ON THE POSSIBLE EXISTENCE OF A DERIVATIVE COUPLING IN QUANTUM ELECTRODYNAMICS

1959 ◽  
Vol 37 (12) ◽  
pp. 1339-1343
Author(s):  
F. A. Kaempffer
Keyword(s):  
Cross Section ◽  
Quantum Electrodynamics ◽  
Mass Difference ◽  
Large Mass ◽  
The Self ◽  
Nucleon Mass ◽  
Muon Scattering ◽  
Derivative Coupling ◽  
Self Energy ◽  
Classical Analogue

Within the framework of quantum electrodynamics there exists the possibility of a derivative coupling between source and photon field, referred to as eΛ-charge, which has no classical analogue. For calculations the usual graph technique can be used, provided the factor eγμ contributed by each vertex in a conventional graph is replaced by ieΛkμ, where Λ is a length characteristic of the new interaction. Using as cutoff the nucleon mass M one finds for a bare source of electronic mass m the self-energy in second order to be Λm/m ≈ 200, if Λ−1 ≈ 60 M. It is argued that the large mass difference between muon and electron may be due to this effect, assuming muon and electron to differ only in that the muon has eΛ-charge whereas the electron has not. An estimate is made of the muon–muon scattering cross section caused by the presence of eΛ-charge on the muon, and it is found that the existence of this derivative coupling may have escaped observation.

scholarly journals On the electrodynamic self-energy of the electron

1948 ◽  
Vol 195 (1041) ◽  
pp. 163-173
Keyword(s):  
Perturbation Theory ◽  
Wave Equation ◽  
Quantum Electrodynamics ◽  
Energy State ◽  
Energy Eigenvalue ◽  
Expansion Method ◽  
Negative Energy ◽  
The Self ◽  
Variation Principle ◽  
Self Energy

The stationary-state wave equation for an electron at rest in a negative-energy state in interaction with only its own electromagnetic field is considered. Quantum electrodynamics, single-electron theory and a ‘cut-off’ procedure in momentum-space are used. Expressions in the form of expansions in powers of e 2 /hc are derived for the wave function ψ and the energy-eigenvalue E by a method which (unlike perturbation theory) is not based on the assumption that the self-energy is small. The convergence of the expansion for E is not proved rigorously but the first few terms are shown to decrease rapidly. For low cut-off frequencies K 0 the expression for E behaves as the equivalent perturbation expression but for large K 0 it behaves as — J(e 2 /hc) hK0. The variation principle is applied to an approximation (obtained from the expansion method) for r/r, and it is proved rigorously that for large K 0 the self-energy is algebraically less than or equal to —J(e 2 /hc) hK 0 . Hence, if the electron wave-equation is considered as the limiting case of the ‘cut-off’ equation as K 0 ->ao, it is established that the divergences obtained are not merely due to improper use of perturbation theory and that the self-energy is indeed infinite.

scholarly journals Systematic study of diphoton resonance at 750 GeV from sgoldstino

2016 ◽  
Vol 31 (26) ◽  
pp. 1650151 ◽  
Author(s):  
Ran Ding ◽  
Yizhou Fan ◽  
Li Huang ◽  
Chuang Li ◽  
Tianjun Li ◽  
...  
Keyword(s):  
Decay Width ◽  
Cross Section ◽  
Production Cross Section ◽  
Production Cross ◽  
Vector Boson ◽  
Mass Difference ◽  
Hadron Collider ◽  
Gluon Fusion ◽  
Large Mass ◽  
Decay Length

The ATLAS and CMS Collaborations of the Large Hadron Collider (LHC) have reported an excess of events in diphoton channel with invariant mass of about 750 GeV. With low energy supersymmetry breaking, we systematically consider the sgoldstino scalar S as the new resonance, which is a linear combination of the CP-even scalar [Formula: see text] and CP-odd pseudoscalar [Formula: see text]. Because we show that [Formula: see text] and [Formula: see text] can be degenerated or have large mass splitting, we consider two cases for all the following three scenarios: (1) Single resonance, [Formula: see text] is the 750 GeV resonance decays to a pair of 1 GeV pseudoscalar [Formula: see text] with suitable decay length, these two [Formula: see text] decay into collimated pair of photons which cannot be distinguished at the LHC and may appear as diphotons instead of four photons. (2) Twin resonances, [Formula: see text] with a mass difference of about 40 GeV and both [Formula: see text] and [Formula: see text] decay into diphoton pairs. For productions, we consider three scenarios: (I) vector-boson fusion; (II) gluon–gluon fusion; (III) [Formula: see text] pair production. In all these scenarios with two kinds of resonances, we find the parameter space that satisfies the diphoton production cross-section from 3 to 13 fb and all the other experimental constraints. And we address the decay width as well. In particular, in the third scenario, we observe that the production cross-section is small but the decay width of [Formula: see text] or [Formula: see text] can be from 40 to 60 GeV. Even if the 750 GeV diphoton excesses were not confirmed by the ATLAS and CMS experiments, we point out that our proposal can be used to explain the current and future diphoton excesses.

STRONG SU(2) BREAKING AND MASS SPLITTINGS IN PSEUDOSCALAR MESONS

1996 ◽  
Vol 11 (29) ◽  
pp. 5245-5259 ◽  
Author(s):  
A. N. MITRA
Keyword(s):  
Mass Difference ◽  
Dynamical Symmetry ◽  
Quark Condensate ◽  
Low Energy ◽  
The Self ◽  
Quark Loop ◽  
Self Energy ◽  
A Value ◽  
Pseudoscalar Mesons ◽  
Vector Exchange

The mass splittings within the SU(2) multiplets of pseudoscalar mesons (π, K, D, B) are used as a laboratory to determine the mass difference between d and u quarks (current), through the simplest (two-point) quark-loop diagrams for the self-energies of the corresponding hadrons, together with the associated quark-condensate diagrams within the loops. The second-order e.m. correction is also calculated with a photon line joining the two opposite quark lines in the self-energy loop. The basic ingredient is a hadron–quark-vertex function generated from a vector-exchange-like (chirally invariant) four-fermion Lagrangian (with current quarks) under dynamical symmetry breaking (DχSB), precalibrated to spectroscopy and other important low-energy amplitudes. The results which are expressed as proportional to the u−d mass difference δc, but are otherwise free from any adjustable parameters, reproduce in a rather accurate way all the SU(2) mass differences (from kaon to bottom) with δc = 4.0 MeV, when all the three self-energy diagrams are included. The pion receives only e.m. contributions with a value 5.24 MeV.

scholarly journals AN ANALYSIS OF THE SELF-ENERGY PROBLEM FOR THE ELECTRON IN QUANTUM ELECTRODYNAMICS

1952 ◽  
Vol 30 (1) ◽  
pp. 70-78
Author(s):  
P. N. Daykin
Keyword(s):  
Quantum Electrodynamics ◽  
The Self ◽  
Positive Energy ◽  
Energy Problem ◽  
Electron Theory ◽  
Hole Theory ◽  
Self Energy ◽  
Virtual Photons ◽  
S Matrix ◽  
The One

Feynman's S-matrix for the self-energy of the free resting electron is evaluated without the restriction that the virtual photons in the intermediate state have only positive energy. Both the one-electron theory and the hole theory of the positron are treated. It is shown that in the one-electron theory the normally quadratically divergent transverse part of the self-energy vanishes if the photon field is assumed to be symmetric in positive and negative energies. A similar theorem does not hold in the hole theory. A particular type of interaction leads to a vanishing self-energy in one-electron theory. However, this does not solve the self-energy problem, as in this case radiation corrections to scattering would vanish as well. The S-matrix for the self-energy of a bound electron is evaluated in a similar manner. The decay probability for an excited state is calculated as the imaginary part of the self-energy. The correct value is obtained only in hole theory and in interaction with positive energy photons. In the special case in which the external field is a uniform magnetic field, again only hole theory with this same interaction gives the correct value for the anomalous magnetic moment.

scholarly journals Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

2005 ◽  
Vol 83 (4) ◽  
pp. 447-454 ◽  
Author(s):  
E -O Le Bigot ◽  
U D Jentschura ◽  
P Indelicato ◽  
P J Mohr
Keyword(s):  
High Precision ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
The Self ◽  
Level Shift ◽  
Atomic Systems ◽  
Self Energy ◽  
Rydberg Constant ◽  
Energy Level Shift ◽  
Nuclear Charge Number

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of quantum electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.PACS Nos.: 12.20.Ds, 31.30.Jv, 06.20.Jr, 31.15.–p

Quantum Electrodynamics: The Self-Energy Problem

1950 ◽  
Vol 78 (2) ◽  
pp. 98-103 ◽  
Author(s):  
Hartland S. Snyder
Keyword(s):  
Quantum Electrodynamics ◽  
The Self ◽  
Energy Problem ◽  
Self Energy

scholarly journals An Algebraic Description of Perturbation Theory in Quantum Electrodynamics

1982 ◽  
Vol 35 (6) ◽  
pp. 661 ◽  
Author(s):  
JD Wright
Keyword(s):  
Quantum Electrodynamics ◽  
Algebraic Approach ◽  
Vacuum State ◽  
The Self ◽  
Energy Calculation ◽  
Field Algebra ◽  
Self Energy ◽  
Algebraic Description ◽  
Feynman Rules ◽  
Algebraic Formulation

We use an algebraic formulation of the electromagnetic field, in which various quantization procedures can be described, to discuss perturbation calculations. We show that the Feynman rules and the second order calculation of the self-energy of the electron can be developed on the basis of the Fermi method of quantization. The algebraic approach clarifies the problems in defining the vacuum and other states, which are associated with calculations in terms of field algebra operators. We demonstrate that the 'vacuum' state defined on the field algebra by Schwinger leads to incorrect results in the self-energy calculation.

scholarly journals Opacity from Loops in AdS

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Alexandria Costantino ◽  
Sylvain Fichet
Keyword(s):  
Imaginary Part ◽  
Quantum Dynamics ◽  
Model Building ◽  
Asymptotic Properties ◽  
The Self ◽  
Effective Theory ◽  
Self Energy ◽  
Higher Dimensional ◽  
Timelike Region ◽  
Spectral Representations

Abstract We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted “conformal” and “momentum”) in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy ImΠ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of ImΠ.Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS5, we determine a universal contribution to opacity from gravity.

scholarly journals Classical gravitational self-energy from double copy

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Gabriel Luz Almeida ◽  
Stefano Foffa ◽  
Riccardo Sturani
Keyword(s):  
Gravitational Field ◽  
Binary System ◽  
The Self ◽  
Gravitational Coupling ◽  
Leading Order ◽  
Body System ◽  
Self Energy ◽  
Composite Systems ◽  
Body Dynamics ◽  
Double Copy

Abstract We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling GN by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion.

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