Nonperturbative photon qqˉq\bar{q} light front wave functions from a contact interaction model

We propose a method to calculate the $q\bar{q}$ light front wave functions (LFWFs) of photon at low-virtuality, i.e., the light front amplitude of $\gamma^*\rightarrow q\bar{q}$ at low $Q^2$, based on a light front projection approach. We exemplify this method using a contact interaction model within Dyson-Schwinger equations formalism and obtain the nonperturbative photon $q\bar{q}$ LFWFs. In this case, we find the nonperturbative effects are encoded in the enhanced quark mass and a dressing function of covariant quark-photon vertex, as compared to the leading order quantum electrodynamics photon $q\bar{q}$ LFWFs. We then use nonperturbative-effect modified photon $q\bar{q}$ LFWFs to study the inclusive deep inelastic scattering HERA data in the framework of the color dipole model. The results demonstrate that the theoretical description of data at low $Q^2$ can be significantly improved once the nonperturbative corrections are included in the photon LFWFs.Comment: 11 pages, 4 figure

The cost of Alzheimer\u27s disease in China and re-estimation of costs worldwide

INTRODUCTION: The socioeconomic costs of Alzheimer\u27s disease (AD) in China and its impact on global economic burden remain uncertain. METHODS: We collected data from 3098 patients with AD in 81 representative centers across China and estimated AD costs for individual patient and total patients in China in 2015. Based on this data, we re-estimated the worldwide costs of AD. RESULTS: The annual socioeconomic cost per patient was US $19,144.36, and total costs were US$167.74 billion in 2015. The annual total costs are predicted to reach US $507.49 billion in 2030 and US$1.89 trillion in 2050. Based on our results, the global estimates of costs for dementia were US $957.56 billion in 2015, and will be US$2.54 trillion in 2030, and US $9.12 trillion in 2050, much more than the predictions by the World Alzheimer Report 2015. DISCUSSION: China bears a heavy burden of AD costs, which greatly change the estimates of AD cost worldwide