scholarly journals Application of a computer algebra systems to the calculation of the \(\pi\pi\)-scattering amplitude

2020 ◽  
Vol 28 (3) ◽  
pp. 216-229
Author(s):  
Yuriy L. Kalinovsky ◽  
Alexandra V. Friesen ◽  
Elizaveta D. Rogozhina ◽  
Lyubov’ I. Golyatkina
Keyword(s):  
Cross Section ◽  
Computer Algebra ◽  
Scattering Amplitude ◽  
Computer Algebra Systems ◽  
Zero Temperature ◽  
Feynman Integrals ◽  
Pion Scattering ◽  
Loop Approximation ◽  
Scattering Lengths ◽  
The One

The aim of this work is to develop a set of programs for calculation the scattering amplitudes of the elementary particles, as well as automating the calculation of amplitudes using the appropriate computer algebra systems (Mathematica, Form, Cadabra). The paper considers the process of pion-pion scattering in the framework of the effective Nambu-Iona-Lasinio model with two quark flavours. The Package-X for Mathematica is used to calculate the scattering amplitude (starting with the calculation of Feynman diagrams and ending with the calculation of Feynman integrals in the one-loop approximation). The loop integrals are calculated in general kinematics in Package-X using the Feynman parametrization technique. A simple check of the program is made: for the case with zero temperature, the scattering lengths \(a_0 = 0.147\) and \(a_2 = -0.0475\) are calculated and the total cross section is constructed. The results are compared with other models as well as with experimental data.

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

ASYMPTOTIC BEHAVIOR OF PHYSICAL AMPLITUDES IN A FINITE FIELD THEORY

1990 ◽  
Vol 05 (10) ◽  
pp. 1861-1880
Author(s):  
J.A. HELAYËL-NETO ◽  
S. RAJPOOT ◽  
A. WILLIAM SMITH
Keyword(s):  
Cross Section ◽  
Scattering Amplitude ◽  
High Energy ◽  
Energy Limit ◽  
Heavy Particles ◽  
Yang Mills ◽  
Physical Amplitude ◽  
Mass Terms ◽  
Scalar Scattering ◽  
The One

Using the N=4 super Yang-Mills theory softly broken by supersymmetric N=1 mass terms for the matter superfields, we compute the one-loop chiral+chiral→antichiral+antichiral scattering amplitude directly in superspace. By suitable choices of the mass parameters, one can endow the model with a hierarchy of light and heavy particles, and the decoupling of the heavy sector from the light-light physical amplitude is studied. We also analyze the high energy limit of the cross section for a two physical scalar scattering and find a (logs) behavior, which then respects the Froissart bound.

Electron Excitation of 21S, 23S, 21P, and 23P States of Helium

1975 ◽  
Vol 53 (20) ◽  
pp. 2289-2295 ◽  
Author(s):  
H. G. P. Lins de Barros ◽  
H. S. Brandi
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Theoretical Calculations ◽  
Electron Excitation ◽  
Wave Functions ◽  
Excitation Cross Sections ◽  
Characteristic Values ◽  
The One

Calculations for the total excitation cross sections of the 21S, 23S, 21P, and 23P states of He by electron impact have been carried out assuming the Born–Ochkur approximation for the scattering amplitude and a parametrization previously proposed by the authors for the total cross section. For the atomic wave functions we used LS coupling and obtained the one electron orbitals using the Xα method for three characteristic values of the parameter α. The results are compared with other experimental and theoretical calculations.

scholarly journals SUPERCRITICAL POMERON AND EIKONAL REPRESENTATION OF THE DIFFRACTION SCATTERING AMPLITUDE

1995 ◽  
Vol 10 (26) ◽  
pp. 1959-1967
Author(s):  
S.V. GOLOSKOKOV ◽  
S.P. KULESHOV ◽  
O.V. SELYUGIN
Keyword(s):  
Experimental Data ◽  
Scattering Amplitudes ◽  
Total Cross Section ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Diffraction Scattering ◽  
Eikonal Representation ◽  
The One ◽  
Qcd Pomeron ◽  
Logarithmic Growth

The intercept of the supercritical pomeron is examined with the use of different forms of the scattering amplitudes of the bare pomeron. The one-to-one correspondence between the eikonal phase and the ratio of the elastic and total cross-section is shown. Based on new experimental data of the CDF collaboration, the intercept and power of the logarithmic growth of the bare and total pomeron amplitude are analyzed. It is shown that as a result of the eikonalization procedure, the bare QCD pomeron becomes compatible with experiment.

scholarly journals Selection rules for the S-Matrix bootstrap

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Anjishnu Bose ◽  
Aninda Sinha ◽  
Shaswat Tiwari
Keyword(s):  
Cross Section ◽  
Regge Trajectory ◽  
Wave Scattering ◽  
P Wave ◽  
Pion Scattering ◽  
Straight Line ◽  
S Matrix ◽  
Total Scattering Cross Section ◽  
Scattering Lengths ◽  
Physical Quantities

We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

scholarly journals The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Nguyen Suan Han ◽  
Do Thu Ha ◽  
Nguyen Nhu Xuan
Keyword(s):  
Perturbation Theory ◽  
Quantum Gravity ◽  
Scattering Amplitude ◽  
High Energy ◽  
Effective Theory ◽  
Potential Equation ◽  
Scalar Particles ◽  
Loop Approximation ◽  
The One ◽  
High Energy Scattering

Abstract The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

Measurement of total cross sections (e+, Ne) and (e+, Ar)

1976 ◽  
Vol 54 (17) ◽  
pp. 1741-1748 ◽  
Author(s):  
J-S. Tsai ◽  
L. Lebow ◽  
D. A. L. Paul
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Scattering Length ◽  
Forward Scattering Amplitude ◽  
Sum Rule ◽  
Total Cross Sections ◽  
Scattering Lengths ◽  
Momentum Integral

The total cross sections for positrons on neon and argon atoms have been measured in the energy ranges 15 eV to 272.5 eV and 25 eV to 300 eV respectively. The cross sections indicate clearly that Born values will not be reached until at least 3 KeV. Interpolating between the measured and the valid Born regions has allowed an application of the sum rule which connects scattering length. Born forward scattering amplitude, and the momentum-integral over the total cross section. This procedure gives scattering lengths as = −0.53 ± 0.15 Bohr radii for neon and as = −2.8 ± 0.7 Bohr radii for argon; the errors include maximum credible uncertainties in the interpolations.

scholarly journals On elastic scattering amplitude of planar charged fermions in a constant magnetic field

2019 ◽  
Vol 34 (30) ◽  
pp. 1950189 ◽  
Author(s):  
V. R. Khalilov
Keyword(s):  
Magnetic Field ◽  
Elastic Scattering ◽  
Constant Magnetic Field ◽  
Quantum Electrodynamics ◽  
Scattering Amplitude ◽  
Total Probability ◽  
Elastic Scattering Amplitude ◽  
Loop Approximation ◽  
Analytical Formulas ◽  
The One

The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the (2[Formula: see text]+[Formula: see text]1)-dimensional quantum electrodynamics (QED[Formula: see text]) for planar charged fermions in an external constant magnetic field. We obtain the elastic scattering amplitude in the corresponding massive theory and then discuss and calculate the massless limit of ESA. The imaginary part of ESA are related to the total probability of photons emission by charged fermions in the considered magnetic field. Simple analytical formulas are obtained when planar charged fermions in initial states occupy high excited Landau levels.

QUANTUM CORRECTIONS EFFECT ON THE COUPLING OF THE GRAVITATIONAL AND SCALAR FIELDS AND SPONTANEOUSLY INDUCED GRAVITY

1989 ◽  
Vol 04 (05) ◽  
pp. 1223-1233 ◽  
Author(s):  
A. B. KAGANOVICH
Keyword(s):  
Gravitational Constant ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Quantum Corrections ◽  
Zero Temperature ◽  
Nonminimal Coupling ◽  
Zero Energy ◽  
Induced Gravity ◽  
Loop Approximation ◽  
The One

Gravity induced by the spontaneous symmetry breaking in gauge theories is studied. All calculations are carried out with an accuracy provided by the one-loop approximation. It appears that in an effective potential of the scalar field φ a parameter ε of a nonminimal coupling of φ with a curvature is a function of φ. Under zero energy density of the stable vacuum <φ>0 = µ it is proved that the induced gravitational constant G ind is finite only if µε′(µ) = −2ε(µ). Hence it follows that if gravity is induced indeed then its theory necessarily has the structure of the Einstein's theory for gravitation: G ind is positive and invariable (at zero temperature). Within the limitations imposed by the model, the T-dependence of G ind is exponentially relaxed.

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