrons has been examined with on-shell gluons at one-loop level. In this work we study the factorization at one-loop level with diagram approach in the most general case, where all TMD gluon distributions at leading twist are involved. We find that the factorization holds and the perturbative effects are represented by one perturbative coefficient. Since the initial gluons from hadrons are off-shell in general, there exists the so-called super-leading region found recently. We find that the contributions from this region can come from individual diagrams at one-loop level, but they are cancelled in the sum. Our factorized result for the differential cross-section is explicitly gauge-invariant.Comment: discussions and references are added. Published version on Phys. Rev.

Linear Gaussian Affine Term Structure Models with Unobservable Factors: Calibration and Yield Forecasting

This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data. When evaluating the one step ahead forecasts, it is shown that a one factor model may be adequate when only the short-dated or only the long-dated yields are considered, but two and three factor models performs significantly better when the entire yield spectrum is considered. Furthermore, the results demonstrate that the predictive ability of multi-factor models remains intact far ahead out-of-sample, with accurate predictions available up to one year after the last calibration for one data set and up to three months after the last calibration for the second, more volatile data set. The experimental data denotes two different periods with different yield volatilities, and the stability of model parameters after calibration in both the cases is deemed to be both significant and practically useful. When it comes to four step ahead predictions, the quality of forecasts deteriorates for all models, as can be expected, but the advantage of using a multi-factor model as compared to a one factor model is still significant. In addition to the empirical study above, we also suggest a nonlinear filter based on linear programming for improving the term structure matching at a given point in time. This method, when used in place of a Kalman filter update, improves the term structure fit significantly with a minimal added computational overhead. The improvement achieved with the proposed method is illustrated for out-of-sample data for both the data sets. This method can be used to model a parameterized yield curve consistently with the underlying short rate dynamics

Polarized Curvature Radiation in Pulsar Magnetosphere

The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and co-rotating with the pulsar magnetosphere. Within the 1/{\deg} emission cone, the waves can be divided into two natural wave mode components, the ordinary (O) mode and the extraord nary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O-mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the co-rotation of relativistic particles with magnetosphere is not considered, the intensity distributions for the X-mode and O-mode components are quite similar within the pulsar beam, which causes serious depolarization. However, if the co-rotation of relativistic particles is considered, the intensity distributions of the two modes are very different, and the net polarization of out-coming emission should be significant. Our numerical results are compared with observations, and can naturally explain the orthogonal polarization modes of some pulsars. Strong linear polarizations of some parts of pulsar profile can be reproduced by curvature radiation and subsequent propagation effect.Comment: 12 pages, 9 figures, Accepted for publication in MNRA

Multiple solutions in extracting physics information from experimental data

Multiple solutions exist in various experimental situations whenever the sum of several amplitudes is used to fit the experimentally measured distributions, such as the cross section, the mass spectrum, or the angular distribution. We show a few examples where multiple solutions were found, while only one solution was reported in the publications. Since there is no existing rules found in choosing any one of these solutions as the physics one, we propose a simple rule which agrees with what have been adopted in previous literatures: the solution corresponding to the minimal magnitudes of the amplitudes must be the physical solution. We suggest test this rule in the future experiments.Comment: 10 pages, 3 figure