Comments on the Sterman-Weinberg jet formula

A simple derivation of the Sterman-Weinberg jet formula (the QCD perturbation theory formula for the 2-jet cross section) is described. Conditions on the jet parameters ? and δ for this formula to be applicable are discussed and the corrections to the formula up to O(?²), O(δ²) are presented.     

Renormalization group approach to Sterman-Weinberg jets

A renormalization group approach is developed for single-jet Sterman-Weinberg cross sections. For small δ², but large Q²δ², the complete δ², Q² and ? dependence of the cross section for e⁺e^? annihilation is shown to be calculable in QCD systematically in powers of α(Q²). ? is not assumed to be small.     

Nondeterministic approach to tree-based jet substructure

Jet substructure is typically studied using clustering algorithms, such as k(T), which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by an appropriate metric. Then each jet in each event produces a distribution for an observable, rather than a single value. Advantages of this approach include (1) observables have significantly increased statistical stability, and (2) new observables, such as the variance of the distribution, provide new handles for signal and background discrimination. For example, we find that employing a set of trees substantially reduces the observed fluctuations in the pruned mass distribution, enhancing the likelihood of new particle discovery for a given integrated luminosity. Furthermore, the resulting pruned mass distributions for (background) QCD jets are found to be substantially wider than that for (signal) jets with intrinsic mass scales, e.g., boosted W jets. A cut on this width yields a substantial enhancement in significance relative to a cut on the standard pruned jet mass alone. In particular the luminosity needed for a given significance requirement decreases by a factor of 2 relative to standard pruning.     

A new formula for the saddle-to-scission time

We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very heavy nuclei.     

理想气体压强公式的一种推导方法

本文从球形容器中理想气体入手，用一种简单易懂且不失一般性的方法，推导出理想气体压强公式。     

A new approach to the Einstein-Podolsky-Rosen paradox

Some new aspects of the EPR paradox are considered. We first show that the authors' argument, leading to the conclusion that quantum theory is incomplete, is based on a tacit assumption that may be questioned. We then investigate the non-local features of the EPR setup and point out an interesting connection between the nonlocality involved in the quantum correlations of pairs of particles and that of a single particle in quantum theory.     

A new approach to the random field problem

A new approach to quenched random problems, based on constructing an equivalent annealed system, is presented. The difficulties with the existing solutions of the random field problem are discussed. The new approach is applied to the random field problem yielding a different new result for the dimensionality shift. A by-product of this result is that the lower critical dimension is 2 for the Ising model.     

计算导热系数的新公式

在传统的一维传热模型下导热系数的计算公式误差较大.本文通过建立试样内部的三维传热模型,更为科学地考虑了侧壁散热的影响,推导出了计算导热系数的新公式.以橡胶为研究材料进行实验,证明了新公式的合理性.引入影响因子P来衡量侧壁散热对系统的影响程度,分析得到P值随着试样厚度增加而增大.     

A new approach to peratization technique

The usual method of peratization technique is to expand scattering lengthA(a) in Born series in powers of the coupling constantg. In this paper a new approach to the peratization technique has been discussed starting with the standard equation for the scattering length. As an application of the theory developed, the cases of inverse fourth power and a logarithmic singular potentials have been discussed.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

A new six-dimensional approach to the Weinberg-Salam model

The bosonic sector of the Weinberg-Salam model is derived from a 6-dimensional Yang-Mills theory by imposing rotational symmetry in the extra, compact dimensions. The Weinberg angle and the mass of the Higgs particle are predicted.     

A new approach to the theory of relativity

The facts that led to establishment of the special theory of relativity are reanalyzed. The analysis leads to the well-known formalism, involving, however, somewhat unusual notations. The object of the analysis is to start more closely from the directly observed experimental facts than is usually done; at the same time, great stress is laid on giving formulations independent of the representation in particular reference systems. A detailed analysis is given as to the actual physical methods involved when introducing three- or four-dimensional reference systems. The orthogonal transformations and also the Lorentz transformations are introduced not so much as coordinate transformations but as operators reflecting physical properties of material systems. The principle of relativity is replaced by a mathematically equivalent principle denoted as theLorentz principle which reflects certain symmetries of the known physical laws.     

A new approach to the quantized electrical conductance

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

研究宇称算符的一种新方法

在量子力学中,宇称算符P^的3种表象积分分别表示为∫d2zπ|z〉〈-z|、∫dq|q〉〈-q|和∫dp|p〉〈-p|.借助Dirac符号法和量子力学表象的完备性,找到了一种非常新颖的方法,给出了宇称算符的积分显式.     

A new approach to particle confinement

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

A new approach to potential scattering

Potential scattering calculations based onCalogero's equation and given in two former papers are now improved to include unitarity of theS-matrix. It is shown that the method gives results better than the second Born approximation and even reasonable in the two limits of very strong coupling and very low energies. As test examples, the square-well potential and the Yukawa potential are discussed.