Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton

The master integrals for the mixed QCD-QED two-loop virtual corrections to the charged-current Drell-Yan process $q\bar{q}^{\prime} \rightarrow \ell \nu$ are computed analytically by using the differential equation method. A suitable choice of master integrals makes it successful to cast the differential equation system into the canonical form. We keep the dependence on charged lepton mass in the building of differential equations and then expand the system against the ratio of small charged lepton mass to large $W$-boson mass. In such a way the final results will contain large logarithms of the form $\log(m_{\ell}^2/m_W^2)$. Finally, all the canonical master integrals are given as Taylor series around $d = 4$ spacetime dimensions up to order four, with coefficients expressed in terms of Goncharov polylogarithms up to weight four.Comment: 34 pages, 6 figure

Formulae of Beurling-Deny and Lejan For Non-Symmetric Dirichlet Forms

By the classical Beurling-Deny formula, any regular symmetric Dirichlet form is decomposed into the diffusion, jumping and killing parts. Further, the diffusion part is characterized by LeJan’s formula. In this paper, both the Beurling-Deny formula and LeJan’s formula are extended to regular non-symmetric Dirichlet forms. In addition, a counterexample is presented to show the gap in the Beurling-Deny formula for non-symmetric Dirichlet forms in the existing literatures

Extensions of Lévy-Khintchine Formula and Beurling-Deny Formula in Semi-Dirichlet Forms Setting

The Lévy-Khintchine formula or, more generally, Courrège’s theorem characterizes the infinitesimal generator of a Lévy process or a Feller process on Rd. For more general Markov processes, the formula that comes closest to such a characterization is the Beurling-Deny formula for symmetric Dirichlet forms. In this paper, we extend these celebrated structure results to include a general right process on a metrizable Lusin space, which is supposed to be associated with a semi-Dirichlet form. We start with decomposing a regular semi-Dirichlet form into the diffusion, jumping and killing parts. Then, we develop a local compactification and an integral representation for quasi-regular semi-Dirichlet forms. Finally, we extend the formulae of Lévy-Khintchine and Beurling-Deny in semi-Dirichlet forms setting through introducing a quasi-compatible metric

The light MSSM neutral Higgs boson production associated with an electron and a jet at the LHeC

We study the light CP-even neutral Higgs boson production in association with an electron and a jet at the possible CERN large hadron-electron collider within the minimal supersymmetric standard model. We investigate the possible supersymmetric effects on this process and compare our standard model numerical results with those in previous work. We present the leading-order and QCD next-to-leading-order corrected total cross sections and the distributions of the transverse momenta of the final electron, the light neutral Higgs boson, and jet in the minimal supersymmetric standard model. Our results show that the scale dependence of the leading-order cross section is obviously reduced by the QCD next-to-leading-order corrections. The K factor of the QCD correction to the total cross section at the large hadron-electron collider varies from 0.893 to 1.048 when the factorization/renormalization scale $\mu$ goes up from $0.2 m_Z$ to $3.8 m_Z$ in our chosen parameter space.Comment: 18pages, 18figure

Viscous damping of nanobeam resonators: humidity, thermal noise and the paddling effect

The nanobeam resonator is the key mechanical component in the nano-electromechanical system. In addition to its high frequency originating from its low dimension, the performance is significantly influenced by the circumstances, especially at nanoscale where a large surface area of the material is exposed. Molecular dynamics simulations and theoretical analysis are used for a quantitative prediction on the damping behavior, such as the critical damping condition and lifetime, of nanobeam resonators that directly maps the fluid-structure properties and interaction information into dynamical behaviors. We show here how the humidity defines the critical damping condition through viscous forces, marking the transition from under-damping to over-damping regime at elevated humidity. Novel phenomena such as the thermal fluctuation and paddling effects are also discussed.Comment: 15 pages, 5 figure

Cross-correlation between the thermal Sunyaev-Zeldovich effect and the Integrated Sachs-Wolfe effect

We present a joint cosmological analysis of the power spectra measurement of the Planck Compton parameter and the integrated Sachs-Wolfe (ISW) maps. We detect the statistical correlation between the Planck Thermal Sunyaev-Zeldovich (tSZ) map and ISW data with a significance of a $3.6\sigma$ confidence level~(CL), with the autocorrelation of the Planck tSZ data being measured at a $25 \sigma$ CL. The joint auto- and cross-power spectra constrain the matter density to be $\Omega_{\rm m}= 0.317^{+0.040}_{-0.031}$, the Hubble constant $H_{0}=66.5^{+2.0}_{-1.9}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ and the rms matter density fluctuations to be $\sigma_{8}=0.730^{+0.040}_{-0.037}$ at the 68% CL. The derived large-scale structure $S_{8}$ parameter is $S_8 \equiv \sigma_{8}(\Omega_{\rm m}/0.3)^{0.5} = 0.755\pm{0.060}$. If using only the diagonal blocks of covariance matrices, the Hubble constant becomes $H_{0}=69.7^{+2.0}_{-1.5}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$. In addition, we obtain the constraint of the product of the gas bias, gas temperature, and density as $b_{\rm gas} \left(T_{\rm e}/(0.1\,{\rm keV}) \right ) \left(\bar{n}_{\rm e}/1\,{\rm m}^{-3} \right) = 3.09^{+0.320}_{-0.380}$. We find that this constraint leads to an estimate on the electron temperature today as $T_{\rm e}=(2.40^{+0.250}_{-0.300}) \times 10^{6} \,{\rm K}$, consistent with the expected temperature of the warm-hot intergalactic medium. Our studies show that the ISW-tSZ cross-correlation is capable of probing the properties of the large-scale diffuse gas.Comment: 25 pages, 15 figures, 2 table

Biochemical and transcriptomic analyses reveal different metabolite biosynthesis profiles among three color and developmental stages in ‘Anji Baicha’ (Camellia sinensis)

Primers used for quantitative reverse transcription polymerase chain reaction analyses. (XLSX 11 kb