Non-relativistic scattering amplitude for a new multi-parameter exponential-type potential

In this paper, we study the scattering properties of s-wave Schrdinger equation for the multi-parameter potential,which can be reduced into four special cases for different values of potential parameters, i.e., Hulthn, Manning–Rosen,and Eckart potentials. We also obtain and investigate the scattering amplitudes of these special cases. Some numerical results are also obtained and reported.

Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method

CP violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders.We study the CP properties of HVV vertexes between Higgs and gauge boson pairs by defining a CP violation phase angle,which indicates the mixture of CP-even and CP-odd Higgs states in HVV in new physics.A series of HVV amplitudes,H→γγ,H-→V→γtt,and H→VV-→4f,with a CP phase angle are studied systematically to explicitly explain why CP violation can only be probed independently in the 4t pro-cess.We obtain a novel amplitude decomposition relation that illustrates that if two preconditions(multilinear mo-mentum dependent vertexes,and the current J_(μ) of V→l^(+)l^(-)is formally proportional to a photon's polarization vec-tor)are satisfied,a higher-point amplitude can be decomposed into a summation of a series of lower-point amp-litudes.As a practical example,the amplitude of the H→γV-→γtt and H→VV→4t processes can be decom-posed into a summation of many H→γγ amplitudes.We calculate these amplitudes in the framework of the on-shell scattering amplitude method,considering both massless and massive vector gauge bosons with the CP viola-tion phase angle.The above two approaches provide consistent results and clearly reveal the CP violation ξ depend-ence in the amplitudes.

Relativistic Bound and Scattering Amplitude of Spinless Particles in Modified Schioberg Plus Manning–Rosen Potentials

By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials for any quantum numbers n and l. Energy eigenvalues and the scattering amplitude are calculated. Some special cases of the problem are also investigated.

Wave Polarization Scattering and Transmission Property in Randomly Distributed Chiral Spheroids

In this paper, the scattering amplitude functions of a spatially-oriented chiral spheroid are derived. Polarization scattering from a layer of randomly distributed chiral spheroids in the Mueller matrix solution is obtained. Co-polarized and de-polarized backscattering and polarization degree for any polarized incidence are numerically calculated. Transmissions of coherent waves with four Stokes parameters through the layer are also discussed. Comparisons of polarization scattering from the chiral and achiral particulate media demonstrate the chirality effect on wave scattering and transmission.

4.2 GeV α-^(12)C Elastic Scattering Based on α-Particle Mode

Based on the α-particle model of ^12C nucleus, the differential cross sections for α-^12C elastic scattering at incident energy of 4.2 GeV have been calculated within the framework of Glauber multiple scattering theory. The results show that the main features of the measured angular distribution of the cross sections can be reasonably described. The parameterized α-α scattering amplitude, which is the basic input to construct the α-^12 C scattering Glauber amplitude in the a-particle model, is obtained by fitting the α-α scattering data.

Quark-Quark Scattering

Scattering process always reveal valuable information. For example scattering of alpha particle in Rutherford＇s well known experiment revealed the existence of nucleus. Physicists have been studying collision process both experimentally as well as theoretically to know much about particle Physics. It is believed that the quark-quark scattering results are same as those of lepton-lepton systems and they are mass independent. The aim of this work was to calculate amplitude cross section for heavy quarks. Our results reveal a mass dependence of these results for heavy quarks.

Inverse Scattering Problem for the Schrodinger’s Equation

The analytic properties of the scattering amplitude are discussed. And, the representation of the potential by the scattering amplitude is obtained.

Navier-Stokes Equations—Millennium Prize Problems

In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.

Standard model effective field theory from on-shell amplitudes

We present a general method of constructing unfactorizable on-shell amplitudes(amplitude basis) and build up their one-to-one correspondence to the independent and complete operator basis in effective field theory(EFT).We apply our method to the Standard Model EFT and identify the amplitude basis in dimensions 5 and 6,which correspond to the Weinberg operator and operators in the Warsaw basis,except for some linear combinations.

Global Estimation of the Cauchy Problem Solutions’the Navier-Stokes Equation

The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided.

Global 1 Estimation of the Cauchy Problem Solutions to the Navier-Stokes Equation

The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.

Some Possible Particles Decays from pp Collisions at LHC Experiment

Some of the possible decays of pp collisions at LHC experiment are considered. The vector bosons mediating in the electroweak interactions and right-handed leptons except neutrinos are assumed to be the most resultant particles from the pp collisions. Neutrinos and anti-neutrinos will be observed when one-double electron charged vector bosons are the resultant particles. The charge conservation is thought to be the dominant factor of these decays. The amplitude transitions for Feynman diagram of these decays are written.

Intersection theory rules symbology

We propose a novel method to determine the structure of symbols for any family of polylogarithmic Feynman integrals.Using the d log-bases and simple formulas for the leading order and next-to-leading contributions to the intersection numbers,we give a streamlined procedure to compute the entries in the coefficient matrices of canonical differential equations,including the symbol letters and the rational coefficients.We also provide a selection rule to decide whether a given matrix element must be zero.The symbol letters are deeply related to the poles of the integrands and also have interesting connections to the geometry of Newton polytopes.Our method can be applied to many cutting-edge multi-loop calculations.The simplicity of our results also hints at the possible underlying structure in perturbative quantum field theories.

Hidden analytic relations for two-loop Higgs amplitudes in QCD

We compute the Higgs plus two-quark and one-gluon amplitudes(H→qqg)and Higgs plus three-gluon amplitudes(H→3 g)in the Higgs effective theory with a general class of operators.By changing the quadratic Casimir CF to CA,the maximally transcendental parts of the H→qqg amplitudes turn out to be equivalent to that of the H→3 g amplitudes,which also coincide with the counterparts in N=4 SYM.This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states,thus the full QCD theory.We further verify that the correspondence applies also to two-loop form factors of more general operators,in both QCD and scalar-YM theory.Another interesting relation is also observed between the planar H→qqg amplitudes and the minimal density form factors in N=4 SYM.

New approach for amplitudes with multiple fermion lines

A new approach for tree-level amplitudes with multiple fermion lines is presented.It primarily focuses on the simplification of fermion lines.By calculating two vectors recursively without any matrix multiplications,the result of a fermion line is reduced to a very compact form depending only on the two vectors.Comparisons with other packages are presented,and the results show that our package FDC provides a very good performance in the processes of multiple fermion lines with this new approach and some other improvements.A further comparison with WHIZARD shows that this new approach has a competitive efficiency in computing pure amplitude squares without phase space integration.

Color-kinematics duality for Sudakov form factor in non-supersymmetric pure Yang-Mills theory

We study the duality between color and kinematics for the Sudakov form factors of tr(F~2)in non-supersymmetric pure Yang-Mills theory.We construct the integrands that manifest the color-kinematics duality up to two loops.The resulting numerators are given in terms of Lorentz products of momenta and polarization vectors,which have the same powers of loop momenta as that from the Feynman rules.The integrands are checked by d-dimensional unitarity cuts and are valid in any dimension.We find that massless-bubble and tadpole topologies are needed at two loops to realize the color-kinematics duality.Interestingly,the two-loop solution contains a large number of free parameters suggesting the duality may hold at higher loop orders.

Resonance properties from a coupled channel meson exchange model

In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.

Strategies for baryon resonance analysis

The analytic properties theoretical investigations of baryon of scattering amplitudes provide a meeting point for experimental and resonances. Pole positions and residues allow for a parameterization of resonances in a well-defined way which relates different reactions. The recent progress made within the Jiilich model is summarized.

Equivalence of coefficients extraction of one-loop master integrals

Now,there have been many different methods to calculate one-loop amplitudes.Two of them are the unitarity cut method and the generalized unitarity cut method.In this short paper,we present an explicit connection between these two methods,especially how the extractions of triangle and bubble coefficients are equivalent to each other.