Dimensional Regularization. Ultraviolet and Infrared Divergences

Author(s):  
Victor Ilisie
2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Simon Caron-Huot ◽  
Einan Gardi ◽  
Joscha Reichel ◽  
Leonardo Vernazza

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.


Author(s):  
I. A. Shershan ◽  
T. V. Shishkina

. 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.


2011 ◽  
Vol 26 (04) ◽  
pp. 289-302 ◽  
Author(s):  
H. G. FARGNOLI ◽  
A. P. BAÊTA SCARPELLI ◽  
L. C. T. BRITO ◽  
B. HILLER ◽  
MARCOS SAMPAIO ◽  
...  

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.


2015 ◽  
Vol 30 (14) ◽  
pp. 1550071
Author(s):  
Amir H. Fariborz ◽  
Renata Jora ◽  
Joseph Schechter

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.


1994 ◽  
Vol 09 (20) ◽  
pp. 3535-3553
Author(s):  
M. RAKOWSKI ◽  
F. SAVATIER

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.


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

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

1992 ◽  
Vol 70 (6) ◽  
pp. 463-466
Author(s):  
A. Y. Shiekh

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.


2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Andreas Ekstedt ◽  
Johan Löfgren

Abstract The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.


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