Nuclear dependence of azimuthal asymmetry in semi-inclusive deep inelastic scattering

Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry $of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of the azimuthal asymmetry$$ is studied. It is shown that the azimuthal asymmetry is suppressed by multiple parton scattering and the transverse momentum dependence of the suppression depends on the relative shape of the twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear dependence of the azimuthal asymmetry and to estimate the smearing effect due to fragmentation.Comment: 9 pages in RevTex with 2 figure

An Examination of Algebra for All through Historic Context and Statewide Assessment Data

Since 2003, California has enacted a policy through its education accountability system that encourages schools and districts to place all 8th grade students into algebra courses and therefore, be tested in algebra in the statewide assessment program. Ten years later, there are a great many more 8th graders taking algebra now. However, there are also many students repeating algebra, instead of going on taking higher level mathematics tests. This article aims to provide the historic context of this policy, previous and recent studies on 8th grade algebra, and our study based on the California Standardized Testing and Reporting (STAR) data. We analyzed 8th grade algebra test-taking and the following years� higher level mathematics test-taking to examine the college preparation course taking pipeline. Our longitudinal study compared two groups of students� performance on 9th grade algebra between those who previously scored below proficient on algebra at 8th grade and those who scored proficient or above on general mathematics at 8th grade. Further, another longitudinal study linked 7th grade mathematics sub-scores to 8th grade algebra achievement. The results show that �algebra for all� policy increased the number of students taking algebra at 8th grade and subsequently, taking higher level mathematics tests. However, the pipeline of the college preparation course taking has a significant leak because the number of students taking higher level mathematics decreased dramatically after algebra. Longitudinal study shows that students who pass the general mathematics test at 8th grade have a 69% greater chance to pass the algebra test at 9th grade compared to their peers who failed the algebra test at 8th grade. We also find that the sub-score rational numbers is a strong predictor of 8th grade algebra achievement. Alternatives to help all students achieve in mathematics learning are also discussed in addition to recommendations for future research

Emergent Mott-insulators at non-integer fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground state properties of an ultracold atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersing in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system being in a self-bound superfluid phase with its particle density distribution manifesting a self-concentrated structure. While in a relatively deep optical lattice, the attractive interaction can drive the system forming the Mott-insulator phase even though the global filling factor is not integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott-insulators with their effective density manifesting a devil's staircase structure with respect to the strength of attractive interaction. Detailed estimation on relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups

Twist-4 contributions to the azimuthal asymmetry in SIDIS

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering (SIDIS) process $e^-+N \to e^-+q+X$ in leading order (LO) of perturbative QCD and up to twist-4 in power corrections and study in particular the azimuthal asymmetry . The final results are expressed in terms of transverse momentum dependent (TMD) parton matrix elements of the target nucleon up to twist-4. %Under the maximal two-gluon correlation approximation, these TMD parton matrix elements in a nucleus %can be expressed terms of a Gaussian convolution of that in a nucleon with the width given by the jet transport %parameter inside cold nuclei. We also apply it to $e^-+A \to e^-+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry by using a Gaussian ansatz for the TMD parton matrix elements.Comment: 9 pages, afigur