scholarly journals ULTRAVIOLET AND INFRARED DIVERGENCES IN IMPLICIT REGULARIZATION: A CONSISTENT APPROACH

2011 ◽  
Vol 26 (04) ◽  
pp. 289-302 ◽  
Author(s):  
H. G. FARGNOLI ◽  
A. P. BAÊTA SCARPELLI ◽  
L. C. T. BRITO ◽  
B. HILLER ◽  
MARCOS SAMPAIO ◽  
...  
Keyword(s):  
Dimensional Regularization ◽  
Present Contribution ◽  
Infrared Divergences ◽  
Consistent Approach

Implicit Regularization is a four-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution, we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover, we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.

scholarly journals Two-parton scattering amplitudes in the Regge limit to high loop orders

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Simon Caron-Huot ◽  
Einan Gardi ◽  
Joscha Reichel ◽  
Leonardo Vernazza
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Dimensional Regularization ◽  
High Energy ◽  
Logarithmic Order ◽  
Finite Radius ◽  
High Loop ◽  
Parton Scattering ◽  
Infrared Divergences ◽  
Regge Limit

Abstract We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary t-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infrared divergences in the amplitude and is therefore computed in dimensional regularization; the latter is computed directly in two transverse dimensions and is expressed in terms of single-valued harmonic polylogarithms of uniform weight. By combining the two we determine exactly both infrared-divergent and finite contributions to the two-to-two scattering amplitude order-by-order in perturbation theory. We study the result numerically to 13 loops and find that finite corrections to the amplitude have a finite radius of convergence which depends on the colour representation of the t-channel exchange.

scholarly journals Modern methods of calculations of bremsstrahlung in the interaction of elementary particles

2020 ◽  
Vol 56 (4) ◽  
pp. 436-448
Author(s):  
I. A. Shershan ◽  
T. V. Shishkina
Keyword(s):  
Dimensional Regularization ◽  
Good Choice ◽  
Radiative Corrections ◽  
Divergent Part ◽  
Calculation Algorithm ◽  
Covariant Calculation ◽  
Modern Methods ◽  
Theoretical Predictions ◽  
Electron Photon ◽  
Infrared Divergences

. The problem of real bremsstrahlung calculation is considered using the modern methods of regularization of divergencies. In particular, we calculate soft photon bremsstrahlung in the most general form using the method of dimensional regularization of infrared divergences. The general calculation algorithm of hard photon bremsstrahlung is described. It is shown that the contribution of hard bremsstrahlung can be separated into the finite and divergent parts. The divergent part can be factorized with the contribution of the initial process in the Born approximation. It is shown that a good choice of kinematic variables makes an analytic covariant calculation of the divergent part of the hard bremsstrahlung possible. In a particular case, an algorithm for determining the kinematic constraints on the invariants is described. A numerical analysis of the radiative corrections for gauge bosons production processes in the case of electron-photon collisions is performed. It is discovered that the contribution of the finite part of bremsstrahlung at high collision energies reaches 20 per cent and must be taken into account in calculations of radiative corrections. The results obtained can be used in various calculations, including covariant ones, performed in the context of confirmation of the Standard Model theoretical predictions or searching for manifestations of alternative gauge models.

scholarly journals How important is iϵ in QFT?

2015 ◽  
Vol 30 (14) ◽  
pp. 1550071
Author(s):  
Amir H. Fariborz ◽  
Renata Jora ◽  
Joseph Schechter
Keyword(s):  
Regularization Parameter ◽  
Dimensional Regularization ◽  
Present Knowledge ◽  
Field Theories ◽  
Optical Theorem ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Infrared Divergences

We discuss the role of iϵ in quantum field theories and suggest that it can be identified with the dimensional regularization parameter iϵ = 4-d thus clarifying and simplifying issues related to the infrared divergences without altering any of the present knowledge in QFT. We further present the relevance of this assumption for the optical theorem.

EXTRACTION OF INFRARED DIVERGENCES IN THE DIMENSIONAL REGULARIZED TWO-LOOP LADDER GRAPH

1994 ◽  
Vol 09 (20) ◽  
pp. 3535-3553
Author(s):  
M. RAKOWSKI ◽  
F. SAVATIER
Keyword(s):  
Dimensional Regularization ◽  
Finite Part ◽  
Feynman Parameter ◽  
Ladder Graph ◽  
Infrared Divergences ◽  
Scalar Integral ◽  
Transfer Momentum

We consider the evaluation of the fundamental scalar integral in the on-shell two-loop ladder graph with different external masses and arbitrary transfer momentum. A method for cleanly extracting the infrared divergences in the Feynman parameter integrals using dimensional regularization is presented, and we analyze one of the finite part contributions to this integral.

Dimensional regularization and infrared divergences

1983 ◽  
Vol 56 (2) ◽  
pp. 770-776 ◽  
Author(s):  
V. A. Smirnov ◽  
K. G. Chetyrkin
Keyword(s):  
Dimensional Regularization ◽  
Infrared Divergences

Dimensional regularization of infrared divergences

1975 ◽  
Vol 88 (1) ◽  
pp. 86-98 ◽  
Author(s):  
W.J. Marciano ◽  
A. Sirlin
Keyword(s):  
Dimensional Regularization ◽  
Infrared Divergences

Finite massless quantum field theory

1992 ◽  
Vol 70 (6) ◽  
pp. 463-466
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Analytic Continuation ◽  
Dimensional Regularization ◽  
Quantum Field ◽  
Four Dimensions ◽  
Infrared Divergences ◽  
Massless Quantum

Massless quantum field theory is usually troubled by both ultraviolet and infrared divergences. With the help of analytic continuation, this fact can be exploited to eliminate, or at least reduce the overall number of divergences. This mechanism is investigated within the context of dimensional regularization for the case of massless [Formula: see text] theory in four dimensions.

High-resolution observations of metastable γ’ precipitation in Al-15at.%Ag

1996 ◽  
Vol 54 ◽  
pp. 1004-1005
Author(s):  
N. V. Larcher ◽  
I. G. Solorzano
Keyword(s):  
Discontinuous Precipitation ◽  
Equilibrium Phase ◽  
Quantitative Description ◽  
Present Contribution ◽  
Α Phase ◽  
The Matrix ◽  
Aging Sequence ◽  
Matrix Precipitation ◽  
Considerable Detail ◽  
Kinetics Of

It is currently well established that, for an Al-Ag alloy quenched from the α phase and aged within the metastable solvus, the aging sequence is: supersaturated α → GP zones → γ’ → γ (Ag2Al). While GP zones and plate-shaped γ’ are metastable phases, continuously distributed in the matrix, formation of the equilibrium phase γ takes place at grain boundaries by discontinuous precipitation (DP). The crystal structure of both γ’ and γ is hep with the following orientation relationship with respect to the fee α matrix: {0001}γ′,γ // {111}α, <1120>γ′,γ, // <110>α.The mechanisms and kinetics of continuous matrix precipitation (CMP) in dilute Al-Ag alloys have been studied in considerable detail. The quantitative description of DP kinetics, however, has received less attention. The present contribution reports the microstructural evolution resulting from aging an Al-Ag alloy with Ag content higher than those previously reported in the literature, focusing the observations of γ' plate-shaped metastable precipitates.

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