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 Relative entropy in scattering and the S-matrix bootstrap

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Anjishnu Bose ◽  
Parthiv Haldar ◽  
Aninda Sinha ◽  
Pritish Sinha ◽  
Shaswat Tiwari
Keyword(s):  
Relative Entropy ◽  
Cross Sections ◽  
High Energy ◽  
Quantum Field Theories ◽  
Superstring Theory ◽  
Information Theoretic ◽  
Pion Scattering ◽  
S Matrix ◽  
Information Theoretic Measures ◽  
Scattering Lengths

We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include \phi^4ϕ4 theory, chiral perturbation theory (\chi PTχPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In \chi PTχPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the \rhoρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop \chi PTχPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin.

THE SCATTERING LENGTHS OF THE DEUTERON

1951 ◽  
Vol 29 (1) ◽  
pp. 36-58 ◽  
Author(s):  
D. G. Hurst ◽  
N. Z. Alcock
Keyword(s):  
Cross Section ◽  
Theoretical Calculations ◽  
Scattering Cross Section ◽  
Angular Variation ◽  
Total Scattering ◽  
Scattering Cross ◽  
Total Scattering Cross Section ◽  
Scattering Lengths ◽  
Deuterium Gas

The angular variation of the scattering of neutrons of 0.0724 ev. energy by deuterium gas has been measured. Comparison with theoretical calculations of this variation gives a ratio of scattering lengths:[Formula: see text]In combination with the known total scattering cross section of the free deuteron of 3.44 ± 0.06 barns this gives for the scattering lengths the two sets of values:[Formula: see text]

Low energy Λp → Λp cross section measurement and determination of S-wave scattering lengths

1966 ◽  
Vol 19 (8) ◽  
pp. 715-719 ◽  
Author(s):  
G. Alexander ◽  
O. Benary ◽  
U. Karshon ◽  
A. Shapira ◽  
G. Yukutieli ◽  
...  
Keyword(s):  
Cross Section ◽  
Wave Scattering ◽  
Low Energy ◽  
S Wave ◽  
Cross Section Measurement ◽  
Section Measurement ◽  
Scattering Lengths

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.

Sum rules for the determination of s- and p-wave pion-pion scattering lengths

1966 ◽  
Vol 87 (5) ◽  
pp. 433-443 ◽  
Author(s):  
J. Pišút ◽  
P. Lichard ◽  
P. Bóna
Keyword(s):  
Sum Rules ◽  
P Wave ◽  
Pion Scattering ◽  
Scattering Lengths

scholarly journals Relativistic Effects in Electron Scattering by Atoms. I. Elastic Scattering by Mercury

1980 ◽  
Vol 33 (2) ◽  
pp. 261 ◽  
Author(s):  
LT Sin Fai Lam
Keyword(s):  
Elastic Scattering ◽  
Momentum Transfer ◽  
Cross Section ◽  
Wave Scattering ◽  
Order Approximation ◽  
Relativistic Effects ◽  
Relativistic Correction ◽  
P Wave ◽  
Shape Resonance ◽  
Momentum Transfer Cross Section

Elastic scattering of electrons in the energy range 0-25 eV by mercury atoms is investigated by applying a perturbation method to the (nonrelativistic) Schrodinger equation. Relativistic correction to the potential is treated using two models: a Pauli approximation and a second-order Dirac potential. The nonrelativistic Hartree-Fock wavefunction is used to describe the target in the zeroth order approximation. Electron exchange is found to be important in the collision. The relativistic correction due to mass variation makes a significant contribution, in particular to p-wave scattering which is dominated by a low energy shape resonance. Phase shifts for s-, p-, d- and f-wave scattering are presented. An analytic expression for the momentum transfer cross section for relativistic scattering is obtained. The total cross section, momentum transfer cross section, differential cross section and spin polarization are calculated and compared with experiment.

scholarly journals On the scattering of fast neutrons by protons

1947 ◽  
Vol 191 (1025) ◽  
pp. 195-209 ◽  
Keyword(s):  
Angular Distribution ◽  
Cross Section ◽  
Cosmic Ray ◽  
Fast Neutrons ◽  
Meson Mass ◽  
Nuclear Forces ◽  
Total Scattering ◽  
Empirical Results ◽  
Meson Theory ◽  
Total Scattering Cross Section

The features of the scattering of fast neutrons by protons are calculated using the Møller- Rosenfeld version of the meson theory of nuclear forces. The experimental results of Occhialini & Powell are used to check the predicted angular distribution of the scattered particles and to determine the mass of the meson; the meson mass indicated is about 215 electronic masses, which agrees with the mass of cosmic ray mesons. The total scattering cross-section predicted by the theory agrees with the empirical results.

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