Analysis of the DDˉ∗KD\bar{D}^*K system with QCD sum rules

In this article, we construct the color singlet-singlet-singlet interpolating current with $I\left(J^P\right)=\frac{3}{2}\left(1^-\right)$ to study the $D\bar{D}^*K$ system through QCD sum rules approach. In calculations, we consider the contributions of the vacuum condensates up to dimension-16 and employ the formula $\mu=\sqrt{M_{X/Y/Z}^{2}-\left(2{\mathbb{M}}_{c}\right)^{2}}$ to choose the optimal energy scale of the QCD spectral density. The numerical result $M_Z=4.71_{-0.11}^{+0.19}\,\rm{GeV}$ indicates that there exists a resonance state $Z$ lying above the $D\bar{D}^*K$ threshold to saturate the QCD sum rules. This resonance state $Z$ may be found by focusing on the channel $J/\psi \pi K$ of the decay $B\longrightarrow J/\psi \pi \pi K$ in the future.Comment: 9 pages, 4 figure

Masses and decay constants of the heavy tensor mesons with QCD sum rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion, study the masses and decay constants of the heavy tensor mesons $D_2^*(2460)$, $D_{s2}^*(2573)$, $B_2^*(5747)$, $B_{s2}^*(5840)$ using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants $\frac{f_{D_{s2}^*}}{f_{D_{2}^*}}\approx\frac{f_{B_{s2}^*}}{f_{B_{2}^*}}\approx\frac{f_{D_{s}}}{f_{D}}\mid_{\rm exp}$, where the exp denotes the experimental value.Comment: 13 pages, 13 figure

GEOMETRIC AND ENVIRONMENTAL CONSIDERATIONS IN HIGHWAY ALIGNMENT OPTIMIZATION

The highway alignment optimization problem is modeled to identify the preferred alignment alternatives which minimize total cost and satisfy the highway design standards. Several mathematical models have been developed during the past decades, among which the Highway Alignment Optimization (HAO) model has been used in several practical highway design projects with satisfactory results. However, several major cost components, such as vehicle operating cost and environmental cost are estimated roughly, and should be improved to yield more precise cost estimates and to allow optimization of lane widths. These are the HAO model features which this thesis seeks to improve. Lane width is an important factor in highway design, which is related to the travel speed, safety, as well as earthwork cost. This thesis employs Newton's method and Finite Difference method to search for the appropriate lane width. The preferred lane width found in the case study is 10.6 feet, for which the total cost is $233 million, and 12.5% less than the total cost at 12 feet lane width. In addition, this thesis improves the vehicle operating cost prediction by calculating the vehicle resistance force and horsepower, and estimating the fuel consumption based on the fuel consumption rate (g/hp-hr). Moreover, the environmental cost, particularly the vehicle emissions cost is incorporated in the newly improved HAO model. It is found that the vehicle emission cost decreases by 9% after including the environmental cost component in the model objective function. The results of the case study and sensitivity analyses indicate that the improved HAO model can find good highway alignments efficiently in tough topographic environmental. Moreover, the model can jointly consider the social, economic and environmental consequences, and result in less fuel consumption and pollutant emissions

Decoupling between gravitationally bounded systems and the cosmic expansion

Recently, it was hypothesized that some supermassive black holes (SMBHs) may couple to the cosmic expansion. The mass of these SMBHs increase as the cubic power of the cosmic scale factor, leaving the energy density of the SMBHs unchanged when the universe expands. However, following general principles of general relativity, namely, locality or junction conditions, we show that the inner part of a gravitationally bounded system is unaware of the cosmic expansion, since the outer solution can be smoothly replaced by an asymptotically flat background. For the same reason, the direct reason that we do not expand with the expansion of the universe is not that we are bound states, but rather we are positioned in a greater gravitationally bounded system, namely the local group.Comment: 14 pages, 2 figures