We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the P z evolution equation for quasi parton distribution functions, and find that the P z evolution kernels are identical to the DGLAP evolution kernels.

Wireless Body Area Networks (WBANs), as a promising health-care system, can provide tremendous benefits for timely and continuous patient care and remote health monitoring. Owing to the restriction of communication, computation and power in WBANs, cloud assisted WBANs, which offer more reliable, intelligent, and timely health-care services for mobile users and patients, are receiving increasing attention. However, how to aggregate the health data multifunctionally and efficiently is still an open issue to the cloud server (CS). In this paper, we propose a privacy-preserving and multifunctional health data aggregation mechanism (PPM-HDA) with fault tolerance for cloud assisted WBANs. With PPM-HDA, the CS can compute multiple statistical functions of users' health data in a privacy-preserving way to offer various services. Specifically, we first propose a multifunctional health data additive aggregation scheme (MHDA + ) to support additive aggregate functions such as average and variance. Then we put forward MHDA ⊕ as an extension of MHDA + to support non-additive aggregations such as min/max, median, percentile and histogram. PPM-HDA can resist differential attacks, which most existing data aggregation schemes suffer from. The security analysis shows that PPM-HDA can protect users' privacy against many threats. Performance evaluations illustrate that the computational overhead of MHDA + is significantly reduced with the assistance of CSs. Our MHDA ⊕ scheme is more efficient than previously reported min/max aggregation schemes in terms of communication overhead when the applications require large plaintext space and highly-accurate data.

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.

Within the framework of large momentum effective theory (LaMET), generalized parton distributions (GPDs) can be extracted from lattice calculations of quasi-GPDs through a perturbative matching relation, up to power corrections that are suppressed by the hadron momentum. In this paper, we focus on isovector quark GPDs, including the unpolarized, longitudinally and transversely polarized cases, and present the one-loop matching that connects the quasi-GPDs renormalized in a regularization-independent momentum subtraction (RI/MOM) scheme to the GPDs in MS scheme. We find that the matching coefficient is independent of the momentum transfer squared. As a consequence, the matching for the quasi-GPD with zero skewness is the same as that for the quasi-PDF. Our results provide a crucial input for the determination of quark GPDs from lattice QCD using LaMET. *

We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at O(αs), both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presence of mixing, and therefore can be used to extract flavor-singlet quark PDFs as well as gluon PDFs from lattice simulations.An explicit one-loop calculation in Ref.[81] has indeed verified the above expectation. Since J µz 2 is not independent, it can be ignored in the studies of operator renormalization. In addition, Eqs. (26) and (27) indicate that J zµ 1 and J ti 1 (i = 1, 2) renormalize independently. As a result, the renormalization pattern can be simplified to J zµ 1,R J zµ 3,R = Z 22 Z 13 0 Z 33 J zµ 1 J zµ 3, J ti 1,R = Z 11 J ti 1 , J ij 1,R = Z 11 J ij 1 .