Pion structure in a modified quark loop model

1980 ◽  
Vol 58 (7) ◽  
pp. 964-968 ◽  
Author(s):  
J. H. Kim ◽  
L. Resnick
Keyword(s):  
Form Factor ◽  
Bound State ◽  
Weak Decay ◽  
Loop Model ◽  
Vector Structure ◽  
Pion Structure ◽  
The One ◽  
System Coupling ◽  
State Nature ◽  
Good Agreement

The pion is assumed as usual to couple to the electroweak currents through its constituent quarks. The bound state nature of the [Formula: see text] system coupling to the electroweak currents is simulated by a form factor at the [Formula: see text] vertex, parametrized by an effective mass M and coupling strength f. Calculations are performed at the one loop level, with a prescription used to ensure electromagnetic gauge invariance. Isospin invariance is assumed. f, M, and the effective quark mass m are determined by the normalization condition for the pion electromagnetic form factor and the charged and neutral pion lifetimes. The charge radius of the pion is calculated and found to be in good agreement with experiment. The ratio of the axial to vector structure functions in the radiative weak decay π → evγ is also determined.

Radiative pion decay in a simple quark loop model

1976 ◽  
Vol 54 (2) ◽  
pp. 158-163 ◽  
Author(s):  
L. Resnick ◽  
J. H. Kim
Keyword(s):  
Basic Assumption ◽  
Dimensional Regularization ◽  
Weak Decay ◽  
Coupling Constants ◽  
Pion Decay ◽  
Loop Model ◽  
Quark Loop ◽  
Quark Masses ◽  
The One ◽  
The Masses

The weak decay of pions into leptons and into leptons plus photon is examined in a simple model at the one loop level. A basic assumption made is that there is more than one pair of quarks to which the pion couples and the masses and coupling constants are such that all amplitudes are finite. The amplitudes are defined by means of dimensional regularization and gauge invariance is rigorously maintained throughout. The experimental lifetimes for charged and neutral pion decay give one constraint among the quark masses and the parameter γ, the ratio of structure dependent axial to vector form factor, gives a second. Quark masses can be found to satisfy either condition, but no solution exists for both constraints simultaneously.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

scholarly journals The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities

2021 ◽  
Author(s):  
Rupert L. Frank ◽  
David Gontier ◽  
Mathieu Lewin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Nonlinear Schrodinger Equation ◽  
Best Constant ◽  
Nonlinear Schrödinger ◽  
The One ◽  
Bound State Case ◽  
Cubic Nonlinear Schrödinger Equation

AbstractIn this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a Schrödinger operator $$-\Delta +V(x)$$ - Δ + V ( x ) are raised to the power $$\kappa $$ κ is never given by the one-bound state case when $$\kappa >\max (0,2-d/2)$$ κ > max ( 0 , 2 - d / 2 ) in space dimension $$d\ge 1$$ d ≥ 1 . When in addition $$\kappa \ge 1$$ κ ≥ 1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo–Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb–Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schrödinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. https://doi.org/10.1007/s00205-021-01634-7). In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.

scholarly journals Estimation of the Noise Source Level of a Commercial Ship Using On-Board Pressure Sensors

2021 ◽  
Vol 11 (3) ◽  
pp. 1243
Author(s):  
Hongseok Jeong ◽  
Jeung-Hoon Lee ◽  
Yong-Hyun Kim ◽  
Hanshin Seol
Keyword(s):  
Noise Source ◽  
Pressure Sensors ◽  
Low Frequency ◽  
Frequency Resolution ◽  
Source Strength ◽  
Recording Time ◽  
Source Level ◽  
The One ◽  
Hydrophone Array ◽  
Good Agreement

The dominant underwater noise source of a ship is known to be propeller cavitation. Recently, attempts have been made to quantify the source strength using on-board pressure sensors near the propeller, as this has advantages over conventional noise measurement. In this study, a beamforming method was used to estimate the source strength of a cavitating propeller. The method was validated against a model-scale measurement in a cavitation tunnel, which showed good agreement between the measured and estimated source levels. The method was also applied to a full-scale measurement, in which the source level was measured using an external hydrophone array. The estimated source level using the hull pressure sensors showed good agreement with the measured one above 400 Hz, which shows potential for noise monitoring using on-board sensors. A parametric study was carried out to check the practicality of the method. From the results, it was shown that a sufficient recording time is required to obtain a consistent level at high frequencies. Changing the frequency resolution had little effect on the result, as long as enough data were provided for the one-third octave band conversion. The number of sensors affected the mid- to low-frequency data.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals Post-liquefaction reconsolidation of sand

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150745 ◽  
Author(s):  
O. Adamidis ◽  
G. S. P. Madabhushi
Keyword(s):  
Void Ratio ◽  
One Dimensional ◽  
Geotechnical Centrifuge ◽  
Significant Damage ◽  
Pore Water Pressures ◽  
The One ◽  
Crucial Parameter ◽  
Excess Pore ◽  
Good Agreement ◽  
Made In

Loosely packed sand that is saturated with water can liquefy during an earthquake, potentially causing significant damage. Once the shaking is over, the excess pore water pressures that developed during the earthquake gradually dissipate, while the surface of the soil settles, in a process called post-liquefaction reconsolidation. When examining reconsolidation, the soil is typically divided in liquefied and solidified parts, which are modelled separately. The aim of this paper is to show that this fragmentation is not necessary. By assuming that the hydraulic conductivity and the one-dimensional stiffness of liquefied sand have real, positive values, the equation of consolidation can be numerically solved throughout a reconsolidating layer. Predictions made in this manner show good agreement with geotechnical centrifuge experiments. It is shown that the variation of one-dimensional stiffness with effective stress and void ratio is the most crucial parameter in accurately capturing reconsolidation.

scholarly journals Kerr-Newman stress-tensor from minimal coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Ming-Zhi Chung ◽  
Yu-tin Huang ◽  
Jung-Wook Kim
Keyword(s):  
Form Factor ◽  
Stress Tensor ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Minimal Coupling ◽  
Massive Spin ◽  
Stress Energy ◽  
Newman Black Hole ◽  
Higher Spin ◽  
The One

Abstract In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

CHIRAL QCD GENERATES CONSTITUENT QUARK MASSES

1988 ◽  
Vol 03 (16) ◽  
pp. 1595-1602 ◽  
Author(s):  
J. PRASCHIFKA ◽  
R.T. CAHILL ◽  
C.D. ROBERTS
Keyword(s):  
Form Factor ◽  
Quark Mass ◽  
Constituent Quark ◽  
Bound State ◽  
Variational Technique ◽  
Quark Masses ◽  
Constituent Quark Mass ◽  
Insight Into

Constituent quark masses are shown to arise naturally in an approximation to chiral QCD. The colour [Formula: see text] diquark component of the nucleon is studied using a new variational technique to solve a Bethe-Salpeter equation for this qq bound state in massless QCD. The resultant diquark form factor Γ(q) exhibits a dramatic peaking for (Euclidean) momentum q2≈(0.2 GeV )2 which, we show, signals the generation of a constituent quark mass of ≈270 MeV , and which provides a significant insight into deep inelastic leptonnucleon scattering results.

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