Differential Equations for Half‐Off‐Shell Matrix Elements

1968 ◽  
Vol 9 (12) ◽  
pp. 2132-2137 ◽  
Author(s):  
M. I. Sobel
Keyword(s):  
Differential Equations ◽  
Matrix Elements ◽  
Shell Matrix

scholarly journals CHARMED MESON PRODUCTION IN PROTON–(ANTI)PROTON COLLISIONS

2007 ◽  
Vol 22 (02n03) ◽  
pp. 555-560
Author(s):  
MARTA ŁUSZCZAK ◽  
ANTONI SZCZUREK
Keyword(s):  
Heavy Quark ◽  
Meson Production ◽  
Experimental Results ◽  
Charmed Meson ◽  
Matrix Elements ◽  
Unintegrated Gluon ◽  
Proton Collisions ◽  
Shell Matrix ◽  
Gluon Distributions

We discuss and compare different approaches to include gluon transverse momenta for heavy quark-antiquark pair and meson production. The results are illustrated with the help of different unintegrated gluon distributions (UGDF) from the literature. We compare results obtained with on-shell and off-shell matrix elements and kinematics. The results are compared with recent experimental results of the CDF collaboration.

EXOTIC ELECTROMAGNETIC TRANSITIONS IN NEUTRON-RICH CARBON ISOTOPES

2009 ◽  
Vol 18 (10) ◽  
pp. 1992-1996 ◽  
Author(s):  
TOSHIO SUZUKI ◽  
TAKAHARU OTSUKA
Keyword(s):  
Shell Model ◽  
Carbon Isotopes ◽  
Magnetic Dipole ◽  
Tensor Force ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Electromagnetic Transitions ◽  
Model Calculations ◽  
Shell Matrix ◽  
Model Hamiltonian

Structure and electromagnetic properties of exotic neutron-rich carbon isotopes are studied by shell model calculations. A p-sd shell model Hamiltonian is modified by enhancing the effects of the tensor force in the p-sd cross shell matrix elements as well as with corrections in the T=1 monopole terms. A considerable suppression of the magnetic dipole (M1) transition in 17 C from the [Formula: see text] state recently observed is found to be well explained by the modified Hamiltonian. The anomalous hindrance of the quadrupole (E2) transitions in 16 C and 18 C is also shown to be reproduced by our new Hamiltonian.

scholarly journals A New Family of Interactions between Clothed Particles in QED

2021 ◽  
Vol 66 (10) ◽  
pp. 833
Author(s):  
A. Arslanaliev ◽  
Y. Kostylenko ◽  
O. Shebeko
Keyword(s):  
Perturbation Theory ◽  
Compton Scattering ◽  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
Energy Shell ◽  
New Family ◽  
Shell Matrix ◽  
Electron Positron ◽  
S Matrix ◽  
Novel Interactions

The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

scholarly journals Three-loop vertex integrals at symmetric point

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrey Pikelner
Keyword(s):  
Renormalization Group ◽  
Differential Equations ◽  
Basis Functions ◽  
Composite Operator ◽  
Operator Matrix ◽  
Matrix Elements ◽  
Root Of Unity ◽  
Loop Level ◽  
Symmetric Point ◽  
Group Functions

Abstract This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

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