scholarly journals REGULARIZATION PARAMETER INDEPENDENT ANALYSIS IN NAMBU–JONA-LASINIO MODEL

2013 ◽  
Vol 28 (31) ◽  
pp. 1350164 ◽  
Author(s):  
T. INAGAKI ◽  
D. KIMURA ◽  
H. KOHYAMA ◽  
A. KVINIKHIDZE
Keyword(s):  
Regularization Parameter ◽  
Dimensional Regularization ◽  
Low Energy ◽  
Leading Order ◽  
Regularization Scheme ◽  
Independent Analysis

Nambu–Jona-Lasinio model used to investigate low energy phenomena is nonrenormalizable, therefore the results depend on the regularization parameter in general. A possibility of the finite in four-dimensional limit and even the in regularization parameter (this is dimension in the dimensional regularization scheme) independent analysis is shown in the leading order of the 1/Nc expansion.

scholarly journals A prescription for projectors to compute helicity amplitudes in D dimensions

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Long Chen
Keyword(s):  
Dimensional Regularization ◽  
Tensor Decomposition ◽  
Regularization Scheme ◽  
Lorentz Index ◽  
Dimensional Splitting ◽  
Lorentz Tensor ◽  
Helicity Amplitudes ◽  
Amplitude Level ◽  
Infrared Singularities

AbstractThis article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

scholarly journals Modern Technique for Real Photon Radiative Correction Calculations

2021 ◽  
Vol 24 (2) ◽  
pp. 184-191
Author(s):  
I. A. Shershan ◽  
T. V. Shishkina
Keyword(s):  
Gauge Boson ◽  
Cross Sections ◽  
Dimensional Regularization ◽  
Real Photon ◽  
Boson Production ◽  
Radiative Corrections ◽  
Hard Photon ◽  
Regularization Scheme ◽  
Modern Technique ◽  
Bremsstrahlung Contribution

The problem of the bremsstrahlung contribution calculation as a part of the radiative corrections in the case of single gauge boson production was discussed. It was shown that the hard photon bremsstrahlung contribution can be divided into the finite and divergent terms. The exact calculation of soft photon bremsstrahlung and infrared part of hard photon bremsstrahlung was presented in frame of the dimensional regularization scheme. Numerical analysis of radiative corrections to the cross sections of single gauge boson production was performed.

ANGLE-SCANNED PHOTOELECTRON DIFFRACTION: FROM CLEAN SURFACES TO COMPLEX ADSORPTION SYSTEMS

2002 ◽  
Vol 09 (02) ◽  
pp. 741-747 ◽  
Author(s):  
F. BONDINO ◽  
G. COMELLI ◽  
A. BARALDI ◽  
R. ROSEI ◽  
S. LIZZIT ◽  
...  
Keyword(s):  
Nitrogen Monoxide ◽  
Quantitative Information ◽  
Low Energy ◽  
Electron Diffraction Data ◽  
Energy Separation ◽  
Photoelectron Diffraction ◽  
Adsorption Sites ◽  
Geometry Model ◽  
Independent Analysis ◽  
Adsorption Geometry

We exploit the capabilities of photoelectron diffraction (PED) to provide quantitative information on the local structure of the first layers of clean and adsorbate-covered surface systems. Selected studies of low-energy PED are presented, highlighting the advantages of the angle-scanning approach. In the first experiment, we evaluate the clean Rh(110) surface layer relaxation by employing the PED of the Rh 3d5/2 surface component. The resulting relaxation is in good accord with previous low energy electron diffraction data. In the second experiment, a system lacking long-range order is examined, namely the saturation layer formed by nitrogen monoxide on Rh(100) at 123 K. Preliminary results confirm the bridge adsorption geometry model. The last example is a chemical shift PED study of the c(4 × 2) phase of carbon monoxide on Pt(111). In this system, CO molecules are coadsorbed at two different adsorption sites, the energy separation of the respective C 1s components being 0.7 eV. Structural determination has been achieved by an independent analysis of the diffraction yield originated by the two chemically shifted C 1s components. The structure of Pt (111) + c(4 × 2)-2CO has been refined with an automated search of the best parameters using a modified version of MSCD (multiple scattering calculation of diffraction) code.

scholarly journals Rb, Rc and New Physics: An Updated Model Independent Analysis

1997 ◽  
Vol 12 (04) ◽  
pp. 723-742 ◽  
Author(s):  
P. Bamert
Keyword(s):  
Standard Model ◽  
Neutral Current ◽  
New Physics ◽  
Low Energy ◽  
Coupling Constant ◽  
A Value ◽  
Independent Analysis ◽  
The Standard Model ◽  
Necessary And Sufficient ◽  
Do So

We analyze LEP and SLC data from the 1995 Summer Conferences as well as from low energy neutral current experiments for signals of new physics. The reasons for doing this are twofold: first to explain the deviations from the Standard Model observed in Rb and Rc and second to constrain nonstandard contributions to couplings of the Z0 boson to all fermions and to the oblique parameters. We do so by comparing the data with the Standard Model as well as with a number of test hypotheses concerning the nature of the new physics. These include nonstandard [Formula: see text]-, [Formula: see text]- and [Formula: see text]-couplings as well as the couplings of the Z0 to fermions of the entire first, second and third generations and universal corrections to all up- and down-type quark couplings (as can arise see for example in Z' mixing models). We find that nonstandard [Formula: see text] couplings are both necessary and sufficient to explain the data and in particular the Rb anomaly. It is not possible to explain Rb, Rc and a value of the strong coupling constant consistent with low energy determinations invoking only nonstandard [Formula: see text]- and [Formula: see text]-couplings. To do so one has to have also new physics contributions to the [Formula: see text] or universal corrections to all [Formula: see text] couplings.

scholarly journals A well-posed multiscale regularization scheme for digital image denoising

2011 ◽  
Vol 21 (4) ◽  
pp. 769-777 ◽  
Author(s):  
V. Prasath
Keyword(s):  
Image Denoising ◽  
Digital Image ◽  
Regularization Parameter ◽  
Input Image ◽  
Smooth Transition ◽  
Functions Of Bounded Variation ◽  
Edge Preserving ◽  
Regularization Scheme ◽  
Adaptive Parameter ◽  
Well Posed

A well-posed multiscale regularization scheme for digital image denoisingWe propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.

scholarly journals Quark and pion condensates at finite isospin density in chiral perturbation theory

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensate ◽  
Independent Analysis ◽  
Model Independent

AbstractIn this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

scholarly journals A NONSINGULAR UNIVERSE IN STRING COSMOLOGY

1999 ◽  
Vol 08 (01) ◽  
pp. 43-49 ◽  
Author(s):  
A. A. AL-NOWAISER ◽  
MURAT ÖZER ◽  
M. O. TAHA
Keyword(s):  
General Relativity ◽  
Central Charge ◽  
Energy Condition ◽  
Homogeneous Solution ◽  
Low Energy ◽  
Leading Order ◽  
Tensor Fields ◽  
Strong Energy Condition ◽  
Four Dimensions ◽  
Strong Energy

We consider the low-energy effective string action in four dimensions including the leading order-α′ terms. An exact homogeneous solution is obtained. It represents a nonsingular expanding cosmological model in which the tensor fields tend to vanish as t→∞. The scale factor a(t) of the very early universe in this model has the time dependence [Formula: see text]. The violation of the strong energy condition of classical General Relativity to avoid the initial singularity requires that the central charge deficit of the theory be larger than a certain value. The significance of this solution is discussed.

scholarly journals GEOMETRICALLY RELATING MOMENTUM CUT-OFF AND DIMENSIONAL REGULARIZATION

2012 ◽  
Vol 10 (02) ◽  
pp. 1250081 ◽  
Author(s):  
SUSAMA AGARWALA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Hopf Algebras ◽  
Dimensional Regularization ◽  
Mass Scale ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coupling Constant ◽  
Regularization Scheme ◽  
Β Function

The β function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the β functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.

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