Tools for Calculation

2019 ◽  
pp. 95-110
Author(s):  
Michael E. Peskin
Keyword(s):  
Elementary Particle ◽  
Phase Space ◽  
Cross Sections ◽  
Feynman Diagrams ◽  
Decay Widths ◽  
Relativistic Phase

This chapter discusses the calculation of quantities observable in elementary particle reactions — cross sections and partial decay widths. It introduces relativistic phase space. It introduces Feynman diagrams and describes their role in visualizing elementary particle reactions.

scholarly journals Higher-twist mechanism and inclusive gluon production in pion–proton collisions

2015 ◽  
Vol 30 (36) ◽  
pp. 1550217
Author(s):  
A. I. Ahmadov ◽  
C. Aydin ◽  
R. Myrzakulov ◽  
O. Uzun
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Production Cross Section ◽  
Production Cross ◽  
Feynman Diagrams ◽  
Proton Collisions ◽  
Running Coupling ◽  
Gluon Production ◽  
Coupling Approach ◽  
Holographic Qcd

We calculate the contribution of the higher-twist Feynman diagrams to the large-[Formula: see text] inclusive gluon production cross-section in [Formula: see text] collisions in case of the running coupling and frozen coupling approaches within perturbative and holographic QCD. The structure of infrared renormalon singularities of the higher-twist subprocess cross-section is obtained and the resummed higher-twist cross-sections (Borel sum) with the ones obtained in the framework of the frozen coupling approach and leading-twist cross-section are compared and analyzed.

scholarly journals GEOMETRIC STRUCTURES OF THE CLASSICAL GENERAL RELATIVISTIC PHASE SPACE

2008 ◽  
Vol 05 (05) ◽  
pp. 699-754 ◽  
Author(s):  
JOSEF JANYŠKA ◽  
MARCO MODUGNO
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Relativistic Particle ◽  
Jet Space ◽  
Geometric Structures ◽  
Geometric Properties ◽  
Geometric Conditions ◽  
General Relativistic ◽  
Relativistic Phase

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1-dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialize these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

scholarly journals Removing phase-space restrictions in factorized cross sections

2015 ◽  
Vol 91 (9) ◽  
Author(s):  
Ilya Feige ◽  
Matthew D. Schwartz ◽  
Kai Yan
Keyword(s):  
Phase Space ◽  
Cross Sections

scholarly journals HIGHER TWIST EFFECTS IN PHOTON–PHOTON COLLISIONS

2008 ◽  
Vol 17 (06) ◽  
pp. 1041-1059 ◽  
Author(s):  
A. I. AHMADOV ◽  
I. BOZTOSUN ◽  
A. SOYLU ◽  
E. A. DADASHOV
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Wave Functions ◽  
Feynman Diagrams ◽  
High Twist ◽  
Higher Twist Effects ◽  
Two Photon ◽  
Pion Wave Function

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, Braun–Filyanov pion wave function, the asymptotic and the Chernyak–Zhitnitsky wave functions are all used in the calculations. For ρ-meson we used the Ball–Braun wave function. The results of the calculations reveal that the high twist cross sections, the ratio R, the dependence transverse momentum pT and the rapidity y of meson in the Φ CLEO (x, Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

Superoperator methods of calculating cross sections: III. Unified description of classical and quantal scattering

1980 ◽  
Vol 58 (8) ◽  
pp. 1171-1182 ◽  
Author(s):  
R. E. Turner ◽  
R. F. Snider
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Dependence ◽  
Stationary State ◽  
Cross Sections ◽  
Differential Cross ◽  
Density Operator ◽  
The Difference ◽  
Unified Description ◽  
Classical And Quantum Mechanics

It is shown how differential cross sections can be obtained from the time dependence of phase space packets. This procedure is valid both for classical and quantum mechanics. Two methods are described. In one the trajectory of the packet is emphasized, while in the second the packet is appropriately spread to infinite size. Both methods are applicable to either mechanics. It is shown how the quantal results agree with those of the stationary state approach as formulated in terms of the density operator. The description is also used to elucidate the difference between the scattered flux and the generalized flux that arises naturally in the superoperator formulation.

scholarly journals Comment on ‘‘Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems’’

1996 ◽  
Vol 53 (4) ◽  
pp. 4240-4241 ◽  
Author(s):  
D. G. Luchinsky ◽  
P. V. E. McClintock ◽  
S. M. Soskin ◽  
N. D. Stein ◽  
A. B. Neiman
Keyword(s):  
Phase Space ◽  
Nonlinear Systems ◽  
Nonlinear Resonance ◽  
Relativistic Phase

scholarly journals Application of the JISP16 potential to the nucleon induced deuteron breakup process at E=13 MeV and E=65 MeV

2020 ◽  
Author(s):  
Volodymyr Soloviov ◽  
Jacek Golak ◽  
Roman Skibiński ◽  
Kacper Topolnicki ◽  
Henryk Witała
Keyword(s):  
Phase Space ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Nucleon Nucleon ◽  
Breakup Reaction ◽  
Breakup Process ◽  
Deuteron Breakup ◽  
Nucleon Potential ◽  
Incoming Nucleon

The JISP16 nucleon-nucleon potential has been applied to investigations of the nucleon induced deuteron breakup reaction at the incoming nucleon laboratory energies E = 13 MeV and E = 65 MeV. We have found that for the studied process the JISP16 force gives a description of the exclusive cross section, which is generally similar to the ones obtained with the standard realistic nucleon-nucleon AV18 interaction. However, there are some regions of the phase space where the differential cross sections predicted by the JISP16 and AV18 models, differ by more than 100 %. These special kinematical configurations may possibly be useful to refit the JISP16 force parameters.

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